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1
H = (2.42)
LS 1+ k
3.16[(ρL−ρG)gθ]0.5
Where k = 2 [ρSV S2fS + ρLDHLF(VT−VF)(VS−VF) + ρGD(1−HLF)(VT−VG)(VS−VG)]
2.5−|sinβ| 2 4lS 4lS
1
H = (2.43)
LS 1+( VS )1.39
8.66
Translational velocity
Zhang et al. (2003) used Equation 2.44 to calculate the translational velocity for horizontal pipe flow.
C is 1.2 for turbulent flow and around 2 for laminar flow.
S
(cid:112)
V =C V +0.54 gD (2.44)
T S S
Poesio et al. (2009a) claim that at lower total superficial velocity, the translational velocity has a linear
relationship with the total superficial velocity as described by Equation 2.44. However, it deviates from
linear relationships at high gas velocities. But they found the dimensionless elongated bubble velocity
collapsed to a master curve for the lower dimensionless total superficial velocity (1+ VSG) as depicted by
VSL
Equation 2.45 and they pointed out that the new relationship was still not enough to depict the complex
flow dynamics at high air velocities.
V V C
T =C (1+ SG)+ P2 (2.45)
V P1 V V
SL SL SL
Zhang et al. (2003) proposed the solution procedure for their unified model of slug flow: continuity
equations (Equation 2.25, Equation 2.26 and Equation 2.27) and liquid entrainment equation (Equation
2.32) are solved simultaneously, based on which the combined momentum equation is solved to find the film
length. Equation 2.46 to Equation 2.48 are some auxiliary equations and are useful for solving the problem.
ρ (1−H −H )+ρ H
ρ = G LF LC L LC (2.46)
G 1−H
LF
ρ =ρ (1−H )+ρ H (2.47)
S G LS L LS
V =V (1−H )+V H (2.48)
S G LF F LF
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2.4 Review of Previous Modeling Studies on Oil-water Flow
This section provides a brief review of the modeling of the oil-water mixture viscosity, which is one of
the most important parameters that impacts the pressure gradient prediction, followed by a discussion of
the modeling considering oil and water interface mixing.
2.4.1 Viscosity Modeling of Liquid Mixture
Viscosity plays a crucial role in predicting pressure gradient, but accurately predicting the effective
mixture viscosity is a significant challenge. There are two primary methods for predicting the mixture
viscosity of oil and water. The first involves using the volume-averaged method to estimate the mixture
viscosity in segregated flow situations. Alternatively, numerous correlations have been proposed for
dispersed flow. Correlations within the second category are reviewed in the following, which have been
developed and applied specifically for multiphase flow purposes.
Brinkman (1952) developed Equation 2.49 for predicting the suspension viscosity. It is widely used for
evaluating liquid mixture viscosity in multi-phase pipe flow (Pan, 1996; Hall, 1992; Hewitt, 2005). k was
shown to be 2.5 for a mono-dispersed system with spherical solid particles in a liquid (Hall, 1992).
µ
µ = c (2.49)
l (1−φ)k
Roscoe(1952) argued that the Einstein equation is valid only when the concentration of suspended
spheres is below 0.05. Further, the authors proposed a new correlation applicable to medium and high
concentrations.
µ
µ = c (2.50)
l (1−1.35φ)k
It is worth mentioning that most of the correlations don’t consider droplet size except for Pal (1996).
The author pointed out that dispersion viscosity would increase if a thick layer adsorbed to the particle
surface with the presence of a surfactant or a trapped continuous phase caused by the solvation effect. In
this case, the effective dispersed-phase volume fraction can be written as Equation 2.51. It is apparent that
a smaller droplet size induces a larger effective dispersed-phase volume fraction, which results in a higher
dispersion viscosity if it is used in those aforementioned viscosity correlations. In fact, Pal (1996) pointed
out that particle size could play an important role even in diluted dispersion.
δ
φ =φ(1+ )3 (2.51)
e R
d
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2.4.2 Previous Modeling Studies Considering Mixing at Interface
In this section, the liquid-liquid stratified flow model is reviewed first, followed by a review of the
modeling studies that consider the mixing oil-water layer. The latter is typically based on the former one.
2.4.2.1 Brauner(1998) Stratified Model
Brauner et al. (1998) published a model for liquid-liquid two-phase stratified flow. Modeling both plane
and curved interfaces was introduced and compared. The momentum equations for the two phases in
liquid-liquid flow are written as Equation 2.52 and Equation 2.53, respectively. Eliminating the pressure
gradient from those two equations, one can get a combined momentum equation represented by Equation
2.54. This is the key equation for solving the problem.
dp
−A −τ S −τ S +A ρ gsinβ =0 (2.52)
adz a a I I a a
dp
−A −τ S +τ S +A ρ gsinβ =0 (2.53)
bdz b b I I b b
S S 1 1
τ a −τ b +τ S ( + )+(ρ −ρ )gsinβ =0 (2.54)
aA bA I I A A b a
a b a b
The equations for the shear stresses are expressed as Equation 2.55. The friction factor f and f can
a b
be evaluated by the Blasius equation (Equation 2.56). The authors also give Equation 2.57 for the
interfacial friction factor and hydraulic diameters based on the relative velocity of the phases. Note, we put
f and ρ for the third case on the right-hand side of Equation 2.57 only for consistency since τ =0 when
I I I
U (cid:39)U and f and ρ are no longer necessary.
a a I I
ρ U2 ρ U2 ρ (U −U )|U −U |
τ =f a a;τ =f b b ;τ =f I a b a b (2.55)
a a 2 b b 2 I I 2
ρ U d ρ U d
f =C( a a a)−n;f =C( b b b)−n (2.56)
a µ b µ
a b
f a,ρ a, Sa4A +a SI,4 SA bb for U a >U b
f I,ρ I,d a,d b = f fb I, ,ρ ρb I, ,4 4S SA Aa aa a, ,S
4
Sb4 A+ bA bSb fI of ro Ur aU (cid:39)a <
U
bU b (2.57)
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2.4.2.2 Vedapuri(1997) Segregated Flow Model with a Mixing Interface
Vedapuri et al.(1997) redefined the phase properties for the gas-oil-water three-phase stratified model
proposed by Taitel et al. (1995) to model oil-water flow with a dispersion layer in the middle, i.e., the new
three phases are oil, dispersion, and water instead of gas, oil, and water. They introduced two new
parameters C and V as the water cut and superficial velocity for the mixing layer, respectively. Two
ML Sm
new mass balance equations due to the introduction of the mixing layer are written as Equation 2.58 and
Equation 2.59. Unfortunately, no equations were available to solve those two new parameters. However,
the authors conducted experimental studies to investigate their variations with flow conditions and
recommended that the in situ velocity of the mixing layer could be approximated with 1.2 times of the
input mixture velocity for low-viscosity oil as the convergence criterion. They also treated the water cut in
the mixing layer as the input water cut for this case. Additionally, they suggested an in situ mixed layer
velocity the same as the input mixture velocity and a 50% water cut for the mixing layer with
high-viscosity oil. Shi (2001) further defined a four-layer stratified model based on the study by Vedapuri
et al. (1997). She introduced two mixing layers between the top oil and bottom water layers with a
water-in-oil layer above an oil-in-water layer in horizontal pipe flow.
V =V +C V (2.58)
SWi SW ML Sm
V =V +(1−C )V (2.59)
SOi SO ML Sm
2.5 Previous Modeling Studies on Three-phase Flow in Horizontal Pipes
This section reviews the available models for three-phase gas-liquid-liquid flow in horizontal pipelines,
which include the stratified model, the drift-flux model, and the unified model. How the two-phase slug
flow model was modified to be applicable to three-phase slug flow is also reviewed. In the end, some
correlations for the liquid holdup and the pressure drop are also summarized.
2.5.1 Stratified Model
Several authors introduced the stratified model for three-phase flow (Hall, 1992; Taitel et al.,1995;
Ghorai et al., 2005). The stratified models introduced by different authors have almost the same
momentum equation for each phase with limited differences. Hall (1992) derived three-phase stratified
model based on Taitel and Dukler (1976) two-phase stratified model and the author assumed τ =τ and
go g
τ was between τ and τ . Taitel et al. (1995) also proposed a three-phase stratified model. In particular,
ow w o
they proposed an explicit formula for both τ and τ in Equation 2.60 and Equation 2.61, with the
go ow
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assumption that knowing the phase that had a higher velocity at the interface was no longer necessary. It
is widely used and hence introduced below in detail. Several assumptions were made in the three-phase
stratified model. It was assumed that the water had the highest density and hence held the bottom
position of the pipe, while oil was in the middle and gas on the top. The second assumption was the gas
dragged the oil and the oil dragged the water phase. The momentum equation for each phase was written
as Equation 2.60, Equation 2.61 and Equation 2.62.
dp
−A −τ S −τ S =0 (2.60)
gdL g g go go
dp
−A −τ S +τ S −τ S =0 (2.61)
odL o o go go ow ow
dp
−A −τ S +τ S =0 (2.62)
wdL w w ow ow
The shear stresses were calculated by Equation 2.63 to Equation 2.67.
ρ V2
τ =f φ φ (2.63)
φ φ 2
ρ V d
f =C ( φ φ φ)−n (2.64)
φ f µ
φ
4A 4A 4A
d = w,d = o,d = g (2.65)
w S o S g S +S
w o g go
ρ (V −V )|V −V |
τ =f o o w o w (2.66)
ow ow 2
ρ (V −V )|V −V |
τ =f g g o g o (2.67)
go go 2
φ denotes the phases (gas, oil or water). The phase wall shear stress can be calculated by Equation
2.63, and C and n are 16 and 1 for laminar flow or 0.046 and 0.2 for turbulent flow. d is the hydraulic
f φ
diameter for each phase. f =0.014 when f ≤0.014, f =f when f >0.014. f =0.014 when
go g go g g ow
f ≤0.014, f =f when f >0.014.
o ow o o
Khor et al. (1997) assessed the accuracy of the hydraulic diameter calculations for three-phase stratified
flow and suggested using Equation 2.68 to calculate hydraulic diameters for a better accuracy. The formula
for d in Equation 2.68 is a new equation proposed by them.
o
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Continuity equations: The continuity equations were obtained from the volumetric flow rate balance by
equaling the volume flow rate flowing out of the slug body with that flowing into the film region for gas, oil
and water as Equation 2.72, Equation 2.73 and Equation 2.74.
(1−H )α (V −V )+H α (V −V )=(1−H −H )(V −V ) (2.72)
WGS OS T OS WGS WS T WS OF WF T G
(1−H )(1−α )(V −V )=H (V −V ) (2.73)
WGS OS T OS OF T OF
H (1−α )(V −V )=H (V −V ) (2.74)
WGS WS T WS WF T WF
The authors gave three other continuity equations for oil, water, and gas by weighting the flow rate
with slug unit length as Equation 2.77, Equation 2.75 and Equation 2.76.
l V =l (1−H )(1−α )V +l V H (2.75)
U SO S WGS OS OS F OF OF
l V =l H (1−α )V +l V H (2.76)
U SW S WGS WS WS F WF WF
l V =l [(1−H )α V +H α V ]+l (1−H −H )V (2.77)
U SG S WGS OS OS WGS WS WS F OF WF G
Momentum equations: In the gas pocket region, the momentum equations for the oil film, water film,
and the gas pocket were written as Equation 2.78, Equation 2.79 and Equation 2.80. The subscripts of
GOF and OWF represent the gas-oil interface and oil-water interface in the film region, respectively.
ρ (V −V )(V −V ) τ S −τ S −τ S p −p
o T OF OS OF + GOF GOF OWF OWF OF OF = 2 1 (2.78)
l H A l
F OF F
ρ (V −V )(V −V ) τ S −τ S p −p
w T WF WS WF + OWF OWF WF WF = 2 1 (2.79)
l H A l
F WF F
τ S +τ S p −p
GOF GOF G G = 2 1 (2.80)
(1−H −H )A l
OF WF F
Using Equation 2.78 and Equation 2.79 to eliminate the pressure drop, a combined momentum equation
for the film flow in the film region was derived, given in Equation 2.81.
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ρ (V −V )(V −V )−ρ (V −V )(V −V )
o T OF OS OF w T WF WS WF
l
F (2.81)
τ S −τ S −τ S τ S −τ S
+ GOF GOF OWF OWF OF OF = OWF OWF WF WF
H A H A
OF WF
By adding Equation 2.78 to Equation 2.79, Equation 2.82 was obtained. Then, another combined
momentum equation Equation 2.83 was obtained by eliminating the pressure drop in Equation 2.80 and
Equation 2.82.
ρ (V −V )(V −V )H +ρ (V −V )(V −V )H
o T OF OS OF OF w T WF WS WF WF+
l (H +H )
F OF WF (2.82)
τ S −τ S −τ S p −p
GOF GOF OF OF WF WF = 2 1
A(H +H ) l
OF WF F
ρ (V −V )(V −V )H +ρ (V −V )(V −V )H
o T OF OS OF OF w T WF WS WF WF+
l (H +H )
F OF WF (2.83)
τ S −τ S −τ S τ S +τ S
GOF GOF OF OF WF WF + GOF GOF G G =0
A(H +H ) A(1−H −H )
OF WF OF WF
In the slug body, the authors also gave two momentum equations (Equation 2.84 and Equation 2.85) for
the stratified flow scenario. By eliminating the pressure drop in those two equations, the third combined
momentum equation Equation 2.86 in the slug body was derived.
ρ (V −V )(V −V ) τ S +τ S p −p
o T OS OF OS − OWS OWS OS OS = 1 0 (2.84)
l (1−H )A l
S WGS S
ρ (V −V )(V −V ) τ S −τ S p −p
w T WS WF WS + OWS OWS WS WS = 1 0 (2.85)
l H A l
S WGS S
ρ (V −V )(V −V )−ρ (V −V )(V −V ) τ S +τ S
o T OS OF OS w T WS WF WS − OWS OWS OS OS
l (1−H )A
S WGS (2.86)
τ S −τ S
= OWS OWS WS WS
H A
WGS
Where H is the holdup of water with entrapped gas in the slug body, V is the local velocity and V
WGS T
is the translational velocity.
Closure relationships: Two types of shear stresses-wall shear stresses and interfacial shear stresses-need
to be obtained. The wall shear stresses including τ , τ , τ , τ , τ were calculated by Equation
OF WF G OS WS
2.87 (where p denotes OF, WF, G, OS and WS), while the interfacial shear stresses were solved separately
by Equation 2.88, Equation 2.89, and Equation 2.90. The subscripts GOF, OWF, and OWS denote the
gas-oil interface in the film region, the oil-water interface in the film region, and the oil-water interface in
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2.5.4 Modeling Three-phase Slug Flow with Two-phase Unified Model
One way to solve three-phase slug flow is to treat oil-water mixture as one liquid phase, which simplifies
the three-phase problem to a two-phase case. Hence, the two-phase unified model for slug flow could be
applied.
Modified Dukler and Hubbard (1975) model
Hall (1992) modified the Dukler and Hubbard (1975) model for three-phase slug flow in horizontal
pipelines. One assumption is that the liquid phases are fully dispersed at the end of the mixing eddy in the
slug body. The volume-averaged density (Equation 2.95) and viscosity calculated by the Brinkman
equation (Equation 2.49) were suggested to be used for liquid slug pressure gradient calculations. The
author derived a formula for the pressure drop associated with the formation of dispersed drops during the
eddy mixing and concluded that this pressure drop was negligible. Further, Hall (1992) argued that it was
common that oil and water flowed separately in the film region despite its dispersion state in the slug body.
Therefore, the author suggested using stratified model to solve for the liquid holdup in the film region. In
terms of the required superficial velocities to solve the stratified model, the author recommended the mean
superficial gas velocity for the gas and proposed two equations (Equation 2.96 and Equation 2.97) to
obtain the superficial velocity for water and oil in the film region by the mass balance.
ρ =φρ +(1−φ)ρ (2.95)
L o w
V =
V SO−V SH LSφ(ω Vl TS)
(2.96)
SOF 1− ωlS
VT
V =
V
SW
−V SH LS(1−φ)(ω Vl TS)
(2.97)
SWF 1− ωlS
VT
Stapelberg and Mewes (1994) also modeled gas-liquid-liquid slug flow in horizontal pipes by assuming a
homogeneous liquid-liquid mixture formed in gas-liquid-liquid three-phase flow and utilized the gas-liquid
two-phase slug models by Dukler and Hubbard (1975) and Aziz et al. (1978).
Modified Zhang et al. (2003) model
Dehkordi et al. (2019b) proposed a model to solve three-phase slug flow based on Zhang et al. (2003)
two-phase unified model for slug flow. They used the Zhang et al. (2006) mixing rule to determine when
the liquid phase could be treated as a homogeneous one-phase and simplified the three-phase slug flow to
two-phase slug flow. In particular, they fitted a new formula for the slug unit length as Equation 2.98,
which was used directly in the modeling. In this way, their model complexity was greatly reduced.
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V
l =7.3(1+ SG)2 (2.98)
U V
SL
2.5.5 Summary
Modeling three-phase flow in pipelines mainly includes the three-phase stratified model, three-phase
unified slug flow model, and drift flux model. The former two are capable of predicting both downstream
pressure drop and liquid holdup, while the drift flux model is mostly used for fitting experimental data and
predicting gas void fraction or liquid holdup. With regard to three-phase slug flow modeling, there are two
main approaches in the literature. The first one is to use Zhang et al. (2006) unified model to model
three-phase slug flow assuming stratified flows both in the slug body and film region for the respective
liquid-liquid mixture. The second method is to use two-phase slug flow models to model three-phase slug
flow assuming a homogeneous liquid-liquid phase.
2.6 Other Empirical Correlations for Three-phase Flow
Although the aforementioned models can predict liquid holdup and pressure drop, those models are
comparatively complicated. This section reviews other simplified models or correlations which can be used
directly to roughly estimate the liquid holdup and pressure drop in three-phase flow.
2.6.1 Liquid Holdup
Lahey (1992) proposed a drift flux model for three-phase flow. The gas void fraction can be predicted
once the phase distribution parameter and drift velocity are determined, and the liquid holdup can
therefore be calculated.
Spedding et al. (2007) measured liquid holdup with quick closing valves for three-phase flow in a 0.0259
m inner diameter horizontal pipeline. They also proposed a method to predict the liquid holdup for
three-phase flow, which was done by predicting the oil holdup and water holdup separately and then
combining them to obtain the total liquid holdup for three-phase flow, given in Equation 2.99 to Equation
2.101. Importantly, this method was based on very limited flow patterns and no slug flow was considered.
log(H )=(554.61V2.0335)V−1+0.9787V −1.7751 (2.99)
Loi SL SG SL
log(H )=(2.5574V−0.0838)V−1+3.6625V −2.006 (2.100)
Lwi SL SG SL
H =0.03857(6.932×10−4Re +0.0206)−8.57×10−5Re (2.101)
Lo SL SL
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Ren et al. (2021) conducted a dimensional analysis to find the relation between water holdup and
dimensionless numbers in three-phase flow. They eventually came up with an equation for predicting the
water holdup in three-phase flow as Equation 2.102 by fitting the equation obtained by a dimensional
analysis with their water holdup data measured at the vertical pipe section. Equation 2.103 to Equation
2.106 are supplementary equations for the water holdup calculation by Equation 2.102.
V
H =0.06Re0.2Fr−0.26 SG (2.102)
W m m V−0.34
Sm
ρ V D
Re = m Sm (2.103)
m µ
m
V2
Fr = Sm (2.104)
m gD
V V
ρ =ρ SW +ρ SO (2.105)
m wV oV
Sm Sm
V V
µ =µ SW +µ SO (2.106)
m wV oV
Sm Sm
2.6.2 Pressure Drop
Lockhart–Martinelli (1949) proposed a correlation Equation 2.107 to predict gas-liquid pressure drop in
(cid:113)
pipes. They introduced a dimensionless number, X = (dp) /(dp) , to which many parameters
dL L dL G
particularly the liquid holdup and φ could be related. The equation to determine X is given in Equation
L
2.108, in which n, m, C and C are based on the flow regimes, provided in Table 2.3. Note, n, and m
BL BG
are the exponents in the Blasius friction factor correlation for the liquid and gas phases, respectively;
Reynolds number smaller than 1000 and higher than 2000 were used as thresholds for laminar and
turbulent flows, respectively. Further, they introduced the empirical plots of φ as a function of X without
L
giving any equations. Later, Chisholm (1967) introduced a theoretical basis for the Lockhart–Martinelli
correlation and fitted an equation Equation 2.109 correlating φ with X (Chisholm, 1967). They
L
introduced the coefficient C based on flow regimes of the involved phases, as shown in Table 2.3. The
C
constituent phase pressure drop was obtained by the Darcy-Weisbach equation (Equation 2.110) (Chisholm
and Laird, 1958), and Equation 2.111 was used to find the friction factor. A key advantage of this method
is its simplicity and accuracy to predict pressure drop without knowing the flow pattern, though this
method is limited to horizontal pipe flow (Rahman et al., 2013). Apparently, this method can be applied to
predict pressure drop for three-phase flow by treating the liquid-liquid mixture as one phase.
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Table 2.3 Exponents n, m and constants C , C (Lockhart, 1949) and the coefficient C (Chisholm,
BL BG C
1967) under different flow regimes
Liquid-gas flow regimes n (-) m (-) C C C
BL BG C
Turbulent-turbulent 0.2 0.2 0.046 0.046 20
Laminar-turbulent 1.0 0.2 16 0.046 12
Turbulent-laminar 0.2 1 0.046 16 10
Laminar-Laminar 1.0 1.0 16 16 5
dp dp
) =φ2 ) (2.107)
dL GL LdL L
C ρ Rem W
X2 = BL G SG( L)2 (2.108)
C ρ Ren W
BG L SL G
C 1
φ2 =1+ C + (2.109)
L X X2
dp f ρ V2
( ) = SL L SL (2.110)
dL L 2D
C
f = BL (2.111)
SL (ρ V D/µ )n
L SL L
Malinowsky (1975) presented the pressure drop for single-phase flow in horizontal pipes as Equation
2.112, which consisted of two pressure drops due to acceleration and friction, respectively. This equation
comes from a derivation of momentum balance and conservation of mass in horizontal pipes for
single-phase flow. The friction factor is expressed by the wall shear stress divided by the kinetic energy per
unit volume as f = 2gτw, and the wall shear stress can be expressed as τ = D(dp) . Combining those
ρv2 w 4 dL f
two, the pressure drop induced by friction can be expressed as Equation 2.113. The author pointed out
that the pressure gradient due to acceleration can be negligible for oil-water two-phase flow. Therefore, the
homogeneous model for oil-water two-phase flow can be expressed as Equation 2.110 with the density and
viscosity evaluated by a volume averaged method.
dp ρVdV dp
= +( ) (2.112)
dL gdL dL f
dp fρV2
( ) = (2.113)
dL f 2gD
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Poesio et al. (2009b) tried to use the Lockhart–Martinelli (1949) model to predict their pressure drop
data for gas-oil-water three-phase core annular flow with elongated gas bubbles for a viscous oil and found
that the model was insensitive to the superficial water velocity and failed to give good performance. So,
they proposed a hybrid model which was a combination of the liquid-liquid core annular flow model by
Brauner (1991) and the Lockhart–Martinelli (1949) model. That is, the pressure gradient of the
liquid-liquid phase used in the Lockhart-Martinelli (1949) model is solved by the Brauner core annular
two-phase model rather than from the Darcy-Weisbach equation by treating the liquid-liquid as one phase.
Hall (1992) modified the two-phase slug flow model proposed by Dukler and Hubbard (1975) to be
applied to three-phase slug flow in a horizontal pipeline. The first modification was to use the volume
average density (Equation 2.95) to calculate the acceleration pressure drop. The author pointed out that
this was not true when the liquid phase right in front of the slug was stratified flow rather than dispersed
flow. In this case, the oil density should be more appropriate. A second modification was to consider the
liquid viscosity in calculating the frictional pressure drop. The author suggested using the Brinkman
equation (Equation 2.49). It should be noted that this is appropriate only when the liquid phases are a
dispersed flow. Additionally, the author argued that the pressure drop in the film region was negligible
based on the experimental observations of the pressure drop variations with time and the low liquid holdup
in the film region that demonstrated stratified flow.
Dehkordi et al. (2019b) introduced a simplified model based on Zhang et al. (2003) unified model for
two-phase slug flow. They treated the oil and water phases in three-phase slug flow as one homogeneous
phase based on Zhang et al. (2006) mixing rule, by which way the three-phase slug flow case was simplified
to a two-phase slug flow model. They used Equation 2.114 to calculate the pressure gradient.
dp τ πD l τ S +τ S l
− = S S + F F G G F (2.114)
dL A l A l
U U
2.6.3 Modeling the Mixing of Liquid-liquid Phases in Three-phase Slug Flow
Zhang et al. (2006) proposed a method to determine the mixing state of the liquid-liquid in three-phase
flow. They contended one phase would be fully dispersed in the other phase when the turbulent energy was
larger than the total surface energy and derived Equation 2.115.
6.325C φ [σ (ρ −ρ )g]0.5
V >{ e inv ow w o }0.5 (2.115)
lm f ρ
lm lm
They also gave the equation for C (Equation 2.116) and suggested the Brauner and Ullmann’s (2002)
e
equation (Equation 2.117) for the critical oil fraction at the inversion point (φ ).
inv
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CHAPTER 3
OBJECTIVES AND TASKS
The objectives of this study are to experimentally understand the effects of a valve at the inlet on
oil-water and gas-oil-water flow behaviors in a horizontal pipe downstream of the valve with a focus on
three-phase flow, and improve the hydraulic modeling for pressure gradient and phase holdup predictions
in two-phase liquid-liquid and three-phase gas-oil-water flow as needed. The modeling study on three-phase
flow will mainly focus on slug flow which is the main flow pattern observed in this current experimental
study.
To accomplish this goal, I have:
1. Conducted a literature review on previous experimental and modeling studies of oil-water two-phase
flow and gas-oil-water three-phase flow in horizontal pipes.
2. Conducted experimental studies on oil-water two-phase and air-oil-water three-phase flows in
horizontal pipelines at various inlet choking levels, flow rates, and water cuts. Major measurements
include the pressure drops across the valve and the test section downstream of the valve, flow pattern
by high-speed camera, and phase distribution at pipe cross-section by an Electrical Capacitance
Volumetric Tomography (ECVT) system.
3. Developed new hydraulic models to better capture the experimental findings for both oil-water and
gas-oil-water three-phase flows.
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CHAPTER 4
EXPERIMENTAL STUDY
This chapter presents the experimental facilities and equipment, test matrix, and experimental results
in terms of various inlet choke openings, water cuts, and superficial velocities for oil-water two-phase and
gas-oil-water three-phase flows respectively.
4.1 Experimental Facilities and Equipment
The following subsections introduce the facility, instrumentation and its calibration, properties of the
testing fluids, and test matrix in the current study.
4.1.1 Facility Description
The three-phase flow loop in this study consists of a horizontal pipe with a length of 43 ft and an inner
diameter of 2.067 in. as shown in Figure 4.3. The system was designed to introduce water and oil
simultaneously through wye connections at the inlet. The experimental setup utilized a progressive cavity
pump to minimize the shear effects in the oil phase and avoid the formation of tight emulsions. The oil
flow rate was controlled by a frequency converter. A submersible pump was employed to introduce water
into the system, and the flow rate was mainly controlled manually by a needle valve at the inlet.
Compressed air from a building compressor was introduced right after the wye-shaped oil connection. The
airflow rate was adjusted automatically by a control valve through Labview. The oil and water flow rates
were metered by a Coriolis flow meter (Emerson Micro Motion R100S) respectively, and the air flow rate
was measured by a vortex flow meter (Rosemount 8800D). To examine the effect of different inlet choke
openings on downstream flow behavior, a 2-in. ball valve was installed immediately after the introduction
of all the phases. The valve was installed in a commonly used position in the field as shown in Figure 4.1.
Figure 4.2 demonstrates the internal structure of the ball valve. The handle and pipe material are different
from the one we have in Figure 4.1, but the internal structure is the same. The black arrow indicates the
fluid flow direction through the valve. Pressure and temperature transducers were installed at the inlet of
the airline and in the test section to monitor the pressure and temperature. Two differential pressure
transducers (Rosemount 3051S differential pressure transducer) were used to measure the pressure drop.
One was installed over a span of 14-in. across the inlet ball valve (the valve is 8 in. to the upstream remote
seals and 6 in. to the downstream remote seals) and the other was set in the test section around 21.2 ft
downstream of the inlet valve over a span of 18 ft. The differential pressure sensors have a pressure range
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Figure 4.3 The schematic of the flow loop.
An Electrical Capacitance Volume Tomography (ECVT) system was deployed downstream of the
pressure drop measurement section to monitor the in-situ phase distribution inside the pipe. The sensor
was clamped around the pipe, as shown in Figure 4.4. Twenty-four sensors were connected to an ECVT
data acquisition system box (Figure 4.5). The system was calibrated with pure water and mineral oil
before the actual measurement was taken. The calibration of the system was typically done with two types
of liquids that would be used during subsequent experiments. In our study, mineral oil and tap water were
used in a dynamic calibration. Pure water first flowed through the pipe that generated a “full” case in the
calibration file, followed by pure oil flowing through the pipe for creating an “empty” case in the
calibration file. These two files were treated as the two ends of the flowing condition spectrum to be tested.
After the calibration files were generated, pure oil and water flowing through the pipe were measured to
evaluate the quality of the data from ECVT (Figure 4.6). As can be seen, the pure oil is indicated in blue
color, whereas the pure water is shown in red color. This verified that the data and calibration were good.
It could also mean that the red color denotes a water-continuous state while the blue color indicates an
oil-continuous state during multi-phase flow. The recorded ECVT data were later analyzed by Tech4
Imaging software, from which the videos of the phase distribution variation with time inside the pipe, and
images of phase distribution at pipe cross-section were obtained and analyzed.
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We used a Phantom high-speed camera (VEO640) coupled with a Canon lens (EF 16-35 mm f/2.8L II
UST & MI) (Figure 4.7) to observe the flow pattern in the test section, focusing on the middle of a
3-foot-long acrylic pipe. The camera was fixed to a metal structure at the closest focus length of 0.92 ft to
obtain the side view of the flow inside the acrylic pipe, as shown in Figure 4.8. A light source was supplied
and set behind the pipe to illuminate the pipe.
Figure 4.7 High-speed video camera with a Cannon lens.
Figure 4.8 High-speed video camera setup.
4.1.2 Fluid Properties
Three types of working fluids were used in this study: air, mineral oil, and tap water. The used mineral
oil is Isopar V which has a density of 810 kg/m3 and a viscosity of 14.6 mPa.s at 20 °C and atmospheric
pressure. The interfacial tension (IFT) between Isopar V and tap water was measured by the Kru¨ss
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tensiometer DSA 100 using the pendant drop method. The measured IFT demonstrated a transient
behavior, i.e., it decreased with time. We observed an initial IFT of 43.61 mN/m with an oil volume of 25.6
µL submersed in the tap water at room temperature and atmospheric pressure and tended to stabilize at
40 mN/m after 5 minutes. More data on the IFT between Isopar V and tap water can be found in Zhou et
al. (2022). The oil density was measured by SVM 3001 Stabinger Viscometer from Anton Paar at various
temperatures and a linear relationship was fitted as shown by Figure 4.9. Its viscosity variation with
temperature was measured by a rheometer (Anton Paar MCR92) and can be fitted well by a logarithmic
relationship as shown in Figure 4.10. Those two equations were used for estimating the in-situ oil density
and viscosity at temperatures in the test section during the experiments.
Figure 4.9 Mineral oil density variation with temperature.
Figure 4.10 Mineral oil viscosity variation with temperature.
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typical techniques for flow pattern identification. In the current study, both high-speed camera videos and
ECVT data were utilized to determine flow patterns for both oil-water two-phase flow and gas-oil-water
three-phase flow.
Determining the flow pattern for oil-water flow is a relatively simple task. However, there is a specific
flow pattern that deserves special attention, which is oil-in-water layer above a free water layer while the
top layer demonstrates a densely packed dispersion. This flow pattern has also been reported by Schu¨mann
et al.(2016). Despite being in a water-continuous state, the densely packed top layer demonstrates a very
high viscosity. Its complex behavior makes it lack deep understanding. In Chapter 5 of this study, a model
is proposed to address this particular flow pattern for pressure gradient predictions. The flow patterns
identified in the study for oil-water flow are illustrated in Figure 4.11, that include stratified flow with a
mixing interface (ST & MI), water-in-oil layer above a free water layer (W/O & W), oil layer above a
water-in-oil layer (O & W/O), oil-in-water layer above a free water layer (O/W & W ), water-in-oil
dispersion (W/O), and oil-in-water dispersion (O/W). W/O & W, O & W/O, and O/W & W are
categorized as semi-dispersed flow since they are all in common to have a pure layer with a dispersion
layer, and O/W & W is most observed among those three in this study.
It is worth noting that Oglesby (1979) introduced the concept of semi-dispersed flow in oil-water
two-phase flow, which is defined as a flow pattern with a steep vertical fluid concentration gradient in the
mixture. The author also defined semi-segregated flow as a flow pattern with some mixing at the
liquid-liquid interface, semi-mixed flow as a segregated flow of a dispersion layer taking less than half of the
total pipe volume with a free phase layer, and mixed flow as an oil-water dispersion occupying more than
half of the pipe volume. In an experimental study, Malhotra (1995) observed both semi-segregated flow
and semi-mixed flow. It is noteworthy that the author claimed the mixing zone could occupy more than
half of the pipe cross-section for semi-mixed flow, which means Malhotra (1995) treated the semi-mixed
flow and mixed flow defined by Oglesby (1979) as semi-mixed flow. However, Vedapuri et al. (1997)
discriminated between semi-segregated, semi-mixed, and semi-dispersed in a slightly different way based on
the mixed layer thickness. Those three flow patterns in their study all have an oil-mixed layer-water
three-layer structure, with an increasing order in the thickness of the mixed layer. Therefore, the
semi-dispersed flow in this study is distinct from the previous definitions and is defined as any flow pattern
with a two-layer structure consisting of a dispersion layer or mixing layer and a pure phase layer in
liquid-liquid two-phase flow.
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procedure consists of three steps:
The first step is to identify the continuous phase in the upper region of the slug body. The videos were
taken from a 3-ft-long acrylic pipe section, which is preferentially wetted by oil no matter if it is originally
water-wetted or oil-wetted (Angeli and Hewitt, 1999). Angeli and Hewitt (1999) observed that when the
pipe material was initially wetted by oil, a contact angle of 84.4 degrees was measured with oil drops in
water, and 121.6 degrees was measured with water drops in oil. On the other hand, if the pipe material
was initially wetted by water, the respective contact angles were 87.6 and 106 degrees. This indicates that
the pipe material is preferentially wetted by oil in all cases. In our study, the top layer of the slug body is
identified as oil continuous if a spread-out film is observed on the wall in the gas pocket region right after
the passage of a slug. On the other hand, it is regarded as water continuous if an almost clear wall shows
without a spread-out film after a passing slug body. This phenomenon can be further described by
Figure 4.13. As can be seen in (a), a spread-out film is left on the wall of the gas pocket region after a slug
body passes and breaks, for the case with a 20% water cut. By contrast, no such phenomenon is observed
for the case with an 80% water cut as shown by (b). Fortunately, we can see whether there is a spread-out
film for all the test points in the current study. It is worth pointing out that the continuous phase
determined this way only tells the continuous phase of the top region in the slug body instead of the whole
slug body, since the bottom part of the pipe is still wetted by the liquid phase in the liquid film region of a
slug flow.
The second step is to identify the flow pattern in the slug body. As introduced by Dukler and Hubbard
(1975), a mixing zone typically exists in the front of a slug body, which is resulted from the acceleration of
the slow-moving liquid film at the slug front to the velocity of the slug body. The mixing zone improves the
mixing between phases. The phase distribution becomes more developed and stable as it moves away from
the mixing zone into the slug body. As such, we determined the flow pattern in the slug body based on the
flow behavior close to the slug tail that represents the flow pattern of the slug body better.
The third step is to determine the flow pattern in the film region. Similar to the flow behavior in the
slug body, the flow pattern in the film region also shows variation in the axial direction. A better mixing
between the liquid phases is observed immediately after the slug body region compared to that in the
region right in front of a slug body that is close to an equilibrium status. The flow pattern in the film
region right in front of a slug body is believed to represent the flow pattern of the film region better and is
therefore used to define the flow pattern of the liquid mixture in the film region.
As an example, the flow pattern depicted in Figure 4.12 is defined as SLUG(O/W-S, O/W & W-F)
using the aforementioned procedure. It means that the flow pattern is slug flow, with oil-in-water
dispersion in the slug body (O/W-S), and oil-in-water layer with a water layer in the film region (O/W &
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W – F). In addition to this flow pattern, six other flow patterns are identified, including SLUG(ST & MI-S,
ST & MI-F), SLUG(ST & MI-S, O/W & W-F), SLUG(O/W & W-S, O/W & W-F), SLUG(O/W-S,
O/W-F), SLUG(W/O-S, W/O-F) and SLUG(DD-S, DD-F), as shown by Figure 4.14. Note, the
liquid-liquid flow patterns in the slug body and in the film region of three-phase slug flow are defined the
same as those observed in liquid-liquid two-phase flow. DD denotes dual dispersion which is not observed
in this study for liquid-liquid two-phase flow.
Figure 4.12 Flow pattern identification and definition for gas-oil-water slug flow.
Figure 4.13 Comparison of the film region with and without the spread-out film at 50% inlet choke opening
at a superficial liquid velocity of 0.5 m/s with a superficial gas velocity of 0.2 m/s (a) oil continuous, a
broken spread-out film is observed in the gas pocket region after a slug body passing for a case with 20%
water cut; (b) water continuous, no spread-out film observed at 80% water cut.
4.2.2 Slug Frequency and Slug Length
The data obtained from ECVT are used to determine the slug frequency in the current study and can
be used to determine the slug body and film lengths in the future. Figure 4.15 shows an example of the 1-D
liquid holdup as a function of frame number. The data was recorded with a frequency of 41.40 frames per
second, meaning that the time interval between two frames is 0.024 s. The liquid holdup peaks correspond
to slug bodies, which can be counted over a certain time period for a given flowing condition to determine
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4.2.3 Oil-water Two-phase Flow in a Horizontal Pipe with Inlet Choking
The effects of inlet choke openings and water cuts on two-phase oil-water flow are discussed in this
section. In particular, the water cut effect is examined at various inlet choke openings. Five different
choking levels and at least four water cuts were investigated, and the results are compared.
4.2.3.1 Effect of Inlet Choke Opening
In this experiment, we observed that the inlet choking could impact the downstream flow pattern
regardless of the water cut. The changes of the flow pattern with inlet choke openings are illustrated by a
series of experiments with a mixture velocity of 0.2 m/s at 20%, 60%, and 80% water cuts as described
below (Figure 4.16, Figure 4.17, and Figure 4.18).
Figure 4.16 Flow pattern and phase distribution at V =0.2 m/s with a 20% water cut (the percentages in
SL
the picture indicate the opening of the ball valve).
Figure 4.16 demonstrates the flow patterns at different inlet choke openings when the input water cut is
20%, captured by the high-speed camera. The images on the right illustrate the phase distribution
captured by the ECVT system at the pipe cross-section. When there is no inlet choke, the flow pattern is
almost stratified flow with a few droplets at the oil-water interface. The flow patterns have minimal
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variations when the inlet choke opening decreases to 75% or 50% except that more droplets are present at
the oil-water interface. The transition in flow pattern occurs when the inlet choke opening reaches 30%, at
which the flow pattern changes from ST & MI to oil layer over a water-in-oil layer with rolling waves at the
interface (O & W/O). The rolling waves get bigger at a further decreased inlet choke opening and the
droplets in the rolling wave become smaller.
Figure 4.17 Flow pattern and phase distribution at V =0.2 m/s with a 60% water cut (the percentages in
SL
the picture indicate the opening of the ball valve).
Figure 4.17 shows the pictures of the flow behaviors for different choke openings from 100% to 20% for
a 60% water cut case. When no choking (100% opening) was applied in the inlet, the flow pattern was
stratified flow with a mixing interface (ST & MI). Clear drops were observed at the oil-water interface.
When a 75% inlet choke opening was applied, the flow pattern remained the same, but with more droplets
at the oil-water interface. A thicker mixing layer with larger droplets occurred with a further 50% inlet
choking. Flow pattern transition from stratified flow with a mixing interface (ST & MI) to oil-in-water &
water (O/W & W) was observed when the inlet valve opening was reduced to 30%. Schu¨mann et al.
(2016) also observed this flow pattern for a liquid mixture velocity of 0.5 m/s at water cuts of 50% and
80% and described the top layer as a densely packed layer (Schu¨mann et al., 2016). They used
quick-closing valves to observe the separation of the top layer, from which they concluded that the top
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layer should be oil droplets in the water phase. Similarly, we also observed a peak pressure gradient at 30%
valve opening, as shown in Figure 4.19.
In Figure 4.18, the results are presented for the case with an 80% input water cut. The figure shows
that at the oil-water interface, more droplets with larger sizes are formed as the water cut increases to 80%.
Notably, the top oil layer almost disappears and is replaced by large oil slugs at a 50% inlet choke opening.
The top oil layer fully disperses at a 30% inlet choke opening. Therefore, it can be concluded that the
dispersion of oil into water is enhanced with a decreased inlet choke opening. Comparing the experimental
results from different water cuts, it also indicates that the inlet choke opening impacts more significantly
the oil dispersion at a higher water cut.
Figure 4.18 Flow pattern and phase distribution at V =0.2 m/s with a 80% water cut (the percentages in
SL
the picture indicate the opening of the ball valve).
Figure 4.19 Pressure gradient in the test section 123 L/D downstream of the inlet valve for V =0.2 m/s
SL
and different water cuts.
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Interestingly, it seems that the flow pattern transition occurs at 30% choke opening for all the three
cases with different water cuts, while the flow pattern after the transition depends on the input water cut.
Similarly, the effect of inlet choke opening on flow pattern transition was also investigated at a higher
liquid mixture velocity at 0.5 m/s. The elevated mixture velocity lifts the flow pattern transition up to a
50% inlet choke opening, from 30% for a mixture velocity of 0.2 m/s. Figure 4.20 shows the corresponding
pictures from the high-speed camera and the images from the ECVT systems for the 0.5 m/s mixture
velocity. The pressure gradient peaks at 50% inlet choking, after which it decreases dramatically with a
further increase in the choking level as shown by Figure 4.21. Such a decrease is caused by the occurrence
of a flow pattern transition from oil-in-water & water flow (O/W & W) to dispersed oil-in-water flow
(O/W). The flow becomes more homogeneous when the inlet choke opening is reduced below 30%, which
can be seen from both the camera side views and the ECVT images. The camera side views do not show a
clear interface. The ECVT images show a red color, indicating a water-continuous phase. It is worth
mentioning that the pressure gradient decreases slightly when the inlet choke opening reduces from 30% to
20%, though they both seem to have a homogeneous water-continuous phase. A possible explanation is
that it is indeed not 100% homogeneous for the 30% inlet choking opening as it seems to be.
Figure 4.20 Flow pattern and phase distribution at V =0.5 m/s with a 60% water cut (the percentages in
SL
the picture indicate the opening of the ball valve).
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Figure 4.21 Pressure gradient in the test section 123 L/D downstream of the inlet valve for V =0.5 m/s
SL
with a 60% water cut.
4.2.3.2 Effect of Water Cut
As indicated in the previous section, the downstream flow pattern, phase distribution, and pressure
gradient are also closely related to the input water cut. In this section, we emphasize on the water cut
effects on the flow pattern, phase distribution, and pressure gradient in the test section downstream of the
inlet valve. Two different mixture velocities and different inlet choke openings were also investigated.
Water cut influences the thickness of different layers, flow pattern transition, pressure gradient, and its
impact is also closely related to inlet choke openings. Figure 4.22, Figure 4.23, and Figure 4.24 show the
water cut effect on the downstream flow behaviors for three choking levels at a mixture velocity of 0.2 m/s.
The corresponding pressure gradient measurement is shown in Figure 4.23. When there is no inlet choking,
the flow patterns are the same for an input water cut range from 20% to 80%, but the increase of input
water cut increases the thicknesses of the mixing layer and the free water layer, as shown by Figure 4.22.
The increased mixing layer thickness could be induced by the increased water phase superficial velocity at
a higher water cut, which enhances its dispersion into the upper oil layer. It is noteworthy that the
pressure gradient increases gradually even as the free water layer thickness increases (Figure 4.25). This
could suggest that the pressure gradient increase resulting from the increased mixing layer thickness
exceeds the decrease caused by the increase in free water layer thickness. This also demonstrates that the
viscosity of the mixing layer is higher and dominates the overall frictional pressure gradients. When either
50% or 30% inlet choke opening was used, flow pattern transition was observed with the increase of input
water cut. In Figure 4.23, the flow pattern changes from ST & MI to O/W & W at an 80% input water
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cut. By contrast, the flow pattern transition is advanced to a 30% input water cut for the case with a 30%
inlet choke opening, as shown by Figure 4.24. After the transition, the increased water cut mainly impacts
the thickness of the bottom free water layer, and a higher input water cut leads to a thicker free water
layer at the pipe bottom. Importantly, a W/O & W flow pattern was identified at 30% input water cut for
the 30% choke opening. The nature of the oil-continuous state in the top dispersion layer could be verified
by the blue color of the ECVT image. Very large droplets were also observed close to the bottom of the
dispersion layer. When the input water cut increases to 40%, it is almost around a flow pattern transition
point. The measured downstream pressure gradient has a very minor variation for an input water cut
change from 30% to 40% (Figure 4.25). It is noteworthy that the pressure gradient increases a lot when the
semi-dispersed flow pattern occurs. This phenomenon is more noticeable at a higher mixing velocity at 0.5
m/s when both semi-dispersed and fully dispersed flow are observed, which is discussed in the following.
Figure 4.22 Downstream flow pattern and phase distribution as a function of the water cut with a 100%
inlet choke opening at V =0.2 m/s (the percentages in the picture denote input water cut).
SL
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Figure 4.25 Pressure gradient in the test section as a function of the water cut of the liquid mixture at
various inlet choke openings with V =0.2 m/s.
SL
For a mixture velocity of 0.5 m/s, similar water cut effects on downstream flow behaviors were
observed, as shown by Figure 4.26 to Figure 4.29. The corresponding pressure gradient measurement in the
test section is shown in Figure 4.30. It can be seen that the flow pattern transition occurs with the
changing of input water cut except for the case of a 100% inlet choke opening. The downstream pressure
gradient changes accordingly as the flow pattern varies. Similar to the observation for a 0.2 m/s mixture
velocity, a significant pressure gradient increase is observed when semi-dispersed flow ( O/W & W ) occurs
at a 50% choke opening, and the pressure gradient is much higher than that for fully-dispersed flow at a
30% inlet choke opening (Figure 4.30). This reveals that the top dispersion layer dominates the frictional
pressure losses due to its higher viscosity. Also, the water cut effect on flow pattern transition is greatly
impacted by the inlet choke opening. The transition occurs at a lower input water cut for a smaller inlet
choke opening. For example, the input water cut at the transition point is around 80% for a 75% inlet
choke opening (Figure 4.27). It changes to 30% water cut for 50% and 30% inlet choke openings
(Figure 4.28 and Figure 4.29). Additionally, it can also be noticed that similar flow pattern variations with
water cut occurs at a larger inlet choke opening for a higher mixture velocity. For instance, the transition
from ST& MI to O/W & W occurs at a 75% inlet choke opening for a mixture velocity of 0.5 m/s, while
this transition shifts to a 50% inlet choke opening when the mixture velocity is 0.2 m/s (Figure 4.27 and
Figure 4.23). Similarly, the flow pattern changes from O & W/O to O/W & W at 50% inlet choke opening
for a mixture velocity of 0.5 m/s, whereas it occurs at 30% inlet choke opening for a 0.2 m/s mixture
velocity (Figure 4.28 and Figure 4.24).
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Figure 4.30 Pressure gradient in the test section as a function of the water cut of the liquid mixture at
various inlet choke openings with V =0.5 m/s.
SL
In summary, the water cut can influence the thicknesses of the dispersion layer and the free water layer,
affect the flow pattern, and impact pressure gradient. Additionally, its impact on downstream flow
behaviors can be greatly influenced by the inlet choking.
4.2.4 Gas-oil-water Three-phase Flow in a Horizontal Pipe with Inlet Choking
Gas-oil-water three-phase flow behaviors were examined using the same superficial liquid velocities as
those for the two-phase oil-water flow tests. Five different inlet choke openings, at least four water cuts,
four superficial liquid velocities, and five superficial gas velocities were investigated, and their impacts on
the downstream fluid flow behaviors were analyzed. With the gas flow rate range investigated in the
current study, slug flow is the dominant flow pattern for three-phase flow. We emphasize on the flow
behavior of the liquid-liquid phase within three-phase flow in the current study, which lacks deep
understanding in previous literature.
4.2.4.1 Effect of Inlet Choke Opening
The effect of inlet choke opening on gas-oil-water three-phase flow is discussed for two superficial liquid
velocities at a 0.2 m/s superficial gas velocity in this section.
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Figure 4.31 Pictures of three-phase slug flow from a high-speed camera for V =0.2 m/s and V =0.2 m/s
SL SG
with a 60% water cut (the percentages in the picture indicate the opening of the valve).
An applied inlet choking can change the mixing state of the liquid-liquid phase in three-phase slug flow,
and thus the pressure gradient. For a V of 0.2 m/s with 60% water cut, when the inlet choke opening is
SL
larger than 30%, the liquid-liquid mixture in the slug body is ST & MI as illustrated in Figure 4.31. It
changes to an O/W dispersed flow when the inlet choke opening is reduced to 30%. The ECVT images also
capture those changes shown by the pictures in the slug body region though only gas and liquid can be
differentiated in the film region (Figure 4.32). The ECVT images in the slug body region show that the
liquid mixture becomes almost dispersed flow when the inlet choke opening reduces to 30%. The
liquid-liquid phase in the slug body region of the three-phase slug flow almost demonstrates the same flow
pattern transition as that for liquid-liquid two-phase flow, however, the three-phase flow demonstrates
better mixing in the liquid phase than just two-phase flow. This is probably due to the low superficial gas
velocities used in this study. For the respective oil-water two-phase flow with the same superficial liquid
velocity and water cut, as previously shown by Figure 4.17, a similar flow pattern was observed, but with
less mixing between the oil and water phases. In addition, the variation of pressure gradient with choke
opening for gas-oil-water three-phase flow also exhibits a peak at 30% as shown in Figure 4.33, which is
consistent with the observation for the two-phase flow with the same flowing conditions (Figure 4.19).
However, the pressure gradient variation with inlet choke opening in three-phase flow is less evident
compared with that in oil-water two-phase flow. This is anticipated to be related to the introduction of the
gas phase that significantly reduces the liquid wetted perimeter at the pipe wall and therefore the frictional
losses.
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Figure 4.33 Pressure gradient of three-phase slug flow in the test section 123 L/D for V =0.2 m/s with a
SL
60% water cut and V =0.2 m/s.
SG
When the superficial liquid velocity increases from 0.2 m/s to 0.5 m/s, the flow pattern transition
advances to a 50% inlet choke opening. Figure 4.34 shows the pictures from the high-speed camera for
different choking levels for a 0.5 m/s superficial liquid velocity with 60% water cut, while Figure 4.36 shows
the phase distribution obtained from the ECVT system, in the liquid film and slug body regions
respectively. For inlet choke openings greater than 50%, the liquid-liquid flow patterns in both the film
region and the slug body are stratified flow with a mixing interface. On the other hand, the liquid-liquid
phase in both the slug body and film regions are dispersed flow for inlet choke openings less than 50%.
This observation could also be verified from the ECVT results, shown in Figure 4.36. For the cases with
100% and 75% inlet choke opening, the slug body demonstrates a two-layer structure that reflects
segregation. The upper layer has a blue-yellow color indicating an oil-continuous phase, while the bottom
layer has a red color implying a water-continuous phase. However, the slug body shows a homogeneous red
color in accordance with an oil-in-water dispersed flow when the inlet choke opening reduces to 50% or less.
It should be mentioning that the slugs shown in the high-speed camera pictures (Figure 4.34) and ECVT
measurement (Figure 4.36) may not be the exact same one, but they all come from the same flow
condition. For each inlet choking opening in either Figure 4.34 or Figure 4.36, the pictures or images are
for the same slug unit. The pressure gradient also shows a peak at a 50% inlet choke opening (Figure 4.35),
which is still consistent with that of the oil-water two-phase flow (Figure 4.21).
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Figure 4.36 Phase distribution at pipe cross-section in the liquid film and slug body regions from the
ECVT system for V =0.5 m/s and V =0.2 m/s with a 60% water cut (the percentages in the picture
SL SG
indicate the opening of the ball valve).
4.2.4.2 Effect of Water Cut
To investigate the effect of water cut on downstream flow behavior in gas-oil-water three-phase flow, the
superficial liquid and gas velocities are fixed in the experiments while the water cut of the respective
liquid-liquid mixture is varied for various inlet choke openings. The observed flow pattern for the gas and
liquid mixture is still slug flow independent of the input water cut.
The water cut mainly influences the flow pattern between the two liquid phases in the gas-liquid-liquid
three-phase flow. Figure 4.37 to Figure 4.42 show the pictures from the high-speed camera and images
from the ECVT system for different water cuts and choke openings.
When the inlet choke opening is 100%, the oil-water generally shows a stratified flow pattern with a
mixing layer at the interface both in the film region and in the slug body region when the input water cut
is smaller than or equal to 60%. The top oil layer becomes very thin and can be hardly read in the film
region when the input water cut reaches 60%, but there still exists a top oil layer in the slug body. This is
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probably induced by the nature of slug flow. The slug body moves like a scoop and collects the oil from the
thin oil layer in the film region. The mixing layer grows with the increase of input water cut in the slug
body and finally disappears when the input water cut reaches 80% (Figure 4.37). This is clearer from the
ECVT results shown in Figure 4.38. It shows an upper oil layer in the slug body with a blue color but an
almost red color at 80% water cut on top in the slug body region. When comparing the flow patterns
observed in the gas-oil-water three-phase flow to those in the respective oil-water two-phase flow at the
same superficial liquid velocity, it is clear that there are notable differences. In the oil-water two-phase
flow, the flow patterns were consistently ST & MI for input water cuts ranging from 60% to 80%
(Figure 4.22). However, a flow pattern transition occurred in gas-oil-water three-phase flow when the input
water cut reached 60%. The introduction of air appears to cause more mixing to the oil-water mixture and
induces the flow pattern transition.
Figure 4.37 Pictures of three-phase slug flow from a high-speed camera at V =0.5 m/s and V =0.2 m/s
SL SG
with 100% inlet choke opening (the percentages in the picture indicate the water cut).
When a 50% inlet choke opening is applied, the aforementioned observations for a 100% inlet choke
opening still hold with a difference that the mixing is better in the slug body and almost becomes fully
dispersed flow for 60% and 80% water cuts (Figure 4.39 and Figure 4.40). The ECVT images in this
situation are more helpful to better understand the flow patterns of the oil-water mixture. When the input
water cut is larger than 40%, the ECVT images exhibit an almost homogeneous red color indicating a
water continuous phase in the slug body.
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Water cut influences the flow pattern and therefore the pressure gradient of gas-oil-water three-phase
flow, which is shown by Figure 4.43. This effect is more obvious when the liquid-liquid mixture of the
three-phase flow has a dispersed state since water cut can greatly influence the viscosity of the liquid-liquid
mixture. The liquid-liquid mixture in gas-oil-water three-phase flow is stratified flow for 50% or higher
inlet choke openings when the water cut is less than 60%. By contrast, the liquid-liquid mixture
demonstrates a dispersed flow for a 30% inlet choke opening with an inversion point at 30% water cut. The
pressure gradient first decreases then increases with increasing water cut before the inversion point and
decreases again with a further water-cut increase after it. The decrease of pressure gradient at 20% input
water cut compared with pure oil could be caused by the drag reduction phenomenon. Pal (1993) studied
both stable and unstable emulsion flow in pipelines and stated that drag reduction could be caused by
droplet coalesce and breakup processes that modified the turbulence. He also argued that the drag
reduction was more evident in water-in-oil emulsion flow.
Figure 4.41 Pictures of three-phase slug flow from a high-speed camera at V =0.5 m/s and V =0.2 m/s
SL SG
with a 30% choke opening (the percentages in the picture indicate the water cut).
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4.2.4.3 Effect of Superficial Velocities
The experimental results at four superficial liquid velocities and five superficial gas velocities are
presented and discussed in this section.
Effect of superficial liquid velocity
An increasing superficial liquid velocity can alter the mixing state of the liquid-liquid mixture in
three-phase slug flow. Figure 4.44 and Figure 4.45 show the flow behaviors for four superficial liquid
velocities at 60% water cut and a superficial gas velocity of 0.2 m/s. When no inlet choking was applied,
the liquid-liquid mixture was stratified flow both in the film region and in the slug body for a V equal to
SL
or lower than 0.8 m/s. It becomes dispersed when the V increases to 1 m/s, as shown by Figure 4.44.
SL
The liquid-liquid mixture should be oil-in-water dispersed flow for a V of 1 m/s according to the ECVT
SL
result, shown in Figure 4.45. For V of 0.8m/s, the ECVT image shows an almost oil-in-water dispersed
SL
flow in the slug body, a water layer can still be observed from the high-speed video camera image. This
reveals the inaccuracy of the ECVT system in differentiating the pure water layer from the oil-in-water
layer. But, it can tell that the top layer in the slug body is not oil continuous for a V of 0.8 m/s.
SL
Figure 4.44 Pictures of slug flow from high-speed camera for different liquid velocities (0.2-1 m/s) at 100%
inlet choke opening, V =0.2 m/s, and 60% water cut of the liquid mixture.
SG
A comparison of the effect of superficial liquid velocity on the flow behavior for different inlet choke
openings reveals that fully dispersed flow forms at a lower superficial liquid velocity for a smaller inlet
choke opening, as shown in Figure 4.46 to Figure 4.49. A dispersed flow starts at a V of 0.8 m/s for a
SL
100% inlet choke opening, whereas a dispersed flow occurs at 0.5 m/s and 0.2 m/s for 50% and 30% inlet
choke openings, respectively.
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CHAPTER 5
MODELING STUDY
This chapter discusses the new hydraulic modeling of oil-water and gas-oil-water flows in horizontal
pipes. The new hydraulic modeling of oil-water flow focuses on the flow of a dispersion layer with a pure
phase layer that lacks specific attention in previous studies. The new hydraulic model of gas-oil-water flow
focuses on the flow pattern that shows some stratifications in the oil and water liquid phase. The following
two subsections discuss each model respectively.
5.1 Modeling Oil-water Two-phase Flow with a Mixing Layer
As discussed in Chapter four, a special flow pattern of oil-in-water over a free water layer was observed
for oil-water two-phase flow in this study. This flow pattern is critical for downstream pressure drop
prediction for liquid-liquid two-phase flow due to the high viscosity of the upper dispersion layer.
A method is proposed in this study to solve this problem based on the oil-water stratified flow model
proposed by Brauner (1998). As illustrated in Figure 5.1, the target flow pattern has a densely packed
oil-in-water layer over a free-water layer. The momentum equations for the dispersion layer and pure phase
layer can be written as Equation 5.1 and Equation 5.2. Eliminating the pressure gradient in the two
equations, one can get the combined momentum equation as in Equation 5.3.
Figure 5.1 Schematic of the flow pattern oil-in-water over a free water layer.
dp
−A −τ S −τ S +A ρ gsinβ =0 (5.1)
ddL d d I I d d
dp
−A −τ S +τ S +A ρ gsinβ =0 (5.2)
pdL p p I I p p
S S 1 1
τ d −τ p +τ S ( + )+(ρ −ρ )gsinβ =0 (5.3)
dA pA I I A A p d
d p d p
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As can be seen from Figure 5.1, the superficial velocities of the dispersion layer V and the free water
Sd
layer V are required to solve this problem. Assuming the water cut of the dispersion layer is WC , the
SW d
following two closure relationships can be obtained. It is apparent that WC is an extra unknown due to
d
the introduction of the dispersion layer. To solve this problem, either another correlation or its measured
data from experimental studies is needed. A closure relationship is proposed in this study as given in
Equation 5.6. At any given superficial velocities of the two pure phases (V and V in this case), the
SWi SOi
dispersion layer water cut, pure phase holdup, and pressure drop can be calculated. The proposed solution
procedure is shown as Figure 5.2.
V =V /(1−WC ) (5.4)
Sd SOi d
V =V +V −V /(1−WC ) (5.5)
SW SOi SWi SOi d
WC =(WC −H )/(1−H ) (5.6)
d i Lp Lp
Figure 5.2 Solution procedure for semi-dispersed flow.
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The data points that show O/W & W flow in this study were used to evaluate the new model. Initially,
the well-known Brinkman correlation is used to estimate the viscosity of the dispersion layer due to its
wide application in multiphase flow modeling. We also evaluated a homogeneous model that treats the oil
and water phases as a homogeneous mixture and compared its performance with the new model.
Figure 5.3 and Figure 5.4 are the cross-plots that show the performance of the homogeneous model and the
new model respectively, with Brinkman correlation for viscosity estimation. As expected, the homogeneous
model significantly underpredicts the pressure gradient. The new method does improve the prediction to
some extent when compared with the homogeneous model, however, the improvement is unsatisfactory.
One of the major uncertainties could be the estimation of the dispersion layer viscosity, which is not well
modeled in previous studies. In this study, we back-calculated the viscosity of the dispersion layer using
the framework of the new model with experimentally measured pressure gradient and compared them with
the prediction from Brinkman correlation. As shown in Figure 5.5, the Brinkman correlation indeed
significantly underestimates the dispersion layer viscosity. We need a better viscosity model to improve the
pressure gradient prediction for this type of flow pattern.
Figure 5.3 Performance of the homogeneous model in pressure gradient prediction when using Brinkman
correlation.
A new empirical correlation that estimates the dispersion layer viscosity is proposed in this study based
on the Brinkman correlation. According to the experimental results, the dispersion layer on top is water
continuous. However, the measured pressure gradient is notably high, suggesting the possibility of a very
high viscosity of the dispersion layer. In the Brinkman correlation, the dispersion viscosity is calculated
using the continuous phase viscosity, which can result in an underestimation of the dispersion layer
viscosity in O/W & W flow. Therefore, it is proposed in this study to multiply the Brinkman correlation
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with a coefficient C for semi-dispersion flow to account for the aforementioned high-viscosity effect
d
(Equation 5.7). It is further found in this study that this coefficient can be correlated with the water cut of
the dispersion layer in the O/W & W flow. The water cut of the dispersion layer is a parameter solved in
the new proposed model. It can also be approximated with the input water cut. The proposed correlation
(Equation 5.8) for C is fitted from the back-calculated viscosity data by the least square method. The new
d
empirical correlation for the dispersion layer viscosity for semi-dispersed flow is represented by Equation
5.7 and Equation 5.8.
The predicted viscosities from this new correlation are compared with those back-calculated from the
pressure gradient data and shown in Figure 5.6. As expected, it improves the viscosity prediction. Utilizing
this new viscosity correlation, we evaluated the performance of the homogeneous model and the newly
proposed model for pressure gradient predictions, and the results are shown in Figure 5.7 and Figure 5.8.
Both models show improved predictions, while the newly proposed method gives better predictions.
Figure 5.4 Performance of the new model in pressure gradient prediction when using Brinkman correlation.
C µ
µ = d c (5.7)
d (1−φ)2.5
C =37.38WC −5.03 (5.8)
d d
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Figure 5.7 Performance of the homogeneous model in pressure gradient prediction when using new viscosity
empirical correlation.
The newly proposed method can predict the pressure gradient and phase holdup if the two input
superficial liquid velocities for semi-dispersed flow are given, along with the fluid properties and pipe
geometrical parameters. It is noteworthy that this model framework can be applied to any flow pattern
that demonstrates a two-layer structure, such as a pure oil layer over water-in-oil dispersion layer.
However, as the range of the flow conditions for semi-dispersed flow is narrow in the current study, more
data are needed to validate the new model and improve the viscosity correlations for semi-dispersed flow in
the future.
5.2 Modeling Gas-oil-water Three-phase Slug Flow
This section describes the new model development for three-phase slug flow that shows stratifications,
followed by the model evaluation.
5.2.1 New Model development
Based on the experimental observations, we developed a three-phase slug flow model for pressure drop
and phase holdup predictions, with a focus on the flow pattern that shows some stratifications of the oil
and water liquid phases. Figure 5.9 shows the schematic of the three-phase slug flow mostly observed in
the current study, while the thicknesses of the top oil layer, mixing layer, and water layer depend on the
water cut, choking opening, liquid, and gas flow rates, etc.
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Figure 5.9 Schematic of three-phase slug flow that demonstrates stratifications in the liquid mixture phase.
A typical slug unit is composed of a liquid film region (also called gas pocket region) and a slug body
region with a length of L and L , respectively (Figure 5.9). The length of the slug unit is L which is the
F S U
summation of L and L . The other slug flow characteristic parameters are also illustrated in Figure 5.9.
F S
V is the translational velocity, which represents the slug front velocity. V and V are the average
T LS GS
liquid and gas velocities within the slug body, while V and V refer to the average liquid and gas
LF GF
velocities in the film region. H and H are the liquid holdup in the slug body and liquid film region
LS LF
respectively. The new hydraulic model is composed of two components, namely phase holdup and pressure
gradient predictions, which are explained in the following subsections respectively.
5.2.1.1 Phase Holdup Prediction
To keep the simplicity in liquid holdup prediction, we adopted the classical framework for slug flow unit
cell model proposed by Taitel and Barnea (1990) for gas-liquid two-phase flow. The oil and water phases
are treated as a single phase. We tested the impacts of mixture properties, especially the viscosity that
mostly influences the model performance, and found insignificant changes in the predictions of the
parameters shown in Figure 5.9. This demonstrates the feasibility of using gas-liquid two-phase flow slug
flow model for three-phase flow by treating the oil and water phases as the single phase with mixture
properties. To solve for the slug flow characteristic parameters listed in Figure 5.9, four continuity
equations and one combined momentum equation are employed, along with four closure relationships. The
continuity equations are developed based on the mass balance of the liquid and gas phases respectively, and
given in Equation 5.9 to Equation 5.12.
H (V −V )=H (V −V ) (5.9)
LS T LS LF T LF
(1−H )(V −V )=(1−H )(V −V ) (5.10)
LS T GS LF T GF
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L V =L H V +L H V (5.11)
U SL S LS LS F LF LF
L V =L (1−H )V +L (1−H )V (5.12)
U SG S LS GS F LF GF
The momentum balance equations for gas and liquid phases within the film region at the equilibrium
conditions are given by:
dp τ S τ S
− = F F − I I +ρ gsinβ (5.13)
dL H A H A L
LF p LF p
dp τ S τ S
− = G G + I I +ρ gsinβ (5.14)
dL (1−H )A (1−H )A G
LF p LF p
The combined momentum equation is given by:
τ S τ S 1 1
F F − G G −τ S ( + )+(ρ −ρ )gsinβ =0 (5.15)
H A (1−H )A I I H A (1−H )A L G
LF p LF p LF p LF p
where τ and τ are the liquid and gas wall shear stresses, Pa; S and S are the liquid and gas
F G F G
wetted perimeters as shown in Figure 5.10, m; A is the pipe cross-sectional area, m2; τ is the interfacial
p I
shear stress, Pa; S is the interfacial perimeter, m; ρ and ρ are the liquid and gas densities, kg/m3; and
I L G
β is the inclination from horizontal.
Figure 5.10 Illustration of pipe cross-section in the film region with wetted parameter listed.
The liquid and gas wall shear stresses, and the interfacial shear stress, can be determined from:
ρ |V |V
τ =f L LF LF (5.16)
F F 2
ρ |V |V
τ =f G GF GF (5.17)
G G 2
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ρ |V −V |(V −V )
τ =f G GF LF GF LF (5.18)
I I 2
where f and f are the liquid and gas wall friction factors that can be determined from correlations
F G
for single-phase flow, such as Blasius correlation, given in Equation 5.19 and Equation 5.20, where C = 16
and n = 1 for laminar flow and C = 0.046, and n = 0.2 for turbulent flow. We tested the sensitivity of
different interfacial friction factor correlations on the model performances and found insignificant changes.
For simplicity, we used the same interfacial friction factor correlation recommended by Taitel and Barnea
(1990), i.e, Cohen and Hanratty (1968) correlation (f = 0.0142), in our model.
I
ρ d |V |
f =C( L F LF )−n (5.19)
F µ
L
ρ d |V |
f =C( G G GF )−n (5.20)
G µ
G
where the hydraulic diameter of the liquid and gas phases, d and d , are determined by:
F G
4A 4A
d = F and d = G (5.21)
F S G S +S
F G I
A and A are the area occupied by the liquid and gas phases in the film region, m2. The geometrical
F G
perimeters, S , S , and S can be determined geometrically by assuming a flat interface which is
F G I
commonly true for gas-liquid horizontal pipe flows. The corresponding equations can be found in the paper
by Taitel and Dukler (1976). For the liquid density and viscosity, we simply used the oil density and
viscosity. The sensitivity analysis shows very minor changes in the liquid holdup predictions with these
fluid properties.
To solve for the parameters listed in Figure 5.9, four closure relationships are needed, namely the
translational velocity (V ), gas velocity in the slug body (V ), liquid holdup in slug body (H ), and slug
T GS LS
body length (L ). We employed the same closure relationships recommended by Taitel and Barnea (1990),
S
except the slug body length. Sensitivity analysis shows that these closure relationships have insignificant
impacts on the liquid holdup and pressure gradient predictions. Those closure relationships are given in
Equation 5.22 to Equation 5.24. For the slug body length, we assumed a constant of 1 m, instead of using
any existing correlations. One of the reasons is that most of the existing correlations significantly
overpredict the slug body length at our experimental conditions. However, it is worth mentioning that the
slug body length itself does not impact the liquid holdup or pressure gradient predictions, but the ratio of
slug body and film lengths, LS does. From the continuity equations, one can notice that LS only depends
LF LF
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on liquid film holdup (and the input liquid velocity) that is determined by the combined momentum
equation regardless of the value of L .
S
(cid:112) (cid:112)
V =c V +0.54 gdcosβ+0.35 gdsinβ (5.22)
T 0 M
gσ(ρ −ρ )
V =c V +1.54( L G )0.25H0.5 (5.23)
GS 0 M ρ2 LS
L
1
H = (5.24)
LS 1+(V /8.66)1.39
M
The calculation procedure to determine the slug flow characteristic parameters is given as follows. The
procedure is similar to the original one by Taitel and Barnea (1990), but with slight modifications for
three-phase flow.
1. Determine the liquid mixture velocity, V =V +V ; where V is the superficial water
SL SW SO SW
velocity, and V is the superficial oil velocity.
SO
2. Determine the mixture velocity, V =V +V .
M SL SG
3. Determine the translational velocity (V ), gas velocity in the slug body (V ), and liquid holdup in
T GS
the slug body (H ) from Equation 5.22 to Equation 5.24. Assume the slug body length to be 1 m.
LS
4. Determine the liquid velocity in the slug body, V , from the continuity equations, Equation 5.9 to
LS
Equation 5.12.
5. Guess a liquid holdup in the film region, H , determine the geometrical parameters, average liquid
LF
and gas phase velocities in the film region, V and V , from the continuity equations (Equation 5.9
LF GF
to Equation 5.12), wall shear stresses from Equation 5.16 and Equation 5.17, and the interfacial shear
stress from Equation 5.18.
6. Check the convergence of the combined momentum equation, Equation 5.15. If the convergence is not
reached, repeat the previous step. When the convergence is reached, proceed to the following step.
7. Determine the average liquid and gas phase velocities in the film region, V and V , and the slug
LF GF
body and film region lengths, L and L , from the continuity equations (Equation 5.9 to Equation
S F
5.12).
8. The average liquid holdup can be determined from either of the following equations:
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V H −V H +V
H = T LS LS LS SL (5.25)
L V
T
V H +V (1−H )−V
H = T LS GS LS SG (5.26)
L V
T
Once all the parameters are solved, we can proceed to the pressure gradient prediction, which is
explained in the next subsection.
5.2.1.2 Pressure Gradient Prediction
To predict the pressure gradient, we proposed a new model that considers the mixing between the oil
and water phases, as indicated previously in Figure 5.9. Figure 5.11 shows the schematic of the framework
of the new model for three-phase slug flow with all the necessary parameters listed. The liquid phase is
separated into two layers, namely a mixing layer and a water layer, to consider the stratifications in the
liquid phase. The mixing layer takes into account the complex mixing behaviors between the oil and water
phases, near the top of the liquid phase, as illustrated in Figure 5.9. In Figure 5.11, H represents the
LFML
average holdup of the mixing layer in the film region, H is the average holdup of the water layer in the
LFW
film region, H refers to the average holdup of the mixing layer in the slug body region, and H is
LSML LSW
the average holdup of the water layer in the slug body region. Figure 5.12 shows the phase distribution in
the new model for the film region and slug body region respectively. In the film region, S , S , S are
G ML W
the wetted perimeters of the gas, mixing layer, and water layer. S and S are the lengths at the
I IML
gas-mixture layer interface and the mixing and water layer interface. For horizontal pipe flow, we assume a
flat interface geometry, similar to the assumptions by Taitel and Dukler (1976) for two-phase flow.
Figure 5.11 Schematic of the three-phase slug flow model with two-layer assumptions in the liquid phase for
pressure gradient prediction.
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Figure 5.12 Schematic of the three-phase slug flow model at the pipe cross-section with two-layer
assumptions in the liquid phase in the film region (left) and slug body region (right).
The pressure drop over a slug unit is composed of two parts, namely the pressure drop in the slug body
region (∆P L ), which is the dominant one, and the pressure gradient in the film region (∆P L ). The
S S F F
total pressure gradient is determined by Equation 5.27.
dp ∆P L +∆P L
= S S F F (5.27)
dLTotal L
U
The pressure drop in the slug body region consists of the pressure drops from the mixture layer and the
water layer, and can be determined from the following equation:
τ S L τ S L
∆P = W W S + ML ML S +ρ gsinβL (5.28)
S A A S S
p p
To determine the wetted perimeters of the water and mixing layer, S and S , we assume that the
W ML
area occupied by the water layer equals the input water cut, i.e.,
H V
LSW =WC = SW (5.29)
H +H V +V
LSW LSML SW SO
One of the advantages of this assumption is that it captures the effect of the water cut on the pressure
drop. This assumption also captures the trend observed in the experimental studies. The wall shear
stresses from the water and mixing layer are determined by:
ρ |V |V
τ =f W LS LS (5.30)
W W 2
ρ |V |V
τ =f W LS LS (5.31)
ML ML 2
where f is the wall friction factor of the water layer, determined by the Blasius correlation:
W
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ρ d |V | 4A
f =C( W W LS )−n and d = W (5.32)
W µ W S
W W
f is the wall friction factor of the mixing layer, which is also determined by the Blasius correlation
ML
given in Equation 5.33. A sensitivity study has shown that the viscosity of the mixture layer, µ , plays a
ML
critical role in determining the pressure drops. We developed an empirical correlation for this parameter
based on our experimental observations, which will be introduced at the end of this section.
ρ d |V | 4A
f =C( W ML LS )−n and d = ML (5.33)
ML µ ML S
ML ML
The pressure drop in the liquid film region includes the pressure drops of the mixture layer, the water
layer, and the gas pocket region, given in Equation 5.34. The geometrical parameters have been illustrated
in Figure 5.12.
τ S L τ S L τ S L
∆P = G G F + W W F + ML ML F +ρ gsinβL (5.34)
F A A A F F
p p p
The shear stress for the gas layer is defined by Equation 5.17. The shear stresses for water and the
mixing layer can be determined by:
ρ |V |V
τ =f W LF LF (5.35)
W W 2
ρ |V |V
τ =f W LF LF (5.36)
ML ML 2
where the gas, water, and mixing layer friction factors can be determined from Blasius correlations, as
given by Equation 5.21 to Equation 5.38. Similar to the slug body, we assume the fraction of the area
occupied by the water layer in the liquid phase equals water cut, i.e., A =A H WC, where WC is the
W p LF
water cut. A flat interface can be assumed to determine the wetted perimeters and interface lengths. The
parameter that mostly impacts the model prediction is the viscosity in the mixing layer, similar to the
pressure drop in the slug body. For simplicity, we assume the viscosity of the mixing layer in the film
region in Equation 5.38 is the same as the one in the slug body. This assumption does not impact much of
the model prediction, due to the insignificant amount of pressure drop in the film region compared to that
of the slug body.
ρ d |V | 4A
f =C( W W LF )−n and d = W (5.37)
W µ W S
W W
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ρ d |V | 4A
f =C( W ML LF )−n and d = ML (5.38)
ML µ ML S
ML ML
Based on our experimental data, we propose a correlation for the mixing layer viscosity, that takes into
account the effects of choke opening, water cut, oil viscosity, and the liquid flow rate, as given in Equation
5.39. In Equation 5.39, µ is the reference viscosity which adopted the form proposed by Brinkman
ML0
(1952) with modified coefficient and exponent, as given in Equation 5.40. It provides a reference viscosity
as a function of dispersed phase fraction. We use the oil viscosity in both formulas in Equation 5.40 which
gives better results than that when using the viscosity of the dispersed phase. In our experiments, the
water cut at the inversion point, WC , is around 30%. The first coefficient (C ) in Equation 5.39, mainly
inv 1
accounts for the liquid mixture velocity effect on the mixing layer viscosity, which is also a function of the
water cut. The second coefficient (C ) accounts for the effect of choke on the mixing layer viscosity.
2
Consistent with the experimental observation, the higher the pressure drop across the choke, the higher the
mixing layer viscosity and therefore a higher pressure drop.
µ =C C µ (5.39)
ML 1 2 ML0
(cid:40)
2.2µ (1−WC)−0.4,WC <WC
µ = o inv (5.40)
ML0 1.6µ WC−0.4,WC ≥WC
o inv
V V
C =[(0.75WC+0.75)( SL −1)2+1]( SL)0.2 (5.41)
1 0.8 0.5
C =0.23(ln∆P +1)0.7+0.9 (5.42)
2 C
where WC is the water cut, -; WC is the water cut at the inversion point, -; µ is the oil viscosity,
inv o
Pa·s; V is the superficial liquid velocity, m/s; and ∆P is the pressure drop across the choke, kPa.
SL C
The following section discusses the model evaluation, as well as the model performance through
parametric studies.
5.2.2 Model evaluation
Besides the new model, we also evaluated other three existing two-phase slug flow models, namely
Zhang et al. (2003) unified model, Taitel and Barnea (1990) slug flow model, and Dukler and Hubbard
(1975) slug flow model, in which the oil and water phases were treated as the single liquid phase with
viscosity predicted by Brinkman (1952)’s correlation. The comparison between the model prediction and
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ε
=(cid:88)N (cid:114) (ε ri−ε 1)2
(5.47)
3 N −1
i=1
N
1 (cid:88)
ε = ( ε ) (5.48)
4 N i
i=1
N
1 (cid:88)
ε = ( |ε |) (5.49)
5 N i
i=1
ε
=(cid:88)N (cid:114) (ε ri−ε 4)2
(5.50)
6 N −1
i=1
where ε is the actual error of the ith data point; ε is the relative error of the ith data point; ε is the
i ri 1
average relative error; ε is the average absolute relative error; ε is the standard deviation of the relative
2 3
error; ε is the average of the actual error; ε is the average of the absolute error; ε is the standard
4 5 6
deviation of the actual error; and N is the number of data points.
To better evaluate the model performance, we assessed the performance of existing models, including
the new one, based on the flow pattern in three categories. We also conducted a parametric study to better
understand how the models capture the effects of different parameters on the pressure gradient. These
evaluations are discussed in the following subsections.
5.2.2.1 Model Evaluation Based on Flow Patterns
The seven identified flow patterns for three-phase slug flow are further categorized into three major flow
patterns based on the differences in the liquid-liquid mixing state, aiming to evaluate the current models’
efficacy for different flow patterns. The dispersed flow consists of oil-in-water and water-in-oil flows. The
semi-dispersed flow includes any flow pattern that has a dispersion layer with a pure oil/water layer. The
ST & MI indicates the existence of a stratified flow with a mixing interface either or both in the film region
and slug body.
The model comparisons are shown by Figure 5.14, Figure 5.15, and Figure 5.16. Both Taitel and
Barnea (1990) model and Zhang et al. (2003) model have a tendency to under-predict pressure gradients in
dispersed flow. Although the Dukler and Hubbard (1975) model has better predictions, the data points are
more scattered. However, the new model improves a lot and gives fairly accurate predictions.
For semi-dispersed and ST & MI flows, the existing three models still underestimate the pressure
gradient. By contrast, the new model gives even better predictions than those for dispersed flow. This is
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Figure 5.16 Comparison of pressure gradient prediction with experimental measurements for liquid-liquid
ST & MI flow in the three-phase slug flow.
5.2.2.2 Choking effect
As discussed in the experimental study section, the inlet choke enhances mixing between the oil and
water phases, which is closely related to the formation of the dispersion layer, the transition of the flow
pattern, and ultimately affects the pressure gradient. Figure 5.17 shows the model performance in
capturing the inlet choking effect on the pressure gradient for a superficial liquid velocity of 0.2 m/s. It is
apparent that both the Taitel and Barnea (1995) model and the Zhang et al. (2003) model largely
underestimate the downstream pressure gradient. Additionally, these existing models fail to capture the
increasing trend of pressure gradient with a decreased inlet choke opening. The Dukler and Hubbard
(1975) model happens to perform better than the other two models not specifically because it considers the
inlet choking effect, but because it has an extra term to consider the pressure drop in the mixing zone at
the slug front. Figure 5.18 represents the model performance at a higher superficial liquid velocity of 0.5
m/s. While all three models exhibit improved performance with increasing superficial liquid velocity, none
of them adequately capture the inlet choking effect on the downstream pressure gradient. Nevertheless, the
new model has the best performance and captures the inlet choking effect well. In summary, previous
models have been found to perform poorly in capturing the inlet choking effect, with the Taitel and Barnea
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Figure 5.20 Pressure gradient as a function of liquid mixture velocity for different choke openings.
5.2.2.5 Effect of Water Cut
Water cut is one of the most important parameters that impact the flow pattern. Flow pattern
transition is also closely linked to water cut, with the impact of water cut being particularly significant in
dispersed flow regimes. When it is dispersed flow, an inversion point exists after which the pressure
gradient demonstrates an abrupt change. Figure 5.21 and Figure 5.22 present the model performance in
capturing the water cut effect on the pressure gradient of three-phase slug flow.
At a superficial liquid velocity of 0.2 m/s, the liquid-liquid mixture exhibits non-dispersed flow, and the
pressure gradient does not vary much with the water cut. However, as the inlet choke opening decreases
from 100% to 30%, the pressure gradient increases. As expected, the three existing models fail to capture
the influence of the inlet choking effect on the downstream pressure gradient (Figure 5.21). The Dukler and
Hubbard (1975) model yields predictions that are closer to the experimental measurements but exhibits
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greater scattering. On the other hand, the Taitel and Barnea (1990) and Zhang et al. (2003) models
significantly underestimate the pressure gradient. The new model developed in this study exhibits the best
performance when water cut is the variable being changed, particularly at such a low superficial liquid
velocity. This can be due to the consideration of the stratification in the liquid mixture in the new model.
At a superficial liquid velocity of 0.5 m/s, all three existing models give close predictions but
underpredict the pressure gradient (Figure 5.22). The liquid-liquid mixture exhibits dispersed flow in the
three-phase slug flow regime when the inlet choke opening of 30% is used. An inversion point was observed
at a 30% water cut, resulting in significant changes in the experimental pressure gradient. All three of the
previous models are able to capture the observed trend, but they tend to underpredict the pressure
gradient. In contrast, the new model significantly improves the prediction. However, it is important to note
that the model’s performance deteriorates when the liquid mixture transitions to dispersed flow at a 30%
inlet choke opening, as this condition no longer meets the assumptions made by our model.
Figure 5.21 Pressure gradient as a function of water cut for different choke openings at V =0.2 m/s.
SL
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While all three of the previous models are capable of capturing the trend of the water cut effect on the
downstream pressure gradient, they struggle in predicting the inlet choking effect on the pressure gradient.
This is especially true when a dispersed flow is present at a small inlet choke opening, as the models
experience a significant deterioration in performance under such conditions. In contrast, the new model
successfully captures the inlet choking effect and shows a significant improvement in pressure gradient
prediction. It is particularly superior when the liquid mixture in three-phase flow is not fully dispersed.
Figure 5.22 Pressure gradient as a function of water cut for different choke openings at V =0.5 m/s.
SL
The efficacy of three slug flow models - Dukler and Hubbard (1975), Taitel and Barnea (1990), and
Zhang et al. (2003) - was evaluated using the experimental data collected in this study for gas-oil-water
three-phase slug flow, and compared with the newly developed model in this study. The evaluation was
multi-faceted, assessing the models’ performance in three flow pattern categories, as well as their responses
to the inlet choking effect, superficial gas velocity effect, superficial liquid velocity effect, and input water
cut effect.
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CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
A horizontal flow loop with a 43-ft long test section was constructed to study the fluid flow behavior of
oil-water two-phase and gas-oil-water three-phase flows downstream of a 2-in. ball valve. The primary goal
of this research is to understand the impact of the inlet choke opening on the downstream fluid flow
behaviors at various flowing conditions, with the ultimate aim of improving the hydraulic models in
horizontal pipelines for better pressure gradient and phase holdup predictions. The significant findings are
summarized below. Recommendations for future research are discussed at the end.
6.1 Oil-water Two-phase Flow
This study identified seven flow patterns for oil-water flow, which include ST & MI, W/O & W, O &
W/O, O/W & W, W/O, and O/W. The W/O & W, O & W/O, and O/W & W can be further categorized
as semi-dispersed flow, which has attracted significant interest due to its very high viscosity and a
corresponding substantial downstream pressure gradient. Notably, most of the observed semi-dispersed
flow is O/W & W in our current experimental conditions. Our experimental study shows that the inlet
choke opening is closely related to interface mixing. Increasing the inlet choking can thicken the mixing
layer until partial inversion occurs, leading to the formation of semi-dispersed flow. Moreover, inlet choking
can affect the droplet size of the mixing layer and influence mixture viscosity. Additionally, we observed a
flow pattern transition from stratified with a mixing interface to oil-in-water dispersion above a water layer
for both a mixture velocity of 0.2 and 0.5 m/s. Increasing the mixture velocity accelerated the flow pattern
transition at a smaller inlet choke opening.
In this study, we proposed a new method to model the semi-dispersed flow in liquid-liquid flow. Our
new method allows for the direct solution of the dispersed volume fraction of the dispersion layer in
semi-dispersed flow given the superficial velocity for each phase. We evaluated the model using all the
collected data of O/W & W in this study and compared it with the homogeneous model. Our new method
showed some improvement compared to the homogeneous model, but it still underpredicted our
experimental data. We identified the viscosity of the dispersion layer as one of the major sources that lead
to underpredictions. We found that the Brinkman (1952) viscosity correlation, which is widely used,
performed poorly for semi-dispersed flow. To address this issue, we proposed a modified Brinkman
equation that significantly improved the model’s performance for semi-dispersed flow. With the new
viscosity empirical correlation, the pressure gradient prediction showed significant improvement, with most
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experimental data falling within a ±20% error range.
6.2 Gas-oil-water Three-phase Flow
In this study, the flow pattern of gas-oil-water three-phase flow was defined by combining the gas-liquid
and liquid-liquid flow patterns. Slug flow was the dominant gas-liquid flow pattern observed in the current
study. The liquid-liquid mixture’s flow pattern was identified in the liquid film region and slug body region
separately. The flow pattern was identified through videos from a high-speed camera and the phase
distribution data from an ECVT system. We identified seven flow patterns in this study, including
SLUG(O/W-S, O/W & W-F), SLUG(ST & MI-S, ST & MI-F), SLUG(ST & MI-S, O/W & W-F),
SLUG(O/W & W-S, O/W & W-F), SLUG(O/W-S, O/W-F), SLUG(W/O-S, W/O-F) and SLUG(DD-S,
DD-F).
The experimental results indicate a close relationship between the inlet choke opening and the mixing
state of the liquid-liquid mixture in three-phase flow at a fixed gas flow rate. The liquid-liquid mixture
mixes better in the gas-oil-water flows compared to the respective liquid-liquid two-phase flow.
Additionally, the water cut is another factor that influences the flow pattern of the liquid-liquid mixture in
three-phase flow at a fixed air flow rate and inlet choke opening. Flow pattern transition was observed as
the water cut varied, and the transition largely depended on the inlet choke opening.
The superficial liquid velocity was found to enhance the mixing state of the liquid-liquid mixture in
three-phase slug flow at a given gas flow rate and inlet choke opening. We also observed that an increased
superficial gas velocity from 0.2 to 0.6 m/s was not sufficient to change the flow pattern at a fixed inlet
choke opening and superficial liquid velocity, but still improved the mixing between the oil and liquid
phases slightly. The pressure drop in the test section increases with increasing liquid velocity or gas
velocity, as expected.
A new hydraulic model was developed in this study to improve the pressure gradient prediction of
three-phase slug flow in a horizontal pipe downstream of a choke. The performance of our new model was
compared with existing slug flow models, including Dukler and Hubbard’s (1975) model, Taitel and
Barnea’s (1990) model, and Zhang et al.’s (2003) model, by evaluating their predictions against our
experimental data on three-phase slug flow downstream of the inlet choke. In general, the comparison
reveals that the existing models significantly underestimate the pressure gradient for our experimental data
and particularly fail to capture the effects of inlet choking. Taitel and Barnea’s (1990) and Zhang et al.’s
(2003) models give close predictions. Dukler and Hubbard’s (1975) model only considers the pressure drop
in the slug body with an extra term to consider the pressure drop from the mixing eddy. Though this
additional term makes their model slightly better, the predictions are more scattered. In contrast, the new
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model demonstrates a significant improvement in pressure gradient predictions. Parametric studies show
that the new model captures well the effects of choking opening, water cut, liquid and gas flow rates on the
pressure gradient. Although the new model was developed for gas-oil-water three-phase flow that shows
stratifications in the liquid mixture, it still provides reasonable predictions for dispersed flow of the
respective liquid-liquid mixture.
6.3 Recommendations for Future Study
The primary focus of this study is to understand the effects of inlet choking on downstream flow
behaviors in oil-water two-phase and gas-oil-water three-phase flows. Based on our current findings, we
suggest several related topics that warrant further investigation. We discuss these areas, which pertain to
oil-water two-phase flow and oil-water-gas three-phase flow, separately in the following two sections.
6.3.1 Oil-water Two-phase Flow
As was found in this study, semi-dispersed flow can exist over a wide range of system conditions when
the mixture flow rate is comparatively low. We observed a mixing interface in all our experiments for
stratified flow. The mixing layer at the interface grows both with increased inlet choking and mixture
velocity before becoming fully dispersed flow. The mixing interface grows with an increased mixing level
till to a point when a partial inversion occurs, leading to the formation of a semi-dispersed flow pattern.
Inlet choking plays a crucial role in the formation of semi-dispersed flow, and we observed both W/O & W
and O/W & W semi-dispersed flows which are of particular interest due to the significant increase in
pressure gradient. It is worth noting that accurate estimation of partial inversion is challenging, even in
experiments. Therefore, more research is necessary to study both inversion and flow pattern transition in
pipe flow, especially for semi-dispersed flow.
Despite the abundance of viscosity models/correlations for liquid-liquid mixtures in the literature, most
of them are empirical correlations for well-mixed flow, and few are developed for fluid flow in pipes. For
example, one of the most commonly used models for liquid-liquid mixture is the Brinkman (1952) model,
originally proposed for suspensions based on Einstein’s (1906) equation. However, this model is an
empirical correlation and does not work well for pipe flow such as our experimental data. It is also
recommended to conduct a thorough and systematic evaluation of other more recent existing predictive
models for liquid-liquid mixture viscosity using the experimental data from the current study, to better
understand their suitability. Moreover, it is crucial to test the validity of the newly proposed model, using
additional data available in the literature. Dense emulsion with a shear-thinning phenomenon can occur,
particularly in the presence of inlet choking. Although some models are proposed to be applicable to
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emulsions, most are based on experimental studies in static mixers. There are few efforts to correlate the
shear in a static mixer to the shear in a pipe flow, especially for turbulent flow. Direct applications of these
models/correlations to multiphase pipe flow can be problematic. There is also no systematic evaluation of
current viscosity models/correlations based on multiphase pipe flow data. Additionally, no existing
viscosity model or correlation accounts for droplet size, which can be a significant factor that is greatly
impacted by the inlet choke opening and subsequently affects the downstream pressure drop. Therefore, a
better understanding of the relationships between the pressure gradient and droplet size in multiphase pipe
flow is critical for improving hydraulic models in this field.
To ensure more accurate and representative data for future modeling studies, advanced measuring
techniques are necessary. While mineral oil is often used in laboratory studies due to its simple
composition and minimal safety concerns, the oil and gas industry has a variety of oils with different
properties and compositions. In order to conduct experimental studies using crude oil, more suitable
devices are needed as the fluid can be very dark and difficult to measure. For instance, measuring droplet
size in such cases can present a significant challenge.
6.3.2 Gas-oil-water Three-phase Flow
While gas-liquid two-phase slug flow has been extensively studied, there is a dearth of literature on
gas-oil-water three-phase slug flow. Three-phase flow is considerably more complex than two-phase flow,
necessitating the use of assumptions when applying gas-liquid slug flow models to three-phase flow.
Therefore, obtaining additional experimental data is still necessary to improve slug flow modeling and
accurately capture the physics in three-phase flow. Furthermore, investigating three-phase slug flow in
inclined pipes can be for future research.
Despite the capability of the current slug flow models, further improvements are necessary as they rely
heavily on empirical correlations. Parameters such as slug length, slug frequency, transnational velocity,
and liquid holdup in the slug body are typically calculated from these correlations, which can lead to a
significant amount of uncertainty. For instance, slug length is actually a distribution, yet current models
often use a constant calculated from an empirical correlation. Utilizing probability modeling for input
parameters can be a more accurate alternative than using an average value. Additionally, further study is
required to investigate friction factors, particularly the interfacial friction factors.
Slugflowisacomplex, transientflow, especiallyinthree-phaseflow, whichposesanumberofchallenges.
As a result, current models approximate the solution by assuming a steady state. However, further
simulations using computational fluid dynamics can aid in a better understanding of three-phase slug flow.
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Our Ref: ldis/03048303 4/1/2023 Dear Requester, Thank you for your correspondence requesting
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Type of use: Academic Article title: Experimental study of the relative effect of pressure drop and
flow rate on the droplet size downstream of a pipe restriction Article DOI:
10.1080/01932691.2016.1207184 Author name: Martin Fossen & Heiner Schu¨mann Journal title:
Journal of Dispersion Science and Technology Volume number: 38 Issue number: 6 Year of
publication: 2017 Name: DENGHONG ZHOU Street address: 1600 Arapahoe St Town: Golden
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this a “Closed” or “Open” deposit?: open
15. Figure 2.26, Figure 2.28 and Figure 2.30 are reprinted from International Journal of Multiphase
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ABSTRACT
The increasing demand for the rare earth elements (REEs) is driven by new
technologies, including computers, automobiles and other advanced technology
applications. Currently, bastnasesite, monazite and xenotime are three major commercial
rare earth minerals throughout the world. China is the biggest rare earth producer,
however, because of the restriction of Chinese rare earth export, the rest of the world has
been to develop proper rare earth resources to replace supply from China. Ancylite, a
rare earth strontium carbonate, is a potentially commercial rare earth mineral. In this
research, the materials obtained from Bear Lodge, Rare Earth Resources, Ltd., were
investigated to develop a proper procedure to efficiently separate rare earth minerals from
their gangue minerals. Mineralogical characterization shows that ancylite is the dominant
rare earth mineral, and calcite is the major gangue mineral, which is strongly associated
with ancylite. The surface chemistry aspects, including electrokinetics, hydroxamic acid
adsorption and microflotation, of ancylite, strontianite and calcite were also investigated.
Fundamental understanding of the flotation chemistry for ancylite, calcite and strontianite
was utilized to delineate the strategy of flotation chemistry for the materials from Bear
Lodge. Magnetic separation combined with flotation was employed to beneficiate ancylite,
and a preliminary evaluation was conducted as well. The end result shows the promising
potential in the separation of ancylite by magnetic separation and froth flotation. This work
was conducted within the Kroll Institute for Extractive Metallurgy (KIEM) and Critical
Materials Institute (CMI).
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CHAPTER 1
INTRODUCTION
Rare earth elements (REEs) are widely used for many commercial applications in
high-technology and national defense over the past four decades. However, there are
several issues of REEs supply for the United States including the dependence on imports
from China and losing its leadership in many areas of REEs technologies. Because of
China’s export restrictions and growing internal demand for its REEs, additional rare earth
capacity has been expected to be developed in the United States, Australia and Canada.
Currently, bastnaesite and monazite are two major economically exploited rare
earth minerals throughout the world. A large amount of literature has been published to
investigate the separation of bastnaesite and monazite from their gangue minerals such
as calcite, barite, and apatite. Nevertheless, other rare earth minerals have been rarely
studied. In this research, ancylite, a rare earth strontium carbonate, will be investigated
for its surface characterization. The fundamental studies of pure ancylite, strontianite and
calcite flotation behaviors in the presence of hydroxamic acid will be also studied. Another
focus of this study will be on the recovery of ancylite from a real ore which contains
ancylite.
The ore containing ancylite was provided by Bear Lodge rare earth deposit,
Wyoming, which is 100% owned by Rare Element Resources Ltd.
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CHAPTER 2
LITERATURE REVIEW
A literature review of rare earth resources, beneficiation methodologies and
flotation reagents related to rare earths and calcite, as well as strontianite was conducted
in order to completely understand the background information and theory of the
experiments.
2.1 Rare Earth
The rare earth elements, as we all know, are a group of lanthanides and yttrium
(atomic number 39), plus scandium (atomic number 21), which are chemically similar to
the lanthanides. The lanthanides contain the following: lanthanide, cerium,
praseodymium, neodymium, promethium, samarium, europium, gadolinium, terbium,
dysprosium, holmium, erbium, thulium, ytterbium, and lutetium (atomic number 57-71).
The group of rare earths could be divided into two subgroups, namely light rare earth
elements (LREEs) and heavy rare earth elements (HREEs), based on the atomic weight.
LREEs normally contain from lanthanide to neodymium, sometimes including samarium,
while HREEs are a group of rare earth elements whose atomic number is from 63 to 71,
and yttrium is considered heavy rare earth because of the chemical similarity as well [1].
Unlike the other elements in the periodic table, the size of lanthanide atoms and ions
steadily decreases with the increase in atomic number, which is named by the term of
lanthanide contraction. Similarity of the size of the yttrium atom and tripositive ion with the
heavier lanthanide can explain that the occurrence of yttrium is associated with the
heavier lanthanide [1]. Besides, lanthanide contraction also contributes to basicity that
determines that rare earth cations can hydrolyze in aqueous solutions [1] and form a
stable complex with certain chelating agents, which will be illustrated the detail in Chapter
2.4.2. Due to the similarity of ionic radii and the trivalent charge, they are commonly
associated with each other.
The rare earth elements are, contrary to the name, relatively abundant in the
Earth’s crust. Cerium which is the most abundant rare earth element, as shown in Figure
2.1, is more plentiful than copper, lead, etc. [1]. The estimated average concentration of
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Table 2.1 Estimates of the crustal abundances of rare earth elements
Hawkesworth and
Taylor [3] Wedepohl [4]
Rare earth elements Kemp [5]
ppm ppm
ppm
lanthanum 30 30 20
Cerium 60 60 43
Praseodymium 8.2 6.7 -
Neodymium 28 27 20
Samarium 6.0 5.3 3.9
Europium 1.2 1.3 1.1
Gadolinium 5.4 4 3.7
Terbium 0.9 0.65 0.6
Dysprosium 3.0 3.8 3.6
Holmium 1.2 0.8 -
Erbium 2.8 2.1 2.1
Thulium 0.48 0.3 -
Ytterbium 3.0 2 1.9
Lutetium 0.5 0.35 0.3
Yttrium 33 24 19
Total 183.68 168.3 119.2
Currently, bastnaesite, monazite and xenotime are the only three rare earth
bearing minerals can be economically exploited. Bastnaesite with the content of 70%
REO, mostly consisting of light rare earth elements, is the primary source of rare earth in
rare earth production [1]. Monazite was the chief source of rare earths before bastnaesite
became the principal source in the world [6]. Monazite, a rare earth phosphate, is mainly
present in beach placers that contain other heavy minerals like ilmenite, rutile and zircon
throughout the world, including Australia, China, India and USA [1]. Nevertheless, most
of monazite extraction is not viable because of the cost associated with the disposal of
thorium and uranium present in the monazite [7]. Other than three major rare earth
minerals, a limited discussion of numerous minerals than contain rare earth has been
published. For instance, ancylite, a group of strontium carbonate minerals enriched by
cerium, lanthanum and minor amount of other rare earth [8], is rarely studied. Ancylite is
a carbonate mineral whose chemical formula is: (RE) x(Sr, Ca) 2-x(CO 3) 2(OH) x● (2-x)H 2O
[9]. Ancylite-(Ce) and ancylite-(La) are common types which occur in some nepheline
syenites and carbonates [10]. The composition of ancylite varies from place to place. It is
distributed throughout the world including in Canada, Russia, U.S.A, Brazil and
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2011 [10][14]. China ranks the first in mine production with 91%; the second is the United
States with 3.64%, and the third is India with about 2.64% [15]. Fig. 2.3 shows Chinese
rare earth production increased steadily until 2006 which is consistent with the global
production trend, while the United States shut down the Mountain Pass Mine in California
in 2003. Since 2010, because of the restriction of Chinese rare earth exports, the
production decreased slightly, while the United States started producing rare earth again
in 2012.
China has been in the dominant position in the rare earth supply market for over
15 years [15]. China is cracking down on illegal rare earth mines and consolidating
legitimate rare earth mines. In 2012, the Ministry of Industry and Information Technology
of the People’s Republic of China reported that more than 600 cases of illegal prospecting
and mining were investigated, and 13 mines and 76 smelting and separation enterprises
were ordered to cease production [25]. However, since the restriction of the supply of
REO has been issued because of the environmental and domestic concerns in China [26],
more efforts have been made all over the world to develop rare earth deposits in order to
make up the decrease of Chinese exports of rare earth and meet the increasing demand
for rare earth end products. Aside from several existing rare earth plants, including Mayan
Obo in Inner Mongolia, and Mountain Pass in the U.S.A., there are still a large number of
projects under development throughout the world.
2.4 Beneficiation of Rare Earth
Commonly, rare earth minerals are separated through gravity separation,
magnetic separation and froth flotation based on their different specific gravity, magnetic
quality and surface chemistry with gangue minerals.
2.4.1 Gravity Separation of Rare Earth
Due to the relatively high specific gravity (4 – 7 g/cm3), rare earth oxides can be
recovered from low density gangue minerals through gravity separation. Gravity methods
currently include jigs, shaking tables, centrifugal gravity concentrators and others [27]. In
order to extract the minerals from heavy, coarse beach sand, gravity separation is
commonly used. The complexity of the minerals contributes to the combination of several
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140000
United States
120000
China
100000 World Total
O 80000
E
R
S
N
O 60000
T
40000
20000
0
Figure 2.3 American, Chinese and the world REO production between 1994- 2013.
(Sources from [10],[14],[16]-[24])
The typical flowsheet of the heavy mineral sand from Congolone, Mozambique is
shown in Fig. 2.4 [28]. Moreover, gravity separation can be used in beneficiation of
bastnaesite as well. Õzbayoğlu et al. (2000) reported that using cyclones and multi-gravity
separators (MGS), a bastnaesite concentrate with around 35.5% REO grade and 48%
recovery was obtained [6]. In the Mianning rare earth plant, gravity separation was
employed in conjunction with flotation. As shown in Fig. 2.5, after gravity separaton, three
different grade bastnaesite concentrates were obtained with the grades of around 30%,
50% and 60%, respectively [29].
2.4.2 Froth Flotation of Rare Earth
Three important rare earth plants, the Bayan Obo rare earth deposit, the Mount
Weld Rare Earth deposit and the Mountain Pass deposit, employ froth flotation to recover
rare earth minerals. Common collectors, such as fatty acid, dicarboxylic acids,
hydroxamic acids and phthalicimide, have been used in flotation of rare earth [30],[28]. In
the Mount Weld Central Lanthanide Deposit, the material with 38µm of particle size was
treated by three-stage flotation to recover approximately 70% of REO with 40% assay
[31]. In the Mountain Pass, the feed for flotation was the product of crushing and grinding.
Using oleic acid as the collector, sodium fluorosilicate and ammonium lignin sulfonate as
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depressants, oil C-30 as the frother, and soda ash as the adjusting reagent, the final
concentrate was obtained at 70°C to 90°C with 60% REO assay and 65% to 70%
recovery [1]. Ren et al. [32] reported that 85% of the bastnaesite was recovered in a
concentrate with 69.5% REO grade that contained 97% bastnaesite in the presence of
bezoic acid as the collector and potassium alum as the depressant. Morrice and Wong
(1982) tested oleic acid, linoleic acid and AERO 845, which is the petroleum sulfonate
product, as the collectors to recover bastnaesite from gangue minerals [33]. The
flowsheet of Bayan Obo plant is described in Fig. 2.6. The feed with 9.78% to 12% grade
REO from high intensity magnetic separation (HIMS) cleaner tailings was conditioned by
naphthyl hydroxamic acid, sodium silicate and J . The final concentrate was obtained at
10
a REO grade of 55% with the combined recovery of 72% to 75%. [29]
Apart from bastnaesite flotation, monazite can be also recovered by froth flotation.
Abeidu (1972) [34] reported that Na S efficiently activated the soap flotation of monazite
2
from zircon, because after adsorption of SH- and S2- onto the monazite surface, the
attachment of oleic acid and SH- was stronger than that of HPO 2- and oleic acid. Cheng
4
et al. (1993) reported that the chemisorption occurred in the interface of monazite and
sodium oleate, and the maximum floatability of both monazite and xenotime happened at
pH values greater than 7 [35].
There have been a number of monographs published on the study of the
hydroxamic acid as the chelating collector for the flotation of sulfide minerals, oxide
minerals and rare earths. Hydroxamic acids, the derivatives of both hydroxyl amines and
carboxylic acids [36], are weak acids, which could be attributed to the polarization of OH
and NH bonds because of the shift of the electron density. Nevertheless, it is less acidic
than fatty acid, because the electronegativity of O connecting with carbonyl is stronger
than that of N in the hydroxamic group [37]. They, represented by the general formula R-
CO-NHOH, exist in two tautomeric forms shown in Fig. 2.7 [38]. Hydroxamic acid is widely
employed in flotation, because it is where chelation occurs, as shown in Fig. 2.8; here, a
metal ion replaces hydrogen, using the carbonyl oxygen atom to create a ring closure
[39]. The pK of the usual hydroxamic acids is close to 9, which is in accordance with pH
a
of the optimum recovery and maximum adsorption achieved.
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Figure 2.7 Two tautomeric forms of hydroxamic acid [38]
Figure 2.8 The formation of a metal complex in addition of hydroxamic acid [39]
The smaller degree of ionization of hydroxamic acids results in the higher melting
point of hydroxamic acids compared with that of fatty acids with the same carbon atoms
and the five orders lower electric dissociation constants in contrast to those of fatty acids
[37]. The results of several investigations showed that the stability constant and solubility
of the chelating agents were two pronounced factors for selectivity and collection power
[40],[41]. In table 2.3, it is very clear that the stability constants of ferrous, non-ferrous
and rare earth elements are much higher than those of the alkali and alkali-earth ions,
which is expected. The reason that hydroxamic acids can complex with various metals is
that hydroxamic acid not only plays a partly covalent character and tends to form biases
covalent chemical adsorption with some transition metals, but also processes an
intermediate base from the viewpoint of classification of Lewis acids and Lewis bases for
collectors [37]. It is also identified by Pradip and Fuerstenau [38] that the strongest
complexes are formed with rare earth elements, while the weakest complexes are those
formed with alkaline earth metal cations. As mentioned earlier, however, the stability that
favors the adsorption density and kinetics is not the only factor that can affect selectivity,
solubility sometimes plays a significant role in increasing the adsorption kinetics, because
adsorption occurrence needs a certain solubility of mineral in order that the hydrolysis of
the lattice cation, chemisorption, and surface reaction, as well as precipitation in the
interface of minerals and collectors take place. Assis S.M. et al. (1996) reported that the
selectivity of minerals flotation with hydroxamates relied on a balance between the
mineral solubility and stability constant of complex hydroxamate/lattice cation, and the
kinetics of hydroxamates adsorption were extremely low. [41] Chander and Fuerstenau
(1975) [43] illustrated that there were three possible ways, chemisorption, surface
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reaction and bulk precipitation, to describe how the reagent-metal can be formed.
Chemisorption is limited to a monolayer owing to the interaction of the reagent with the
interface without movement of metal atoms from their lattice sites, and the difference
between surface reaction and bulk precipitation is that surface reaction involves the
interaction of reagents in the interface of the minerals with the metal ion moved from the
lattice sites, whereas bulk precipitation occurs in the solution involving reagents with
metal ions. Pradip and Fuerstenau [38] reported a series of equations to illustrate these
chemisorption and surface reaction mechanisms (Figure 2.9). In Fig. 2.9, the metal ion to
the left of the dotted line means that it is in its lattice position, while the metal ion to the
right of the dotted line indicates that it is moved from the lattice position.
Table 2.3 Stability constant of hydroxamic acid salt at 20°C and I = 0.1 (NaNO )
3
[42]
ion Log K LogK LogK
1 2 3
H+ 9.35
Ca2+ 2.4
Mn2+ 4.0 2.9
Fe2+ 4.8 3.7
Co2+ 5.1 3.8
Ni2+ 5.3 4.0
Zn2+ 5.4 4.2
Pb2+ 6.7 4.0
Cu2+ 7.9
La3+ 5.16 4.17 2.55
Ce3+ 5.45 4.34 3.0
Sm3+ 5.96 4.77 3.68
Gd3+ 6.10 4.76 3.07
Dy3+ 6.52 5.39 4.04
Yb3+ 6.61 5.59 4.29
Al3+ 7.95 7.34 6.18
Fe3+ 11.42 9.68 7.23
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temperature. They identified that hydroxamic acids were favorably specific to rare earth
elements instead of alkaline earth elements, and the formation of complex between rare
earth and hydroxamic acid was endothermic by calculating the free energy. Fuerstenau
et al. (1970) compared flotation of iron oxide in the presence of hydroxamate and fatty
acid, and found that the usage of hydroxamate was much lower than that of fatty acids,
even though the adsorption of fatty acids and hydroxamates were chemisorption. [47]
Liang et al. [48] made a comparison of properties of carboxyl and hydroxyl oxime groups
based on the effect of chelation and the energy of conjugated Pi bonding for active group
of specific collectors. The results showed that the hydroxyl oxime group ranked the top in
energy of conjugated Pi bonding, followed by carboxyl group and carbonyl, which
suggested the highest stability of the rare earth complex could be achieved by the
hydroxyl oxime group and carboxyl that constituted the hydroxamic acid. Ren et al. (1997)
showed that MOHA, modified hydroxamic acid, was a selective and efficient collector for
bastnaesite flotation with chemisorption accompanied with the non-homogeneous and
physical adsorption [49]. Xu et al. [50] found 1–hydroxyl-2-naphthaldoximic acid as a new
collector to float bastnaesite and monazite from silicate minerals in the presence of water
glass as the depressant efficiently. Pavez et al. (1996) suggested that the adsorption
mechanism of hydroxamic acid on monazite and bastnaesite was chemisorption at pH =
9 and pH = 9.3, respectively, while physical adsorption of sodium oleate on monazite and
bastnaesite occurred throughout the pH and chemisorption of sodium oleate on
bastanesite occurred at pH = 3. [51] Moreover, C. A. Pereira et al. [52] reported that the
recovery of xenotime in microflotation tests could be reaching 93.9% and 96.5%,
respectively, in the presence of hydroxamic acid as the collector, and sodium silicate and
starch as the depressants.
As the main gangue mineral associated with rare earth minerals, calcite has been
extensively studied for several decades, including its PZC (point of zero charge),
adsorption in hydroxamic acid and fatty acid, the performance in the presence of various
depressants, and flotation behavior as a function of temperature. Different isoelectric
points of calcite were reported in the literature. There is a considerable variance, ranging
from 5 to 10.5 ([53], [[54], [55] and [56]). Mountain Pass employed sodium fluorosilicate
and ammonium lignin sulphonate as the reagents to depress calcite and barite. Hernainz
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et al. [57] reported that quebracho and sodium silicate were more effective on depression
of calcite than of celectite, in the presence of sodium oleate. As reported, sodium silicate
was also employed in Bayan Obo rare earth deposit to depress calcite with the collector
of H205. Compared with plenty of monographs on calcite, there is a limited literature on
strontianite, probably because strontianite in industry is commonly regarded as the end-
product. Martínez and Uribe (1995) reported that, from the view of thermodynamics, the
isoelectric point (defines as the pH of equilibrium of salt-type mineral slurry) of strontianite
aqueous suspension took place at pH 8 and the IEP (defines as the zeta potential at the
plane of shear is zero) occurred at pH 7.4. [58]
2.5 Beneficiation of Bear Lodge Ore, Wyoming
The Bear lodge project, located in northeast Wyoming, is held by Rare Element
Resources, Inc. Based on the Measured & Indicated (M&I) resource in March 2013 [59],
the total combined resource for both Greater Bull Hill deposit and Whitetail Ridge deposit
is 31.8 million tons assaying 2.58% REO at a 1.5% cutoff grade. Currently, the proposed
operations at the Bear Lodge Project [59] consists of the following: (1) a small open pit
mine at both the Bull Hill and Whitetail deposits; (2) a physical upgrading plant (PUG),
including crushing, washing, screening and magnetic separation, for pre-concentration of
the rare earth-bearing fines and reduction of the associated physical mass; (3) a
hydrometallurgical plant for further concentration of the rare earth elements. A couple of
both PUG batch tests and pilot tests were completed by SGS, Lakefield. Four composites
with different feed assays of REO were used to run PUG pilot tests. Depending on the
various mineralogical characterizations of deposits, three different flowsheets, shown in
Fig. 2.10, Fig. 2.11 and Fig. 2.12, were employed. In Fig. 3.0, primary screens, a primary
rougher gravity separator and a primary magnetic scavenger were employed, the circuit
also contained secondary screens, a secondary rougher gravity separator and a
secondary magnetic separator. Compared with composite 1 flowsheet, a secondary
gravity separator was used as a scavenger in the composite 2 flowsheet. The composite
3 flowsheet contained primary and secondary screening followed by primary and
secondary magnetic separation. The tailing from the primary magnetic separation went
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CHAPTER 3
INTERFACIAL CHEMISTRY OF FLOTATION
Flotation is a physic-chemical separation process on the basis of the differences in
the wettability of particles [61]. The floatation basically involves three phases: solid, liquid
and air phases. Since the first patent of floatation in 1906, many efforts have been made
to comprehensively understand the theory of floatation, and its applications have been
widely studied for complex minerals, such as lead-zinc, copper-zinc and rare earth
minerals [62]. The theory of flotation that takes place is that the mineral particle can attach
to the bubble, and can be lifted up to the water surface, which can be attributed to the
hydrophobicity. However, only a few minerals are naturally hydrophobic, most minerals
are hydrophilic, thus certain reagents should be used to render hydrophilic surface of
minerals to hydrophobic. There are three important factors for surface chemistry of
floatation in the laboratory scale: contact angle, adsorption density and zeta potential.
3.1 Contact Angle
Whether or not the hydrophobicity occurs depends on the degree of contact angle
(Figure 3.1) between the mineral surface and the bubble surface. Contact angle, θ,
related to interfacial tension, γ, is commonly expressed by the Young equation (Eq. 3.1)
between the gas (G), solid (S) and liquid (L).
γSG = γSL + γLG cos θ (Eq. 3.1)
The free energy change on bubble-particle contact can be referred to as Dupre’s
equation: (Eq. 3.2)
ΔG = γSG - (γSL + γLG) (Eq. 3.2)
Combining Eq. 3.1 and Eq. 3.2,
ΔG = γLG (cos θ – 1) (Eq. 3.3)
According to Eq. 3.3, the free energy can be expressed in term of contact angle. The
negative free energy is achieved as long as the contact angle is more than zero. Thus the
free energy becomes more negative as the contact angle increases, which means that
the bigger contact angle is, the more hydrophobic mineral-bubble interface is.
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Figure 3.1 Contact angle between bubble and particle in an aqueous medium [63]
3.2 Adsorption
It is well-known that hydrophobicity is rendered to the mineral by means of collectors
selectively adsorbing on the mineral, which means that collectors, shown in Figure 3.2,
absorb on the particles with their non-polar ends orientated towards the bulk solution,
thereby imparting hydrophobicity to the particle, because of chemical, physical, and
electrical forces between the polar portions and surface sites [63]. An adsorption
characteristic will be very helpful to deeply understand how collectors and modifiers affect
adsorption of minerals and make the selective attachment between bubble and minerals
steady enough. Increasing the strength the interface between bubbles in order to make
bubbles more elastic is the other function of surfactants [61]. Adsorption is commonly
distinguished into chemisorption and physical adsorption in terms of the interactive force
between mineral surface and collectors. Physical adsorption is defined as adsorption
caused by weak forces such as van der waals forces and hydrogen bonding [61].
Whereas, chemisorption happens if specific chemical interactions in the interface
between minerals and collectors take place, which lead to the formation of the compound
[62]. Thus, adsorption density with different pH along with certain applications of
spectrometer, such as FTIR and UV-visible spectrometer, can identify the mechanism of
adsorption of reagents on particles in order to optimize the flotation parameter, including
reagent scheme and conditioning time.
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Figure 3.2 Collector adsorption on mineral surface (Wills, 2006)
3.3 Electrical Double Layer
In the study of the surface chemistry, an electrical double layer (Figure 3.3) governs
whether adsorption mechanism is chemisorption or physical adsorption. In system where
the surfactant is physically adsorbed, flotation occurs depending on the mineral surface
being charged oppositely, whereas a high surface charge could inhibit the chemisorption
of collectors on minerals. An electrical double layer is the charge in solution together with
the charge on the solid surface [62]. Since the solution should be neutral, the surface
charge acquires equivalent amounts of opposite ions from the solution, called counter
ions, to compensate. Owing to the electrostatic attraction, the counter ions are absorbed
around the solid surface. The potential of stern plane determines the maximum adsorption,
although it is impossible to measure the potential of stern plane directly, however, it is
possible to measure the potential of shear plane that is called ζ potential [61]. ζ potential
is defined as the potential at the shear plane where the liquid phase will move past the
solid when forced using electrokinetic methods [61]. The isoelectric point (IEP) is the
characteristic point for ζ potential measurement, since IEP can predict the sign of the
charge on a mineral surface in different pH range [7].
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CHAPTER 4
MATERIAL CHARACTERIZATION
Material characterization is the fundamental parameter used for completely
understanding the materials including their chemical composition, size distribution,
association and sulfur content, as well as carbon content. Materials employed in this
thesis are rare earth carbonate (carbonatite) provided by Bear Lodge Ore, Wyoming,
calcite obtained through Ward’s Natural Science Establishment, New York, ancylite and
strontianite which are obtained from Ebay. Mineral liberation analysis (MLA) of
carbonatite are conducted by the Center for Advanced Mineral and Metallurgical
Processing (CAMP), Montana Tech of the University of Montana. Quantitative evaluation
of mineralogy by scanning electron microscope (QEMSCAN), X-ray diffraction (XRD),
inductively coupled plasma optical emission spectroscopy (ICP-OES) and X-ray
fluorescence (XRF) are conducted by Colorado School of Mines. Characterization
information may qualitatively and quantitatively guide the methodology to efficiently
separate ancylite from gangue minerals.
4.1 Theories of Analytical Techniques
An illustration of theories for the analytical techniques will be helpful to better and
more clearly understand and identify the mineralogical information of minerals presented
in this thesis.
4.1.1 Mineral Liberation Analysis (MLA)
The MLA is an automated mineral analysis system combined by a large specimen
chamber automated Scanning Electron Microscope (SEM), multiple Energy Dispersive
X-ray detectors with automated quantitative mineralogy software [65]. It rapidly identifies
and quantifies mineral characteristics, such as size distribution, mineral association and
abundance, presented as flat polished surfaces, coated with a thin conductive film,
usually carbon. In the late 1990s, the JKMRC Mineral Liberation Analyzer was firstly
presented and commercialized with a unique method of combining back-scattered
electron (BSE) image analysis and X-ray mineral identification. [66][67] Identification can
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be achieved by imaging mineral grains, where the BSE brightness of the minerals are
varied; however, particle X-ray mapping can analyze elemental information by collecting
X-ray data at each grid point when minerals have similarly bright BSE images.
The stable BSE signals from a modern SEM can meet the prerequisite of a high-
resolution and a low noise image for image identification. Spatial resolution of BSE with
0.1 to 0.2 micron is much higher when compared with that of an X-ray of 2 to 5 microns
[66]. Besides, there is a difference of almost two orders of magnitude for BSE analysis
speed over X-ray analysis [66]. The advantages contribute to reliable detail generated of
fine grains and mineral intergrowth. The main image analysis functions are known as de-
agglomeration and segmentation. De-agglomeration function is involved to detect
agglomerates and separate them to avoid biased results generated owing to particles not
separating individually [66]. Segmentation is employed to identify mineral phases and
define their boundaries properly, after individual particles are defined by de-
agglomeration. The MLA segmentation outlines the regions of homogeneous grey level
in a particle level [66]. The average BSE grey value of each region is corresponding to a
mineral of certain average atomic number (AAN) that is related to the number of
backscatter electrons emitted by the mineral [67].
The seven basic measurement modes are listed [66]:
1. Standard BSE liberation analysis (BSE).
2. Extended BSE liberation analysis (XBSE).
3. Sparse liberation analysis (SPL).
4. Particle X-ray mapping (PXMAP).
5. Selected particle X-ray mapping (SXMAP).
6. X-ray modal analysis (XMOD).
7. Rare phase search (RPS).
4.1.2 Quantitative Evaluation of Minerals by Scanning Electron Microscope
(QEMSCAN)
QEMSCAN is a fully automated micro-analysis system performed with a Carl Zeiss
EVO 50 Scanning Electron Microscope (SEM) combined with four Bruker X275HR silicon
drift X-ray detectors, and the iMeasure-iDiscover ® software is employed to process all
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analytical information. The QEMCAN provides quantitative mineralogical and textual data,
as well as false-color mineral maps, including highly accurate mineral maps, elemental
X-ray mapping, particle size, mineral association, etc.
An image of a sample based on chemical composition is created by back-scattered
electrons (BSE) and energy dispersive (EDS) X-ray spectra. Accurate mineral
identification is obtained by X-ray spectra over BSE brightness. The EDS spectrum is
analyzed by windowing, background subtraction, overlap correction, thresholding, and
the calculation of peak ratios [68]. A database complements the identification of minerals
that cannot be identified from EDS alone.
A number of different analysis modes are available. Bulk mineralogical analysis
(BMA) is used on drill core, rock and particulate particles by linear scans to identify the
number and length of intercepts with mineral species and the number or type of transitions
between phases for determination of mineral associations, mineral size, mineral surface
area and model abundance [68]. Particle mineralogical analysis (PMA) is used for the
detailed characterization of fine particles up to 1mm in size. BSE images are obtained to
determine particle diameter, perimeter and whether it is touching each other. Data from
PMA is primarily used for liberation analysis, although model association is usually less
accurate than bulk mineralogical analysis [68]. Specific mineral particle analysis, often in
conjunction with BMA, are divided into specific mineral search (SMS) and trace mineral
search (TMS). Specific mineral search performs the same way as PMA except that
images are only selected for those particles that contain specific BSE brightness. This is
only used for minerals present at about 0.5 vol% or less [68]. While, TMS is used when
only trace amounts of the mineral of interest are present.
4.1.3 X-Ray Diffraction Analysis
X-ray diffraction are mainly used in the identification of crystalline and
determination of crystalline structure, since each crystalline has its unique characteristic
X-ray powder pattern.
X-rays are produced by bombarding a metal target with a beam of electrons
emitted from a cathode by heating a filament. After filtering, monochromatic X-rays are
collimated and directed onto the sample. The intensity of the reflected radiation is
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It is well-known that samples have to be introduced into the plasma chamber in the form
that can be effectively vaporized and atomized [69].
The sample preparation was performed as Broton proposed in 1999 [70]. A 0.1
grams sample was placed directly on top of a 0.5 grams flux, consisting of 60 wt% lithium
metaborate and 40 wt% lithium tetraborate, to minimize the effect of the walls and bottom
of a graphite crucible; a 0.5 grams flux was placed on the top of the sample to protect the
sample from air with 2 to 3 drops of 20mg/L lithium borate solution. Then the crucible was
placed at 1000°C in a muffle furnace for an hour. The final solution was obtained by
diluting 200 µL sample that was made by dissolving molten melt in 25 vol% nitric acid with
10 mL 2 vol% nitric acid.
4.1.5 X-ray Fluorescence Spectroscopy (XRF)
X-ray fluorescence is an analytical technique that is used as a fast characterization
tool in many analytical labs throughout the world. It is based on the interaction of x-rays
with a material to determine its elemental composition. High energy x-rays or gamma rays
transfer enough energy to core level electron, which will be ejected from the inner orbitals
of the atom. The removal of the electron will contribute to the unstable structure of the
atom. Thus, in order to make the structure stable, the electron in high energy level will
drop to the vacant core hole. In falling, the atom can rid itself of excess energy by either
ejecting an electron from a higher energy level, referred as an Auger electron, or emitting
an x-ray photon, which is called x-ray fluorescence [71]. In terms of different
methodologies of detection for the photon, energy dispersive x-ray fluorescence (EDXRF)
and wavelength dispersive x-ray fluorescence (WDXRF) are commonly used. The
detection range for WDXRF is from beryllium to uranium, and WDXRF has the wide
dynamic ranges from 100% down to ppm, and in some cases sub-ppm levels [71].
WDXRF is available for both solid and liquid. Insofar as the fundamental principle is
concerned, Bragg diffraction of single crystal or multilayer are utilized to disperse
fluorescence x-rays, and Bragg’s equation is written as Eq. 4.2:
nλ=2dsinθ (Eq.4.2)
Here, n is the reflection order, λ is the wavelength of incident X-rays, d is the lattice
spacing of the crystal and θ is the incident angle.
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Table 4.1 Continued
Uranium 0.01
Copper 0.01
Tantalum P
Niobium P
Chromium P
Neodymium -
P – element calculated at less than 0.01%
Table 4.2 Content of rare earth by ICP-OES
Wt% Element Wt%
Element
Cerium 34.73 Erbium 1.66
Lanthanum 18.59 Dysprosium 1.14
Neodymium 15.92 Thulium 0.75
Praseodymium 10.02 Europium 0.71
Samarium 6.53 Holmium 0.60
Uranium 2.81 Ytterbium 0.32
Gadolinium 2.24 Scandium 0.19
Yttrium 1.90 Lutetium 0.17
Terbium 1.72
Mineral identification was carried out by MLA, QEMSCAN, and XRD. Ancylite is
the dominant rare earth mineral, however, the content of ancylite is varied from 7.64% by
MLA to 8.32% by QEMSCAN. Bastnaesite and monazite are also found, all occurring
below 0.5%. According to MLA data, the ancylite content increases as sieve size fraction
decreases. Calcite is the primary gangue mineral, which is in accordance with the
elemental analysis result that calcium has the highest content among the metal elements.
Strontianite is the second most abundant gangue mineral from QEMSCAN, followed by
pyrite. However, MLA shows that pyrite is the second most abundant mineral at 7.64%.
Except for calcite, strontianite and pyrite, other minor gangue minerals, such as
potassium feldspar, biotite and pyrrhotite, are identified as well. In the MLA test, since
cerium, theoretically, has the same content as lanthanum in the formula of rare earth
minerals, the cerium distribution can be used as a representative to study rare earth
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distribution in rare earth minerals. The results show that ancylite contains around 97% of
the cerium. About 1% cerium is found in each of bastnaesite and monazite, respectively.
The XRD results, performed in the size fraction of 200 Χ 400 mesh, illustrate that calcite
has a higher content associated with lower contents of ancylite, strontianite and pyrite in
comparison with the MLA results, even though calcite is still the primary mineral.
Table 4.3. Model mineral content (wt%)
Minerals Formula MLA QEMSCAN
Calcite CaCO 59.7 52.03
3
Pyrite FeS 7.64 3.86
2
Ancylite Sr(Ce,La)(CO 3) 2(OH)●H2O 7.31 8.32
Strontianite SrCO 5.77 4.01
3
K_Feldspar KAlSi O 4.77 1.05
3 8
Biotite K(Mg,Fe) (AlSi O )(OH) 4.21 1.92
3 3 10 2
Pyrrhotite FeS 2.37 0.18
Siderite FeCO 1.72 -
3
Apatite Ca (PO ) F 1.35 0.63
5 4 3
Wollastonite CaSiO 0.89 -
3
Barite BaSO 0.75 0.69
4
Galena PbS 0.71 0.55
Rutile TiO 0.63 0.09
2
Celestine SrSO 0.46 0.16
4
Sphalerite ZnS 0.39 0.97
Dolomite CaMg(CO ) 0.21 0.14
3 2
Monazite (La,Ce)PO 0.06 0.25
4
Bastnaesite (Ce,La)(CO )F 0.02 0.31
3
Quartz SiO 0.01 0.5
2
Allanite (Ca,Ce) (Al,Fe) (SiO )(Si O )O(OH) 0.02 -
2 3 4 2 7
4.2.2 Ancylite Grain Size and Liberation
It is well known that mineral grain size distribution is the key to predict and optimize
the performance of mineral processes. The more liberated the mineral is, the better
performance of separation will be obtained. Thus, there is a parameter, referred to as P ,
80
to make an assumption for a proper size of the mineral.
The carbonatite and ancylite size distributions are displayed by sieve fraction as
shown in Fig. 4.2, Fig.4.3 and Fig. 4.4. The overall carbonatite and ancylite grain size
distributions, P , were 100 and 50µm, respectively. It indicates that the carbonatite may
80
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4.3 Characterization of Materials for Flotation Fundamentals
For these experiments, calcite, strontianite and ancylite were obtained from Ward’s
Science Establishment, Rochester, New York and Ebay, respectively. Strontianite and
ancylite were hand-sorted under UV-light. They were dry-ground in a pulverizer and the
fraction of minus 325 mesh was obtained by sieving, corresponding to P value of 325
80
mesh for Bear Lodge carbonatite, as mentioned in Chapter 4.2.2. They were analyzed
chemically and spectroscopically to determine the approximate compositions and the
impurities present.
4.3.1 Characterization of Calcite
Semi-quantitative X-ray fluorescence spectroscopic analysis shows that calcium is
the primary element with 97% content, followed by fluorine with 1.5% (Table 4.5). XRD
shows that the sample is essentially pure calcite (Figure 4.7).
Table 4.5 Elemental analysis of calcite
Content (%) Element Content (%)
Element
Ca 97.17 Al 0.13
F 1.50 Mn 0.07
Mg 0.28 Pb 0.07
Si 0.28 Zn 0.02
Sr 0.23 Others 0.12
Fe 0.13
4.3.2 Characterization of Strontianite
The elemental composition of strontianite was measured by XRF. Strontium is
found to be at 95.32%, followed by calcium (3.09%), fluorine (0.49%) and magnesium
(0.182%), as well as some trace elements. The XRD result, shown in Figure 4.8,
illustrates that strontianite is the dominant mineral, with minor amount of serendibite and
ringwoodite.
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CHAPTER 5
EXPERIMENTAL PROCEDURES
Experimental procedures are presented here to fully illustrate how experiments are
conducted and guide others who may investigate this subject in the future.
The minerals, including calcite, strontianite, ancylite and the sample from Bear
Lodge Ore (carbonatite), were ground to minus 325 mesh for zeta potential, adsorption,
and microflotation. Batch scale flotation and wet high intensity magnetic separation were
performed by minus 100 mesh carbonatite. The BET nitrogen specific surface areas of
the minus 325 mesh fractions for ancylite, strontianite, calcite and carbonatite were found
to be 3.8025, 3.3602, 5.0928 and 1.6211m2/g, respectively. All the reagents used in the
study were analytical grade chemical reagents. Octanohydroxamic acid was purchased
from Tokyo Chemical Industry Co., Ltd. It was identified by Fourier Transform Infrared
Spectroscopy (Fig. 5.1) that the characteristic bond (C=O) took place at 1660 cm-1.
Moreover, three bands for N-H and O-H stretchings happened in the range from 3300-
2800 cm-1, and two strong amide II bands were observed near 1550 cm-1 and 970 cm-1.
5.1 Sampling
The representative sampling is the essential requirement for the entire research to
insure that the results produced are reasonable and representative.
In this research, the ore, provided by Bear Lodge, Wyoming, was about 90 pounds
with size fraction of around 1.5 inch. On the basis of the relationship between sample
mass and particle size (Fig. 5.2), the entire ore was crushed to certain size by a jaw
crusher and a roll crusher, as well as sieves. The end products were separated to small
portions by a Jones riffle splitter. Around 2 pound minus 100 mesh ore was obtained,
followed by another grinding and sieving to minus 325 mesh as the representative sample
to be employed in the following fundamental experiments.
5.2 Zeta Potential Experiments
Zeta potential experiments were carried out using a Stabino® (Fig. 5.3) distributed by
Microtrac Europe GmbH. The principle of the Stabino® measurement is that the particles
are immobilized by attaching to the cell wall when a suspension is brought into the cell,
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5.3 Adsorption Experiments
The adsorption of octanohydroxamic acid as functions of concentration, time and
pH was performed by the determining difference in the concentration of the collectors in
solution before and after the addition of mineral powders. The experiments at room
temperature were carried out in 15mL polyethylene bottles at a solid: liquid ratio of 8g/L
for pure calcite, strontianite and ancylite, as well as carbonatite. Conditioning time was
determined from adsorption kinetics experiments. The suspension was agitated using a
shaker at 650 rpm. After equilibration, the slurry was centrifuged in a VWR clinical 100
centrifuge for 20 minutes at 6500 rpm in order to separate solid from liquid. The
concentration of hydroxamic acid was measured by a Shimadzu UV160U spectrometer
(Fig. 5.5) with the well-known ferric hydroxamate method, mentioned in Pradip’s thesis
[73]. The theory is that the purple-colored ferric hydroxamate complex has the unique
peak at 510 nm measured by UV-visible spectrometer. The ferric hydroxamate was made
by mixing hydroxamic acid with ferric perchlorate at a volume radio 1:2. At 50 °C,
adsorption experiments were performed in 7mL tubes that are made by special materials,
and conditioning was carried out in a Benchmark multi-therm shaker at 900rpm at 50 °C.
The separation of solid from liquid and measurement of the concentration of hydroxamic
acid were performed with the same way as those at room temperature. The slurry pH was
recorded before and after adsorption. KOH and HCl solutions were used as the pH
adjustment reagents. The adsorption density of minerals is expressed by Eq. 5.1.
δ = ΔC*V/(A*S) (Eq. 5.1)
Where ΔC is the change of concentration of surfactant, V is the original volume of solution,
A is the specific area of the mineral, and S is the amount of solid.
The specific area was measured by BELSORP-mini II purchased from BEL Japan
Inc. BELSORP-mini II is a compact, volumetric adsorption measurement instrument used
for specific area measurement. The measurement principles are volumetric gas
adsorption and advanced free space measurement, which can contribute to high
precision and high reproducible data [74]. BET theory is usually used as the calculation
of the specific surface area. The theory is that the adsorptive absorbs on the strong
energy sites on the surface first, and then the adsorptive absorbs on the next energy level
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sites as the pressure is increased. The advanced free space measurement, developed
by BEL Japan, Inc., is a measurement of adsorption amount, which can continuously
measure the change of free space without maintaining the coolant level [75].
Figure 5.5 Shimadzu UV160U spectrometer
5.4 Microflotation
Floatability studies were performed with a modified Hallimond tube, shown in
Fig.5.6. Octanohydroxamic acid and potassium ethyl xanthate were used as a collector.
For the pure minerals flotation tests, 0.4 g of minus 325 mesh pure mineral samples were
pulped to 52mL with the collector and conditioned with the chosen reagents at a desired
pH for 15 minutes using a magnetic stirrer at 600rpm. Then the sample was transferred
to the Hallimond tube and agitated by another magnetic stirrer at 800rpm. Two minutes
flotation was achieved by passing air gas at the rate of 39.7 cc/minute. . The concentration
range of octanohydroxamic acid was from 5Χ10-4 M to 2Χ10-3 M, and the pH range was
from 5.5 to 11.5. After flotation, the concentrate and the tailing fractions were separately
filtered, dried and weighed. The recoveries for pure minerals were expressed on a weight
basis. In terms of carbonatite flotation test, 0.5 grams carbonatite with minus 100 mesh
and minus 325 mesh were employed in the presence of different collectors, depressants
and activators, as well as frothers. All the experimental procedures were the same as that
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for pure minerals, except that the recovery of carbonatite was conducted by a combination
of weight and element concentration that was measured by XRF.
Figure 5.6 A modified Hallimond tube set-up
5.5 FT-IR Measurement
Spectra were recorded using Nicolet isTM50 FT-IR spectrometer obtained from
Thermo Fisher Scientific Inc. Typical measurement was carried out at a resolution of 4
cm-1. After 15 minutes adsorption in the presence of 10-3 M hydroxamic acid, solids were
washed three times with DI water (18Ω) and allowed to air-dried at room temperature
overnight. The pure minerals both before and after adsorption were measured by FTIR-
ATR. Atmospheric water was always subtracted.
5.6 Wet High Intensity Magnetic Separation
The Eriez lab model wet intensity magnetic separator was employed to remove
iron oxide, primarily for hematite and magnetite. The separator consists of two
electromagnetic coils with a stainless steel canister containing a flux-converging element
located between magnetic poles. Even though there are several parameters, such as
magnetic field, feed rate, pulp density and flow rate of the rinse water, that can affect the
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performance of magnetic separation, only two parameters which are magnetic field and
matrices were tested in this study. Two matrices were used, which are grooved plates
and steel balls. Tests were run by pouring a 100 grams sample with 20 wt% pulp density
into the separator with the magnetic energized. 0.4, 0.8, 1.2 and 1.6 amperes were
employed as a factor to be optimized. The recovery of carbonatite was conducted by a
combination of weight and element concentration that was measured by XRF.
Figure 5.7 WHIMS
5.7 Bench Scale Floatation
A series of batch tests were undertaken in the 1L Denver flotation cell. In the
rougher stages, a 250g tailing from WHIMS was fed to the Denver cell with 20% pulp
density. Distilled water was used throughout the tests. The air flow rate was around 380
ccm. The temperature during experimentation was 21± 1°C. In the experiments which
were only involved with pH adjustments and collector concentration change, each sample
was conditioned in 1L certain concentration octanohydroxamic acid for 15 minutes at the
required pH. In the experiments which required the addition of modifiers, the modifier
addition time was tested in the experiments. Two minutes conditioning was made for
frother. AF 70 (Cytec AEROFROTH 70) was used as the frother in subsequent tests.
Likewise, in the cleaner stage, the conditioning procedures were same as the rougher
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CHAPTER 6
EXPERIMENTAL DATA AND DISCUSSION
The flotation fundamentals of ancylite, strontianite and calcite are presented here,
including zeta potential, adsorption and microflotation. The flotation fundamental and
bench flotation of carbonatite are included as well.
6.1 Flotation Fundamental of Pure Minerals
The fundamentals of surface chemistry can give a better prediction and
understanding of ancylite flotation. The measurement of the zeta potential of the minerals
in various conditions and adsorption mechanism of mineral/collector interface were
studied. Microflotation experiments were also employed to establish the chemical
conditions for flotation separation of minerals.
6.1.1 Zeta Potential Measurement
Being of considerable importance on the wetting characteristics and collector
adsorption, investigations of electrokinetic behavior for ancylite and calcite as well as
strontianite are undoubtedly attractive to help deeply understand the flotation mechanism
and optimize the flotation performance. It is well-known that the surface charge of the
semi-soluble minerals is not only dependent on the pH of the suspension system, but
sensitive to solution composition owing to hydrolysis and metathetic exchange. Lattice
ions in the mineral structure can alter the surface properties. As Miller mentioned in 2004
[76], the common theories of surface charging mechanisms are summarized as follows:
dissociation of surface acid groups, lattice substitution and preferential hydration of
surface lattice ions, as well as lattice hydration theory.
The experimental results shown in Fig. 6.1 were obtained by initially equilibrating
ancylite, strontianite and calcite in distilled water. The isoelectric points (I.E.P) of ancylite,
strontianite and calcite are around 5.46, 4.50 and 5.50, respectively. As expected, the
electrokinetic behavior of ancylite in aqueous solution reveals that pH plays a significant
role. At pH below 5.46, the zeta potential of ancylite particles becomes positive, while
zeta potential is more negative as pH increases. The effects of CO 2-, HCO - and Sr2+ on
3 3
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the electrokinetic behavior of ancylite were also investigated and it is found that, Sr2+,
CO 2- and HCO - are the potential determining ions. The addition of Sr2+ contributes to an
3 3
increase of zeta potential compared with ancylite in water. That could be explained by a
fact that strontium, one of the lattice ions in the ancylite crystal, could undergo hydrolysis
to form a strontium hydroxyl complex. Since little is known on the solubility product of
ancylite, it is difficult to thermodynamically calculate the solid-aqueous solution equilibria
for the ancylite-H O system. Whereas, investigations on calcite-H Oand strontianite-H O
2 2 2
solution equilibriums were conducted and presented in several literature citations. In an
aqueous suspension of strontianite and calcite particles, both cations and anions from the
minerals lattice will dissolve and interact with the ions of the water based on the following
reactions at room temperature.
SrCO = Sr2+ + CO 2- pK = 9.1534 (6.1)
3(S) 3
CO + 2OH- = CO 2- + H O pK = -9.8724 (6.2)
2(g) 3 2
CO 2- + H O = HCO - + OH- pK = 3.6700 (6.3)
3 2 3
CO 2- + 2H O = H CO + 2OH- pK = 11.3024 (6.4)
3 2 2 3(aq)
Sr2+ + OH- = Sr(OH)+ pK = -0.820 (6.5)
Sr2+ + 2OH- = Sr(OH) pK = 0.4327 (6.6)
2(S)
CaCO = CaCO pK = 5.1488 (6.7)
3(S) 3(aq)
CaCO = Ca2+ + CO 2- pK = 3.1979 (6.8)
3(aq) 3
Ca2+ HCO - = CaHCO + pK = -0.8655 (6.9)
3 3
Ca2+ + OH- = Ca(OH)+ pK = -1.3019 (6.10)
The inconsistency of I.E.P for calcite and strontianite could be attributed to several
factors, such as different sources, incorporation of different cations into the mineral crystal,
and various methodologies of electrokinetic measurements. The varied I.E.P or point of
zero charge (PZC) in the previous studies are shown in Table 6.1. It is also found that the
determining ions for calcite are Ca2+, CO 2- and HCO -, while Sr2+, CO 2-, and HCO - are
3 3 3 3
the determining ions of strontianite.
A series of investigations were conducted in mineral supernatants as well as in
water in order to confirm the effect of dissolved species of the ancylite-strontianite and
ancylite-calcite system. The supernatant was prepared by shaking the mineral in distilled
water for 24 hours followed by centrifugation. The supernatant obtained was used for 24
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hours conditioning of the desired mineral prior to zeta potential measurements. It is
presented in Fig. 6.5 that the ancylite surface is more negatively charged in both
strontianite and calcite supernatant than in water and that isoelectric point of ancylite in
strontianite supernatant has shifted from around 5.46 in water to 4.26. Similarly, the zeta
potential of calcite and strontianite in ancylite supernatant was measured as well, and Fig.
6.7 shows that the zeta potential of strontianite in the ancylite supernatant behaves the
same trend as that in water, except the IEP in ancylite supernatant is slightly lower than
that in water. However, the IEP of calcite is only slightly affected by ancylite supernatant.
This scenario is in agreement with previous studies by Amankonah et al. [80] and
Somasundaran et al. [81]. In mixed mineral systems, the interfacial behavior of minerals
is quite different from that of individual mineral due to the dissolved species present in the
supernatants. The following microflotation of the mixed minerals also shows different
results using the same condition as that for individual mineral.
Table 6.1 Summary of PZC for calcite and strontianite
Mineral PZC Measurement Reference
9.5 Streaming potential [77]
8.2 Streaming potential [56]
Electrophoretic
11 [78]
mobility
10.5 (I.E.P) Streaming potential [55]
Calcite
Electrophoretic
10 [73]
mobility
5.5 Streaming potential [79]
Electrophoretic
8.2 [58]
mobility
Electrophoretic
Strontianite 8.0 [58]
mobility
The electrokinetic behaviors of ancylite, strontianite and calcite in the presence of
hydroxamic acid were investigated to delineate the adsorption mechanism of hydroxamic
acid on the surface of minerals. Fig. 6.8 shows that as the concentrtation of hydroxamic
acid increases, IEP of ancylite decreases, and the zeta potential range in the entire pH
becomes narrow compared with that in distilled water. The effect of hydroxamic acid
addition for strontianite is as same as ancylite. However, the addition of hydroxamic acid
has a slight effect on calcite, compared with strontianite and ancylite, which could be
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6.1.2 Adsorption Studies
As mentioned earlier, the measurement of the zeta potential can make clear that
adsorption mechanism of hydroxamic acid on pure ancylite, calcite and strontianite are
chemisorption. Adsorption studies was also employed to investigate the underlying
mechanism of hydroxamate interaction in these mineral systems. High temperature
adsorption studies were carried out as well.
Figure 6.11 shows the results of uptake of octanohydroxamic acid on ancylite,
calcite and strontianite as a function of time with the initial concentration of 10-3 M at room
temperature. Clearly, calcite reaches the equilibrium in about 2 hours with the lowest
adsorption. Strontianite takes as long as 48 hours to reach equilibrium, while ancylite
takes 29 hours to reach equilibrium to get the highest adsorption among three minerals.
The reason that calcite can reach equilibrium so fast with low adsorption is probably that
calcite is more soluble in comparison with strontianite and ancylite.
The uptake of octanohydroxamic acid by ancylite at pH values 9 ± 0.3 is presented
in Fig. 6.12. The adsorption isotherm curve is characterized by three well-defined regions:
(a) at low collector concentrations the adsorption displays a marked dependence on the
hydroxamic acid concentration; (b) the adsorption remains relatively constant; and (c) the
adsorption increases with increasing concentration of hydroxamic acid. The adsorption
density of hydroxamic acid on ancylite is 20 µmol/m2. Assuming a surface area of the
hydroxamic acid head group of 20.5Å [38], according to calculation, it is found that the
ancylite to hydroxamate ratio is approximately 1:2.5, which could be in concordance with
theoretical expectation in terms of the composition of ancylite. Because the lattice of
ancylite contains both rare earth ions and strontium ions, which contributes to a fact that
the cationic ion to hydroxamate radio should be theoretically in the range of 1:3 to 1:2. At
high concentration, however, there seems to be another plateau where the amount of
hydroxamic acid absorbed is far more than needed for the formation of a close-packed
vertically oriented monolayer. It could be expected based on a consideration that a
multilayer adsorption occurs, which is probably due to physical adsorption by hydrogen
bonding after the surface chelation (Eq. 6.11 and Eq. 6.12), mentioned by Raghavan and
Fuerstenau [36]. The adsorption of hydroxamic acid on rare earth minerals, such as
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bastnaesite, has been ascribed ([38], [51], and [49]) to the formation of a rare earth-
hydroxamate complex on the mineral surface, and a similar mechanism might be
applicable in the present system.
(Eq. 6.11)
(Eq. 6.12)
The adsorption isotherm of calcite and strontianite at pH 9 ± 0.3 (Fig. 6.12) displays
a typical S-type shape as well; however, the adsorption densities are significantly lower
than that for ancylite. The adsorption density plateau of calcite obtained is far less than
that needed for the formation of a close-packed monolayer where all the molecules are
horizontally oriented, attaining an adsorption density of 3.02 µmol/m2. The adsorption
density of strontianite increases sharply at lower hydroxamic acid concentration, but is
constant at around 7 µmol/m2 in the concentration range from 6 Χ 10-4 M to 1.8 Χ 10-3 M.
Then a linear increase in the uptake of hydroxamic acid on the strontianite is obtained at
higher concentration. The reason that the plateaus for uptake of hydroxamic acid on
calcite and strontianite are much lower than that for ancylite is that Sr2+ and Ca2+ are
divalent ions, in comparison, the rare earth ions are trivalent ions, which suggests that
the formation of the metal-hydroxamate complex for rare earth ions consumes many
times more hydroxamate than that for divalent ions.
The adsorption of hydroxamic acid on three minerals at various pH values are
presented in Fig. 6.13, Fig. 6.14 and Fig. 6.15. The experiments were conducted at
collector concentration of both 10-3 M and 5 Χ 10-4 M. Among these three figures, there is
a common characterization that at pH below 7, adsorption density increases abruptly as
pH decreases, in the presence of 10-3 M hydroxamic acid. It might be attributed to the
presence of CO . Several literature reported that the presence of such species as
2
CaHCO + and CaOH+ could increase the flotation recovery of calcite, which is attributed
3
to an increase of electrostatic attraction by carbonation inducing a positive charge on the
calcite interface through the adsorption of CaHCO + and CaOH+ [82][73]. Fig. 6.13
3
indicates that adsorption of strontianite has a slight decrease in the range of pH 6.5 to pH
9 at 10-3 M hydroxamic acid, followed by a sharp increase above pH 9. A minimum
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adsorption density is obtained where the pH is around 7.4 at the collector concentration
of 5 Χ 10-4 M. There is a drop happening above pH 11, which is probably due to a formation
of strontium carbonate precipitated on the surface of strontianite to prevent the adsorption
of hydroxamic acid.
Calcite behaves similarly to strontianite, except that there is a relatively constant
adsorption density from pH 7 to 9 in the presence of 10-3 M hydroxamic acid and pH 7.8.
However, the drop in adsorption density at around pH 7.5 in the presence of 5 Χ 10-4 M
hydroxamic acid could not be easily explained. Perhaps some other strontium and
calcium species are formed and are responsible for hydroxamic acid uptake.
The adsorption of hydroxamic acid on ancylite as a function of pH is presented in
Fig. 6.15. It is apparent that adsorption of the collector on ancylite is relatively independent
with pH variation in the range of pH 7 to 10 compared with those for calcite and strontianite.
At 10-3 M concentration, the predominate ion species that might be responsible for the
plateau are MOH2+, M3+, M(OH) + and M(OH) (aq) (Fig. 6.16), in which M represents rare
2 3
earth metal. Pradip et al. [38] also observed this plateau in their bastnaesite flotation study.
In an alkaline environment, especially above pH 10, there is a drop of adsorption density,
which could be attributed to formation of M(OH) and M(OH) - that precipitated on the
3 4
surface of mineral particles.
35
30 Ancylite
) calcite
2
m
/ 25 strontianite
lo
m
µ
(
y
20
t
is
n
e
d 15
n
o
it
p
r 10
o
s
d
A
5
0
0 20 40 60 80 100 120
Equilibrium time (hour)
Figure 6.11 Adsorption density of calcite, strontianite and ancylite as a function of time
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Figure 6.16 Aqueous solution equilibrium for cerium at 10-3 M total concentration [73]
Since the uptake of hydroxamic acid on minerals indicates the interaction between
hydroxamic acid and minerals, some adsorption experiments at 50°C were also carried
out to investigate the effect of temperature, and a series of thermodynamic calculations
were also made to theoretically illustrate the mechanism of adsorption of hydroxamic acid
on minerals. From the results given in Fig. 6.17, it could be seen that the time required to
attain equilibrium at high temperature is much longer than that at room temperature and
the amount of hydroxamic acid adsorbed increases with temperature increases. It might
be attributed to the higher solubility of these minerals at elevated temperature and the
endothermic reactions for the adsorption of hydroxamate on these minerals. Fig. 6.18
indicates that the high temperature plays a more important role in adsorption for
strontianite than ancylite. And interestingly, there are two plateau to be observed in the
adsorption isotherm plots for calcite, ancylite and strontianite. Adsorption isotherm of
calcite has the two plateaus which take place at 7.31 and 14.76 µmol/m2, respectively.
Ancylite has the same trend as calcite has, and the two plateaus happen at 22.5 and
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39.05 µmol/m2, respectively, which could be attributed to a lower plateau corresponding
to the horizontal monolayer of hydroxamic ion. The second plateau occurs when
hydroxamic ion vertically adsorbs on the mineral surface area.
The comparison is shown in Fig. 6.19 to illustrate the different trends for the
adsorption of hydroxamic acid on ancylite at room temperature and 50°C. At 50°C, it is
apparent that as pH increases, adsorption density of ancylite increases until pH is 7, and
then remains constant, in contrast with the trend at room temperature. Adsorption of
calcite at elevated temperature (Fig. 6.20) is higher than that at room temperature when
pH is above 7, whereas the adsorption at higher temperature behaves the similar trend
as the room temperature. It is probably due to the unstable species, such as CaHCO +
3
and CaOH+, at elevated temperature, which contributes to no activation by CO for
2
flotation. Clearly, Fig. 6.21 indicates that the adsorption behavior of strontianite at room
temperature has relatively the same trend as that at 50°C, except that there is a higher
adsorption density compared with that at room temperature.
35
Calcite
30
Strontianite
)
2 m 25 Ancylite
/
lo
m
µ
(
y
20
t
is
n
e
d
n
15
o
it
p
r
o
s d 10
A
5
0
0 20 40 60 80 100 120
Equilibrium time (hour)
Figure. 6.17 Adsorption density of calcite, strontianite and ancylite as a function of time
at 50°C
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The free energies of adsorption for hydroxamic acid on ancylite, calcite and
strontianite were calculated using the Stern-Grahame equation shown in Eq. 6.13.
Τ
δ
= 2rCexp(-ΔG° ads/RT) (Eq. 6.13)
where Τ is the adsorption density in the stern plane, and r is the effective radius of the
δ
adsorbed ion, C is the equilibrium concentration, ΔG°
ads
is the standard adsorption free
energy.
The free energies of adsorption for hydroxamic acid are found to be -6.15, -4.93,
and -5.58 Kcal/mole for ancylite, calcite and strontianite, respectively. The values for free
energies are in agreement with the experimental results showing that hydroxamic acid
has the strongest affinity with ancylite, followed by strontianite, whereas calcite
hydroxamate complex has the weakest affinity.
Based on the adsorption density results in two different temperatures, the
enthalpies (ΔH° ads) and entropies (ΔS° ads) for the adsorption of three minerals were
estimated by Eq. 6.15 and Eq. 6.16.
For any adsorption process, the standard free energy change is given by
ΔG° ads= ΔH° ads – TΔS° ads (Eq. 6.14)
Assuming enthalpy and entropy are independent of temperature in this study,
Thus
ΔH° ads = [(ΔG° 1/T 1) – (ΔG° 2/T 2)] / (1/T 1 – 1/T 2) (Eq. 6.15)
ΔS° ads = (ΔG° 1 - ΔG° 2) / (T 2 – T 1) (Eq. 6.16)
Where ΔG°
1
and ΔG°
2
are the standard free energies of mineral adsorptions at two
different temperatures T and T , respectively.
1 2
The adsorption standard free energies of three minerals with different
temperatures are plotted in Fig. 6.22. And the thermodynamic parameters are shown in
Table 6.2. The enthalpy of ancylite is the lowest among the three minerals, which could
explain why the adosprtion density of ancylite has the smallest increase in comparison
with the other minerals. Furthermore, a conclusion could be made that the adsorptions of
hydroxamic acid on the surface of these minerals are endothermic.
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8
7
6
lo
m 5
/
la
c
K 4
,s
d
a
°
G 3
Δ
-
Ancylite
2
Strontianite
1
Calcite
0
290 300 310 320 330
Temperature, °K
Figure 6.22 The adsorption standard free energies for calcite, ancylite and strontianite
at two temperature.
Table 6.2 Thermodynamic parameters for adsorption of hydroxamic acid on minerals
Minerals Enthalpy (Kcal/mole) Entropy (Cal/mole K)
Ancylite 0.44 22.41
Strontianite 5.98 39.30
Calcite 7.13 40.00
6.1.3 Microflotation for Pure Minerals
As is clear from the result given in Fig. 6.23, the recovery of pure ancylite is
extremely sensitive to various concentrations of hydroxamic acid. Particularly, at a low
concentration from 3 Χ 10-4 to 5 Χ 10-4 M, there is a sharp increase in recovery of 8% to
94%. Nevertheless, the recovery of strontianite is around 85% at pH 9.5 in the presence
of 2 Χ 10-4 M hydroxamic acid, compared with the ancylite recovery of 5.2%. However,
the maximum recovery of calcite is obtained at around 2 Χ 10-3 M, which is in agreement
with adsorption studies that calcite has the lowest adsorption density among the three
minerals studied.
Fig. 6.24 shows that at higher collector concentration, above 5 Χ 10-4 M, recoveries
of ancylite are relatively independent with pH variation and have the same trend as the
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collector concentration increases. In comparison with trends at high concentration, there
is a difference occurring at low collector concentration when pH increases. A drop is found
from pH 7 to pH 8.5, which also could be found in previous adsorption density studies. It
is attributed to the fact that carbon dioxide plays a more significant role in activation of
flotation at lower collector concentration than that at higher concentration. The
resemblance of recovery vs. pH trends for strontianite in the presence of varied
concentration is found in Fig. 6.25. The relatively low recovery of strontianite is obtained,
even though the recovery is still above 60%. While calcite recovery is extremely
dependent with pH at all range concentrations (Fig. 6.26). Compared with strontianite
and ancylite, calcite appears to be more sensitive with alkaline environment, which could
be explained by the fact, shown in Fig. 6.27, that CaCO and Ca(OH) precipitate on the
3 2
surface of calcite to prevent the uptake of hydroxamic acid. Less than 20% recovery takes
place when pH is below 7.5. Thus, it is clear to see (Fig. 6.28) that there is a potential
methodology that could separate calcite from strontianite and ancylite. The method could
be illustrated that at pH 7.5, where calcite separation (Fig. 6.29) could be theoretically
achieved in the presence of 5 Χ 10-4 M hydroxamic acid, then strontianite could be
separated from ancylite in the presence of 2 Χ 10-4 M hydroxamic acid at pH 9.5. However,
a microflotation for a mixture of ancylite and strontianite with ratio 1:1 was conducted on
the basis of the environment mentioned before. The results show that strontianite cannot
successfully be separated from ancylite. And another microflotation with a mixture of
calcite, ancylite and strontianite also confirms that calcite separation is not successful as
single mineral flotation. The zeta potential tests, mentioned in Chapter 6.1.1, also show
that the isoelectric point of the each mineral is altered by the supernatant of the other
mineral. The discrepancies between the single mineral and mixed minerals could result
from the existence of dissolved species, since the solubility of semi-soluble minerals is
drastically higher than in other systems. Amankonah J. O. et al. [80] observed that the
shifts in the isoelecric point of calcite and apatite in the supernatants of each other were
the result of many complex surface reactions. Somasundaran P. et al. [81] investigated
that calcite might reprecipitate under certain pH conditions to convert the surface of
apatite to calcite, when apatite was accommodated in the supernatant of calcite.
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100
90
Ancylite
80
Strontianite
70
) % 60
(
y
r e 50
v
o
c
e 40
R
30
20
10
0
5 6 7 8 9 10 11 12
pH
Figure 6.29 Recovery of strontianite and ancylite at 2Χ10-4 M octanohydroxamic acid as
the function of pH
6.1.4 FT-IR Measurement
IR spectra of the pure ancylite and ancylite-hydroxmate are shown in Fig. 6.30.
There is a difference, shown in Fig. 6.30, between pure ancylite before and after
adsorption. It is also a confirmation that chemisorption happens when hydroxamate
adsorbs on the surface of ancylite particles. However, in this case, the IR spectra could
not represent the true adsorbed formation of ancylite-hydroxamate complex.
Chemisorption of hydroxamate on strontianite and calcite are also identified from Fig.
6.31 and 6.32, respectively, which is in agreement with both electrokinetic measurements
and adsorption experiments.
6.2 Flotation Fundamentals of Bear Lodge Ore
As mentioned in Section 6.1.1, the flotation behavior of pure minerals is different
from ore, it is necessary to study the surface chemistry fundamentals of the sample from
Bear Lodge Ore. Zeta potential, adsorption and thermodynamic calculations were
conducted to have a better interpretation for flotation behavior and make a comparison
with the flotation performance of individual pure minerals.
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Figure 6.32 IR spectra of calcite (a. calcite before adsorption; b. calcite after adsorption;
c. difference between calcite after and before adsorption)
The electrokinetic response of the sample in the presence of distilled water, as a
function of pH, is shown in Fig. 6.33. The isoelectric point is observed at around pH 5.27,
which is lower than that of pure ancylite. It could be attributed to the fact that the
composition of the sample is complex. Electrokinetic tests in different electrolytes are also
performed and the results show that Sr2+ and CO 2- considerably affect zeta potential in
3
the entire pH range, while HCO - has a minor effect on zeta potential of the sample. The
3
effects of zeta potential in the presence of strontium and carbonate ions provide a
potential guidance for batch flotation tests.
The effect of hydroxamic acid on the electrokinetic behavior of the sample is shown
in Fig. 6.34. It is clearly observed that the addition of hydroxamic acid lowers the
isoelectric point of the sample, and isoelectric point decreases as the concentration of
hydroxamic acid increases. However, the addition of hydroxamic acid makes the range
of zeta potential narrow, compared with the sample in distilled water, and the zeta
potential of the sample becomes less negative as the collector concentration increases.
These results clearly indicate that hydroxamic acid chemisorbs onto the sample surface,
which is in accordance with individual minerals studies.
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30
1 X 10-3 M NaHCO3
20
1 X 10-3 M Na2CO3
10
water
0
1 X 10-3 M Sr(NO3)2
la -10
it
n
e
t o -20
p
a
t e -30
Z
-40
-50
-60
-70
0 2 4 6 8 10 12 14
pH
Figure 6.33 Zeta potential of the sample in different electrolytes
Fig. 6.35 shows the results on the adsorption of hydroxamic acid onto the sample
as a function of time at both room temperature and 50°C. It is observed that the uptake
of hydroxamic acid on the sample surface takes around 45 hours to reach the equilibrium,
which is faster than that at 50°C. The adsorption density of hydroxamic acid on the sample
surface as a function of the equilibrium surfactant concentration (0 to 3.6Χ10-3 M) was
determined at the room temperature and 50°C. The results obtained are presented in an
adsorption isotherm plot. Fig 6.36 indicates that adsorption isotherms at both
temperatures behave strangely. At room temperature, a relative plateau happens at the
low collector concentration, followed by a sharp increase. Then a plateau takes place,
before adsorption density rises up with the increase of collector concentration. The reason
that the adsorption plateau happens at low concentration of hydroxamic acid is that
hydroxamic acid preferably horizontally adsorbs on the surface of iron minerals and rare
earth minerals. The second adsorption density plateau obtained is designated as the
formation of a close-packed monolayer where all the molecules are vertically oriented.
Another increase of adsorption density could be attributed to the formation of the complex.
It is also clear to show that temperature plays a significant effect on adsorption of
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200
180 at room temperature
160 at 50 C
)
2
m 140
/
lo
m
µ 120
(
y
t
is
n 100
e
d
n o 80
it
p
r
o 60
s
d
A
40
20
0
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
Equilibrium concentration (mol/L)
Figure 6.36 Adsorption density of the sample as a function of concentration
On the basis of Eq. 6.13, the free energies of adsorption for hydroxamic acid were
calculated to be -6.00 and -51.83 Kcal/mole at room temperature and 50°C, respectively.
The free energy at high temperature is more negative than that at room temperature,
which is in agreement with adsorption density results.
On the basis of the adsorption density results at two different temperatures, the
enthalpies (ΔH°ads) and entropies (ΔS°ads) for the adsorption of the sample were
estimated by Eq. 6.14 and Eq. 6.15. The thermodynamic parameters are shown in Table
6.3.
Table 6.3 Thermodynamic parameters for adsorption of hydroxamic acid on the sample
Thermodynamic parameters sample
Enthalpy (Kcal/mole) 7.99
Entropy (Cal/mole K) 47.59
The effect of pH for the collector uptake on the sample surface is also studied. The
same trends take place at room temperature with 1Χ10-3 M and 5Χ10-4 M hydroxamic acid.
It could be attributed to the fact that in the range between 5Χ10-4 to 1Χ10-3 M, the
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adsorption mechanism is same. As expected, at pH below 7, adsorption density sharply
increases as pH decreases, which might be explained by the presence of CO . At 50°C,
2
however, at pH above 10, there is a peak happening at approximately pH 11. It might be
attributed to the high solubility of CaCO , SrCO and Ce(OH) at high temperature. Since
3 3 3
CaCO , SrCO and Ce(OH) could be formed in an alkaline environment, those
3 3 3
compounds could precipitate on the surface of the sample to prevent the adsorption of
hydroxamic acid at room temperature; however, as temperature increases, the solubility
of these compounds increases, which contributes to the fact that no compound
precipitates on the mineral surface to prevent adsorption.
6.3 Wet High Intensity Magnetic Separation (WHIMS)
As shown in Table 2.3, the stability constant of iron hydroxamate is much higher
than that of rare earth hydroxamate. Thus, hydroxamate favorably adsorbs on the iron
mineral surface, rather than rare earth minerals, which not only consumes a large amount
of hydroxamic acid, but decreases the flotation selectivity. It is postulated that removal of
iron as much as possible before the flotation process could be beneficial. Therefore, a
wet high intensity magnetic separator (WHIMS) was employed to extract iron minerals
from using the feed containing approximately 4.5% REO.
Table 6.4 shows the grade and recovery of iron as well as rare earth loss as a
function of different magnetic field strengths when the grooved plates were used as the
matrix. The recovery of iron increases as current increases. This is due to the fact that
the higher the current is, the greater the magnetic force applied to the particles, which in
turn are captured within the matrix. However, likely because of liberation effects, as the
recovery of iron increases, the loss of the REO increases. The experimental results
indicate that magnetic extraction of 42.8% of the iron minerals results in 5.6% REO loss
at the current of 4 amperes.
Table 6.5, on the other hand, shows the recovery of iron and rare earth loss as a
function of magnetic current in the matrix of 4,042 steel balls with the diameter of ¼’’. It
is found that the recovery of iron and the loss of rare earth increases with increasing
magnetic current. The recovery of iron when steel balls were employed as the matrix is
higher than that in the grooved plate matrix. It could be attributed to the fact that the larger
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surface area steel balls has, the more amount of iron could be collected. Nevertheless,
the loss of rare earth in the steel ball matrix is higher than that in the grooved plate matrix.
A compromise has to be made between the iron extraction and rare earth loss. In an
attempt to achieve the relatively high iron extraction with lower rare earth loss, 4 ampere
current and the steel ball matrix were employed as the final magnetic parameters; 55.7%
of iron recovery and 14.9% of REO loss were obtained. The non-magnetic product
containing 6.9% REO after WHIMS processing were regarded as the feed of batch
flotation tests.
60
5Χ10-4 M HXY
50
1Χ10-3 M HXY
)
2
m
/
lo 40
m
µ
(
y
t
is
n 30
e
d
n
o
it
p 20
r
o
s
d
A
10
0
4 5 6 7 8 9 10 11 12 13
pH
Figure 6.37 Adsorption density of the sample as a function of pH in the presence of
5Χ10-4 M and 1Χ10-3 M octanohydroxamic acid at room temperature
Table 6.4 Results for WHIMS with grooved plate
Current (ampere) Iron assay (%) Iron recovery (%) REO loss (%)
4 39.6 42.8 5.6
8 29.8 46.5 12.3
12 26.7 48.0 14.2
16 25.0 57.4 20.7
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