text: # Correlation for devolatilization time accounting for moisture content within
  # a wood particle. Refer to Equations 2-7 in the paper for more details. 
  # -- Reference (Diego2003) --
  # De Diego, L. F., et al. "Effect of moisture content on devolatilization times
  # of pine wood particles in a fluidized bed." Energy & fuels 17.2 (2003): 285-290.
  
  import numpy as np
  import matplotlib.pyplot as py
  
  py.close('all')
  
  # Parameters
  # -----------------------------------------------------------------------------
  
  d = 2       # diameter of particle, mm
  n = 1.5     # exponent n
  b = 1.7e-2  # factor for moisture content
  
  # coefficient a at various temperatures
  a1 = 1.69   # for 923 K
  a2 = 1.38   # for 1023 K
  a3 = 1.03   # for 1123 K
  a4 = 0.89   # for 1223 K
  
  # Calculate devolatilization time
  #------------------------------------------------------------------------------
  
  # range of moisture content from 0-50%
  mc = np.linspace(0, 50) # moisture content, %
  
  # general equation for devolatilization time tv = a*(d)^n per Eq. 2
  # tv = tvo*(1+b*mc) per Eq. 5
  tv1 = a1*d**n*(1 + b*mc)
  tv2 = a2*d**n*(1 + b*mc)
  tv3 = a3*d**n*(1 + b*mc)
  tv4 = a4*d**n*(1 + b*mc)
  
  # Plot results
  #------------------------------------------------------------------------------
  
  # this figure should have similar trends as Fig. 4 in Diego2003
  py.figure(1)
  py.plot(mc, tv1, lw=2, label='923 K')
  py.plot(mc, tv2, lw=2, label='1023 K')
  py.plot(mc, tv3, lw=2, label='1123 K')
  py.plot(mc, tv4, lw=2, label='1223 K')
  py.xlabel('Moisture Content (%)')
  py.ylabel('tv (s)')
  py.legend(loc='best', numpoints=1, fontsize=12)
  py.title('d = {} mm particle size'.format(d))
  py.grid()
  py.show()
  
  # plot the (a) coefficients vs temperature
  T = [923, 1023, 1123, 1223]
  a = [a1, a2 ,a3 ,a4]
  
  py.figure(2)
  py.scatter(T, a, s=60, c='red')
  py.ylabel('Coefficient  a')
  py.xlabel('Temperature (K)')
  py.title('d = {} mm particle size'.format(d))
  py.grid()
  py.show()