CROSS-REFERENCE TO RELATED APPLICATIONS 
   This application claims the benefit, pursuant to 35 U.S.C. §120, to U.S. patent application Ser. No. 10/970,808, now U.S. Pat. No. 7,302,374, filed on Oct. 21, 2004, which is a continuation of U.S. patent application Ser. No. 09/640,219, now U.S. Pat. No. 6,527,068, filed on Aug. 16, 2000 and of U.S. patent application Ser. No. 10/352,490, now U.S. Pat. No. 6,827,161, filed Jan. 28, 2003. 
   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The invention relates generally to the field of drill bits used to drill earth formations. More specifically, the invention relates to methods for designing, and to designs, for drill bits having improved drilling performance. 
   2. Description of the Related Art 
   Roller cone drill bits used to drill wellbores through earth formations generally include a plurality of roller cones rotatably mounted to a bit body. The bit body is turned by a drilling apparatus (drilling rig) while axial force is applied to the bit to drill through the earth formations. The roller cones include a plurality of cutting elements disposed at selected locations thereon. The types, sizes and shapes of the cutting elements are generally selected to optimize drilling performance of the drill bit in the particular earth formations through which the formation is to be drilled. 
   The cutting elements may be formed from the same piece of metal as each of the roller cones, these being so-called “milled tooth” bits. Other types of cutting elements consist of various forms of “inserts” (separate bodies formed from selected materials) which can be affixed to the roller cones in a number of different ways. 
   Some types of cutting elements, both milled tooth and insert type, have cutting edges (“crests”) which are not symmetric with respect to an axis within the body of the cutting element. These are called non-axisymmetric cutting elements. Some types of roller cone drill bits have non-axisymmetric cutting elements oriented so that the crests are oriented in a selected direction. The purpose of such crest orientation is to improve the drilling performance of the roller cone bit. 
   One such method for improving drill bit performance by orienting cutting element crests along a particular direction is described in published patent application PCT/US99/19992 filed by S. Chen. The method disclosed in this application generally includes determining an expected trajectory of the cutting elements as they come into contact with the earth formation. The expected trajectory is determined by estimating a rotation ratio of the roller cones, this ratio being the cone rotation speed with respect to the bit rotation speed. The crests of the cutting elements are then oriented to be substantially perpendicular to, or along, the expected trajectory. Whether the crests are oriented perpendicular or along the expected trajectory depends on the type of earth formation being drilled. 
   Yet another method for orienting the crests of the cutting elements on a roller cone bit is described in U.S. Pat. No. 5,197,555 issued to Estes. As explained in the Estes &#39;555 patent, the crests of the cutting elements are oriented within angle ranges of 30 to 60 degrees (or 300 to 330 degrees) from the axis of rotation of the cone. 
   It is desirable to provide a drill bit wherein non-axisymmetric cutting elements are oriented to optimize a rate at which the drill bit cuts through earth formations. 
   SUMMARY OF THE INVENTION 
   One aspect of the invention is a roller cone drill bit having roller cones rotatably attached to a bit body. Each of the cones includes a plurality of cutting elements, at least one of the cutting elements being non-axisymmetric and oriented so that a value of at least one drilling performance parameter is optimized. In one embodiment, the at least one parameter include rate of penetration of the drill bit. 
   In one embodiment, the crest of the at least one cutting element is oriented at an angle of about 10 to 25 degrees from the direction of movement of the cutting element as it contacts the earth formation when the cutting element is disposed in a position outboard of the drive row location on the cone. In another embodiment, the angle is about 350 to 335 degrees when the cutting element is disposed in a position inboard of the drive row location. 
   Another aspect of the invention is a method for designing a roller cone drill bit including simulating the bit drilling earth formations. The drill bit includes roller cones rotatably attached to a bit body. Each of the cones includes a plurality of cutting elements, at least one of the cutting elements being non-axisymmetric. In the method, an orientation of the cutting element is adjusted, and the drilling is again simulated. The adjustment and simulation are repeated until the value of at least one drilling performance parameter is optimized. In one embodiment, the at least one performance parameter includes the rate of penetration of the drill bit. 
   Other aspects and advantages of the invention will be apparent from the description which follows. 


   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  shows one example of a prior art roller cone drill bit having non-axisymmetric cutting elements. 
       FIG. 2  shows a bottom view of one example of a roller cone bit having cutting elements oriented according to the invention. 
       FIG. 3  shows one example of how to approximate a location of a drive row on a cone. 
       FIG. 4  shows one embodiment of a cutting element which has more than one direction of a long dimension. 
   


   DETAILED DESCRIPTION OF THE INVENTION 
   Referring to  FIG. 1 , a typical prior art roller cone drill bit  20  includes a bit body  22  having an externally threaded connection at one end  24 , and a plurality of roller cones  26  (usually three as shown) attached to the other end of the bit body  22  and able to rotate with respect to the bit body  22 . Attached to the cones  26  of the bit  20  are a plurality of cutting elements  28  typically arranged in rows about the surface of the cones  26 . The cutting elements  28  can be any type known in the art, including tungsten carbide inserts, polycrystalline diamond compacts, or milled steel teeth. The cutting elements shown in  FIG. 1  at  28  are non-axisymmetric, meaning that the crest  28 A of the cutting element is not symmetric with respect to an axis (not shown) of the cutting element  28 . Typically, the crest  28 A of a non-axisymmetric cutting element such as shown at  28  will define a long dimension, shown along line L. An orientation of the long dimension L is generally defined as an angle subtended between the direction of the long dimension L and a selected reference. In this example the reference is the rotational axis of the cone, shown at A. Any other suitable reference can be used to define the orientation of the cutting element. The non-axisymmetric cutting elements  28  on the bit  20  shown in  FIG. 1  are arranged so that the long dimension L is substantially parallel (at zero degrees subtended angle) with respect to the axis rotation A. 
   It should be noted that the long dimension L for the crest  28 A shown in  FIG. 1  is substantially parallel to the crest  28 A because the crest  28 A is linear. Other shapes of crest are known in the art which will have different definitions of the long dimension. For example, crescent shaped crests on some cutting elements may have the long dimension defined as along a line connecting the endpoints of the crescent. Referring briefly to  FIG. 4 , for example, a special type of cutting element  28  has a long dimension L 2  across its crest which as shown in this example is oriented differently than the long dimension L 1  of the base of the cutting element  28 . For the description of the invention which follows, the orientation of the crest of such cutting elements will be determined by the direction of L 2 . As will be further explained, the individual orientation of both L 2  and of L 1  can be optimized to provide improved drilling performance. 
   Referring back to  FIG. 1 , although the bit  20  has been shown wherein substantially all the cutting elements  28  include the long dimension L, it is within the scope of this invention if only one such cutting element, or any other number of such cutting elements, is non-axisymmetric and includes long dimension L. The rest of the cutting elements may be axisymmetric. Therefore, the number of non-axisymmetric cutting elements is not intended to limit the invention. 
   It has been determined that the orientation of the long dimension L with respect to the axis of the cone A has an effect on drilling performance of the bit  20 . In one aspect of the invention, drilling with the bit  20  through a selected earth formation is simulated. The simulation typically includes determination of a rate at which the bit penetrates through the selected earth formation (ROP), among other performance measures. In this aspect of the invention, the angle of the long dimension L with respect to the selected reference is adjusted, the drilling simulation is repeated, and the performance of the bit is again determined. The adjustment to the angle and simulation of drilling are repeated until the drilling performance is optimized. In one embodiment of the invention, optimization is determined when the rate of penetration (ROP) is determined to be maximum. 
   One such method for simulating the drilling of a roller cone drill bit such as shown in  FIG. 1  is described in U.S. Pat. No. 6,516,293, filed on Mar. 13, 2000, and assigned to the assignee of this invention. The method of the &#39;293 patent is hereby incorporated by reference. The method for simulating the drilling performance of a roller cone bit drilling an earth formation may be used to optimize the design of roller cone drill bits, and to optimize the drilling performance of a roller cone bit. The method includes selecting bit design parameters, selecting drilling parameters, and selecting an earth formation to be drilled. The bit design parameters generally include at least the shape of the cutting elements on the drill bit. The method further includes calculating, from the bit design parameters, drilling parameters and earth formation, the parameters of a crater formed when one of the cutting elements contacts the earth formation. The method further includes calculating a bottomhole geometry, wherein the crater is removed from a bottomhole surface. The method also includes incrementally rotating the bit and repeating the calculating of crater parameters and bottomhole geometry based on calculated roller cone rotation speed and geometrical location with respect to rotation of said roller cone drill bit about its axis. 
   In the present embodiment, the simulation according to the previously described program is performed. At least one drilling performance parameter, which can include the rate of penetration, is determined as a result of the simulation. The angle of the long dimension L of the at least one non-axisymmetric cutting element is adjusted. The simulation is repeated, typically including maintaining the values of all the other drilling control and drill bit design parameters, and the value of the at least one drilling performance parameter is again determined. This process is repeated until the value of the drilling performance parameter is optimized. In one example, as previously explained, the drilling performance parameter is optimized when rate of penetration is determined to be at a maximum. 
   For the special cutting element  28  shown in  FIG. 4 , the orientation of the crest long dimension L 2  and the orientation of the base long dimension L 1  can both be adjusted, the simulation repeated, and the results compared until the value of the at least one drilling performance parameter is optimized. It is believed that in some drill bits, the direction of the velocity vector may be different at the crest of the cutting elements than at the base of the cutting elements. Specially shaped cutting elements such as shown at  28  in  FIG. 4  provide the bit designer with the ability to optimize the orientation of the long dimension at both the crest and at the base of the cutting elements to further improve drilling performance. As for the other embodiments of a bit according to the various aspects of the invention, the number of such special cutting elements as shown in  FIG. 4  is not meant to limit the scope of the invention. 
   Another aspect of non-axisymmetric cutting elements is that some types of such cutting elements may not be symmetric with respect to a bisecting plane. Other types of such cutting elements may be symmetric with respect to a bisecting plane. Referring briefly to  FIG. 1 , typical prior art cutting elements such as  28 A which are not axisymmetric nonetheless have a bisecting plane about which the cutting element is symmetric. In the prior art, such cutting elements  28 A are oriented such that the bisecting plane is substantially perpendicular to the surface of the roller cone. Another aspect of the invention is that in addition to orienting the cutting element crest at a selected angle with respect to the cone axis, the bisecting plane is oriented at a selected angle with respect to the surface of the cone. An example of this orientation is shown in  FIG. 2 , where bisecting plane P subtends an angle θ 4  with respect to perpendicular to the surface of the cone  26 . As with other aspects of the invention, the orientation of the subtended angle θ 4  is preferably determined by selecting an initial value of the subtended angle, simulating performance of the bit, adjusting the angle, and repeating the simulating performance until an optimal value of the at least one drilling performance parameter is determined. 
   Referring to  FIG. 2 , through drilling simulation according to the method described in the &#39;088 patent application, it has been determined that drilling performance of a certain type of roller cone bit known as a tungsten carbine insert (TCI) bit having “chisel” shaped inserts, is optimal when the angle, shown as θ 1 , of the long dimension L is in a range of about 10 to about 25 degrees with respect to the axis A, when the cutting element  28  is disposed in a position on the cone radially outboard (away from the center of the cone) of the radial position of a “drive row” on the cone. If the cutting element, for example, as shown at  29 , is disposed in a row radially interior to the drive row position, it has been determined that drilling performance is improved when the angle, shown in  FIG. 2  as θ 2 , is within a range of about 350 to 335 degrees. The definition of the size of the angle used herein is that the angle increases in a direction of the “leading” edge (toward the direction of rotation of the cone). 
   It has been determined through simulation of drilling with the bit that a more preferred value for the angle θ 1  is about 25 degrees, and that a more preferred value for angle θ 2  is about 335 degrees. 
   In the event that the cutting element is radially positioned at the drive row location, the angle may be either approximately 10 to 25, or 350 to 335 degrees, (or more preferably 25 or 335 degrees) depending on which value of the angle provides a more optimized value of the drilling performance parameter, such as higher rate of penetration. 
   One method for estimating the position of the drive row is illustrated in  FIG. 3 . The rotation ratio of each of the cones  26  can be determined, for example, using force calculations such as described in the &#39;293 patent referred to earlier, or by simulating the drilling of the bit as in the &#39;293 patent. Having determined or otherwise estimated the rotation ratio of the cone  26 , a ratio of drive row distance r 2  from the axis of the bit B with respect to effective cone radius r 1  will be approximately related to the position of the drive row. The drive row position for purposes of this invention will be located approximately at the position along the cone axis A where the ratio r 2 /r 1  is approximately the same as the rotation ratio of the cone  26 . In any particular bit design, there may or may not be a row of cutting elements disposed at the drive row location. The angle for orienting the at least one cutting element can be selected, as previously explained, by considering the location of the at least one cutting element with respect to the drive row location estimated according to the previously described method. 
   Referring again to  FIG. 3 , a particular feature of the invention is shown which has as its purpose further improvement of drilling performance. At least one of the cutting elements  30 , in a row in which all the other cutting elements are oriented at the preferred angle θ 1 , preferably is oriented at a different angle θ 3  so that the row of cutting elements will resist “tracking”. The magnitude of the difference in the angles is not important, but only need be selected to avoid tracking. In particular, whether the selected difference in angle between the at least one cutting element and the other cutting elements on the same row is enough to avoid tracking can be determined, among other methods, by using the drilling simulation technique described in the &#39;293 patent referred to earlier. 
   This feature of the invention can work with other embodiments of a drill bit. For example, substantially all of the cutting elements on the bit may have long dimension L parallel to the respective axis A of the cone on which each cutting element is disposed. At least one cutting element on any one row of cutting elements on the bit may be disposed so that its long dimension L subtends an angle other than parallel to the cone axis. In another example, at least one cutting element on each row on one cone can be disposed so that its long dimension is other than parallel to the respective cone axis. In yet another example, at least one cutting element on each cone, or alternatively, at least one cutting element on each row of each cone can be oriented so that its long dimension is other than parallel to the cone axis. In each of the foregoing examples, orienting the at least one cutting element so that its long dimension other than parallel to the cone, when all the other cutting elements in the same row are parallel to their respective cone axis is intended to reduce tracking. This aspect of the invention will also work where the other ones of the cutting elements on the same row are not parallel to the cone axis but are disposed at some selected angle (such as the previously described preferred angle). As long as at least one cutting element is disposed at a different angle than all the other cutting elements on one row of cutting elements on the bit, such configuration is within the contemplation of this aspect of the invention. In another example, each row of cutting elements on each of the cones includes at least one cutting element disposed at an angle different from all the other cuffing elements on the row to avoid tracking. 
   The invention has been described with respect to particular embodiments. It will be apparent to those skilled in the art that other embodiments of the invention can be devised which do not depart from the spirit of the invention as disclosed herein. Accordingly, the invention shall be limited in scope only by the attached claims.
A method for designing a drill bit that involves simulating a drill bit having cutting elements disposed thereon is provided. In particular, the method involves determining at least one drilling performance parameter while simulating drilling in a selected earth formation.