Abstract:
A method for designing a roller cone drill bit comprising selecting initial bit design parameters, selecting initial earth formations parameters, selecting initial drilling parameters, simulating drilling a selected earth formation, determining stress on at least one of the group of cutting element, cone, and drill bit, determining velocity of at least one of the group of cutting element, cone, and drill bit, calculating wear, varying at least one of the bit design parameters and repeating the simulating and the calculating until the wear meets a selected criterion. The method further comprises normalizing said calculated wear, and converting said normalized wear into a visual representation.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a continuation of U.S. patent application Ser. No. 09/635,116 (“the &#39;116 application”) which was filed on Aug. 9, 2000 as a continuation of U.S. Pat. No. 6,516,293 (“the &#39;293 patent”), filed Mar. 13, 2000. This application claims benefit, pursuant to 35 U.S.C. §120, from both the &#39;116 application and the &#39;293 patent. The disclosures of the &#39;116 application and the &#39;293 patent are expressly incorporated by reference in their entireties. 
     
    
     BACKGROUND OF INVENTION  
     Background Art  
       [0002]     Roller cone rock bits and fixed cutter bits are commonly used in the oil and gas industry for drilling wells.  FIG. 1  shows one example of a conventional drilling system drilling an earth formation. The drilling system includes a drilling rig  10  used to turn a drill string  12 , which extends downward into a well bore  14 . Connected to the end of the drill string  12  is roller cone-type drill bit  20 , shown in further detail in  FIG. 2 .  
         [0003]     As shown in  FIG. 2 , a roller cone bit  20  typically comprises 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 roller cones  26  of the bit  20  are a plurality of cutting elements  28 , typically arranged in rows about the surface of the roller cones  26 . The cutting elements  28  can be tungsten carbide inserts, polycrystalline diamond compacts, or milled steel teeth. If the cutting elements  28  are milled steel teeth, they may be coated with a hardfacing material.  
         [0004]     The bit body includes one or more legs, each having thereon a bearing journal. The most commonly used types of roller cone drill bits each include three such legs and bearing journals. A roller cone is rotatably mounted to each bearing journal. During drilling, the roller cones rotate about the respective journals while the bit is rotated. The roller cones include a number of cutting elements, which may be press fit inserts made of tungsten carbide and other materials, or may be milled steel teeth.  
         [0005]     The cutting elements engage the formation in a combination of crushing, gouging, and scraping or shearing actions which remove small segments of the formation being drilled. The inserts on a cone of a three-cone bit are generally classified as inner-row inserts and gage-row inserts. Inner-row inserts engage the bore hole bottom, but not the well bore wall. Gage-row inserts engage the well bore wall and sometimes a small outer ring portion of the bore hole bottom. The direction of motion of inserts engaging the rock on a two or three-cone bit is generally in one direction or within a very small range of directions, i.e., within a range of 10 degrees or less.  
         [0006]     When a roller cone bit is used to drill earth formations, the bit may experience abrasive wear. Abrasive wear occurs when hard, sharp formation particles slide against a softer surface of the bit and progressively remove material from the bit body and cutting elements. The severity of the abrasive wear depends upon, among other factors, the size, shape, and hardness of the abrasive particles, the magnitude of the stress imposed by the abrasive particles, and the frequency of contact between the abrasive particles and the bit.  
         [0007]     Abrasive wear may be subclassified into three categories: low-stress abrasion, high-stress abrasion, and gouging abrasion. Low-stress abrasion occurs when forces acting on the formation are not high enough to crush abrasive particles. Comparatively, high-stress abrasion occurs when forces acting on the formation are sufficient to crush the abrasive particles. Gouging abrasion occurs when even higher forces act on the formation and the abrasive particles dent or gouge the bit body and/or the cutting elements of the bit.  
         [0008]     As a practical matter, all three abrasion mechanisms act on the bit body and cutting elements of drill bits. The type of abrasion may vary over different parts of the bit. For example, shoulders of the bit may only experience low-stress abrasion because they primarily contact sides of a wellbore. However, drive-row cutting elements, which are typically the cutting elements that first contact a formation, may experience both high-stress and gouging abrasion because these cutting elements are exposed to high axial loading.  
         [0009]     Drill bit life and efficiency are of great importance because the rate of penetration of the bit through earth formations is related to the wear condition of the bit. Accordingly, various methods have been used to provide abrasion protection for drill bits in general, and specifically for roller cones and cutting elements. For example, roller cones, cutting elements, and other bit surfaces may be coated with hardfacing material to provide more abrasion resistant surfaces. Further, specialized cutting element insert materials have been developed to optimize longevity of the cutting elements. While these methods of protection have met with some success, drill bits still experience wear.  
         [0010]     As a bit wears, its cutting profile can change. One notable effect of the change in cutting profile is that the bit drills a smaller diameter hole than when new. Changes in the cutting profile and in gage diameter act to reduce the effectiveness and useful life of the bit. Other wear-related effects that are less visible also have a dramatic impact on drill bit performance. For example, as individual cutting elements experience different types of abrasive wear, they may wear at different rates. As a result, a load distribution between roller cones and between cutting elements may change over the life of the bit. These changes may be undesirable if, for example, a specific roller cone or specific rows of cutting elements are exposed to a majority of axial loading. This may cause further uneven wear and may perpetuate a cycle of uneven wear and premature bit failure.  
         [0011]     For the foregoing reasons, there exists a need for an effective method to design drill bits having good wear characteristics.  
       SUMMARY OF INVENTION  
       [0012]     In one aspect, the invention provides a method for designing a drill bit. The method comprises selecting initial bit design parameters, selecting initial earth formation parameters, and selecting initial drilling parameters. The method further comprises simulating drilling a selected earth formation, determining stress on a least one from the group of cutting element, cone, and drill bit, determining velocity of at least one from the group of cutting element, cone, and drill bit, and calculating wear. At least one of the bit design parameters is varied, and the simulating, the determining, and the calculating are repeated until the wear meets a selected criterion.  
         [0013]     In another aspect, the invention provides a method for designing a drill bit further comprising normalizing said calculated wear.  
         [0014]     In another aspect, the invention provides a method for designing a drill bit further comprising converting a normalized wear into a visual representation. In some embodiments, the visual representation is in tabular form. In other embodiments, the visual representation is a graphical display of the drill bit showing said normalized wear.  
         [0015]     In another aspect, the invention provides a drill bit designed by a method comprising selecting initial bit design parameters, selecting initial earth formation parameters, and selecting initial drilling parameters. The method further comprising simulating drilling a selected earth formation, determining stress on a least one from the group of cutting element, cone, and drill bit, determining velocity of at least one from the group of cutting element, cone, and drill bit, calculating wear, and varying the bit design parameters and repeating the simulating, the determining stress, the determining velocity, and the calculating until the wear meets a selected criterion.  
         [0016]     Other aspects and advantages of the invention will be apparent from the following description and the appended claims. 
     
    
     BRIEF DESCRIPTION OF DRAWINGS  
       [0017]      FIG. 1  shows a schematic diagram of a conventional drilling system for drilling earth formations having a drill string attached at one end to a roller cone drill bit.  
         [0018]      FIG. 2  shows a perspective view of a conventional roller cone drill bit.  
         [0019]      FIG. 3A  and  FIG. 3B  show a flowchart of an embodiment of the invention for generating a visual representation of a roller cone bit drilling earth formations.  
         [0020]      FIG. 4  shows an output of an embodiment of the invention in tabular form.  
         [0021]      FIG. 5  shows a flowchart of an embodiment of the invention. 
     
    
     DETAILED DESCRIPTION  
       [0022]     In order to account for the effects of wear on drill bit performance, it is desirable to be able to analyze bit wear in a drilling operation. After a detailed analysis, bit design parameters may be modified to minimize or compensate for bit wear. Embodiments of the inventions use a model to analyze relative wear and to design drill bits with improved wear characteristics.  
         [0023]     In one aspect, embodiments of the present invention relate to methods of simulating relative wears of cutting elements, roller cones, and/or drill bits. In another aspect, embodiments of the invention relate to drill bits having optimized wear characteristics.  
         [0024]     Significant expense is involved in the design and manufacture of drill bits. Therefore, having accurate models for simulating and analyzing the drilling characteristics of bits can greatly reduce the cost associated with manufacturing drill bits for testing and analysis purposes. For this reason, several models have been developed and employed for the analysis and design of 2, 3, and 4 roller cone bits. See, for example, U.S. Pat. Nos. 6,213,225, 6,095,262, 6,412,577, and 6,401,839. In addition, U.S. Pat. No. 6,516,293 (“the &#39;293 patent”) discloses a simulation method for multiple cone bits, which is assigned to the assignee of the instant application, and is incorporated by reference in its entirety.  
         [0025]     The simulation model disclosed in the &#39;293 patent is particularly useful in that it provides a means for analyzing the forces acting on individual cutting elements on the bit, thereby allowing for the design of, for example, faster drilling bits or the design of bits having optimal spacing and placing of cutting elements thereon. By analyzing forces acting on individual cutting elements of a bit prior to making the bit, it is possible to avoid expensive trial and error in designing effective and long-lasting bits.  
         [0026]      FIGS. 3A and 3B  show a flow chart of one embodiment of the invention for simulating a roller cone drill bit drilling a selected earth formation. The parameters in the simulation may include drilling parameters  310 , bit design parameters  312 , cutting element/earth formation interaction data  314 , and bottomhole geometry data  316 . In addition, an initial bit speed/cone speed rotation ratio may be included. Typically, the bottomhole geometry prior to drilling simulation will be a planar surface, but this is not a limitation on embodiments of the invention. The input data  310 ,  312 ,  314 ,  316  may be stored in an input library and later retrieved as needed during simulation calculations.  
         [0027]     Drilling parameters  310  which may be used include the axial force applied on the drill bit (commonly referred to as the weight on bit, “WOB”), and the rotational speed of the drill bit (typically provided in revolutions per minute, “RPM”). It should be understood that drilling parameters are not limited to these variables, but may include other variables, such as, rotary torque and mud flow volume. Additionally, drilling parameters  310  provided as input may include the total number of bit revolutions to be simulated, as shown in  FIG. 3A . However, it should be understood that the total number of revolutions is provided simply as an end condition to signal the stopping point of simulation and is not necessary for the calculations required to simulate or visually represent the drilling operation. Alternatively, another end condition may be employed to determine the termination point of simulation, such as the total drilling depth (axial span) to be simulated or any other final simulation condition. Alternatively, the termination of simulation may be accomplished by operator command, or by performing any other specified operation.  
         [0028]     Bit design parameters  312  used as input may include bit cutting structure information, such as the cutting element location and orientation on the roller cones, and cutting element information, such as cutting element size(s) and shape(s). Bit design parameters  312  may also comprise at least one of cutting element count, cutting element height, cutting element geometrical shape, cutting element spacing, cutting element orientation, cone axis offset, cutting element material, cutting element location, cone diameter profile, and bit diameter. The cutting element and roller cone geometry can be converted to coordinates and used as input for the invention. Preferred methods for bit design parameter inputs include the use of 3-dimensional CAD solid or surface models to facilitate geometric input.  
         [0029]     Cutting element/earth formation interaction data  314  used as input may include data that characterize the interactions between a selected earth formation (which may have, but need not necessarily have, known mechanical properties) and an individual cutting element having known geometry.  
         [0030]     Bottomhole geometry data  316  used as input may include geometrical information regarding the bottomhole surface of an earth formation, such as the bottomhole shape. As previously explained, the bottomhole geometry may be planar at the beginning of a simulation, but this is not a limitation on embodiments of the invention. The bottomhole geometry can be represented as a set of axial (depth) coordinates positioned within a defined coordinate system, such as in a cartesian coordinate system. In accordance with one embodiment of the invention, the bottomhole surface may be represented as a mesh shape having a suitable mesh size, e.g. 1 millimeter.  
         [0031]     As shown in  FIG. 3A , once the input data  310 - 316  are entered or otherwise made available, calculations in the main simulation loop  320  can be carried out. In the main simulation loop  320 , drilling simulation is performed by incrementally “rotating” the bit through an incremental angle and determining an approximate vertical (axial) displacement of the bit corresponding to the incremental bit rotation. Once the approximate vertical displacement is obtained, the lateral forces on the cutting elements may be calculated and used to determine the current rotation speed of the cones. Finally, the bottomhole geometry is updated by removing the deformed earth formation resulting from the incremental drilling calculated in the simulation loop  320 . A more detailed description of the elements in the simulation loop  320  is as follows.  
         [0032]     The first step in the simulation loop  320  in  FIG. 3A , involves “rotating” the roller cone bit (numerically) by a selected incremental angle amount, Δθ bit,i ,  322 . In one example embodiment, the selected incremental angle is 3 degrees. It should be understood that any incremental angle may be chosen for the convenience of a system designer and should not limit the invention. The incremental rotation of the bit results in an incremental rotation of each cone on the bit, Δθ cone,i . In one example, the rotational speed of the cones is determined by the rotational speed of the bit, Δθ bit,i , and the effective radius of the “drive row” of the cones. The effective radius is generally related to the radial extent of the cutting elements that extend axially the farthest from the axis of rotation of the cones; these cutting elements are located on a so-called “drive-row.” Thus, the rotational speed of the cones can be defined or calculated based on the known rotational speed of the bit and the defined geometry of the cones provided as input (e.g., the cone diameter profile and cone axial offset). Then, the incremental rotation of the cones, Δθ cone,i , may be calculated based on incremental rotation of the bit, Δθ bit,i , and the calculated rotational speed of the cones  324 .  
         [0033]     Once the incremental rotation of each cone Δθ cone,i  is calculated, the new locations of the cutting elements, p θ,i , are computed based on bit rotation, cone rotation, and the immediately previous locations of the cutting elements p i-1 . The new locations of the cutting elements  326  can be determined by any method for geometric calculations known in the art. In addition to new locations of the cutting elements, vertical displacements of the bit resulting from the incremental rotations of the bit may be, in one embodiment, iteratively computed in a vertical force equilibrium loop  330 .  
         [0034]     In the vertical force equilibrium loop  330 , the bit is “moved” (axially) downward (numerically) a selected initial incremental distance Δd i  and new cutting element locations p i  are calculated, as shown at  332  in  FIG. 3A . In this example, the selected initial incremental distance is 2 mm. It should be understood that the initial incremental distance selected is a matter of convenience for the system designer and is not intended to limit the invention. Then, the cutting element interference with the existing bottomhole geometry is determined, at  334 . This includes determining the depth of penetration of each cutting element into the earth formation, and a corresponding interference projection area. The depth of penetration is defined as the distance from the formation surface a cutting element penetrates into an earth formation. The depth of penetration can range from zero (no penetration) to the full height of the cutting element (full penetration). The interference projection area is the fractional amount of surface area of the cutting element which actually contacts the earth formation. Upon first contact of a cutting element with the earth formation, such as when the formation presents a smooth, planar surface to the cutting element, the interference projection area is substantially equal to the total contact surface area corresponding to the depth of penetration of the cutting element into the formation.  
         [0035]     However, upon subsequent contact of cutting elements with the earth formation during simulated drilling, each cutting element may have subsequent contact area less than the total available contact area on a cutting element. This less than full area contact results from the formation surface having “craters” (deformation pockets) made by previous contact with a cutting element. Fractional area contact on any of the cutting elements reduces the interference and axial force acting on the cutting element, which can be accounted for in the simulation calculations.  
         [0036]     Once the cutting element/earth formation interaction is determined for each cutting element, the vertical force, f V,i  applied to each cutting element may be calculated based on the calculated penetration depth, the projection area, and the cutting element/earth formation interaction data  312 . This is shown at  336  in  FIG. 3B . Thus, the axial force acting on each cutting element is related to the cutting element penetration depth and the cutting element interference projection area. One of ordinary skill in the art would appreciate that a drilling simulation may be performed with a constant RPM or a constant WOB. In accordance with one embodiment of the invention, the simulation is driven by a constant WOB. In this embodiment, a simplifying assumption used in the simulation is that the WOB is equal to the summation of vertical forces acting on each cutting element. Therefore, the vertical forces, f V,i , on the cutting elements are summed to obtain a total vertical force F V,i  on the bit, which is then compared with the selected axial force applied to the bit (the WOB) for the simulation, as shown at  338 . If the total vertical force F V,i  is greater than the WOB, the initial incremental distance Δd i  applied to the bit is larger than the incremental axial distance that would result from the selected WOB. If this is the case, the bit is moved up a fractional incremental distance, (i.e., the incremental axial movement of the bit is reduced), and the calculations in the vertical force equilibrium loop  330  are repeated for the resulting incremental distance.  
         [0037]     If the total vertical force F V,i  on the cutting elements, using the resulting incremental axial distance is less than the WOB, the resulting incremental distance Δd i  applied to the bit is smaller than the incremental axial distance that would result from the selected WOB. In this case, the bit is moved further down, and the calculations in the vertical force equilibrium loop  330  are repeated. The vertical force equilibrium loop  330  calculations iteratively continue until a proper axial displacement for the bit is obtained that results in a total vertical force on the cutting elements substantially equal to the selected WOB, or within a selected error range.  
         [0038]     Once the proper axial displacement, Δd i , of the bit is obtained, the lateral movement of the cutting elements may be calculated based on the previous, p i-1 , and current, p i , cutting element locations, as shown at  340 . Then, the lateral force, f L,i , acting on the cutting elements is calculated based on the lateral movement of the cutting elements and cutting element/earth formation interaction data, as shown at  342 . Then, the cone rotation speed is calculated based on the forces on the cutting elements and the moment of inertia of the cones, as shown at  344 .  
         [0039]     Finally, the bottomhole pattern is updated, at  346 , by calculating the interference between the previous bottomhole pattern and the cutting elements during the current incremental drilling step, and based on cutting element/earth formation interaction, “removing” the formation resulting from the incremental rotation of the selected bit with the selected WOB. In this example, the interference can be represented by a coordinate mesh or grid having 1 mm grid blocks.  
         [0040]     This incremental simulation loop  320  can then be repeated by applying a subsequent incremental rotation to the bit  322  and repeating the calculations in the incremental simulation loop  320  to obtain an updated bottomhole geometry. Using the total bit revolutions to be simulated as the termination command, for example, the incremental displacement of the bit and subsequent calculations of the simulation loop  320  will be repeated until the selected total number of bit revolutions to be simulated is reached. Repeating the simulation loop  320  as described above will result in simulating the performance of a roller cone drill bit drilling earth formations with continuous updates of the bottomhole pattern drilled, simulating the actual drilling of the bit in a selected earth formation. Upon completion of a selected number of operations of the simulation loops  320 , results of the simulation can be programmed to provide output information at  348  characterizing the performance of the selected drill bit during the simulated drilling, as shown in  FIG. 3B . It should be understood that the simulation can be stopped using any other suitable termination indicator, such as a selected axial displacement.  
         [0041]     Referring back to the embodiment of the invention shown in  FIGS. 3A and 3B , drilling parameters  310 , bit design parameters  312 , and bottomhole parameters  316  required as input for the simulation loop of the invention are distinctly defined parameters that can be selected in a relatively straight forward manner. On the other hand, cutting element/earth formation interaction data  314  are not defined by a clear set of parameters, but can be obtained in a number of different ways.  
         [0042]     In one embodiment of the invention, cutting element/earth formation interaction data  314  may comprise a library of data obtained from actual tests performed using selected cutting elements, each having known geometry, on selected earth formations. In this embodiment, the tests include impressing a cutting element having known geometry on the selected earth formation with a selected force. The selected earth formation may have known mechanical properties, but it is not essential that the mechanical properties be known. Then, the resulting grooves formed in the formation as a result of the interaction between the inserts and the formation are analyzed. These tests can be performed for different cutting elements, different earth formations, and different applied forces, and the results analyzed and stored in a library for use by a simulation method of the invention. These tests can provide good representation of the interactions between cutting elements and earth formations under selected conditions.  
         [0043]     In one embodiment, these tests may be repeated for each selected cutting element in the same earth formation under different applied loads, until a sufficient number of tests are performed to characterize the relationship between interference depth and impact force applied to the cutting element. Tests are then performed for other selected cutting elements and/or earth formations to create a library of crater shapes and sizes and information regarding interference depth/impact force for different types of bits in selected earth formations.  
         [0044]     Alternatively, single insert tests, such as those described in the &#39;293 patent, may be used in simulations to predict the expected deformation/fracture crater produced in a selected earth formation by a selected cutting element under specified drilling conditions.  
         [0045]     In another embodiment of the invention, techniques such as Finite Element Analysis, Finite Difference Analysis, and Boundary Element Analysis may be used to determine the cutting element/earth formation interaction. For example, the mechanical properties of an earth formation may be measured, estimated, interpolated, or otherwise determined, and the response of the earth formation to cutting element interaction may be calculated using Finite Element Analysis.  
         [0046]     After the simulation phase is complete, the data collected from the simulation may be used to analyze wear of cutting elements, cones, and/or bits (Step  352  in  FIG. 3B ). The following description uses a cutting element to illustrate wear analysis. One of ordinary skill would appreciate that similar analysis may be applied to a roller cone or a drill bit.  
         [0047]     Wear is a function of the velocity of a cutting element, the stress on the cutting element, and the properties (e.g. hardness) of the material used to manufacture the cutting element (e.g., tungsten carbide). In other words, wear may be determined as follows:  
             Wear   =     A   ×       v   ⁢           ⁢   σ       H   ⁢           ⁢   ɛ                 (   1   )             
 
 where ν is the velocity of a given cutting element, σ is the stress encountered by the cutting element, H is the hardness of the material of the cutting element, ε is a material coefficient of the cutting element, and A is a constant. Because, A, H, and ε are constants for a selected cutting element, the wear can be redefined as: 
 
Wear= K ×νσ  (2) 
 
 where K is a constant. In other words, the wear is a linear function of the product of ν and σ. Thus, the wear may be referred to as “linear wear” in this description. 
 
         [0048]     In one embodiment, the stress may be determined by calculating the force acting on the cutting elements and/or cones per unit area. In another embodiment, the stress may be determined experimentally. In another embodiment, the stress may be calculated from the Modulus of Elasticity, Poisson&#39;s Ratio, and strain values. One of ordinary skill in the art would appreciate that the stress encountered by the cutting element may be determined by different methods commonly known in the art. The velocity of a given cutting element may be calculated from the rotational speed of the drill bit and the cone, as well as the linear movement speed of the whole bit in the simulation. The stress and velocity are then used to calculate the wear of the bit as shown above in Equations 1 and 2.  
         [0049]     The linear wear induced on the roller cone cutting elements and on the cones can be displayed in tabular form, as shown in  FIG. 4 . Alternatively, the linear wear may be displayed graphically, for example, by a color coded plot of the relative wear on the cutting elements and cones.  
         [0050]     The maximum, median, and average wear seen by a given cutting element or row, may be displayed. In accordance with some embodiments of the invention, the wear is a “relative” quantity. In these embodiments, the calculated wear values are normalized, for example, with the highest wear set to 1 and all of the other cutting elements normalized with respect to the highest wear.  
         [0051]     The simulation output may display a table of the linear wear induced on each cutting element, marked by cone and row numbers. In one embodiment of the invention, as show in  FIG. 4 , the maximum, median, and average wear are displayed in tabular form for each cone, and each row of cutting elements on each cone. In another embodiment, the normalized, or relative, wear may be displayed in tabular form, similar to that of  FIG. 4 . In this embodiment, the highest linear wear is represented by the value “1.000” and each linear wear measurement in normalized with respect to that value.  
         [0052]     Thus, the above methodology provides a method for simulating a drill bit drilling a formation. Some embodiments of the invention include graphically displaying the simulation of the drill bit, and other embodiments relate to methods for designing drill bits having improved wear characteristics. In one embodiment, a method of the invention includes selecting an initial bit design, calculating the performance of the initial bit design, then adjusting one or more design parameters and repeating the performance calculations until an optimal set of bit design parameters is obtained. In another embodiment, this method can be used to analyze relationships between bit design parameters and wear performance of a bit. In another embodiment, the method can be used to design roller cone bits having enhanced drilling characteristics. For example, the method can be used to analyze row spacing optimization, intra-insert spacing optimization, tracking, and forces acting on rows and cutting elements.  
         [0053]     Output information that may be considered in identifying bit designs having enhanced drilling characteristics or an optimal set of parameters include relative linear wear values. This output information may be in the form of visual representation parameters calculated for the visual representation of selected aspects of wear performance for each bit design, or the relationship between values of a bit parameter and the wear performance of a bit. Alternatively, other visual representation parameters may be provided as output as determined by the operator or system designer. Additionally, the visual representation of drilling may be in the form of a visual display on a computer screen. It should be understood that the invention is not limited to these types of visual representation, or the type of display. The means used for visually displaying aspects of simulated drilling is a matter of convenience for the system designer, and is not intended to limit the invention.  
         [0054]     Thus, in one embodiment of the invention, as shown in  FIG. 5 , a designer imports a bit design  560  into a computer containing the simulation software in accordance with an embodiment of the invention. The performance of this bit design is then simulated  562 . During the simulation, the relative wear induced on the cutting elements, cones, and/or drill bit may be monitored by the designer  564 . At the end of the simulation step, the stress induced on the cutting elements, cones, and/or drill bit is determined  566 , as described above. The velocity of the cutting elements, cones, and or drill bit is also determined  568  from the simulation. Using the stress and velocity determined from the simulation, the wear is calculated  570  according to Equation 2 above. The performance of the bit, specifically, the wear on the simulated cutting elements, cones, and/or bit, is analyzed  572 . After analyzing the performance of the bit, the design may be accepted or rejected  574 . In one embodiment of the invention, the designer may determine a “stop” point for the design. That is, the individual designer makes a determination as to when a bit is optimized for a given set of conditions. In other embodiments, however, the process may be automated to reach a pre-selected end condition. If the bit is rejected, the bit may be redesigned  576 . The bit design may be modified, for example, by modifying the initial bit parameters. For example, the orientation, spacing, number, material, location of the cutting elements and/or rows may be modified. Those having skill in the art will appreciate that bit designs may be changed in a variety of ways, and no limitation on the scope of the present invention is intended by listing specific changes. If the design is accepted, the design process is halted.  
         [0055]     As described above, the invention can be used to analyze wear of cutting elements, roller cones, and drill bits, or as a design tool to simulate and optimize the performance of roller cone bits drilling earth formations. The invention enables the analysis of drilling characteristics of proposed bit designs prior to their manufacturing, thus, minimizing the expense of trial and error designs of bit configurations. The invention enables the analysis of the effects of adjusting drilling parameters on the drilling performance of a selected bit design. Further, the invention permits studying the effect of bit design parameter changes on the drilling characteristics of a bit and can be used to identify a bit design which exhibits desired drilling characteristics. Furthermore, use of the invention leads to more efficient designing and use of bits having enhanced performance characteristics and enhanced drilling performance of selected bits.  
         [0056]     While the invention has been described with respect to a limited number of embodiments, those skilled in the art, having benefit of this disclosure, will appreciate that other embodiments can be devised which do not depart from the scope of the invention as disclosed herein. Accordingly, the scope of the invention should be limited only by the attached claims.