ESTIMATION OF ROCK ABRASIVENESS AND ROCK STRENGTH USING BIT RESPONSE DATA

Description

BACKGROUND

Knowledge of rock mechanical properties, including unconfined compressive strength (UCS) and confined compressive strength (CCS), allows for accurate geomechanical evaluations. Two important rock properties include rock abrasiveness and rock strength. The estimation of rock abrasiveness and rock strength after drilling a well may be useful in understanding dysfunctions that may have occurred in drilling and useful in selecting a bit or drilling conditions for future well drilling. Usually, these rock properties may be measured by measurement while drilling (MWD) and/or logging while drilling (LWD) tools indirectly.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 an elevation view (partially cross sectional) of an example well system, according to some implementations.

FIG. 2 is a block diagram of an example computer, according to some implementations.

FIGS. 3-4 are flowcharts depicting example operations for calculating an estimated rock strength along drilling depth, according to some implementations.

FIG. 5 is a plot depicting the relationship between input bit energy and drilling depth, according to some implementations.

FIG. 6 is a plot depicting depth of cut vs. weight on bit at various wear levels, according to some implementations.

FIG. 7 is a plot depicting depth of cut vs. torque on bit at various wear levels, according to some implementations.

FIG. 8 is a plot depicting depth of cut vs. drilling efficiency at various wear levels, according to some implementations.

FIG. 9 is a plot depicting weight on bit vs. torque on bit at various wear levels, according to some implementations.

FIG. 10 is a plot depicting contributions to WOB between various components of a drill bit, according to some implementations.

FIG. 11 is a plot depicting the weight on bit experienced by the primary cutters across a plurality of bit wear levels, according to some implementations.

FIG. 12 is an illustration depicting a spherical coordinate system and cartesian coordinate system for determining bit drilling efficiency based on cutter wear, according to some implementations.

FIG. 13 is a plot depicting the relationship between sharp bit drilling efficiency as a function of depth of cut, according to some implementations.

FIG. 14 is a trio of plots depicting drilling properties that vary with depth, according to some implementations.

FIG. 15A is an example graph depicting an input bit energy versus a drilling depth, according to some implementations.

FIG. 15B is an example graph depicting a required bit energy to wear primary cutters versus a pre-defined bit wear level, according to some implementations.

FIG. 16 is a plot depicting an example method of operations, according to some implementations.

FIGS. 1-16 and the operations described herein are examples meant to aid in understanding example implementations and should not be used to limit the potential implementations or limit the scope of the claims. None of the implementations described herein may be performed exclusively in the human mind nor exclusively using pencil and paper. None of the implementations described herein may be performed without computerized components such as those described herein. Some implementations may perform additional operations, fewer operations, operations in parallel or in a different order, and some operations differently.

DESCRIPTION

The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. In some instances, well-known instruction instances, protocols, structures, and techniques have not been shown in detail in order not to obfuscate the description.

As described herein, example implementations may use down hole bit response data including weight on bit (WOB), torque on bit (TOB), rate of penetration (ROP), and rotations per minute (RPM) of the bit to directly estimate rock abrasiveness and rock strength. Example implementations may include a method to estimate rock abrasiveness and a new method to estimate rock strength. The estimation of rock abrasiveness and rock strength may be useful to understand bit performance and, hence, to redesign a bit or to select another bit for future drilling.

Bit response data may be obtained using one or more in-bit sensors configured to provide direct, in-bit measurements of weight, torque, bending, vibration, rotational speed, etc. A final bit cutter dull severity may also be obtained by a cutter wear analysis tool. For example, a cutter wear analysis tool utilizing computer vision and one or more machine learning algorithms may be used to capture and precisely dull grade every cutter on the drill bit. The tool may be configured to determine the final bit cutter dull severity through rapid analysis of hundreds, or even thousands of individual cutter dull grades. However, other techniques may also be possible.

In some implementations, the in-bit sensors within the drill bit may measure different drill bit response data. Examples of such drill bit response data measured may include Weight on Bit (WOB), Torque on Bit (TOB), Rate of Penetration (ROP), rotations per unit of time (e.g., Rotations Per Minute (RPM). Additionally, rock strength index and rock abrasiveness index along drilling depth may be available using logging while drilling (LWD) tools (such as gamma ray, sonic logging, etc.). Data regarding final cutter and bit dull of the drill bit after drilling may also be available. Using this different data as input, a bit-rock interaction simulation may be developed that simulates drilling along drilling depth of the offset well.

The bit-rock interaction tool may be used for simulation at different distances (such as foot by foot) along the drilling depth of the section of the offset well that was drilled. The performance of the base drill bit (also referenced as a base drill bit performance) may be evaluated using this simulation. This simulation may, for example, include estimating energy input to the drill bit and energy required by the drill bit.

Example implementations may include calculating an input energy to the bit along drilling depth from mechanical specific energy (MSE). A required energy to wear the cutters may be calculated from the cutter dull severity as determined via the cutter wear analysis tool above. An average rock abrasiveness may then be calculated by equating the total input energy to the total required energy.

In drilling, the mechanical specific energy (MSE) that is required for a sharp cutter to successfully drill through rock may be proportional to the unconfined compressive strength of the rock. This same relationship, modeled by Equation (1), may be used to estimate confined compressive strength (CCS) during drilling of a wellbore:

CCS = η ⁢ MSE ( 1 )

wherein MSE is the specific energy and n is the bit drilling efficiency.

MSE may be calculated from measured Weight on Bit (WOB), Torque on Bit (TOB), Rotations per Minute (RPM), Rate of Penetration (ROP), etc. (as shown in Equation (2)):

MSE = WBO / A + 120 * π * TOB * RPM / ( A * ROP ) ( 2 )

wherein MSE is the specific energy, WOB is the weight on bit, A is the cross-sectional area of the hole drilled by the bit, TOB is the torque on bit, RPM is the revolutions per minute of the drill bit, and ROP is the rate of penetration of the drill bit.

In Equation (1), η is related to bit drilling efficiency. However, this may lead to inaccuracies as η may change along the drilling depth of the wellbore. Furthermore, such a conventional approach for determining the CCS (using Equation (1) may be not accurate enough to be used in drilling optimization. This lack of accuracy may arise for multiple reasons. For example, traditional techniques may assume a constant drilling efficiency between 0.3-0.4, as stated above. This however is not true, as drill bit drilling efficiency (bit DE, also referred to as η) changes with depth when drilling a well and is not a constant. The bit DE may depend heavily on the design and wear of the drill bit. Therefore, the estimation of η should consider the design and wear of the drill bit. A second reason that Equation (1) may not be accurate enough to be used in drilling optimization is that the measured MSE during drilling includes two parts. The first part is related to pure drilling. This first part neglects cutter wear. The second part is related to wear of the cutter(s) along the bit face (i.e., frictional forces in drilling).

Therefore, a two-part solution may include calculating bit DE along the drilling depth of a well and calculating an MSE for pure drilling, MSE_c. Using MSE_c in Equation (1) may provide a more accurate estimation of rock strength along the drilling depth.

Example Well System

FIG. 1 an elevation view (partially cross sectional) of an example well system, according to some implementations. In particular, FIG. 1 is a schematic diagram of a well system 100 that includes a drill string 180 having a drill bit 112 disposed in a wellbore 106 for drilling the wellbore 106 in the subsurface formation 108. While depicted for a land-based well system, example implementations may be used in subsea operations that employ floating or sea-based platforms and rigs. The drill bit 112 is an example drill bit for which simulation of abrasive wear and damage as described herein may be performed.

The well system 100 may further include a drilling platform 110 that supports a derrick 152 having a traveling block 114 for raising and lowering the drill string 180. The drill string 180 may include, but is not limited to, drill pipe, drill collars, and down hole tools 116. The down hole tools 116 may comprise any of a number of different types of tools including measurement while drilling (MWD) tools, logging while drilling (LWD) tools, mud motors, and others. A kelly 115 may support the drill string 180 as it may be lowered through a rotary table 118. The drill bit 112 may include roller cone bits, polycrystalline diamond compact (PDC) bits, natural diamond bits, any hole openers, reamers, coring bits, and the like. As the drill bit 112 rotates, it may crush or cut rock to create and extend a wellbore 106 that penetrates various subterranean formations. The drill bit 112 may be rotated by various methods including rotation by a downhole mud motor and/or via rotation of the drill string 180 from the surface 120 by the rotary table 118. Attributes of drilling the wellbore may be adjusted to increase, decrease, and/or maintain the rate of penetration (ROP) of the drill bit 112 through the subsurface formation 108. Attributes may include weight-on-bit (WOB) and rotations-per-minute (RPM) of the drill string 180. In some implementations, the drill bit 112 may become dull and lose efficiency, thus requiring more WOB and/or RPM to maintain a target ROP. A pump 122 may circulate drilling fluid through a feed pipe 124 to the kelly 116, downhole through interior of the drill string 180, through orifices in the drill bit 112, back to the surface 120 via an annulus surrounding the drill string 180, and into a retention pit 128.

The well system 100 includes a computer 170 that may be communicatively coupled to other parts of the well system 100. The computer 170 may be local or remote to the drilling platform 110. A processor of the computer 170 may perform simulations (as further described below). In some implementations, the processor of the computer 170 may control drilling operations of the well system 100 or subsequent drilling operations of other wellbores.

An example of the computer 170 is now described. FIG. 2 is a block diagram of an example computer, according to some implementations. FIG. 2 depicts a computer 200 that includes a processor 201 (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer 200 includes a memory 207. The memory 207 may be system memory or any one or more of the above already described possible realizations of machine-readable media. The computer 200 also includes a bus 203 and a network interface 205.

The computer 200 also includes a simulation processor 211 and a controller 215. The simulation processor 211 and the controller 215 may perform one or more of the operations described herein. For example, the simulation processor 211 may perform data processing and simulation operations as further described below. The controller 215 may perform various control operations to a wellbore operation based on the simulations. For example, the controller 215 may modify a drilling operation based on the simulations.

Any one of the previously described functionalities may be partially (or entirely) implemented in hardware and/or on the processor 201. For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the processor 201, in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in FIG. 2 (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor 201 and the network interface 205 are coupled to the bus 203. Although illustrated as being coupled to the bus 203, the memory 207 may be coupled to the processor 201.

Example Operations

Example operations are now described with reference to a bit-rock interaction simulation software tool (also referred to as the “bit rock interaction tool” and “bit rock interaction model”) used in determining rock abrasiveness, bit drilling efficiency of a sharp bit with sharp cutters and worn bit with worn cutters, and estimating rock strength. The simulation processor 211 of FIG. 2 may be coupled with the bit rock interaction tool.

In some implementations, a bit-rock interaction simulation software tool may be used to calculate bit drilling efficiency for any bit with cutter wear. The bit wear may be divided into several levels. For example, bit wear may be divided into 9 levels from 0 to 8. At each bit wear level, a cutter wear profile for each cutter may be calculated, including a wear contact area and wear depth. A value of bit drilling efficiency may be calculated at each depth of cut and at each wear level. This procedure may be referred to as the pre-calculation.

During drilling, the accumulated input energy to bit at a drilling depth may be calculated using MSE and accumulated removed volume at that depth. Therefore, input energy as a function of drilling depth is available. Cutter wear volume may be proportional to input energy to cutter. Therefore, bit wear level is also proportional to the input energy to bit. This relationship is used to determine, at a drilling depth, the bit wear level. Once bit wear level at a depth is determined, and depth of cut is known, DE is available from pre-calculations. Therefore, the bit drilling efficiency or coefficient n in Equation (1) may then be available at a drilling depth.

Example Operations to Estimate Rock Strength Using a Mechanical Specific Energy for Pure Drilling

FIGS. 3-4 are flowcharts depicting example operations for calculating an estimated rock strength along drilling depth, according to some implementations. Operations of a flowchart 300 of FIG. 3 and a flowchart 400 of FIG. 4 are described in reference to the well system 100 of FIG. 1 and the computer 200 of FIG. 2. Also, operations of the flowchart 300 of FIG. 3 and the flowchart 400 of FIG. 4 continue between each other through transition point A. Operations of the flowcharts 300-400 start at block 302.

At block 302, a bit response file and measured bit dull file are retrieved. Data regarding the drilling parameters and drilling conditions from the drilling of the section of the offset well may be retrieved for input via the bit-rock interaction model. For example, with reference to FIG. 2, the processor 201 may retrieve the data from any type of machine-readable media (local or remote). For example, with reference to FIG. 1, the data may be related to drilling of the wellbore 106 (which may be an offset well). The data may include a bit response file (including WOB, TOB, RPM and ROP), a rock abrasive index of the subsurface formation, and a measured bit dull file. At least a portion of the data may be provided via simulation, via one or more in-bit sensors, etc. Flow progresses to block 304.

At block 304, the processor 201 may retrieve WOB, TOB, RPM, ROP, and may calculate bit MSE. For example, the WOB, TOB, RPM, ROP, etc. may be retrieved alongside the bit response file and measured bit dull file of block 302. The MSE may be calculated with reference to Equation 2 using the retrieved WOB, TOB, RPM, and ROP of the drill bit of interest. Flow progresses to block 306.

At block 306, the processor 201 may calculate an energy input into the drill bit along the drilling depth. For example, an energy input (or spent) after drilling through a layer with thickness ΔS (in ft) may be calculated using Equation 3:

Δ ⁢ E bit = MSE_layer * ( Δ ⁢ S * 12 ) * ( Π * R 2 ) ( 3 )

wherein R is the hole radius in inches, MSE_layer is the mechanical specific energy of the layer of formation rock, and ΔS is the formation layer thickness.

The processor 201 may calculate a total input energy to the drill bit via a summation of energy spent after drilling through the various layers of a simulated well, offset well, etc., as shown in Equation 4:

Ebit ⁢ = ∑ Δ ⁢ Ebit ( 4 )

where Ebit is the total input energy to the bit at a drilling depth.

Therefore, input bit energy may be modeled as a function of drilling depth. The drilling depth refers to the measured depth (MD) of at least a portion of an example well (real-world or simulated). In some implementations, the processor 201 may obtain a relationship between input energy as a function of drilling depth via one or more in-bit sensors after the drilling of an offset well. This relationship is depicted in FIG. 5. FIG. 5 is a plot depicting the relationship between input bit energy and drilling depth, according to some implementations. A plot 500 includes an X-axis depicting drilling depth 502 (in ft) and a spent (total) bit energy 504 measured in lb-in. As expected, the total input energy to the bit increases with drilling depth. Flow progresses to block 308.

At block 308, the processor 201 may retrieve the pre-calculated following values at each bit wear level and at each depth of cut: 1) WOB, 2) TOB, 3) drilling efficiency 4) WOB to the primary cutters, 5) TOB to the primary cutters, 6) WOB friction, 7) TOB friction, 8) pure cutting WOB, 9) pure cutting TOB, and 10) scaled cutter force distributions. For example, FIGS. 6-9 include various drilling parameters calculated at different levels of bit wear as part of the pre-calculation step of block 308.

FIG. 6 is a plot depicting depth of cut vs. weight on bit at various bit wear levels, according to some implementations. A plot 600 includes an X-axis of depth of cut 602 (in inches per revolution of the bit) and a Y-axis of a weight on bit 604 (WOB) in kilo-pound force (klbf).

FIG. 7 is a plot depicting depth of cut vs. torque on bit at various bit wear levels, according to some implementations. A plot 700 includes an X-axis depicting a depth of cut 702 in inches/revolution and a Y-axis depicting a torque on bit 704 in kilo foot-pounds (kft-lb).

FIG. 8 is a plot depicting depth of cut vs. drilling efficiency at various bit wear levels, according to some implementations. A plot 800 includes an X-axis depicting a depth of cut 802 in inches/revolution and a Y-axis depicting a bit drilling efficiency 804 (Bit DE) as a percentage of a theoretical perfect drilling efficiency. A sharp-bit drilling efficiency 806 depicts a drilling efficiency of a bit with a wear level of 0 as a function of cut depth, and a worn-bit drilling efficiency 808 depicts a drilling efficiency of a bit with a wear level of 8.

FIG. 9 is a plot depicting weight on bit vs. torque on bit at various wear levels, according to some implementations. A plot 900 includes an X-axis depicting a weight on bit 902 (measured in klbf) and a Y-axis depicting a torque on bit 904 measured in kft-lb.

As determined via block 306, the energy input to the drill bit along the drill depth may be spread amongst various components of the cutting face of the drill bit. For example, the energy input to the bit of block 306 may include the primary cutters, backup cutters, depth of cut controllers (DOCCs) and blades. However, the energy input to primary cutters may be of particular interest. The bit dull analysis tool may be configured to record only cutter dull severity measurements for primary cutters; therefore, drill bit optimization via the bit-rock interaction tool may be performed with reference to the primary cutters.

To calculate the energy input to the primary cutter(s), the processor 201 may estimate how much of the WOB (and/or the TOB) is only applied to primary cutters. The processor 201 may perform this calculation by first determining a ratio of the WOB and TOB experienced only by the primary cutters to the total WOB and TOB exerted on the drill bit, as shown in Equations 5-6:

λ ⁢ w = WOB_p / WOB * 100 ⁢ % ( 5 ) λ ⁢ t = TOB_p / TOB * 100 ⁢ % ( 6 )

where WOB_p is the weight on bit experienced by the primary cutters, TOB_p is the torque on bit experienced by the primary cutters, λw is the ratio of the weight on bit experienced by the primary cutters to the total WOB on the drill bit, and λw is the ratio of the torque on bit experienced by the primary cutters to the total TOB on the drill bit.

Both λw and λt may depend on the depth of cut (DOC) of the primary cutters and on bit wear level. These values may be pre-calculated and saved for use in later calculations. Examples of the above relationships may be depicted via FIGS. 10 and 11.

FIG. 10 is a plot depicting contributions to WOB between various components of a drill bit, according to some implementations. At an example bit wear level of 5, the plot 1000 includes an X-axis of depth of cut 1002 (measured in inches/revolution) and a Y-axis of WOB 1004 in lbs. The total WOB may be decomposed into numerous trends. For example, a primary cutter trend 1006 models the WOB experienced by the primary cutters (WOB_p) with respect to depth of cut, a backup cutter trend 1008 models the WOB experienced by the backup cutters, and a DOCCs +Blades trend 1010 models the WOB experienced by the DOCCs and blades.

FIG. 11 is a plot depicting the weight on bit experienced by the primary cutters across a plurality of bit wear levels, according to some implementations. A plot 1100 includes an X-axis of depth of cut 1102 (measured in in/rev) and a Y-axis depicting a ration 1104 of WOB_p/WOB (also referred to as λw). In some implementations, the processor 201 may calculate λw and λt across all bit wear levels as part of the pre-calculations.

The cutter dull severity (Sd) may be estimated from cutter wear depth (Wd) and cutter diameter (Dc) using Equation 7:

Sd == 8 * Wd / Dc ( 7 )

If, for example, Sd=4, this means that half of the PDC (Polycrystalline Diamond Compact) cutter is worn out.

Once the cutter dull severity is known, the cutter wear depth (Wd) may be calculated using Equation 8:

Wd = Sd * Dc / 8 . 0 ( 8 )

wherein Dc is a cutter diameter (that may be measured in inches). In some implementations, Wd is the possible maximal cutter wear distribution (final bit wear level). In some implementations, the bit profile may be divided into N bit wear levels.

At each bit wear level, and at each depth of cut, the following may be calculated: 1) WOB and TOB; 2) WOB_p and TOB_p (WOB for the primary cutter and the TOB for the primary cutter, respectively); scaled cutter axial forces; scaled cutter drag forces; drilling efficiency; and required bit energy at each bit wear level. At a given bit wear level, cutter wear depth is known, and cutter wear volume may be calculated. On the other hand, cutter wear volume is proportional to cutter energy. Therefore, the required cutter energy to wear a cutter to a wear depth may be calculated. The sum of the required energy of all cutters may be defined as the bit required energy. As described above, some implementations, the bit wear levels may be defined from 0-8. However, some implementations of the bit wear level and the depth of cut may be divided into 10 or more points. Flow progresses to block 310.

At block 310, the processor 201 may calculate an estimated total energy input to the primary cutters. For example, the processor 201 may perform this calculation of the estimated total energy input to the primary cutters based on the pre-calculated values (such as WOB_p and TOB_p) calculated as part of the operations at block 308. Flow progresses to block 312.

At block 312, the processor 201 may calculate a cutter wear volume based on the measured bit dull severity. In some implementations, bit dull severity may be measured using a dullness index or a similar metric. The dullness index may be based on visual inspection, measurements, etc. In some implementations, the bit wear analysis tool may perform the dull grading of the bit. For example, a cutter wear analysis tool may utilize computer vision and one or more algorithms to capture and precisely dull grade every cutter on the drill bit. Some implementations of the bit-rock interaction tool may include the results from the cutter wear analysis tool. The cutter wear analysis tool may be configured to determine the final bit cutter dull severity through rapid analysis of hundreds, or even thousands of individual cutter dull grades. However, other techniques may also be possible. For example, visual inspection may be used. Visual inspection may involve examining the bit's cutting edges under a microscope or using specialized tools to assess wear patterns. Measurements may include assessing the width of the worn area on the cutting edge or measuring the reduction in the cutting edge's original geometry (e.g., flank wear land width).

The cutter wear volume may be calculated based on the measured bit dull severity. For example a cutter wear volume may be calculated based on Equations (9a-13) below:

Vw = K ⁢ 1 * F * Ls ( 9 ⁢ a )

where Vw is cutter wear volume, Ls is sliding distance. F is force on cutter, and K1 is a factor related to rock abrasiveness and cutter wear resistance.

Equation 9a relates to determining a cutter wear volume due to mechanical loading. However, cutter wear may be related to both mechanical loading and thermal loading. If the temperature around a cutter is below a critical temperature, Tc, cutter wear may be dominated by mechanical loading. Equation 9a may be rewritten as:

Vw = 3600 * K ⁢ 1 * F * Vc * T = K * F * Vc * T = K ⁢ Pc ⁢ T ( 9 ⁢ b )

where Vc is cutter velocity, T is a unit of time, Pc is cutter power, and Pc T is the energy input to the cutter. Therefore, equations 9a and 9b reveal that cutter wear is proportional to the cutter energy input to the cutter. In some implementations, only mechanical loading induced cutter wear is considered in the drilling simulation via the bit-rock interaction tool.

A plurality of variables during drilling may be decomposed into an axial component and a drag component. For example, the cutter power, Pc, may be calculated according to Equation 10:

Pc = Fa * Va + Fd * Vd ( 10 )

where Fa is the axial force on the cutter, Va is the axial velocity of the cutter, Fd is the drag force on the cutter, and Vd is the drag velocity of the cutter.

The axial and drag forces in Equation 10 may be used to calculate a cutter energy, as shown in Equation 11:

Ec = Fa * La + Fd * Ld = Ea + Ed ( 11 )

where La is the axial distance of the cutter and Ld is the drag distance of the cutter.

A change in cutter energy, ΔEc, may be described as the cutter power, Pc, multiplied by a change in time (Δt). This is depicted in Equation 12:

Δ ⁢ Ec = Pc ⁢ Δ ⁢ t ( 12 )

If the cutter volume, Vw, is known, the cutter energy, Ec, may be calculated via Equation 13:

Vw ⁢ = K ⁢ Ec ( 13 )

where K is the product of an average rock abrasiveness factor (Ka) and cutter wear resistance (Kw). Flow progresses to block 314.

At block 314, the processor 201 may calculate an averaged rock abrasiveness factor. For example, a rock abrasiveness may be calibrated by equaling the total input energy to the primary cutters to the required energy by the primary cutters at the drilling end a well (e.g., an offset well). In some implementations, the processor 201 may perform this calibration of the rock abrasiveness factors based on the pre-calculated values as part of the operations at block 308.

The input energy to the primary cutters may be determined via Equation 14:

Ep = ∑ Ec ( 14 )

where the input energy to the primary cutters at a drilling depth, Ep, is equal to the sum of all cutter energies to that drilling depth. If the axial force and drag force of the primary cutters are known at any drilling depth, the input energy to the primary cutters may then be calculated using Equation 12 for any drilling depth. The total input energy to primary cutter at the drilling end may be referred to as E_pf.

The bit dull analysis tool may be used to determine a cutter dull severity (Sd) for each of the primary cutters at the end of drilling, as determined via Equations 7-8. Therefore, the processor 201 may calculate a cutter wear depth of the primary cutters using Equations 8. The cutter wear volume may then be calculated as a function of cutter wear depth (Wd), back rake (BR), Dc, chamfer of the primary cutters, and shape of the primary cutters according to Equation 15:

Vw = f ⁡ ( Wd , BR , Dc , Chamfer , Shape ) ( 15 )

A total energy required to wear all primary cutters may be determined via Equation 16 as the sum of cutter wear volume (Vw) along the drilling depth:

Epr = ∑ ( Vw K ) ( 16 )

where Epr is the total energy required to wear all cutters.

With reference to Equations 9b and 13, the K-factor may be divided into a rock abrasiveness factor (Ka) and a cutter wear resistance factor (Kw). Therefore, according to Equation 17:

K = Ka * Kw ( 17 )

Assuming Ka is a constant (i.e., an average rock abrasiveness factor), equation 17 may be rewritten as:

Epr = ( 1 / Ka ) ⁢ ∑ ( Vw / Kw ) ( 18 )

By allowing the total energy to wear all primary cutters to equal the total energy to wear the primary cutters at the drilling end (because the primary cutters are of interest, and assuming a constant value of Ka), an equation for the average rock abrasiveness factor may then be produced:

Ka = ∑ ( Vw Kw ) / Epf ( 19 )

As shown, Equation 19 models the average rock abrasiveness along the drilling depth, where Ka is the average rock abrasiveness factor.

If the formation abrasive index (or relative abrasive index) along drilling depth is known, an absolute or a calibrated formation abrasive factor along drilling depth is calculated based on the average rock abrasiveness according to Equation 20a:

Ka * St = λ * ∑ ( Ks ⁢ Δ ⁢ S ) ( 20 ⁢ a )

where St is the total drilling length, ΔS is length of a section, Ks is the scaled formation abrasive index for that section (the maximal abrasive index is scaled to 1.0), and lambda (λ) is a constant obtained by solving Equation 20a. Once λ is solved from Equation 20a, the calibrated abrasive factor for each section is obtained via Equation 20b:

Kab = λ ⁢ Ks ( 20 ⁢ b )

Operations of the flowchart 300 continue at transition point A, which continues at transition point A of the flowchart 400 of FIG. 4. From transition point A of the flowchart 400 of FIG. 4, operations continue at block 402.

At block 402, the processor 201 may determine a bit wear level using the energy input to the bit of block 306. As previously stated, bit wear may be divided into several levels. Bit wear may be divided into 9 levels, for example, ranging from 0 to 8. Each bit wear level includes a calculated cutter wear profile for each cutter including wear contact area and wear depth. Bit DE is then calculated at each depth of cut and at each wear level. During drilling, the accumulated input energy to bit at a drilling depth may be calculated using MSE and an accumulated removed rock volume at that depth. Therefore, input energy as a function of drilling depth is available, and the cutter wear volume is proportional to the input energy to the cutter(s). Therefore, bit wear level is also proportional to the input energy to bit. This relationship is used by the processor 201 to determine, at a drilling depth, the bit wear level. Flow progresses to block 404.

At block 404, the processor 201 may retrieve a bit drilling efficiency along the drilling depth for a bit wear level and a depth of cut at a drilling depth.

The pre-calculated responses at various bit wear levels measured in FIGS. 9-12 may be used in determining a pre-calculated WOB, TOB, and drilling efficiency (η) as a function of depth of cut and bit wear level. For a given RPM, ROP, and rock strength (σ), the bit-rock interaction tool may be used to calculate WOB and TOB at various drilling depths. The mechanical specific energy (MSE) may be calculated based on the WOB and TOB. Once the MSE is calculated, a drilling efficiency of the bit may be calculated. Even though rock strength (σ) is included in the calculation of drilling efficiency (η), drilling efficiency is independent of rock strength. Therefore, for any given rock strength, σ, the ratio of σ/MSE is the same.

In some implementations, the bit-rock interaction tool/simulator may be used to calculate a bit drilling efficiency for any bit with cutter wear. For example, FIG. 12 is an illustration depicting a spherical coordinate system and cartesian coordinate system for determining bit drilling efficiency based on cutter wear, according to some implementations. Example implementations may use one or more in-bit sensors may be used to provide direct, in-bit measurements of WOB, TOB, bending forces, vibration, RPM, etc. Data from the in-bit sensors may be used to generate bit wear simulations, cutter wear simulations, etc. In some implementations, a simulation may simulate one or more cutters of a drill bit. The bit wear may be divided into several pre-defined levels (e.g., nine levels from 0 to 8). A plurality of cutter wear profiles may include a drill bit with no wear (bit wear level 0) and a bit with maximum wear (bit wear level 8). At each bit wear level, a cutter wear profile for each cutter is then calculated, including wear contact area and wear depth. Bit drilling efficiency (DE) may then be calculated at each depth of cut and at each wear level.

A spherical coordinate system 1250 has an x-axis 1230, a y-axis 1231, and a z-axis 1232. The x-axis 1230 and the y-axis 1231 are the radius of the drill bit in their respective directions and having units of inches (in.). The z-axis 1232 is the height of the drill bit and also has units of inches (in.). The spherical coordinate system 1250 depicts the distribution of primary cutters 1201 and backup cutters 1202. Similar methods described in block 402 of flowchart 400 may be used to project the distribution of primary cutters 1201 and backup cutters 1202 on to a cartesian coordinate system 1260 to create final primary cutter profiles 1203 and backup cutter profiles 1204, as displayed by a cartesian coordinate system 1260 having an x-axis 1240 that is the radius of the drill bit and a y-axis 1241 that is the height of the drill bit. Both the x-axis 1240 and the y-axis 1241 have units of inches (in.). As shown by final primary cutter profiles 1203 and backup cutter profiles 1204, even though a portion of the final primary cutter wear profiles 1203 are flat due to damaged primary cutters, final backup cutter wear profiles 1204 may extend past the final primary cutter wear profiles (i.e., have a radius/height greater than the final primary cutter wear profiles). In some instances, one or more backup cutters may also be damaged such that the one or more final backup cutter wear profiles may appear similar to the final primary cutter wear profiles that are on the same radial track. Based on the wear of the primary cutters, a bit wear profile may be determined.

With reference to FIG. 12, such(s) simulations may be used to determine how and what causes abrasive wear and/or damage of a drill bit. Example implementations may perform such simulation based on an initial profile of a drill bit prior to drilling and a final profile of the drill bit after drilling. Some implementations may be performed without using a cutter wear or damage model.

For example, for abrasive wear simulation, the initial bit wear may be zero and represented by a new bit profile. The final condition of the drill bit may be represented by a digital dull after drilling at least a portion of a wellbore. In some implementations, for each cutter of the drill bit, the wear depth may be nonlinearly divided into N steps (N>1). At each step, a bit wear profile and profiles for different elements of the drill bit may be determined. For example, the elements may include primary cutters, backup cutters, and depth of cut controllers (DOCC). Additionally, the bit-rock interaction model may be executed to obtain bit design characteristics for the drill bit. Flow progresses to block 406.

At block 406, the processor 201 may calculate a weight on bit for pure cutting (WOB_c) and the torque on bit for pure cutting (TOB_c). For a single cutter, the axial force and the drag force may be divided into two parts, respectively, as shown in Equations 21a and 21b:

Axial ⁢ force : Fa = Fa_c + Fa_w ( 21 ⁢ a ) Drag ⁢ force : Fd = Fd_c + Fd_w ( 21 ⁢ b )

where Fa_c is axial force related to the sharp cutter, Fa_w is axial force related to cutter wear, Fd_c is the drag force related to the sharp cutter and Fd_w is the drag force related to cutter wear.

Similarly, for a bit, the WOB and TOB may be divided into two parts, respectively:

WOB = WOB_c + WOB_w ( 22 ⁢ a ) TOB = TOB_c + TOB_w ( 22 ⁢ b )

where WOB_c is the weight on bit for pure cutting, WOB_w is the weight on bit related to bit wear, TOB_c is the torque on bit for pure cutting, and TOB_w is the torque on bit related to bit wear. For a sharp bit or a new bit, WOB_w=0 and TOB_w=0. WOB_c and TOB_c may be used in calculations relating purely to cutting. Flow progresses to block 408.

At block 408, the processor 201 may calculate an MSE_c used for pure cutting. MSE_c may be related purely to drilling and distinct from factors such as frictional forces, wear, etc. Mechanical specific energy may be divided into two parts, as shown in Equation 23:

MSE = MSE_c + MSE_w ( 23 )

where MSE is the mechanical specific energy of the bit, MSE_c is an MSE related to pure cutting, and MSE_w is the MSE related to cutter wear, frictional forces, etc. For a sharp bit or a new bit, MSE_w=0.

While both MSE_c and MSE_w are used to calculate MSE, only MSE_c is used in calculating the rock strength at each depth based purely on drilling. A modified version of Equation 23 may be used to calculate MSE_c in Equation 24:

MSE_c = WOB_c / A + 120 * π * TOB_c * RPM / ( A * ROP ) ( 24 )

where WOB_c is the weight on bit for pure cutting and TOB_c is the torque on bit for pure cutting. Flow progresses to block 410.

At block 410, the processor 201 may calculate an estimated rock strength along the drilling depth of the bit. For example, the processor 201 may use each value of MSE_c determined via Equation 24 to calculate values of rock strength along the drilling depth drilled or to be drilled by a drill bit of interest (via simulation). The processor 201 may output a value of confined compressive strength of a rock at each drilling depth based on the MSE_c and drilling efficiency (η) at that depth, as shown in Equation 25:

CCS = η ⁢ MSE_c ( 25 )

where CCS is the confined compressive strength of the rock, η is the bit drilling efficiency, and MSE_c is the mechanical specific energy for pure drilling/cutting. Using MSE_c rather than MSE may lead to more accurate simulations, bit selections, etc. This is because MSE_c behaves differently than MSE during drilling. When using a sharp cutter (e.g., PDC), MSE_c may behave differently with depth of cut. Initially, as the cutter penetrates deeper (increasing DOC), the cutting force dominates over frictional/drag forces, resulting in a decreasing MSE. However, beyond a certain depth, cutter wear becomes significant, leading to a leveling off of the MSE. This behavior is characteristic of a sharp cutter that efficiently shears the rock. Flow of the flowchart 400 ceases.

In some implementations, because the above calculations relate to a sharp bit with cutters used in pure drilling (i.e., disregarding frictional forces and wear), the drilling efficiency, η, of Equation 25 may also be referred to as the sharp bit drilling efficiency, ηc. The sharp bit drilling efficiency may depend only on bit design and depth of cut—therefore, ηc may be pre-calculated as a function of depth of cut. This relationship is depicted in FIG. 13.

FIG. 13 is a plot depicting the relationship between sharp bit drilling efficiency as a function of depth of cut, according to some implementations. A plot 1300 includes an X-axis of depth of cut 1302 measured in in/rev and a Y-axis of (sharp) bit drilling efficiency measured as a percentage. As shown, the sharp bit drilling efficiency increases linearly as a function of depth of cut above ˜0.1 in/rev.

FIG. 14 is a trio of plots depicting drilling properties that vary with depth, according to some implementations. A measured MSE plot 1400 includes an X-axis depicting drilling depth 1402 (measured in ft) and a Y-axis depicting a measured MSE 1404 (measured in kilopounds per square inch, ksi). A sonic log plot 1410 includes an X-axis depicting drilling depth 1412 measured in ft and a Y-axis depicting travel times 1414 of a sonic log (measured in microseconds/ft or μs/ft). A rock strength plot 1420 includes an X-axis 1422 depicting drilling depth in ft and a Y-axis depicting rock confined compressive strength (rock CCS) in units of ksi. In the figure, the MSE 1404 is used to calculate the rock strength of plot 1420. The change of rock strengths, as shown in plot 1420 and which may be predicted via operations similar to block 410, match closely with the change of the inverse measured sonic log of plot 1410.

Example Operations to Estimate Bit Wear Level

In the estimation of formation strength using Equation 25, a key operation is to determine bit wear level at a drilling depth during drilling. To illustrate, FIG. 15A is an example graph depicting an input bit energy versus a drilling depth, according to some implementations, and FIG. 15B is an example graph depicting a required bit energy to wear primary cutters versus a pre-defined bit wear level, according to some implementations. FIGS. 15A-15B depict a graph 1500 and a graph 1550, respectively. The graph 1500 includes an x-axis 1502 that is a drilling depth (ft) and a y-axis 1504 that is an input drill bit energy (lb-in). The graph 1550 includes an x-axis 1552 that is a pre-defined bit wear level and a y-axis 1554 that is a required bit energy (lb-in) to wear the primary cutter to a given level. The graph 1500 may be a result of the simulation. Whereas the graph 1500 may be part of the pre-calculation (prior to the simulation).

The graph 1500 includes a plot 1506 that may be calculated from a bit response measured by in-bit sensors or MWD tools. The plot 1506 includes a point 1508 that corresponds to an input bit energy of 6×10¹⁰ lb-in at a drilling depth of approximately 7400 ft. The graph 1550 includes a plot 1556 that may be calculated from each primary cutter wear volume at a given bit wear level. The plot 1556 includes a point 1558 that corresponds to the point 1508. In particular, the point 1558 is a required bit energy of 6×10¹⁰ lb-in (same as the input bit energy at point 1508). The corresponding pre-defined bit wear level at the point 1558 is approximately 6.5. Accordingly, the bit wear level at a drilling depth of 7400 ft is 6.5.

Bit wear level at a drilling depth may also be determined based on cutter wear depth of all cutters. From a pre-defined bit wear level, for example, bit wear level 6, the predefined cutter wear depth for each cutter at cutter wear level 6 is known. In drilling at a drilling depth, the actual cutter wear depth for each cutter can be estimated using cutter accumulated energy at the drilling depth. If the actual average cutter wear depth is close (i.e., within a preset threshold value) to the pre-defined average cutter wear depth at level 6, then the bit wear level is determined to be 6.

Example Method of Operations

FIG. 16 is a plot depicting an example method of operations, according to some implementations. Operations of a method 1600 are described in FIGS. 1-4. However, other systems and components may be used to perform the operations now described. Operations of the method 1600 begin at block 1602.

At block 1602, the processor 201 of FIG. 2 may determine a drilling efficiency of a drill bit at a first depth in a first wellbore formed in a subsurface formation based, at least in part, on a bit wear level of the drill bit. For example, the processor 201 may calculate a weight on bit and torque on bit during the pre-calculations of block 308. The pre-calculations may be determined at each bit wear level and at each depth of cut given a known RPM of the bit, ROP of the bit, and a known rock strength, σ. Because bit wear level is proportional to the input energy to the bit, and input energy as a function of drilling depth is known, the bit drilling efficiency may be determined. Flow progresses to block 1604.

At block 1604, the processor 201 may determine a cutting force mechanical specific energy of the drill bit at the first depth. For a sharp cutter of a drill bit, the force transmitted through the cutter may be utilized for cutting rocks—i.e., the cutting force. However, for cases utilizing a blunt or dull cutter, part of the force exerted onto the cutter is utilized in overcoming friction. Equation 1 is only concerned with the cutting force and disregards frictional forces. This is reflected in Equation 25 which includes MSE_c.

The cutting force mechanical specific energy, MSE_c, may be defined as the portion of the MSE related purely to cutting, breaking, and/or removing rock during drilling. The cutting force MSE, (MSE_c) accounts for the mechanical work required to shear or crush the formation. Factors affecting this energy component may include a weight on bit related to pure drilling, WOB_c (also referred to as the cutting force WOB), the rotational speed of the bit (RPM), and a cutting force torque on bit, TOB_c. Similarly to the WOB_c, TOB_c may also be referred to as the cutting force torque on bit. The processor 201 may use Equation 24 to determine MSE_c at the first depth and at a plurality of other drilling depths. Flow progresses to block 1606.

At block 1606, the processor 201 may determine a rock strength of the subsurface formation at the first depth based on the drilling efficiency and the cutting force mechanical specific energy of the drill bit. For example, the processor 201 may use Equation 25 to determine the confined compressive strength of the subsurface formation at the first depth. In some implementations, the processor 201 may calculate the CCS as a function of drilling depth along the length of a wellbore. The rock strength (CCS) may be calculated using a sharp bit drilling efficiency and MSE_c, yielding an estimation of rock strength irrespective of frictional forces, drag forces, etc. experienced during drilling. In some implementations, the determined rock strength may be used in selecting a drill bit to drill a portion of the current wellbore, an offset well, etc. Flow of the method 1600 ceases.

Accordingly, example implementations may select a new drill bit for drilling a target well based on simulation with same or similar drilling parameters and drilling conditions, such that the new drill bit has both a better drill bit efficiency and a better drill bit durability to drill through rock having the determined rock strength. For example, the new drill bit (as compared to the base drill bit) may be different in terms of the number and/or type of cutters, the cutter geometry, the composition of the drill bit (such as cobalt steel, carbide, diamond-coated, etc.), etc.

While the aspects of the disclosure are described with reference to various implementations and exploitations, it will be understood that these aspects are illustrative and that the scope of the claims is not limited to them. Many variations, modifications, additions, and improvements are possible.

The various illustrative logics, logical blocks, modules, circuits, and algorithm processes described in connection with the implementations disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. The interchangeability of hardware and software has been described generally, in terms of functionality, and illustrated in the various illustrative components, blocks, modules, circuits and processes described throughout. Whether such functionality is implemented in hardware or software depends upon the particular application and design constraints imposed on the overall system.

The hardware and data processing apparatus used to implement the various illustrative logics, logical blocks, modules and circuits described in connection with the implementations disclosed herein may be implemented or performed with a general purpose single-or multi-chip processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor or any conventional processor, controller, microcontroller, or state machine. A processor also may be implemented as a combination of computing devices, e.g., a combination of a DSP and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a DSP core, or any other such configuration. In some implementations, particular processes and methods may be performed by circuitry that is specific to a given function.

In one or more implementations, the functions described may be implemented in hardware, digital electronic circuitry, computer software, firmware, including the structures disclosed in this specification and their structural equivalents thereof, or in any combination thereof. Implementations of the subject matter described in this specification also may be implemented as one or more computer programs, e.g., one or more modules of computer program instructions stored on a computer storage media for execution by, or to control the operation of, a computing device.

If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. The processes of a method or algorithm disclosed herein may be implemented in a processor-executable instructions which may reside on a computer-readable medium. Computer-readable media includes both computer storage media and communication media including any medium that may be enabled to transfer a computer program from one place to another. Storage media may be any available media that may be accessed by a computer. By way of example, and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that may be used to store desired program code in the form of instructions or data structures and that may be accessed by a computer. Also, any connection may be properly termed a computer-readable medium. Disk and disc, as used herein, includes compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-Ray™ disc where disks usually reproduce data magnetically, while discs reproduce data optically with lasers. Combinations also may be included within the scope of computer-readable media. Additionally, the operations of a method or algorithm may reside as one or any combination or set of codes and instructions on a machine readable medium and computer-readable medium, which may be incorporated into a computer program product.

In the context of this document, a machine-readable storage medium may be any tangible medium that may contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. A machine-readable storage medium is not a machine-readable signal medium.

A machine-readable signal medium may include a propagated data signal with machine readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A machine-readable signal medium may be any machine-readable medium that is not a machine-readable storage medium and that may communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

Program code embodied on a machine-readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

Computer program code for carrying out operations for aspects of the disclosure may be written in any combination of one or more programming languages, including an object oriented programming language such as the Java® programming language, C++ or the like; a dynamic programming language such as Python; a scripting language such as Perl programming language or PowerShell script language; and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on a stand-alone machine, may execute in a distributed manner across multiple machines, and may execute on one machine while providing results and or accepting input on another machine.

The program code/instructions may also be stored in a machine-readable medium that may direct a machine to function in a particular manner, such that the instructions stored in the machine-readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

Various modifications to the implementations described in this disclosure may be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other implementations without departing from the spirit or scope of this disclosure. Thus, the claims are not intended to be limited to the implementations shown herein but are to be accorded the widest scope consistent with this disclosure, the principles and the novel features disclosed herein.

Certain features that are described in this specification in the context of separate implementations also may be implemented in combination in a single implementation. Conversely, various features that are described in the context of a single implementation also may be implemented in multiple implementations separately or in any suitable sub-combination. Moreover, although features may be described as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination may in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or variation of a sub-combination.

While operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. Further, the drawings may schematically depict one more example process in the form of a flow diagram. However, some operations may be omitted and/or other operations that are not depicted may be incorporated in the example processes that are schematically illustrated. For example, one or more additional operations may be performed before, after, simultaneously, or between any of the illustrated operations. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the implementations described should not be understood as requiring such separation in all implementations, and the described program components and systems may generally be integrated together in a single software product or packaged into multiple software products. Additionally, other implementations are within the scope of the following claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve desirable results.

Unless otherwise specified, use of the terms “up,” “upper,” “upward,” “uphole,” “upstream,” or other like terms shall be construed as generally away from the bottom, terminal end of a well; likewise, use of the terms “down,” “lower,” “downward,” “downhole,” or other like terms shall be construed as generally toward the bottom, terminal end of the well, regardless of the wellbore orientation. Use of any one or more of the foregoing terms shall not be construed as denoting positions along a perfectly vertical axis. In some instances, a part near the end of the well may be horizontal or even slightly directed upwards. Unless otherwise specified, use of the terms “subsurface formation” or “subterranean formation” shall be construed as encompassing both areas below exposed earth and areas below earth covered by water such as ocean or fresh water.

Plural instances may be provided for components, operations or structures described herein as a single instance. Finally, boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure.

The flowcharts are provided to aid in understanding the illustrations and are not to be used to limit the scope of the claims. The flowcharts depict example operations that may vary within the scope of the claims. Additional operations may be performed; fewer operations may be performed; the operations may be performed in parallel; and the operations may be performed in a different order. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, may be implemented by program code. The program code may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable machine or apparatus.

Use of the phrase “at least one of” preceding a list with the conjunction “and” should not be treated as an exclusive list and should not be construed as a list of categories with one item from each category, unless specifically stated otherwise. A clause that recites “at least one of A, B, and C” may be infringed with only one of the listed items, multiple of the listed items, and one or more of the items in the list and another item not listed. As used herein, the term “or” is inclusive unless otherwise explicitly noted. Thus, the phrase “at least one of A, B, or C” is satisfied by any element from the set {A, B, C} or any combination thereof, including multiples of any element.

Example Implementations

Implementation #1: A method comprising: determining a drilling efficiency of a drill bit at a first depth in a wellbore formed in a subsurface formation based, at least in part, on a bit wear level of the drill bit; determining a cutting force mechanical specific energy of the drill bit at the first depth; and determining a rock strength of the subsurface formation at the first depth based on the drilling efficiency and the cutting force mechanical specific energy of the drill bit.

Implementation #2: The method of Implementation 1, further comprising: determining an average rock abrasiveness factor based, at least in part, on a cutter wear volume of a plurality of primary cutters disposed along a face of the drill bit.

Implementation #3: The method of any one or more of Implementations 1-2, further comprising: determining, via a bit-rock interaction tool, a cutter dull severity for each primary cutter of the plurality of primary cutters; determining a cutter wear depth of the plurality of primary cutters based on the cutter dull severity; and determining the cutter wear volume of the plurality of primary cutters based on the determined cutter wear depth.

Implementation #4: The method of any one or more of Implementations 1-3, further comprising: determining a weight on bit (WOB) and a torque on bit (TOB) on the drill bit along a drilling depth of the wellbore based, at least in part, on a given rate of penetration of the drill bit, a given quantity of revolutions per minute of the drill bit; determining a mechanical specific energy of the drill bit based on the WOB and TOB of the drill bit along the drilling depth; and determining a plurality of values of the drilling efficiency of the drill bit along the drilling depth of the wellbore.

Implementation #5: The method of any one or more of Implementations 1-4, further comprising: determining an input energy to a primary cutter of the drill bit at the first depth along a drilling depth of the wellbore; determining a required energy for the primary cutter of the drill bit to wear to a bit wear level; and determining a bit wear level at the first depth along the drilling depth of the wellbore.

Implementation #6: The method of any one or more of Implementations 1-5, wherein determining the cutting force mechanical specific energy of the drill bit at the first depth comprises determining the cutting force mechanical specific energy based on a cutting force weight on bit and a cutting force torque on bit.

Implementation #7: The method of any one or more of Implementations 1-6, wherein the rock strength is a confined compressive strength of the subsurface formation at the first depth.

Implementation #8: One or more non-transitory, machine-readable media having instructions stored thereon that are executable by a processor, the instructions comprising: instructions to determine a drilling efficiency of a drill bit at a first depth in a wellbore formed in a subsurface formation based, at least in part, on a bit wear level of the drill bit; instructions to determine a cutting force mechanical specific energy of the drill bit at the first depth; and instructions to determine a rock strength of the subsurface formation at the first depth based on the drilling efficiency and the cutting force mechanical specific energy of the drill bit.

Implementation #9: The one or more non-transitory, machine-readable media of Implementation 8, further comprising: instructions to determine an average rock abrasiveness factor based, at least in part, on a cutter wear volume of a plurality of primary cutters disposed along a face of the drill bit.

Implementation #10: The one or more non-transitory, machine-readable media of any one or more of Implementations 8-9, further comprising: instructions to determine, via a bit-rock interaction tool, a cutter dull severity for each primary cutter of the plurality of primary cutters; instructions to determine a cutter wear depth of the plurality of primary cutters based on the cutter dull severity; and instructions to determine the cutter wear volume of the plurality of primary cutters based on the determined cutter wear depth.

Implementation #11: The one or more non-transitory, machine-readable media of any one or more of Implementations 8-10, further comprising: instructions to determine a weight on bit (WOB) and a torque on bit (TOB) on the drill bit along a drilling depth of the wellbore based, at least in part, on a given rate of penetration of the drill bit, a given quantity of revolutions per minute of the drill bit, and a known rock strength; instructions to determine a mechanical specific energy of the drill bit based on the WOB and TOB of the drill bit along the drilling depth; and instructions to determine a plurality of values of the drilling efficiency of the drill bit along the drilling depth of the wellbore.

Implementation #12: The one or more non-transitory, machine-readable media of any one or more of Implementations 8-11, further comprising: instructions to determine an input energy to a primary cutter of the drill bit at the first depth along a drilling depth of the wellbore; instructions to determine a required energy for the primary cutter of the drill bit to wear to a bit wear level; and instructions to determine a bit wear level at the first depth along the drilling depth of the wellbore.

Implementation #13: The one or more non-transitory, machine-readable media of any one or more of Implementations 8-12, wherein the instructions to determine the cutting force mechanical specific energy of the drill bit at the first depth comprise instructions to determine the cutting force mechanical specific energy based on a cutting force weight on bit and a cutting force torque on bit.

Implementation #14: An apparatus comprising: a processor; and one or more machine-readable media having instructions stored thereon that are executable by the processor, the instructions comprising: instructions to determine a drilling efficiency of a drill bit at a first depth in a wellbore formed in a subsurface formation based, at least in part, on a bit wear level of the drill bit; instructions to determine a cutting force mechanical specific energy of the drill bit at the first depth; and instructions to determine a rock strength of the subsurface formation at the first depth based on the drilling efficiency and the cutting force mechanical specific energy of the drill bit.

Implementation #15: The apparatus of Implementation 14, further comprising: instructions to determine an average rock abrasiveness factor based, at least in part, on a cutter wear volume of a plurality of primary cutters disposed along a face of the drill bit.

Implementation #16: The apparatus of any one or more of Implementations 14-15, further comprising: instructions to determine, via a bit-rock interaction tool, a cutter dull severity for each primary cutter of the plurality of primary cutters; instructions to determine a cutter wear depth of the plurality of primary cutters based on the cutter dull severity; and instructions to determine the cutter wear volume of the plurality of primary cutters based on the determined cutter wear depth.

Implementation #17: The apparatus of any one or more of Implementations 14-16, further comprising: instructions to determine a weight on bit (WOB) and a torque on bit (TOB) on the drill bit along a drilling depth of the wellbore based, at least in part, on a given rate of penetration of the drill bit, a given quantity of revolutions per minute of the drill bit, and a known rock strength; instructions to determine a mechanical specific energy of the drill bit based on the WOB and TOB of the drill bit along the drilling depth; and instructions to determine a plurality of values of the drilling efficiency of the drill bit along the drilling depth of the wellbore.

Implementation #18: The apparatus of any one or more of Implementations 14-17, further comprising: instructions to determine an input energy to a primary cutter of the drill bit at the first depth along a drilling depth of the wellbore; instructions to determine a required energy for the primary cutter of the drill bit to wear to a bit wear level; and instructions to determine a bit wear level at the first depth along the drilling depth of the wellbore.

Implementation #19: The apparatus of any one or more of Implementations 14-18, wherein the instructions to determine the cutting force mechanical specific energy of the drill bit at the first depth comprise instructions to determine the cutting force mechanical specific energy based on a cutting force weight on bit and a cutting force torque on bit.

Implementation #20: The apparatus of any one or more of Implementations 14-19, wherein the rock strength is a confined compressive strength of the subsurface formation at the first depth.