RATE OF PENETRATION PREDICTION AND USES THEREOF

Abstract

System and methods are disclosed herein for rate of penetration (ROP) predictions and uses thereof. A ROP model representing a rate at which a drill bit can penetrate one or more formation layers can be computed based on a mechanical efficiency and bit wear model representing drill bit wear of the drill bit. In some examples, the ROP model can be combined with a geomechanical model representing the one or more formations to generate a drilling performance model that can represent (or predict) drilling efficiencies of the drill bit with respect to the one or more formations. Potential well trajectories through the one or more formations can be formed using the drilling performance model and one or more candidate well trajectories be selected from the potential well trajectories, for example, for use in formation drilling.

Description

FIELD OF THE DISCLOSURE

This disclosure relates generally to subterranean drilling, and more particularly, to a system and method for rate of penetration (ROP) prediction and use thereof.

BACKGROUND OF THE DISCLOSURE

Subterranean formations refer to various layers of rock and soil that exist beneath an earth's surface. These formations can vary widely in composition, structure, and depth, and can include sedimentary, igneous, and metamorphic rocks, as well as soils and other geological materials. Subterranean formations can contain valuable resources as well, such as oil, gas, and minerals. Drilling operations are often conducted to extract these resources. The properties of subterranean formations can vary greatly within a geological area (or basin), which can affect a performance of drilling operations. For example, some formations may be harder and more resistant to drilling, while others may be softer and more porous.

A rate of penetration (ROP) in subterranean formation drilling refers to a speed at which a drill bit advances through a formation being drilled. The ROP is related to properties of a formation being drilled, including its strength, density, and porosity. In areas with harder and more compact formations (e.g., rocks), the ROP may be slower due to increased resistance to a drilling bit, which can lead to increased drilling costs and longer drilling times. In contrast, in areas with softer and more porous formations, the ROP can be faster, but the risk of hole collapse or other drilling issues is also greater. Thus, understanding a heterogeneity of subterranean formation properties is needed so that drilling performance can be optimized. In existing approaches to predict ROP for a new well based on offset well data, the subterranean formations are often assumed homogeneous in horizontal directions. Since subterranean formations are heterogeneous in both vertical and horizontal directions data at one location may not represent data at another and drilling performance prediction based on offset well data may be misleading.

SUMMARY OF THE DISCLOSURE

Various details of the present disclosure are hereinafter summarized to provide a basic understanding. This summary is not an extensive overview of the disclosure and is neither intended to identify certain elements of the disclosure nor to delineate the scope thereof. Rather, the primary purpose of this summary is to present some concepts of the disclosure in a simplified form prior to the more detailed description that is presented hereinafter.

According to an embodiment, a computer implemented can include computing, by a processor, a mechanical efficiency for a drill bit, computing, by the processor, a bit wear model representing drill bit wear of the drill bit, and generating, by the processor, a rate of penetration (ROP) model representing a rate at which the drill bit will penetrate one or more formation layers based on the mechanical efficiency and the bit wear model.

In another embodiment, a system can include memory to store machine-readable instructions and one or more processors to access the memory and execute the machine-readable instructions. The machine-readable instructions cause the processor to identify one or more regions defined by formation sections that a baseline well trajectory intersects in a drilling performance model. The drilling performance model can be generated based on a ROP model. The ROP model can be generated based on a mechanical efficiency for a drill bit, and a bit wear model representing drill bit wear of the drill bit. The machine-readable instructions further cause the processor to insert potential well trajectories into the drilling performance model that intersects one or more regions of the drilling performance model, and output well trajectory data identifying a candidate well trajectory of the inserted potential well trajectories for drilling by the drill bit.

In a further embodiment, a computer implemented method can include generating, by a processor, a ROP model representing a rate at which the drill bit will penetrate one or more formation layers based on a precomputed mechanical efficiency and bit wear model, receiving, by the processor, a geomechanical model representing the one or more formations, combining, by the processor, the geomechanical model and the ROP model to provide a drilling performance model with a ROP for the one or more formations, and outputting, by the processor, well trajectory data identifying a well trajectory through the drilling performance model representative of a potential trajectory through the one or more formations.

Any combinations of the various embodiments and implementations disclosed herein can be used in a further embodiment, consistent with the disclosure. These and other aspects and features can be appreciated from the following description of certain embodiments presented herein in accordance with the disclosure and the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an example of a rate of penetration (ROP) engine.

FIG. 2 is an example of a well trajectory planner.

FIG. 3 is an example of a graph illustrating ROP predictions based on well data.

FIG. 4 is an example of a graph illustrating bit dull grade predictions.

FIG. 5 is an example of a portion of a drilling performance model illustrating ROP predictions in a reservoir.

FIG. 6 is an example of another portion of a drilling performance model with well trajectories.

FIG. 7 is an example of a method for computing mechanical efficiency data.

FIG. 8 is an example of a method for generating a bit wear model.

FIG. 9 is an example of a method for computing a ROP model.

FIG. 10 is an example of a method for ROP optimization.

FIG. 11 depicts an example computing environment that can be used to perform methods according to an aspect of the present disclosure.

FIG. 12 depicts a cloud computing environment that can be used to perform one or more actions according to an aspect of the present disclosure.

DETAILED DESCRIPTION

Embodiments of the present disclosure will now be described in detail with reference to the accompanying Figures. Like elements in the various figures may be denoted by like reference numerals for consistency. Further, in the following detailed description of embodiments of the present disclosure, numerous specific details are set forth in order to provide a more thorough understanding of the claimed subject matter. However, it will be apparent to one of ordinary skill in the art that the embodiments disclosed herein may be practiced without these specific details. In other instances, well-known features have not been described in detail to avoid unnecessarily complicating the description. Additionally, it will be apparent to one of ordinary skill in the art that the scale of the elements presented in the accompanying Figures may vary without departing from the scope of the present disclosure.

Embodiments of the present disclosure relate to rate of penetration (ROP) prediction and well (or wellbore) placement optimization, in some examples. Subterranean formations are heterogeneous in both vertical and horizontal directions and well data obtained for a respective well location may not be representative of the rock properties and drilling performance at a new well location. This can lead to inaccurate predictions of the ROP and other drilling performance parameters. In addition to variations in subterranean formation properties, other factors such as changes in geological structures, formation pressures, and wellbore conditions can also affect drilling performance and ROP. Therefore, relying on offset well data to predict drilling performance can be misleading and can result in suboptimal drilling outcomes. Some existing approaches use offset well modeling to represent the predicted ROP; however, such models fail to take into account variations in well data from well location to well location, thereby making it difficult to know where to place a wellbore to achieve optimal drilling performance.

According to the examples disclosed herein, a three-dimensional (3D) model can be created that takes into account variations in well data using a ROP model. The ROP model can be used for an oil and gas reservoir in subterranean formations. However, other uses of the ROP model outside of oil and/or gas reservoir subterranean formation is contemplated by the examples disclosed herein. The ROP model can be constructed (or generated) taking into consideration various factors that can impact ROP while drilling, including, but not limited to, rock strength, wellbore pressure, pore pressure, rock permeability, in-situ stresses, formation abrasiveness, bit wear, weight on bit, rotations per minute (RPM), flow rate, and/or total nozzle flow area of the drill bit. Accordingly, the ROP model provided according to this disclosure is more accurate in contrast to ROP models generated using some existing techniques. The ROP model of the present disclosure has a greater fidelity and thus is more reliable than some existing ROP models, providing a more accurate representation of ROP for drilling operations. Because the ROP model is higher in fidelity than some existing ROP models, the ROP model provides for improved or more accurate wellbore placement. With such a ROP model, a trajectory design for a well (or wellbore) can be improved (e.g., optimized) to achieve optimum drilling performance. As such, well (or wellbore) trajectories for new wellbores can be optimized in the well planning stage based on predicted ROP according to the examples disclosed herein so that an actual well or wellbore can be placed in an optimum location and direction. In some examples, the systems and methods disclosed herein can be used to predict a 3D distribution of ROP for a reservoir. With such a 3D model, new wells can be planned to be in higher ROP regions (or zones), thereby improving drilling performance.

Rate of Penetration (ROP) Engine

FIG. 1 is an example of a ROP engine 100 that can be used for modeling a ROP of a drilling operation in one or more formations (referred to herein as formations, or formation layers). The term formation as used herein can include any type of earth layer. Thus, while examples are presented herein in which the formation is a rock layer, in other examples, the formation can be a different earth layer, or a combination of earth layers. In some examples, the ROP engine 100 can be embodied as machine-readable instructions that can define a software plugin or tool. For example, the ROP engine 100 can be implemented as a part of software used for modeling, or a stand-alone module that can be activated in response to the software, or by a user (e.g., using an input device, as disclosed herein). Thus, in some instances, the ROP engine 100 can be incorporated into one or more systems and/or applications.

The ROP engine 100 can be implemented using one or more modules, shown in block form in the drawings in the example of FIG. 1. The one or more modules can be in software or hardware form, or a combination thereof. In some examples, the ROP engine 100 can be implemented as machine-readable instructions for execution on a computing device 102, as shown in FIG. 1. The computing device 102 can include any computing device, for example, a desktop computer, a server, a controller, a blade, a mobile phone, a tablet, a laptop, a personal digital assistant (PDA), or other types of portable (or stationary) devices. The computing device 102 can include a processor 104 and a memory 106. By way of example, the memory 106 can be implemented, for example, as a non-transitory computer storage medium, such as volatile memory (e.g., random access memory), non-volatile memory (e.g., a hard disk drive, a solid-state drive, a flash memory, or the like), or a combination thereof. The processor 104 can be implemented, for example, as one or more processor cores. The memory 106 can store machine-readable instructions (e.g., the ROP engine 100) that can be retrieved and executed by the processor 104. Each of the processor 104 and the memory 106 can be implemented on a similar or a different computing platform. The computing platform could be implemented in a computing cloud and thus on a cloud computing architecture. In such a situation, features of the computing platform could be representative of a single instance of hardware or multiple instances of hardware executing across the multiple of instances (e.g., distributed) of hardware (e.g., computers, routers, memory, processors, or a combination thereof). Alternatively, the computing platform could be implemented on a single dedicated server or workstation.

As disclosed herein, the ROP engine 100 can provide a ROP model 108 representing a rate at which a drill bit will penetrate the formation layers (during a drilling operation) based on a mechanical efficiency and the bit wear model computed according to the examples disclosed herein. The ROP model 108 can be used to predict the ROP of the drill bit while taking into consideration variables that can affect a drilling performance of the drill bit. In some examples, the ROP model 108 can predict a number of ROPs for formation sections of each of the formation layers. A formation section can refer to an interval or section of a formation (or one or more formations). In some examples, the ROP model 108 can predict ROPs for zones or regions in the formation layers. A zone or region as used herein can refer to an interval or section of a formation that includes one or more formation sections from the formation layers. Thus, in some examples, a zone or region can correspond to a section of a formation that has particular properties or characteristics. In some examples, the zones or regions are referred to as locations of interest (representing locations typically where drilling is expected to occur).

The ROP engine 100 includes a model generator 126 that can provide the ROP model 108 based on mechanical efficiency data 112 and a bit wear model 114. The mechanical efficiency data 112 can be provided by a parameter adjuster 116 and the bit wear model 114 can be provided by a bit wear predictor 118 based on the well data 120 (e.g., relevant portions of the well data 120), as shown in FIG. 1. The parameter adjuster 116 can communicate with a drilling efficiency calculator 122 to provide the mechanical efficiency data 112 based on ROP field data 124.

The well data 120 can represent subsurface geology and hydrocarbon potential assessments. At least some of the well data 120 can be captured by one or more instruments (e.g., devices and/or sensors) employed in a field (e.g., at a wellbore). Well logs can be recorded by various types of downhole instruments and data can be provided by these downhole instruments, which can be provided as a continuous plot or record that can show changes in measured properties with depth. The well logs can include, for example, Gamma ray (GR) logs, resistivity logs, density logs, neutron logs, sonic logs, caliper logs, and/or formation pressure test result logs. The type of log information that is part of the well data 120 can depend on drilling operation and objectives, a geological setting, and an availability of downhole instruments.

For example, the well data 120 can include well logs and formation evaluation results including Gamma ray (GR) log (e.g., providing an estimate of a lithology (e.g., rock type) of the formation), spectral gamma ray logs (e.g., enhanced gamma ray logs to estimate clay content), total porosity evaluation results, effective porosity evaluation results, water saturation (or resistivity) evaluation results (e.g., estimating an amount of water present in the formation), and/or volume of minerals (or density) evaluation results (e.g., estimating a mineralogy of formation). Total porosity can refer to a total void space within the formation (e.g., rock), whereas effective porosity can refer to an interconnected void space that can hold fluids (e.g., oil and/or gas). The well data 120 can further include drilling parameters, such as weight on bit (WOB) (e.g., specifying a downward forced applied to a drill bit by a drill string), RPM (e.g., specifying a rotational speed of the drill bit), flow rate (e.g., specifying a rate at which drilling fluids (e.g., mud) are pumped down the drill string and circulated through a wellbore), and/or mud weight (e.g., specifying a density of a drilling mud). The well data 120 can also include bit parameters, such as a bit manufacturer, a bit model number, a bit size (e.g., specifying a diameter of the drill bit), running hours (e.g., specifying an amount of time that the drill bit has been in operation), a total number of feet drilled (e.g., specifying a total distance that the drill bit drilled) and/or a dull grade (e.g., specifying a condition of the drill bit according to a dull grade rating system).

In some examples, the model generator 126 can receive geomechanical data 128, which can be used for providing a drilling performance model 130. While examples are disclosed herein, in which the drilling performance model 130 is provided by the ROP engine 100, in other examples, functionality described herein for providing the drilling performance model 130 can be implemented by a different module, device, and/or system. For example, a well trajectory planner 200, as shown in FIG. 2, can be configured to provide the drilling performance model 130. The geomechanical data 128 can represent subsurface geomechanical properties along one or more axes within the formation. In some examples, the geomechanical data 128 represents subsurface geomechanical properties along a single vertical axis (e.g., depth) within the formation. In some examples, the gcomechanical data 128 is a one-dimensional (1D) model with a number of parameters characterizing a mechanical behavior of each formation (and thus the formations).

The parameters (or the geomechanical data 128) can include, but is not limited to, unconfined compressive strength (UCS) (e.g., specifying a maximum amount of compressive stress that the formation (or rock) can withstand without undergoing permanent deformation or failure), a friction angle (e.g., specifying a physical property of earth materials or the slope of a linear representation of the shear strength of earth materials, and thus can characterize a resistance of a rock to shear failure), a pore pressure (e.g., specifying a pressure of fluids (e.g., water or hydrocarbons) within pore spaces of the formation), and/or in-situ stresses (e.g., specifying the stresses that exist in the formation due to overburden pressure, tectonic forces, and other geological factors). In some examples, the geomechanical model can include other parameters, such as rock porosity, rock density, rock fabric, rock anisotropy, and other mechanical properties.

In some examples, the drilling efficiency calculator 122 can implement a well-based ROP analysis based on the well data 120. Using the well-based ROP analysis, the drilling efficiency calculator 122 can calculate (or compute) a number of ROP with consideration of mechanical specific energy (MSE) (for a selected or given mechanical efficiency), MSE and hydraulic energy, and consideration of bit wear. Using the computed ROPs, the parameter adjuster 116 can provide the mechanical efficiency data 112 based on the ROP field data 124, as shown in FIG. 1. Thus, the drilling efficiency calculator 122 can compute a number of ROPs according to different factors or variables of ROP influence.

In some examples, the ROP engine 100 implements the well-based ROP analysis for a bit type. The ROP engine 100 can receive bit type data 132 identifying the bit type (e.g., a bit model number), and which can be provided based on user input at an input device (e.g., as disclosed herein). In some examples, the bit type data 132 can be provided as part of the well data 120. Once the bit type (using the bit type data 132) has been specified, the ROP engine 100 can perform the well-based ROP analysis, and track all relevant data for that bit for generating one or more models, as disclosed herein.

For example, the drilling efficiency calculator 122 can calculate a ROP due to MSE. In some examples, to predict a ROP for drilling subterranean formations, the drilling efficiency calculator 122 can use a concept of specific energy, which can be defined as an energy required to remove a unit volume of rock (or formation) in rotary drilling and can be expressed as follows:

$\begin{array}{cc}{E}_s=\frac{W_b}{A_b}+\frac{120\pi \mathrm{NT}}{A_b\mathrm{ROP}},& \left(1\right)\end{array}$

wherein E_S is a specific energy, psi, ROP is a rate of penetration, ft/hr, T is a torque at bit, N is a rotational speed of drill bit, revolutions per minute, and A_b is an area of bit (e.g., in square inches).

The specific energy reaches its minimum value when the specific energy is equal to the compressive strength of rock. The mechanical efficiency can be expressed as follows:

$\begin{array}{cc}{E}_M=\frac{E_{\mathrm{Smin}}}{E_S},& \left(2\right)\end{array}$

wherein E_M is a mechanical efficiency, dimensionless, and, E_Smin is a minimum specific energy, in psi.

The mechanical efficiency reaches its maximum when the specific energy reaches its minimum. In some examples, the minimum specific energy can be equal to a confined compressive strength (CCS), and expression (2) therefore becomes:

$\begin{array}{cc}{E}_S=\frac{{\xi }_c}{E_M},& \left(3\right)\end{array}$

wherein 86_c is the CCS, in psi.

In some examples, the MSE can be computed according to the following expression;

$\begin{array}{cc}\mathrm{MSE}=W_b\left(\frac{1}{A_b}+\frac{13\text{.33}{\mu }_{b}N}{d_b\mathrm{ROP}}\right),& \left(4\right)\end{array}$

wherein μ_b is a bit-specific coefficient of sliding friction, dimensionless, d_b is a bit diameter, in inches, W_b is a weight on bit, in lbf,

The bit specific coefficient μ_b can be computed according to the following expression:

$\begin{array}{cc}{\mu }_b=36\frac{T}{d_b{W}_b}.& \left(5\right)\end{array}$

In some instances, if the weight on bit W_b is not available, the following expression can be used to estimate the weight on bit from a surface weight on bit:

$\begin{array}{cc}{W}_b={\mathrm{WOBe}}^{-\mathrm{\mu \beta }},& \left(6\right)\end{array}$

wherein WOB is a surface weight on bit, in lbf, β is a well inclination angle, in radian, and μ is a friction coefficient between drill pipe and wellbore wall that is dimensionless.

In some examples, ROP can be solved and expressed according to the following expression, in which expressions (3) and (6) have been introduced into expression (4):

$\begin{array}{cc}{\mathrm{ROP}}_M=\frac{13.33{\mu }_{b}N}{d_b\left(\frac{{\xi }_c}{E_M\times \mathrm{WOB}\times e^{-\mathrm{\mu \beta }}}-\frac{1}{A_b}\right)},& \left(7\right)\end{array}$

wherein ROP_M is used to indicate that the rate of penetration is due to mechanical energy input.

Mechanical efficiency E_M can vary from bit to bit and formation to formation, and in some instances in a range of 10% to 40% in the expression (7). The drilling efficiency calculator 122 can use a given (or initial) mechanical efficiency for computing the ROP in expression (7).

In some instances, the drilling efficiency calculator 122 can predict ROP according to CCS, as shown in expression (7). CCS can be estimated with rock strength measurement at various confining pressures in triaxial tests. In some examples, the drilling efficiency calculator 122 estimates CCS based on UCS, friction angle and the confining pressure on the rock ahead of the drill bit (and thus based on the geomechanical data 128). Depending on the permeability of the formation, the confining pressure can be calculated differently. For example, for permeable formations, the confining pressure on the rock ahead of the bit can be equivalent to the difference between wellbore pressure and pore pressure. In impermeable formations, the pore pressure in the rock ahead of the drill bit can decrease due to stress release and rock expansion. The reduction in pore pressure can be a function of the in-situ earth stress in a direction of drilling and a Skempton pore pressure coefficient. The effective confining pressure can be greater than the differential pressure between the well pressure and pore pressure. In some examples herein, a formation can be considered permeable if an effective porosity is greater than 0.2, and impermeable if the effective porosity is less than 0.05. In formations with an effective porosity between 0.05 and 0.2, the CCS can be interpolated by the drilling efficiency calculator 122 between the permeable case and the impermeable case.

For example, the drilling efficiency calculator 122 can calculate CCS for permeable formations according to the following expression:

$\begin{array}{cc}{\xi }_{\mathrm{cdp}}={\xi }_u+d_p+2d_p\frac{\sin \psi }{1-\sin \psi },& \left(8\right)\end{array}$

wherein ξ_cdp is a confined compressive strength in permeable formation, in psi, ξ_u is an unconfined compressive strength, in psi, d_p is a differential pressure between the wellbore and the pore pressure ahead of the drill bit where the formation is permeable, in psi, and ψ is a friction angle of the formation, in degrees.

A differential pressure between the wellbore and the pore pressure ahead of the drill bit where the formation is permeable can be calculated by the drilling efficiency calculator 122 according to the following expression:

$\begin{array}{cc}{d}_p=P_w=P_p,& \left(9\right)\end{array}$

wherein P_w is a well pressure, in psi, and P_p is a pore pressure, in psi.

In some examples, the drilling efficiency calculator 122 can calculate CCS for impermeable formations according to the following expression:

$\begin{array}{cc}{\xi }_{\mathrm{csk}}={\xi }_u+d_{\mathrm{psk}}+2d_{\mathrm{psk}}\frac{\sin \psi }{1-\sin \psi },& \left(10\right)\end{array}$

wherein ξ_csk is a confined compressive strength in impermeable formation, in psi, and d_psk is a differential pressure between the wellbore and the pore pressure ahead of the drill bit where the formation is impermeable, in psi.

In some examples, the drilling efficiency calculator 122 can calculate a differential pressure between the wellbore and the pore pressure ahead of the drill bit where the formation is impermeable according to the following expression:

$\begin{array}{cc}{d}_{\mathrm{psk}}=P_w-P_p+\frac{B\left({\sigma }_n-P_w\right)}{3},& \left(11\right)\end{array}$

wherein σ_n is an earth stress normal to a bottom of the wellbore, in psi, and B is a Skempton pore pressure coefficient that is dimensionless.

In some examples, the drilling efficiency calculator 122 can calculate a CCS in formations regardless of effective porosity according to the following expression:

$\begin{array}{c}\begin{array}{cc}\begin{array}{ccc}{\xi }_{\mathrm{cmix}}={\xi }_{\mathrm{cdp}}\mathrm{if}{\varphi }_e\ge 0.2& ={\xi }_{\mathrm{csk}}\mathrm{if}{\varphi }_e\le 0.05& =\frac{{\xi }_{\mathrm{cdp}}\left({\varphi }_e-0.05\right)+{\xi }_{\mathrm{csk}}\left(0.2-{\varphi }_e\right)}{0.15}\mathrm{if}0.05<{\varphi }_e\le 0.2\end{array}& \left(12\right)\end{array}\\ =\frac{{\xi }_{\mathrm{cdp}}\left({\varphi }_e-0.05\right)+{\xi }_{\mathrm{csk}}\left(0.2-{\varphi }_e\right)}{0.15}\mathrm{if}0.05<{\varphi }_e\le 0.2\\ =\frac{{\xi }_{\mathrm{cdp}}\left({\varphi }_e-0.05\right)+{\xi }_{\mathrm{csk}}\left(0.2-{\varphi }_e\right)}{0.15}\mathrm{if}0.05<{\varphi }_e\le 0.2\end{array}$

wherein ξ_cmix is a confined compressive strength in formations of any effective porosity, in psi, and ϕ_e is an effective porosity that is dimensionless.

Accordingly, the drilling efficiency calculator 122 can compute (or calculate) the CCS according to expression (12) for the formation.

In some examples, the ROP can be computed by the drilling efficiency calculator 122 according to expression (7) and thus without consideration of hydraulic energy. In other examples, the drilling efficiency calculator 122 can compute the ROP due to both MSE and hydraulic energy. Thus, in some examples, in addition to the mechanical energy input to drilling from weight on bit and torque, the drilling efficiency calculator 122 can consider hydraulic energy from a hydraulic force exerted by a drilling fluid. Hydraulic force is used to remove cuttings from a space between a drill bit and the formation. To incorporate the effect of hydraulic energy on ROP, the drilling efficiency calculator 122 can compute a hydro mechanical specific energy (HMSE) according to the following expression:

$\begin{array}{cc}\mathrm{HMSE}=W_b\left(\frac{1}{A_b}+\frac{13.33{\mu }_{b}N}{d_b\mathrm{ROP}}\right)+\frac{1154\mathrm{\Gamma \Delta }{P}_{b}Q}{A_b\mathrm{ROP}},& \left(13\right)\end{array}$

wherein Γ is a hydraulic energy reduction factor, which is dimensionless, ΔP_b is a pressure drop across the bit, in psi, and Q is a flow rate, in gallon/min.

The drilling efficiency calculator 122 can calculate the pressure drop across the bit according to the following expression:

$\begin{array}{cc}\Delta P_b=\frac{MW\times Q^2}{12775\times {\mathrm{TNFA}}^2},& \left(14\right)\end{array}$

wherein MW is a mud weight, in pound per gallon and TNFA is a total nozzle flow area, in square inches

The drilling efficiency calculator 122 can calculate the ROP according to the following expression:

$\begin{array}{cc}{\mathrm{ROP}}_H=\frac{\frac{13.33{\mu }_{b}N\times \mathrm{WOB}\times e^{-\mathrm{\mu \beta }}}{d_b}\left(1+\frac{\frac{1154\mathrm{\Gamma \Delta }{P}_{b}Q}{A_b}}{\frac{13.33{\mu }_b{N}_c\times \mathrm{WOB}\times e^{-\mathrm{\mu \beta }}}{d_b}}\right)}{\frac{{\xi }_c}{E_m}-\frac{{\mathrm{WOBe}}^{-\mathrm{\mu \beta }}}{A_b}},& \left(15\right)\end{array}$

wherein ROP_H is a rate of penetration considering both MSE and hydraulic energy, in ft/hr, N_c is a mean rotational speed of drill bit in a bit run, in revolutions per minute, and WOB_c is a mean surface weight on bit in a bit run, in lbf.

Accordingly, the drilling efficiency calculator 122 can compute or calculate the ROP due to both MSE and hydraulic energy using expression (15).

In some examples, the drilling efficiency calculator 122 can calculate ROP due to bit wear. Drill bits wear out with drilling and rate of penetration decreases with drill bit wear. Drill bits are usually inspected for a severity of wear after removal from the well. Dull grade is a common index used for evaluating the severity of bit wear and provides information about the severity of wear for different parts of the bit, characteristics of the wear, and the reasons for pulling the bit out of the well. Dull grade can be between 0 and 8 with 0 for brand new bits and 8 for completely worn out bits. If the dull grades of drill bits are available, either from bit inspection from drilled wells or from prediction in planned wells, the drilling efficiency calculator 122 can approximate the ROP according to the following expression:

$\begin{array}{cc}{\mathrm{ROP}}_W=\left(1-\frac{\Delta d\times \mathrm{DG}}{8d}\right){\mathrm{ROP}}_H,& \left(16\right)\end{array}$

wherein ROP_W is a rate of penetration considering mechanical specific energy, hydraulic energy and bit wear, in ft/hr, DG is an average dull grade of a bit, which is dimensionless, Δd is a footage drilled by a bit, in ft, and d is a total footage drilled by a bit, in ft.

In some examples, the drilling efficiency calculator 122 can consider the adverse effects of weight on bit (WOB) on ROP. In the derivation of ROP equations based on MSE, it is assumed that weight on bit has a positive impact on ROP. In some instances, field data of ROP and drilling parameters frequently show a reverse trend in certain types of formations when the weight on bit is above a given (or critical) value, sometimes referred to as flounder point. ROP instead of increases with WOB, it decreases, even for fresh (or new) bits or slightly worn bits. The possible reasons for such behavior can include bit vibrations, bit balling, and/or insufficient hole cleaning. In formations exhibiting such behavior, the drilling efficiency calculator 122 can use the following expression to compute a modified WOB:

$\begin{array}{cc}{\mathrm{WOB}}_m=2{\mathrm{WOB}}_c-\mathrm{WOB},& \left(17\right)\end{array}$

wherein WOB_m is a modified weight on bit, in lbf, and WOB_c is a critical weight on bit, in lbf.

Identifying such adverse effects of WOB on ROP provides an opportunity to enhance drilling performance by optimizing WOB.

In some examples, the drilling efficiency calculator 122 can predict a bit wear as represented by bit dull grade. For example, the drilling efficiency calculator 122 can predict ROP for planned wells and consider the effect of bit wear. For example, the drilling efficiency calculator 122 can predict the bit wear based on UCS, a rock grain size, a volume of quartz, a total porosity, a water saturation, a weight on bit, an RPM, and a bit running hours. The drilling efficiency calculator 122 can calculate or estimate the rock grain size according to the following expression:

$\begin{array}{cc}T=20-19.9\frac{\log 10\mathrm{CGR}-\log 10{\mathrm{CGR}}_{\min }}{\log 10{\mathrm{CGR}}_{\max }-\log 10{\mathrm{CGR}}_{\min }},& \left(18\right)\end{array}$

wherein T is a parameter representing the relative rock grain size, which is dimensionless, CGR is gamma ray readings of thorium and potassium from spectral gamma ray logs, CGR_max is the maximum CGR value in clay rich formation, and CGR_min is the minimum CGR value in quartz rich formation.

In some instances, bit wear represented as bit dull grade can be computed by the drilling efficiency calculator 122 according to the following expression:

$\begin{array}{cc}D=f_1{W_b}^a{N}^b{A}^c{H}^d,& \left(19\right)\end{array}$

wherein H is a running hour of the bit, hour, A is formation abrasiveness, N is an RPM and a, b, c, d and f₁ are correlation coefficients.

The formation abrasiveness can be calculated by the drilling efficiency calculator 122 according to the following expression:

$\begin{array}{cc}A=f_2{T}^e{V_q}^g{{\xi }_c}^h{{\varphi }_t}^i{\eta }^j,& \left(20\right)\end{array}$

wherein V_q is a volume of quartz, which is dimensionless, ϕ_t is total porosity, which is dimensionless, and η is a water saturation, which is dimensionless.

In some examples the bit wear can be calculated by the drilling efficiency calculator 122 according to the following expression in which expressions (19) and (20) have been combined:

$\begin{array}{cc}D=f_3{W_b}^a{N}^b{T}^k{V_q}^l{{\xi }_c}^m{{\varphi }_t}^n{\eta }^o{H}^d.& \left(21\right)\end{array}$

Accordingly, the drilling efficiency calculator 122 can calculate a fresh bit ROP using expression (15) and a worn bit ROP of increasing dull grade from bit run start to end depth using expression (16). Data characterizing the fresh bit ROP and the worn bit ROP can be received by the parameter adjuster 116. The parameter adjuster 116 can receive the ROP field data 124, as shown in FIG. 1. The ROP field data 124 can reflect recorded ROP in a field for the bit from fresh at the start depth to about the end depth. The ROP field data 124 can include actual drilling data collected during drill of a well in the field. This data can include information on the ROP of the drilling bit. The ROP field data 124 can be referred to as a recorded ROP. Thus, the recorded ROP can reflect an actual drilling rate measured at a rig that can be expressed as a distance drilled per unit of time. Ideally, the recorded ROP should be between the fresh bit ROP and the worn bit ROP.

The parameter adjuster 116 can compare the calculated ROP due to bit wear with the recorded bit ROP. If the calculated ROP due to bit wear does not match the recorded bit ROP, the parameter adjuster 116 can adjust (shown as 132 in the example of FIG. 1) one or more parameters of the drilling efficiency calculator 122 until the calculated ROP due to bit wear matches the recorded bit ROP. For example, the parameter adjuster 116 can adjust a mechanical efficiency parameter and repeat ROP calculation(s) due to bit wear until the calculated ROP due to bit wear matches the recorded ROP to provide the mechanical efficiency data 112. The mechanical efficiency data 112 can characterize a value of the mechanical efficiency parameter when the calculated ROP due to bit wear matches the recorded bit ROP. Accordingly, the parameter adjuster 116 can adjust one or more drilling efficiency calculator parameters until the predicted ROP matches the recorded ROP. Drill bit mechanical efficiency is a parameter that varies with different bit types. It may also vary in different formations. Based on the well-based ROP analysis, as disclosed herein, mechanical efficiencies of different bit types can be determined. This data can be used for ROP model generation, such as the ROP model 108.

In some examples, increasing a WOB (applied to the drill bit over a drilling distance) leads to an increase in the ROP, which can indicate that the drill bit is more efficiently removing rock. In some examples, increasing the WOB does not lead to an increase in the ROP, which can limit drilling performance, and thus there can be an adverse impact of WOB on the ROP over a drilling distance as WOB is increased. In some examples, the parameter adjuster 116 can take into account the adverse impact of the WOB on the ROP by modifying a WOB parameter used for predicting the ROP due to bit wear. For example, the parameter adjuster 116 can determine whether the recorded ROP increases with the WOB over the drilling distance and the flounder point. The parameter adjuster 116 can modify a WOB parameter used for providing the ROP due to bit wear in response to determining that the recorded ROP does not increase with the WOB over the drilling distance (or a new drilling distance) based on the ROP field data 124. As such, the parameter adjuster 116 can adjust (or modify) the WOB parameter (e.g., of expression (17)) until a predicted ROP matches the recorded ROP.

The bit wear predictor 118 can provide a prediction of dull grade corresponding to the bit wear model 114 based on the well data 120 using (or employing) expressions of the drilling efficiency calculator 122 (e.g., by invoking the calculator 122 for relevant data calculations). In some examples, the bit wear predictor 118 can implement bit wear prediction functionality as disclosed in U.S. patent application Ser. No. 17/810,208, filed June 2022, and incorporated herein by reference in its entirety. For example, the bit wear predictor 118 can predict dull grade for the specified bit type. In some examples, the specified bit type is a type of Polycrystalline Diamond Compact (PDC) bit. For example, the bit wear predictor 118 can receive the bit type data 132 and provide a dull grade prediction for the bit type as specified by the bit type data 132. In some examples, another module (or block) as shown in FIG. 1 can provide data identifying the bit type. For the bit type, the bit wear prediction 118 can compute a corresponding bit wear model 114.

For example, to predict bit wear, the bit wear predictor 118 can calculate an average bit dull grade from both inner and outer rows of cutters of a drill bit based on one or more bit parameters of the well data 120. For example, the one or more parameters can include average dull grades (values) for the inner (I) and outer (O) rows of cutters. I is the average dull grade for the inner rows of cutters, and O is average dull grade for the outer rows of cutters. The bit wear predictor 118 can determine the average bit dull grade based on the average dull grades for the inner (I) and outer (O) rows of cutters.

The bit wear predictor 118 can estimate a downhole WOB using surface WOB according to expression (6). For example, the bit wear predictor 118 can employ expression (6) implemented by the drilling efficiency calculator 122 to estimate the downhole WOB based on the one or more parameters of the well data 120. In some examples, the bit wear predictor 118 can receive RPM data. The well data 120 can include a surface RPM and a rotary speed of a rotary steerable system (RSS) or downhole motor if it is rotating, in some instances. The bit predictor 118 can use the RPM data for bit wear prediction. For example, the RPM data can be used to populate parameter N in expressions (19) and (21) above. The bit wear predictor 118 can calculate a rock grain size using CGR logs (from the well data 120), or use another rock grain size log, if available, employing expression (18) implemented by the drilling efficiency calculator 122. The bit wear predictor 14 can calculate confined compressive strength (ξ_c) using ξ_u, ψ, wellbore (well) pressure, pore pressure and in-situ stresses (σ_n) (from the geomechanical data 128) employing expression (12) implemented by the drilling efficiency calculator 122. For example, in-situ stresses can be factored in the σ_n in expression (11), wherein σ_n is a stress in the direction of drilling. In-situ stresses are three stresses in the vertical and horizontal directions. With the direction of the well, σ_n can be calculated from the three in-situ stresses.

The bit wear predictor 118 can calculate bit run parameters based on a starting depth and end depth for one or more drill bits, which can be provided from field data, in some instances, can be part of the bit parameters of the well data 120. The bit run parameters can include, for example, but not limited to, an average grain size, ξ_c, V_q, ϕ_t, η, W and N for each bit run based on a starting depth and end depth for the drill bit. The starting depth can represent a depth at which a drilling process begins with a specific drill bit. The end depth can represent a depth at which the drilling process with a particular drill bit is completed. It is typically the point where the drill bit is pulled out of the wellbore, and the drilling with that specific bit is finished. The bit wear predictor 118 can normalize bit running hours and average the bit run parameters with mean values of the parameters in all bit runs and all wells analyzed. The bit wear predictor 118 can calculate a logarithm of the normalized parameters and a logarithm of the average dull grade of each bit run. The bit wear predictor 118 can perform multi-linear regression for all the parameters in the logarithm calculation with the logarithm of the average dull grade as Y and the logarithm of all other parameters on the right-hand side of expression (21) as X. The bit wear predictor 118 can create (or assemble) the bit wear model 114 (corresponding to expression (21)) with correlation coefficients (e.g., parameters in expression (21), f₃, a, b, k, l, m, n, o, and d) derived from the multi-linear regression. The rock abrasiveness and bit wear for new drill bits (e.g., PDC bits) in a same reservoir of a same field can be predicted using bit wear models calculated according to the examples disclosed herein. The predicted rock abrasiveness and bit wear can be used for 3D ROP prediction (e.g., for new bits), as disclosed herein. The predicted rock abrasiveness and bit wear can be used in the 3D ROP prediction to account for bit wear effect (of a new bit) on ROP.

The model generator 126 can use one or more bit wear models (for one or more respective bits) provided as the bit wear model 114, the mechanical efficiency data 112 (e.g., for each bit type) to provide the ROP model 108, and the geomechanical data 128. In some examples, the ROP model 108 provided by the model generator 126 is a ROP prediction in 3D space and provides ROP predictions in a 3D volume of the one or more formations (e.g., the rock). The ROP prediction in the 3D space allows for identification of new well paths and well planning to be adjusted to target higher ROP regions and layers according to the examples disclosed herein.

In some examples, the model generator 126 can provide the drilling performance model 130 based on the ROP model 108 and the geomechanical data 128. For example, to generate drilling performance model 130, the model generator 126 can construct a 3D geomechanical model based on formation properties (or data) using the geomechanical data 128 and the well data 120. The 3D geomechanical model can include a 3D distribution of the formation properties. The formation properties can include, but not limited to, pore pressure, in-situ stresses, UCS, friction angle, total porosity, effective porosity, volume of quartz, water saturation, spectral gamma ray. Relevant values for the formation properties can be extracted from the well data 120 and the geomechanical data 128. The model generator 126 can assign constant values to the parameters of mud weight, weight on bit. RPM, bit running hours, bit size, coefficient of sliding friction, mechanical efficiency, total nozzle flow area, friction coefficient between drill pipe and wellbore wall, Skempton pore pressure coefficient and vertical drilling direction. The model generator 126 can calculate CCS based on an input of UCS, pore pressure, well pressure (from mud weight) and the vertical stress using (or employing) expression (12) of the drilling efficiency calculator 122 (e.g., by invoking the calculator 122 to execute the expression (12) with relevant input parameter data provided by the model generator 126).

The model generator 126 can predict ROP considering mechanical and hydraulic energy by employing expression (15) of the drilling efficiency calculator 122 using the mechanical efficiency data 112 for a given (e.g., specific) bit type. This ROP predicted based on the mechanical efficiency data 112 can be equivalent to that can be produced by a new bit, and thus can be referred to as new bit ROP. In some examples, the model generator 126 can predict dull grade (e.g., providing an indication of bit wear) for the given bit type using the bit wear model 114 provided by the bit wear predictor 118, assuming a given bit running hour. The model generator 126 can predict ROP considering bit wear by employing expression (16) of the drilling efficiency calculator 122, and this predicted ROP can be referred to as a worn bit ROP. The model generator 126 can construct the drilling performance model 130 with each location on a well path (or outside the well path) with a corresponding ROP prediction, which can include new bit ROP and/or worn bit ROP computed according to the examples disclosed herein. As disclosed herein, the drilling performance model 130 can be used for well (or wellbore) trajectory placement (or planning) to optimize ROP.

In some examples, the model generator 126 can provide a geomechanical model representing the formations based on the geomechanical data 128. Each formation can be formed from one or more sub-formations, which can be referred to as formation sections. The formation sections can include vertical and/or horizontal formation sections. The model generator 126 can combine the geomechanical model with the ROP model 108 to provide the drilling performance model 130. For example, the model generator 126 can assign (e.g., logical link) each formation section of the geomechanical model a (predicted) ROP value, which can be provided according to one or more examples disclosed herein. For example, ROP values can be predicted using the gcomechanical data and drilling parameters, as explained above. The prediction can be in 3D, the vertical cross sections and horizontal cross sections can be used for visualizing a distribution of the predicted ROP values. By visualizing ROP in the cross-sections, wellbores can be planned in higher ROP regions. In some examples, the ROP model 108 can be provided with computed ROP (according to the examples disclosed herein) with formation section location information that can be used for assigning a corresponding computed ROP to a given formation section or formation sections of the geomechanical model. Accordingly, in some examples, the model generator 126 can combine the ROP model 108 and the geomechanical model (of the geomechanical data 128) to provide the drilling performance model 130 with a ROP assigned to each formation section.

Well (Or Wellbore) Trajectory Planner

FIG. 2 is an example of a well (or wellbore) trajectory planner 200 that can be used for ROP optimization. The well trajectory planner 200 can be implemented (e.g., executed) on a computing device, such as the computing device 102, as shown in FIG. 1. Thus, reference can be made to the example of FIG. 1 in the example of FIG. 2. The well trajectory planner 200 can receive the drilling performance model 130, which can be generated according to the examples disclosed herein. The well trajectory planner 200 includes a well trajectory integrator 202 that can import or include an initial well (wellbore) trajectory into the drilling performance model 130. The initial well trajectory can be representative of a horizontal well (wellbore) trajectory that has been initially planned (e.g., by a user, or a different system) as intersecting one or more regions (or zones) where formation properties indicate a presence of a hydrocarbon (e.g., oil, gas, etc.).

The well trajectory integrator 202 can receive well trajectory data 204 characterizing the initial well trajectory and process this data with respect to the drilling performance model 130 to provide a trajectory model 206, which can correspond to a version of the drilling performance model 130 having one or more well trajectories therein. The well trajectory planner 200 includes a formation analyzer 208 that can analyze the trajectory model 206 to identify candidate formation layers from the one or more formation layers of the trajectory model 206. For example, the formation analyzer 208 can inspect a variation of ROP in a vertical cross section intersecting the initial wellbore to identify candidate formation layers. In some examples, the variation of ROP in both vertical and horizontal directions can be visualized (e.g., on a display, for example, as disclosed herein) and a user can identify the candidate formation layers. In some examples, if the ROP along each trajectory is averaged, the candidate formation layers can be identified having a highest average ROP. In some examples, the candidate formation layers can include or correspond to reservoir layers. Thus, the formation analyzer 208 can identify candidate formation layers from the formation layers using a baseline well trajectory inserted in the drilling performance model 130. The candidate formation layers can have a number of candidate formation sections.

The formation analyzer 208 can evaluate the candidate formation layers to identify one or more regions 210 in the trajectory model 206. In some examples, the one or more regions are identified based on user input (e.g., at an input device, for example, as disclosed herein). For example, the user can evaluate variation of ROP values in (or associated with) the candidate formation layers to identify the one or more regions. The identified regions 210 can be provided to the well trajectory integrator 202. The well trajectory integrator 202 can create one or more horizontal well trajectories that intersect the one or more regions 210 associated with the candidate formation layers to provide the trajectory model 206 with the initial (or baseline) well trajectory and the created one or more horizontal well trajectories. The one or more inserted horizontal well trajectories can be referred to as potential (or candidate) well trajectories. Thus, the formation analyzer 208 can identify one or more regions defined by a subset of candidate formation sections of the candidate formation sections in a drilling performance model (the trajectory model 206) that the baseline well trajectory intersects. The well trajectory integrator 202 can insert one or more potential well trajectories into the drilling performance model 130 that intersects the one or more regions. The drilling performance model 130, for example, can consist of a number of grid cells. Each grid cell can have a single value of any parameter in the drilling performance model 130. A region can be a volume with a minimum of one grid cell, but can be consisted of multiple grid cells, in some instances. For example, each grid cell can be assigned (e.g., by the model generator 126) one value for each parameter in the drilling performance model 130. The value can be different in different grid cells, it is also different for different parameters. The value can be distributed in the drilling performance model 130 using measured/interpreted point data (well data) and geostatistical methods. Thus, a volume of material can be discretized by the model generator 126 into a multitude of grid cells. Multiple properties can be populated into the grid cells and each grid cell can be assigned one value for each property by the model generator 126. The discrete values contained in all grid cells are a numerical representation of the continuous medium.

In some examples, a well trajectory selector 212 of the well trajectory planner 200 can receive the trajectory model 206 having the one or more horizontal well trajectories inserted therein. The well trajectory selector 212 can calculate a CCS property for grid cells that are intersected by the proposed wellbores, which can be referred to as intersecting grid cells. The well trajectory selector 212 can calculate new CCS properties associated with each proposed wellbore using an average well inclination and average well azimuth in each intersecting grid cell. The well trajectory selector 212 can compute the CCS property according to the examples disclosed herein. The well trajectory selector 212 can update each ROP prediction for each intersecting grid cell using a new computed CCS property for that intersecting grid cell. The reason for calculating a CCS property and update the ROP in one or more examples described above is because of the expressions (11) and (12). Where CCS is a function of σ_n, and σ_n is a function of the drilling direction or well direction. Thus, the well trajectory selector 212 can update ROP predictions for grid cells associated with each proposed wellbore using the new computed CCS property. As such, the well trajectory selector 212 can calculate an updated CCS for each candidate formation of a subset of candidate formations sections forming the one or more regions. The well trajectory selector 212 can calculate an updated ROP for each candidate formation of the subset of candidate formations based on the updated CCS. A candidate potential well trajectory can be identified based on an evaluation of the updated ROP calculated for each candidate formation of the subset of candidate formations sections, as disclosed herein.

The well trajectory selector 212 can compare the updated ROP predictions and effective porosity logs along the proposed wellbore trajectories and identify a given (or best) proposed well (or wellbore) trajectory along which an updated ROP prediction are the best, which can be referred to as the candidate potential well trajectory. For example, the effective porosity can be a property distributed in the drilling performance model 130. It is therefore available in every grid cell, same as ROP which is predicted. Because ROP indicates drilling performance and effective porosity indicates reservoir quality these two parameters (or values) can be compared. In some examples, the updated ROP predictions and the effective porosity logs are compared by a user. In examples, the well trajectory selector 212 (or the user) can compare the ROP and effective porosity logs along each planned well trajectory, or the average ROP and effective porosity along each trajectory to identify the best proposed wellbore trajectory. The well trajectory selector 212 can provide well trajectory data identifying each candidate potential well trajectory as a selected well (or wellbore) trajectory 214, as shown in FIG. 2.

In some examples, the well trajectory planner 200 includes a visualization engine 216, which can receive the trajectory model 206 (or the drilling performance model 130) and the selected well trajectory 214 and render on an output device 218 (e.g., a display, a computer, a mobile device, a portable device, etc.) the trajectory model 206 with the selected well trajectory 214 identified therein. For example, a unique color can be used to identify each candidate potential well trajectory. In examples in which other proposed wellbore trajectories are identified, these proposed trajectories can have a different color from the candidate well trajectories. In some examples, the well trajectory selector 212 can update the updated trajectory model 206 so that the selected well trajectory 214 is differentiated therein. The updated trajectory model 206 can be provided to the visualization engine 216, or to a different system or application for use therein.

Graphs

FIG. 3 is an example of a graph 300 illustrating ROP predictions based on well data, such as the well data 120, as shown in FIG. 1, for a particular bit type. Thus, reference can be made to one or more examples of FIGS. 1-2 in the example of FIG. 3. In the example of FIG. 3, the ROP predictions can be used for determination of mechanical efficiency (e.g., the mechanical efficiency data 112, as shown FIG. 1) for specific bit types. The graph 300 illustrates relevant data (captured and/or computed over time) in a horizontal well and all the bits used are of a same type and model. From left to right, the eight tracks in the figure display the following parameters: reference depth (Track 1), gamma ray (Track 2), WOB (Track 3), RPM (Track 4), flow rate (Track 5), UCS (Track 6), dull grade (Track 7), the predicted ROP_W (identified as “ROP_W” in FIG. 3), ROP_H (identified as “ROP_H” in FIG. 3) and the recorded ROP (Track 8). By way of example, the mechanical efficiency was estimated to be 0.25 for this type of bit in a respective formation according to the graph 300.

FIG. 4 is an example of a graph 400 illustrating bit dull grade predictions that can be provided according to the examples disclosed herein. For example, the bit dull grade predictions can be provided by the bit wear predictor 118, as shown in FIG. 1. Thus, reference can be made to the example of FIG. 1 in the example of FIG. 4. An x-axis of the graph 400 represents a predicted bit dull grade (identified as “DG_REG” in the example of FIG. 4), and a y-axis of the graph 400 represents a measured dull grade (identified as “DG” in the example of FIG. 4) for a specific bit type and model. Regression parameters can be derived using the graph 400 and used to predict bit dull grade for modeling (e.g., in generation of the ROP model 108 and/or the drilling performance model 130, as shown in FIG. 1).

Exemplary Drilling Performance Model(s)

FIG. 5 is an example of a portion of a drilling performance model 500 illustrating ROP predictions in a reservoir. The drilling performance model 500 can correspond to the drilling performance model 130, as shown in FIGS. 1-2. Thus, reference can be made to one or more examples of FIGS. 1-2 in the example of FIG. 5. The drilling performance model 500 illustrates ROP predictions with a different color shading with a dark color shading indicating a reduced rate of penetration across a number of formation layers (and thus for corresponding formation regions). The predicted ROP compute according to the examples herein, is based on the MSE, hydraulic energy and bit wear. A variation of ROP within a reservoir (e.g., formation regions) can reflect a variation of rock mechanical and reservoir properties.

FIG. 6 is an example of another portion of a drilling performance model 600 with well trajectories 602-606 (e.g., potential well trajectories) inserted according to the examples herein and ROP predictions computed according to the examples herein. In some examples, the drilling performance model 600 can correspond to the drilling performance model 130, as shown in FIGS. 1-2, or the ROP model 500, as shown in FIG. 5. Thus, reference can be made to one or more examples of FIGS. 1-2 and 5 in the example of FIG. 6.

The portion of the drilling performance model 600 is an example of ROP distribution in one horizontal layer 608 and one vertical cross section 610. The horizontal layer 608 includes a number of cells forming a checker pattern therein and can correspond to a region. One or more cells of the horizontal layer 608 can be part of a formation section of one or more horizontal formations. In other examples, the cells can have a different shape. For example, a representative cell or region is shown at 612. Each cell can be assigned a ROP value computed according to the examples disclosed herein. In the example of FIG. 6, the vertical cross section includes a number of formation layers through which each of the well trajectories 902-906. The vertical cross section can be representative of vertical formation layers. Each formation layer in the vertical cross section can be assigned a ROP value computed according to the examples disclosed herein.

The determination of optimized well trajectory can be based on the variation of ROP in both directions. The trajectory with the best ROP can be selected as the optimized well trajectory. In the example of FIG. 6, three well trajectories 602-606 have been inserted according to the examples disclosed herein. As shown in the example of FIG. 6, the well trajectories 602-606 intersect one or more cells of the horizontal layer. For example, the well trajectory 906 intersects cell 908, as shown in FIG. 6. A given one of the well trajectories 602-606 can be identified as the best well trajectory among the well trajectories 602-606 according to the examples disclosed herein. Exemplary Methods

In view of the foregoing structural and functional features described above, example methods will be better appreciated with reference to FIGS. 7-10. While, for purposes of simplicity of explanation, the example methods of FIGS. 7-10 are shown and described as executing serially, it is to be understood and appreciated that the present examples are not limited by the illustrated order, as some actions could in other examples occur in different orders, multiple times and/or concurrently from that shown and described herein. Moreover, it is not necessary that all described actions be performed to implement the methods.

FIG. 7 is an example of a method 700 for computing mechanical efficiency data (e.g., the mechanical efficiency data 112, as shown in FIG. 1). The method 700 can be implemented by the ROP engine 100, as shown in FIG. 1. Thus, reference can be made to one or more examples of FIG. 1 in the example of FIG. 7. The method 700 can begin at 702 by selecting a bit type (e.g., based on bit type data 132, as shown in FIG. 1). At 704, data for computing mechanical efficiency can be received (or prepared). The data can include, for example, the well data 120, the geomechanical data 128, and the ROP field data 124, as shown in FIG. 1. At 706, a CCS can be computed (e.g., by the drilling efficiency calculator 122). At 708, a given (assumed) mechanical efficiency can be selected (or assigned) and a ROP can be calculated (e.g., by the drilling efficiency calculator 122) due to MSE.

At 710, a ROP can be calculated due to MSE and hydraulic energy (e.g., by the drilling efficiency calculator 122) using the ROP calculated due to MSE. At 712, a ROP can be calculated due to bit wear (e.g., by the drilling efficiency calculator 122) using the ROP calculated due to MSE and hydraulic energy, which can be referred to as a bit wear ROP. At 714, a determination can be made (e.g., by the parameter adjuster 116, as shown in FIG. 1) to determine whether the bit wear ROP increases with (measured) WOB. The method 700 can proceed (as indicated with an “N” in the example of FIG. 7) to step 716 in response to determining that the bit wear ROP does not increase with WOB. In some examples, the method 700 can proceed (as indicated with a “Y” in the example of FIG. 7) to step 718 in response to determining that the bit wear ROP does increase with WOB. A WOB parameter (of the drilling efficiency calculator 122) can be modified (e.g., by the parameter adjuster 116, as shown in FIG. 1) and the method 700 can proceed to step 718.

At step 718, a determination can be made (e.g., by the parameter adjuster 116) to determine whether the bit wear ROP matches a recorded ROP (e.g., based on the ROP field data 124, as shown in FIG. 1). The method 700 can proceed (indicated with a “N” in the example of FIG. 7) back to step 708 in response to a determination being made that the bit wear ROP does not match the recorded ROP. At step 708, the mechanical efficiency parameter can be adjusted and the method 700 can proceed through steps 710 to 718 for another determination. The method 700 can proceed (indicated with a “Y” in the example of FIG. 7) to step 720 in response to determining that the bit wear ROP matches the recorded ROP. At step 720, the mechanical efficiency data can be outputted (e.g., by the parameter adjuster 116) characterizing a value of the mechanical efficiency parameter when there was a match.

FIG. 8 is an example of a method for generating a bit wear model, such as the bit wear model 114, as shown in FIG. 1. The method 800 can be implemented by the ROP engine 100, as shown in FIG. 1. For example, at least some of the method 800 can be implemented by the bit wear predictor 118, as shown in FIG. 1. Thus, reference can be made to one or more examples of FIG. 1 in the example of FIG. 8. The method 800 can begin at 802 by classifying (e.g., by the bit wear predictor 118) drill bits (e.g., PDC bits) by bit type and manufacturer. At 802, a determination can be made (e.g., by the bit wear predictor 118) to determine whether classified drill bits are similar (or same) bit types. The method 800 can proceed (as indicated with a “No” in the example of FIGS. 8) to 806 in response to determining that the classified drill bits are not same bit types. At 806, a separate study can be conducted. As the analysis (the method 800) is done for a specific bit type, if a bit is a different type, it will not be included in the analysis. If there are enough data for that bit type, the same analysis following step 808 can be done for that bit type as well according to one or more examples disclosed herein. The method 800 can proceed (as indicated with a “Yes” in the example of FIG. 8) to step 808.

At step 808, data for determining bit wear and abrasiveness can be received (or prepared) by the ROP engine 100. The data can include, for example, the well data 120, the geomechanical data 128, and the ROP field data 124, as shown in FIG. 1. At 810, an average bit dull grade from both inner and outer cutters can be determined (e.g., by the bit wear predictor 118). At 814, bit running hours can be retrieved or selected from the data (e.g., by the bit wear predictor 118). At 816, downhole WOB and RPM (for both a surface RPM and rotary speed of an RSS, or downhole motor if it is rotating) can be estimated, as disclosed herein. At 818, a CCS can be calculated (e.g., by the bit wear predictor 118) according to the examples herein. At 820, an average grain size, CCS, total porosity, quartz volume, and water saturation can be calculated (e.g., by the bit wear predictor 118). At 822, values for parameters from steps 816-820 in each bit run are averaged (e.g., by the bit wear predictor 118). At 824, the bit running hours and average values from step 822 can be normalized by a mean value of all bit runs (e.g., by the bit wear predictor 118). At 826, multi-linear regression can be performed (e.g., by the bit wear predictor 118) using normalized values from step 824 and the average bit dull grade computed from step 812 to provide a bit wear model (e.g., the bit wear model 114, as shown in FIG. 1). In some examples, at step 826, the rock abrasiveness and bit wear can be predicted using the bit wear model.

FIG. 9 is an example of a method 900 for generating a ROP model, such as the ROP model 108, as shown in FIG. 1. The method 900 can be implemented by the ROP engine 100, for example, by the model generator 126 of the ROP engine 100, as shown in FIG. 1. Thus, reference can be made to one or more examples of FIG. 1 in the example of FIG. 9. The method 900 can begin at 902 by receiving (e.g., at the model generator 126) a 3D geomechanical model, which can be provided as or as part of geomechanical data, such as the geomechanical data 128, as shown in FIG. 1. At 904, constant values can be assigned (e.g., by the model generator 126) to drilling parameters. The drilling parameters and other data can include for example, but not limited to, mud weight, weight on bit, RPM, bit running hours, bit size, coefficient of sliding friction, mechanical efficiency, total nozzle flow area, friction coefficient between drill pipe and wellbore wall, Skempton pore pressure coefficient and vertical drilling direction. At 906, a CCS can be calculated (e.g., by the model generator 126) based on formation (or rock) mechanical properties. The formation mechanical properties and other data can include, but not limited to, UCS, pore pressure, well pressure (from mud weight) and vertical stress. For example, the CCS can be calculated according to expression (16), as disclosed herein.

At 908, a ROP can be predicted (e.g., by the model generator 126) due MSE and hydraulic energy using mechanical efficiency data (e.g., the mechanical efficiency data 112, as shown in FIG. 1). In some examples, the mechanical efficiency data can be provided or generated according to the method 700, as shown in FIG. 7. Thus, reference can also be made to the example of FIG. 7 in the example of FIG. 9. At 910, a dull grade for a given bit type can be predicted (e.g., by the model generator 126) using a bit wear model (e.g., the bit wear model 114, as shown in FIG. 1). In some examples, the bit wear model is provided or generated according to the method 800, as shown in FIG. 8. Thus, reference can also be made to the example of FIG. 8 in the example of FIG. 9. At 912, ROP considering bit wear can be predicted (e.g., by the model generator 126) based on the dull grade from step 910. The model generator 126 can predict ROP considering bit wear by employing expression (16) of the drilling efficiency calculator 122. In some examples, at 914, the ROP model (e.g., the ROP model 108, as shown in FIG. 1) can be provided using the predicted ROP due MSE and hydraulic energy and/or the predicted ROP due to bit wear.

FIG. 10 is an example of a method 1000 for ROP optimization. The method 1000 can be implemented by the well trajectory planner 200, as shown in FIG. 2. Thus, reference can be made to one or more examples of FIGS. 1-2 in the example of FIG. 10. The method 1000 can begin at 1002 by importing (or integrating) (e.g., by the well trajectory integrator 202, as shown in FIG. 2) initial well trajectory data (e.g., the well trajectory data 204, as shown in FIG. 2) characterizing an initial well trajectory into a drilling performance model (e.g., the drilling performance model 130, as shown FIGS. 1-2) to provide a trajectory model (e.g., the trajectory model 206, as shown in FIG. 2). At 1004, identifying (or selecting) (e.g., by the formation analyzer 208, as shown in FIG. 2) candidate formation layers. In some examples, the candidate formation layers can include or correspond to reservoir layers. At 1006, identifying (or selecting) (e.g., by the formation analyzer 208, as shown in FIG. 2) one or more regions in trajectory model 206 associated with the candidate formation layers.

At 1008, well (or wellbore) trajectories (e.g., horizontal well trajectories) can be created (e., by the well trajectory integrator 202) that intersect the one or more regions. At 1010, CCS properties can be calculated (e.g., by the drilling efficiency calculator 122, as shown in FIG. 1, or the well trajectory selector 212, as shown in FIG. 2) for the well trajectories that intersect the one or more regions. At 1010, well directions can be used as well. For example, well directions can be made available from a well trajectory plan. A well trajectory can be defined by a measured depth, a deviation angle and an azimuth angle. At any point in the trajectory, these values are available. CCS can be calculated at step 1010 based on the well direction. At 1012, a ROP due to MSE and hydraulic energy, and/or a ROP due to bit wear can be calculated (e.g., by the drilling efficiency calculator 122 or the well trajectory selector 212) according to the example disclosed herein. At 1014, (e.g., by the well trajectory selector 212) ROP and effective porosity logs along with the created (or proposed) wellbore trajectories can be compared. At 1016, a well trajectory (e.g., the selected well trajectory 214, as shown in FIG. 2) can be identified (e.g., by the well trajectory selector 212) from the created well trajectories based on a result of the comparison at step 1014.

Further Computer-Implemented Embodiments and Example Implementations

Various embodiments (including the ROP engine 100, as shown in FIG. 1, and the well trajectory planner 200, as shown in FIG. 2 can be implemented on one or more computing devices. The computing devices may be at the same or different locations. A computing device can be any type of device having one or more processors and memory, for example, the computing device 102. as shown in FIG. 1. For example, a computing device can be a workstation, mobile device (e.g., a mobile phone, personal digital assistant, tablet or laptop), computer, server, computer cluster, server farm, game console, set-top box, kiosk, embedded system, or other device having at least one processor and computer-readable memory. In addition to at least one processor and memory, such a computing device may include software, firmware, hardware, or a combination thereof. Software may include one or more applications and an operating system. Hardware can include, but is not limited to, a processor, memory and user interface display or other input/output device.

In view of the foregoing structural and functional description, those skilled in the art will appreciate that portions of the embodiments may be embodied as a method, data processing system. or computer program product. Accordingly, these portions of the present embodiments may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware, such as shown and described with respect to the computer system of FIG. 11. Furthermore, portions of the embodiments may be a computer program product on a computer-usable storage medium having computer readable program code on the medium. Any non-transitory, tangible storage media possessing structure may be utilized including, but not limited to, static and dynamic storage devices, hard disks, optical storage devices, and magnetic storage devices, but excludes any medium that is not eligible for patent protection under 35 U.S.C. § 101 (such as a propagating electrical or electromagnetic signal per se). As an example and not by way of limitation, a computer-readable storage media may include a semiconductor-based circuit or device or other IC (such, as for example, a field-programmable gate array (FPGA) or an ASIC), a hard disk, an HDD, a hybrid hard drive (HHD), an optical disc, an optical disc drive (ODD), a magneto-optical disc, a magneto-optical drive, a floppy disk, a floppy disk drive (FDD), magnetic tape, a holographic storage medium, a solid-state drive (SSD), a RAM-drive, a SECURE DIGITAL card, a SECURE DIGITAL drive, or another suitable computer-readable storage medium or a combination of two or more of these, where appropriate. A computer-readable non-transitory storage medium may be volatile, nonvolatile, or a combination of volatile and non-volatile, where appropriate.

In this regard, FIG. 11 illustrates one example of a computer system 1100 that can be employed to execute one or more embodiments of the present disclosure. Computer system 1100 can be implemented on one or more general purpose networked computer systems, embedded computer systems, routers, switches, server devices, client devices, various intermediate devices/nodes or standalone computer systems. Additionally, computer system 1100 can be implemented on various mobile clients such as, for example, a personal digital assistant (PDA), laptop computer, pager, and the like, provided it includes sufficient processing capabilities.

Computer system 1100 includes processing unit 1102, system memory 1104, and system bus 1106 that couples various system components, including the system memory 1104, to processing unit 1102. Dual microprocessors and other multi-processor architectures also can be used as processing unit 1102. System bus 1106 may be any of several types of bus structure including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. System memory 1104 includes read only memory (ROM) 1110 and random access memory (RAM) 1112. A basic input/output system (BIOS) 1114 can reside in ROM 1110 containing the basic routines that help to transfer information among elements within computer system 1100.

Computer system 1100 can include a hard disk drive 1116, magnetic disk drive 1118, e.g., to read from or write to removable disk 1120, and an optical disk drive 1122, e.g., for reading CD-ROM disk 1124 or to read from or write to other optical media. Hard disk drive 1116, magnetic disk drive 1118, and optical disk drive 1122 are connected to system bus 1106 by a hard disk drive interface 1126, a magnetic disk drive interface 1128, and an optical drive interface 1130, respectively. The drives and associated computer-readable media provide nonvolatile storage of data, data structures, and computer-executable instructions for computer system 1100. Although the description of computer-readable media above refers to a hard disk, a removable magnetic disk and a CD, other types of media that are readable by a computer, such as magnetic cassettes, flash memory cards, digital video disks and the like, in a variety of forms, may also be used in the operating environment; further, any such media may contain computer-executable instructions for implementing one or more parts of embodiments shown and described herein.

A number of program modules may be stored in drives and RAM 1110, including operating system 1132, one or more application programs 1134, other program modules 1136, and program data 1138. In some examples, the application programs 1134 can include the ROP engine 100, as shown in FIG. 1, and/or the well trajectory planner 200, as shown in FIG. 1. The application programs 1134 can include functions and methods disclosed according to the examples described herein.

A user may enter commands and information into computer system 1100 through one or more input devices 1140, such as a pointing device (e.g., a mouse, touch screen), keyboard, microphone, joystick, game pad, scanner, and the like. These and other input devices are often connected to processing unit 1102 through a corresponding port interface 1142 that is coupled to the system bus, but may be connected by other interfaces, such as a parallel port, serial port, or universal serial bus (USB). One or more output devices 1144 (e.g., display, a monitor, printer, projector, or other type of displaying device) is also connected to system bus 1106 via interface 1146, such as a video adapter.

Computer system 1100 may operate in a networked environment using logical connections to one or more remote computers, such as remote computer 1148. Remote computer 1148 may be a workstation, computer system, router, peer device, or other common network node, and typically includes many or all the elements described relative to computer system 1100. The logical connections, schematically indicated at 1150, can include a local area network (LAN) and a wide area network (WAN). When used in a LAN networking environment, computer system 1100 can be connected to the local network through a network interface or adapter 1152. When used in a WAN networking environment, computer system 1100 can include a modem, or can be connected to a communications server on the LAN. The modem, which may be internal or external, can be connected to system bus 1106 via an appropriate port interface. In a networked environment, application programs 1134 or program data 1138 depicted relative to computer system 1100, or portions thereof, may be stored in a remote memory storage device 1154.

Although this disclosure includes a detailed description on a computing platform and/or computer, implementation of the teachings recited herein are not limited to only such computing platforms. Rather, embodiments of the present disclosure are capable of being implemented in conjunction with any other type of computing environment now known or later developed.

Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models (e.g., software as a service (SaaS, platform as a service (PaaS), and/or infrastructure as a service (IaaS)) and at least four deployment models (e.g., private cloud, community cloud, public cloud, and/or hybrid cloud). A cloud computing environment can be service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability.

FIG. 12 is an example of a cloud computing environment 1200 that can be used for implementing one or more modules and/or systems in accordance with one or more examples, as disclosed herein. Thus, reference can be made to one or more examples of FIGS. 1-11 in the example of FIG. 12. As shown, cloud computing environment 1200 can include one or more cloud computing nodes 1202 with which local computing devices used by cloud consumers (or users), such as, for example, personal digital assistant (PDA), cellular, or portable device 1204, a desktop computer 1206, and/or a laptop computer 1208, may communicate. The computing nodes 1202 can communicate with one another. In some examples, the computing nodes 1202 can be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds, or a combination thereof. This allows the cloud computing environment 1200 to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. The devices 1204-1208 are intended to be illustrative and that computing nodes 1202 and cloud computing environment 1200 can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser). In some examples, the one or more computing nodes 1202 are used for implementing one or more examples disclosed herein for processing and computing data. Thus, in some examples, the one or more computing nodes can be used to implement modules, platforms, and/or systems, as disclosed herein.

In some examples, the cloud computing environment 1200 can provide one or more functional abstraction layers. It is understood that the cloud computing environment 1200 need not provide all of the one or more functional abstraction layers (and corresponding functions and/or components), as disclosed herein. For example, the cloud computing environment 1200 can provide a hardware and software layer that can include hardware and software components. Examples of hardware components include: mainframes; RISC (Reduced Instruction Set Computer) architecture based servers; servers; blade servers; storage devices; and networks and networking components. In some embodiments, software components include network application server software and database software.

In some examples, the cloud computing environment 1200 can provide a virtualization layer that provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers; virtual storage; virtual networks, including virtual private networks; virtual applications and operating systems; and virtual clients. In some examples, the cloud computing environment 1200 can provide a management layer that can provide the functions described below. For example, the management layer can provide resource provisioning that can provide dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. The management layer can also provide metering and pricing to provide cost tracking as resources are utilized within the cloud computing environment 1200, and billing or invoicing for consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. The management layer can also provide a user portal that provides access to the cloud computing environment 1200 for consumers and system administrators. The management layer can also provide service level management, which can provide cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment can also be provided to provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA.

In some examples, the cloud computing environment 1200 can provide a workloads layer that provides examples of functionality for which the cloud computing environment 1200 may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation; software development and lifecycle management; virtual classroom education delivery; data analytics processing; and transaction processing. Various embodiments of the present disclosure can utilize the cloud computing environment 1200.

The present disclosure is also directed to the following exemplary embodiments:

Embodiment 1: a computer-implemented method comprising: computing, by a processor, a mechanical efficiency for a drill bit; computing, by the processor, a bit wear model representing drill bit wear of the drill bit; and generating, by the processor, a ROP model representing a rate at which the drill bit will penetrate one or more formation layers based on the mechanical efficiency and the bit wear model.

Embodiment 2: the computer-implemented method of embodiment 1, wherein said computing comprises: predicting, by the processor, a first ROP due to an MSE for the drill bit; predicting, by the processor, a second ROP due to MSE and hydraulic energy using the first ROP for the drill bit; and predicting, by the processor, a third ROP due to bit wear using the second ROP for the drill bit, the third ROP being used for computing the mechanical efficiency.

Embodiment 3: the computer-implemented method of embodiment 2, further comprising deciding, by the processor, whether the third ROP equals a recorded ROP representative of ROP due to bit wear on the drill bit over a drilling distance.

Embodiment 4: the computer-implemented method of embodiment 3, wherein said deciding comprises a determining, by the processor, whether the recorded ROP increases with a WOB indicative of an amount weight applied to the drill bit over the drilling distance.

Embodiment 5: the computer-implemented method of embodiment 4, further comprising: modifying, by the processor, a WOB parameter used for predicting the third ROP in response to determining that the recorded ROP does not increase with the WOB over the drilling distance; and repeating, by the processor, the predicting of the third ROP and the deciding steps until the third ROP matches the recorded ROP over a given drill distance.

Embodiment 6: the computer-implemented method of any of the embodiments 1-5, further comprising generating, by the processor, a geomechanical model representing the one or more formations.

Embodiment 7: the computer-implemented method of embodiment 6, wherein said generating the ROP model comprises: computing, by the processor, a CCS for the one or more formations in the geomechanical model, wherein the CCS is computed for a number of sections or intervals of each formation; and predicting, by the processor, a ROP due to MSE and hydraulic energy using a computed CCS for each formation section in the geomechanical model, wherein the ROP due to MSE and hydraulic energy is representative of a ROP produced by a new version of the drill bit through a respective formation section.

Embodiment 8: the computer-implemented method of embodiment 7, wherein the ROP model is generated based on the ROP computed for each formation section in the geomechanical model.

Embodiment 9: the computer-implemented method of any of the embodiments 6-8, wherein said generating the ROP model further comprises: predicting, by the processor, a bit dull grade using the bit wear model for each formation in the geomechanical model, wherein the bit dull grade is predicted for a number of sections or intervals of each formation; and predicting, by the processor, a ROP due to bit wear using the predicted bit dull grade for each formation section in the geomechanical model, wherein the ROP due to bit wear is representative of a ROP produced by a worn version of the drill bit through a respective formation section.

Embodiment 10: the computer-implemented method of embodiment 9, wherein the ROP model is generated based on the ROP due to bit wear computed for each formation section in the geomechanical model.

Embodiment 11: the computer-implemented method of any of the embodiments 1-10, further comprising combining, by the processor, the geomechanical model and the ROP model to provide a drilling performance model with a ROP for formation sections of the geomechanical model.

Embodiment 12: the computer-implemented method of embodiment 11, further comprising outputting, by the processor, well trajectory data identifying a potential well trajectory through the drilling performance model.

Embodiment 13: the computer-implemented method of embodiment 12, wherein said outputting comprises: identifying, by the processor, candidate formation layers from the one or more formation layers using a baseline well trajectory inserted in the drilling performance model, the candidate formation layers having candidate formation sections; identifying, by the processor, one or more regions defined by a subset of candidate formation sections of the candidate formation sections in the drilling performance model that the baseline well trajectory intersects; inserting, by the processor, one or more potential well trajectories into the drilling performance model that intersects the one or more regions; and identifying, by the processor, a candidate potential well trajectory from the one or more potential well trajectories.

Embodiment 14: the computer-implemented method of embodiment 13, further comprising: calculating, by the processor, an updated CCS for each candidate formation of the subset of candidate formations sections forming the one or more regions; and calculating, by the processor, an updated ROP for each candidate formation of the subset of candidate formations based on the updated CCS, the candidate potential well trajectory being identified based on an evaluation of the updated ROP calculated for each candidate formation of the subset of candidate formations sections.

Embodiment 15: the computer-implemented method of any of the embodiments 1-14, further comprising evaluating, by the processor, an effective porosity and for each candidate formation of the subset of candidate formations sections along the one or more potential well trajectories to identify the candidate potential well trajectory, wherein the well trajectory data is provided in response to the evaluating.

Embodiment 16: a system comprising: memory to store machine-readable instructions; one or more processors to access the memory and execute the machine-readable instructions, the machine-readable instructions causing the processor to: identify one or more regions defined by formation sections that a baseline well trajectory intersects in a drilling performance model, wherein the drilling performance model is generated based on an ROP model, the ROP model being generated based on a mechanical efficiency for a drill bit, and a bit wear model representing drill bit wear of the drill bit; insert potential well trajectories into the drilling performance model that intersects one or more regions of the drilling performance model; and output well trajectory data identifying a candidate well trajectory of the inserted potential well trajectories for drilling by the drill bit.

Embodiment 17: the system of embodiment 16 further comprising an output device, the machine-readable instructions further causing the processor to output the drilling performance model on the output device with the candidate trajectory well based on the well trajectory data.

Embodiment 18: the system of any of the embodiments 15-16, wherein the machine-readable instructions further cause the processor to combine a geomechanical model representing one or more formations and the ROP model to provide the drilling performance model with a ROP for formation sections of the geomechanical model.

Embodiment 19: a computer-implemented method comprising: generating, by the processor, a ROP model representing a rate at which the drill bit will penetrate one or more formation layers based on a precomputed mechanical efficiency and bit wear model; receiving, by the processor, a geomechanical model representing the one or more formations combining, by the processor, the geomechanical model and the ROP model to provide a drilling performance model with a ROP for the one or more formations; and outputting, by the processor, well trajectory data identifying a well trajectory through the drilling performance model representative of a potential trajectory through the one or more formations.

Embodiment 20: the computer-implemented method of embodiment 19: wherein said outputting comprises: identifying, by the processor, candidate formation layers from the one or more formation layers using a baseline well trajectory inserted in the drilling performance model, the candidate formation layers having candidate formation sections; identifying, by the processor, one or more regions defined by a subset of candidate formation sections of the candidate formation sections in the drilling performance model that the baseline well trajectory intersects; inserting, by the processor, one or more candidate well trajectories into the drilling performance model that intersects the one or more regions; and identifying, by the processor, the well trajectory from the one or more candidate well trajectories.

The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire.

Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device.

Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention.

Certain embodiments have also been described herein with reference to block illustrations of methods, systems, and computer program products. It will be understood that blocks of the illustrations, and combinations of blocks in the illustrations, can be implemented by computer-executable instructions. These computer-executable instructions may be provided to one or more processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus (or a combination of devices and circuits) to produce a machine, such that the instructions, which execute via the processor, implement the functions specified in the block or blocks.

These computer-executable instructions may also be stored in computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory result in an article of manufacture including instructions which implement the function specified in the flowchart block or blocks. The computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks.

These computer readable program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks.

The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions.

The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, for example, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “contains”, “containing”, “includes”, “including,” “comprises”, and/or “comprising,” and variations thereof, when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. In addition, the use of ordinal numbers (e.g., first, second, third, etc.) is for distinction and not counting. For example, the use of “third” does not imply there must be a corresponding “first” or “second.” Also, as used herein, the terms “coupled” or “coupled to” or “connected” or “connected to” or “attached” or “attached to” may indicate establishing either a direct or indirect connection, and is not limited to either unless expressly referenced as such. Furthermore, to the extent that the terms “includes,” “has,” “possesses,” and the like are used in the detailed description, claims, appendices and drawings such terms are intended to be inclusive in a manner similar to the term “comprising” as “comprising” is interpreted when employed as a transitional word in a claim. The term “based on” means “based at least in part on.” The terms “about” and “approximately” can be used to include any numerical value that can vary without changing the basic function of that value. When used with a range, “about” and “approximately” also disclose the range defined by the absolute values of the two endpoints, e.g. “about 2 to about 4” also discloses the range “from 2 to 4.” Generally, the terms “about” and “approximately” may refer to plus or minus 5-10% of the indicated number.

What has been described above include mere examples of systems, computer program products and computer-implemented methods. It is, of course, not possible to describe every conceivable combination of components, products and/or computer-implemented methods for purposes of describing this disclosure, but one of ordinary skill in the art can recognize that many further combinations and permutations of this disclosure are possible. The descriptions of the various embodiments have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A computer implemented method comprising: computing, by a processor, a mechanical efficiency for a drill bit;computing, by the processor, a bit wear model representing drill bit wear of the drill bit; andgenerating, by the processor, a rate of penetration (ROP) model representing a rate at which the drill bit will penetrate one or more formation layers based on the mechanical efficiency and the bit wear model.

2. The computer implemented method of claim 1, wherein said computing comprises: predicting, by the processor, a first rate of penetration (ROP) due to mechanical specific energy (MSE) for the drill bit;predicting, by the processor, a second ROP due to MSE and hydraulic energy using the first ROP for the drill bit; andpredicting, by the processor, a third ROP due to bit wear using the second ROP for the drill bit, the third ROP being used for computing the mechanical efficiency.

3. The computer implemented method of claim 2, further comprising deciding, by the processor, whether the third ROP equals a recorded ROP representative of ROP due to bit wear on the drill bit over a drilling distance.

4. The computer implemented method of claim 3, wherein said deciding comprises a determining, by the processor, whether the recorded ROP increases with a weight on bit (WOB) indicative of an amount weight applied to the drill bit over the drilling distance.

5. The computer implemented method of claim 4, further comprising: modifying, by the processor, a WOB parameter used for predicting the third ROP in response to determining that the recorded ROP does not increase with the WOB over the drilling distance; andrepeating, by the processor, the predicting of the third ROP and the deciding steps until the third ROP matches the recorded ROP over a given drill distance.

6. The computer implemented method of claim 1, further comprising generating, by the processor, a geomechanical model representing the one or more formations.

7. The computer implemented method of claim 6, wherein said generating the ROP model comprises: computing, by the processor, a confined compressive strength (CCS) for the one or more formations in the geomechanical model, wherein the CCS is computed for a number of sections or intervals of each formation; andpredicting, by the processor, a ROP due to mechanical specific energy (MSE) and hydraulic energy using a computed CCS for each formation section in the geomechanical model, wherein the ROP due to MSE and hydraulic energy is representative of a ROP produced by a new version of the drill bit through a respective formation section.

8. The computer implemented method of claim 7, wherein the ROP model is generated based on the ROP computed for each formation section in the geomechanical model.

9. The computer implemented method of claim 6, wherein said generating the ROP model further comprises: predicting, by the processor, a bit dull grade using the bit wear model for each formation in the geomechanical model, wherein the bit dull grade is predicted for a number of sections or intervals of each formation; andpredicting, by the processor, a ROP due to bit wear using the predicted bit dull grade for each formation section in the geomechanical model, wherein the ROP due to bit wear is representative of a ROP produced by a worn version of the drill bit through a respective formation section.

10. The computer implemented method of claim 9, wherein the ROP model is generated based on the ROP due to bit wear computed for each formation section in the geomechanical model.

11. The computer implemented method of claim 6, further comprising combining, by the processor, the geomechanical model and the ROP model to provide a drilling performance model with a ROP for formation sections of the geomechanical model.

12. The computer implemented method of claim 11, further comprising outputting, by the processor, well trajectory data identifying a potential well trajectory through the drilling performance model.

13. The computer-implemented method of claim 12, wherein said outputting comprises: identifying, by the processor, candidate formation layers from the one or more formation layers using a baseline well trajectory inserted in the drilling performance model, the candidate formation layers having candidate formation sections;identifying, by the processor, one or more regions defined by a subset of candidate formation sections of the candidate formation sections in the drilling performance model that the baseline well trajectory intersects;inserting, by the processor, one or more potential well trajectories into the drilling performance model that intersects the one or more regions; andidentifying, by the processor, a candidate potential well trajectory from the one or more potential well trajectories.

14. The computer-implemented method of claim 13, further comprising: calculating, by the processor, an updated confined compressive strength (CCS) for each candidate formation of the subset of candidate formations sections forming the one or more regions; andcalculating, by the processor, an updated ROP for each candidate formation of the subset of candidate formations based on the updated CCS, the candidate potential well trajectory being identified based on an evaluation of the updated ROP calculated for each candidate formation of the subset of candidate formations sections.

15. The computer implemented method of claim 1, further comprising evaluating, by the processor, an effective porosity and for each candidate formation of the subset of candidate formations sections along the one or more potential well trajectories to identify the candidate potential well trajectory, wherein the well trajectory data is provided in response to the evaluating.

16. A system comprising: memory to store machine-readable instructions;one or more processors to access the memory and execute the machine-readable instructions, the machine-readable instructions causing the processor to: identify one or more regions defined by formation sections that a baseline well trajectory intersects in a drilling performance model, wherein the drilling performance model is generated based on a rate of penetration (ROP) model, the ROP model being generated based on a mechanical efficiency for a drill bit, and a bit wear model representing drill bit wear of the drill bit;insert potential well trajectories into the drilling performance model that intersects one or more regions of the drilling performance model; andoutput well trajectory data identifying a candidate well trajectory of the inserted potential well trajectories for drilling by the drill bit.

17. The system of claim 16, further comprising an output device, the machine-readable instructions further causing the processor to output the drilling performance model on the output device with the candidate trajectory well based on the well trajectory data.

18. The system of claim 16, wherein the machine-readable instructions further cause the processor to combine a geomechanical model representing one or more formations and the ROP model to provide the drilling performance model with a ROP for formation sections of the geomechanical model.

19. A computer-implemented method comprising: generating, by the processor, a rate of penetration (ROP) model representing a rate at which the drill bit will penetrate one or more formation layers based on a precomputed mechanical efficiency and bit wear model;receiving, by the processor, a geomechanical model representing the one or more formations;combining, by the processor, the geomechanical model and the ROP model to provide a drilling performance model with a ROP for the one or more formations; andoutputting, by the processor, well trajectory data identifying a well trajectory through the drilling performance model representative of a potential trajectory through the one or more formations.

20. The computer-implemented method of claim 19, wherein said outputting comprises: identifying, by the processor, candidate formation layers from the one or more formation layers using a baseline well trajectory inserted in the drilling performance model, the candidate formation layers having candidate formation sections;identifying, by the processor, one or more regions defined by a subset of candidate formation sections of the candidate formation sections in the drilling performance model that the baseline well trajectory intersects;inserting, by the processor, one or more candidate well trajectories into the drilling performance model that intersects the one or more regions; andidentifying, by the processor, the well trajectory from the one or more candidate well trajectories.