CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims priority under 35 U.S.C. § 119 (e) to U.S. Provisional Application No. 63/508,326, entitled “ROP OPTIMIZATION,” by Varadaraju GANDIKOTA et al., filed Jun. 15, 2023, which is assigned to the current assignee hereof and incorporated herein by reference in its entirety.

FIELD OF THE DISCLOSURE

The present invention relates, in general, to the field of drilling and processing of wells. More particularly, present embodiments relate to a system and method for optimizing rate of penetration (ROP) of a drill bit during subterranean operations.

BACKGROUND

Optimum rate of penetration (ROP) is commonly predicted based on minimizing Mechanical Specific Energy (MSE). This method does not appear to provide clear insight of the drilling behavior. Because driving inefficiencies are omitted when calculating MSE, significant errors in determining an optimum ROP will occur when its calculation is based on the MSE method. Therefore, improvements in methods and systems for determining an optimum ROP are continually needed.

SUMMARY

This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify indispensable features of the claimed subject matter, nor is it intended for use as an aid in limiting the scope of the claimed subject matter.

A system of one or more computers can be configured to perform particular operations or actions by virtue of having software, firmware, hardware, or a combination of them installed on the system that in operation causes or cause the system to perform the actions. One or more computer programs can be configured to perform particular operations or actions by virtue of including instructions that, when executed by data processing apparatus, cause the apparatus to perform the actions. One general aspect includes a method of optimizing a rate of penetration (ROP) in real-time in a subterranean operation. The method also includes determining, via a rock strength simulator, an equivalent confined compressive rock strength (ECCRS) profile along a future wellbore; receiving the ECCRS profile at an ROP optimizer; receiving physical parameters of a bottom hole assembly (BHA) at the ROP optimizer; and simulating in real-time, via the ROP optimizer, a simulated ROP of a drill bit of the BHA through a portion of a subterranean formation based on the ECCRS profile, the physical parameters of the BHA, and drilling parameters of a rig. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

Implementations may include one or more of the following features. The method where the ROP optimizer is a physics-based model. The future wellbore is defined by the well plan. The method may include varying the simulated ROP of the drill bit by adjusting one or more of the drilling parameters; and determining an optimum simulated ROP by comparing various simulated ROPs. The method selecting, via the rock strength simulator, one or more previously drilled wellbores from a rock strength database. Simulating the simulated ROP may include simulating a plurality of ROP simulations; ranking, via a ranking engine, each of the plurality of ROP simulations; and selecting, via the ROP optimizer, from the plurality of ROP simulations the simulated ROP with a highest ranking from the ranking engine. The method may include receiving a well plan for the future wellbore at the ROP optimizer; and simulating the simulated ROP based on the well plan. The method may include predicting, via the ROP optimizer, an ROP along the future wellbore prior to drilling the future wellbore and during drilling of the future wellbore. Implementations of the described techniques may include hardware, a method or process, or computer software on a computer-accessible medium.

One general aspect includes a system for optimizing a rate of penetration (ROP) in real-time in a subterranean operation. The system also includes a rig; a tubular string extending from the rig into a subterranean formation, where the tubular string may include a bottom hole assembly (BHA) with a drill bit; and a rig controller configured to: determine, via a rock strength simulator, an equivalent confined compressive rock strength (ECCRS) profile along a future wellbore; receive the ECCRS profile at an ROP optimizer of the rig controller; receive physical parameters of the bottom hole assembly (BHA) at the ROP optimizer; and simulate in real-time, via the ROP optimizer, a simulated ROP of the drill bit of the BHA through a portion of the subterranean formation based on the ECCRS profile, the physical parameters of the BHA, and drilling parameters of the rig. Other embodiments of this aspect include corresponding computer systems, apparatus, and computer programs recorded on one or more computer storage devices, each configured to perform the actions of the methods.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of present embodiments will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein:

FIG. 1 is a representative view of a rig used to perform subterranean operations, in accordance with certain embodiments;

FIG. 2 is a representative partial cross-section view of a rig used to perform subterranean operations, in accordance with certain embodiments;

FIG. 3 is a representative partial cross-section view of wellbore being drilled using a bottom hole assembly (BHA), in accordance with certain embodiments;

FIG. 4 is a representative functional block diagram of a rig controller that can control rig equipment of the rig 10 and perform methods of the current disclosure (e.g., ROP optimization), in accordance with certain embodiments;

FIG. 5 is a representative flow diagram of a method for determining an equivalent confined compressive rock strength (ECCRS) profile of a future wellbore, in accordance with certain embodiments; and

FIG. 6 is a representative flow diagram of a method for predicting a real-time optimized rate of penetration (ROP) for a rig (or drill bit) drilling a future wellbore, in accordance with certain embodiments.

DETAILED DESCRIPTION

The following description in combination with the figures is provided to assist in understanding the teachings disclosed herein. The following discussion will focus on specific implementations and embodiments of the teachings. This focus is provided to assist in describing the teachings and should not be interpreted as a limitation on the scope or applicability of the teachings.

As used herein, the terms “comprises,” “comprising,” “includes,” “including,” “has,” “having,” or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of features is not necessarily limited only to those features but may include other features not expressly listed or inherent to such process, method, article, or apparatus. Further, unless expressly stated to the contrary, “or” refers to an inclusive-or and not to an exclusive-or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

The use of “a” or “an” is employed to describe elements and components described herein. This is done merely for convenience and to give a general sense of the scope of the invention. This description should be read to include one or at least one and the singular also includes the plural, or vice versa, unless it is clear that it is meant otherwise.

The use of the word “about”, “approximately”, “generally”, or “substantially” is intended to mean that a value of a parameter is close to a stated value or position. However, minor differences may prevent the values or positions from being exactly as stated. Thus, differences of up to ten percent (10%) for the value are reasonable differences from the ideal goal of exactly as described. A significant difference can be when the difference is greater than ten percent (10%).

As used herein, “tubular” refers to an elongated cylindrical tube and can include any of the tubulars manipulated around a rig, such as tubular segments, tubular stands, tubulars, and tubular string, but not limited to the tubulars shown in FIG. 1. Therefore, in this disclosure, “tubular” is synonymous with “tubular segment,” “tubular stand,” and “tubular string,” as well as “pipe,” “pipe segment,” “pipe stand,” “pipe string,” “casing,” “casing segment,” or “casing string.”

FIG. 1 is a representative view of a rig 10 at a rig site 11 that can be used to perform subterranean operations, in accordance with certain embodiments. The rig 10 is shown as an offshore rig, but it should be understood that the principles of this disclosure are equally applicable to onshore rigs as well. The example rig 10 can include a platform 12 with a derrick 14 extending above the platform 12 from the rig floor 16. The platform 12 and derrick 14 provide the general super structure of the rig 10 from which the rig equipment is supported. The rig 10 can include a horizontal storage area 38, pipe handlers 30, 32, 34, a drill floor robot 26, an iron roughneck 40, a crane 20, fingerboard storage 36, and a plurality of sensors 70 distributed at various locations on the rig 10. The sensors 70 can be any type of sensors that can detect various characteristics of the subterranean operation being performed by the rig 10.

The sensors 70 can be two dimensional (2D) cameras, three dimensional (3D) cameras, infrared cameras, closed circuit television (CCTV) cameras, X-ray sensors, light detection and ranging (LiDAR) sensors, proximity sensors, strain gauges, torque sensors, accelerometers, optical sensors, laser sensors, physical contact sensors, contact sensors with encoders, audio sensors, pressure sensors, temperature sensors, environmental sensors, gas sensors, liquid sensors, or other suitable sensors for detecting characteristics of the rig environment or rig operations. The sensors 70, as well as other rig environment on the rig 10, can be communicatively coupled to a rig controller 150 via a network 154, with the network 154 being wired or wirelessly connected to the sensors 70 or rig environment.

The sensors 70 can be disposed on stationary locations (such as on or above the horizontal storage area 38, at various points along the fingerboard storage 36, on the derrick 14, on the platform 12, etc.). The sensors 70 can also be disposed on robotic equipment, such as the drill floor robot 26, the iron roughneck 40, the pipe handlers 30, 32, 34, a top drive 18 (see FIG. 2), and the crane 20. Some of the tubulars that can be used during subterranean operations is shown in the horizontal storage area 38 and the fingerboard storage 36, such as the tools 52, the bottom hole assembly (BHA) 60, and the tubulars 54. The tools 52 can include centralizers, subs, slips, subs with sensors, adapters, etc. The BHA 60 can include drill collars 62, mud motor 64, instrumentation, and a drill bit 68 (see FIG. 2).

FIG. 2 is a representative partial cross-sectional front view of a rig 10 at a rig site 11 being used to drill a wellbore 15 in a subterranean formation 8, in accordance with certain embodiments. FIG. 1 shows a land-based rig 10 located on a surface 6, but the principles of this disclosure can equally apply to off-shore rigs, as well, where “off-shore” refers to a rig with water between the rig floor and the earth surface 6. Rig 10 can include a top drive 18 with a drawworks 44, sheaves 19, traveling block 28, anchor 47, and reel 48 used to raise or lower the top drive 18 via drilling cable 46. A derrick 14 extending from the rig floor 16, can provide the structural support of the rig equipment for performing subterranean operations (e.g., drilling, treating, completing, producing, testing, etc.).

The rig can be used to extend a wellbore 15 through the subterranean formation 8 by using a tubular string 58 having a bottom hole assembly (BHA) 60 at its lower end. The BHA 60 can include a drill bit 68 and multiple drill collars 62, with one or more of the drill collars including one or more sensors 70 or one or more tools 69 for Logging While Drilling (LWD) or Measuring While Drilling (MWD) operations. During drilling operations, drilling mud can be pumped from the surface 6 into the tubular string 58 (e.g., via pumps 84 supplying mud to the top drive 18 via the standpipe 86) to cool and lubricate the drill bit 68 and to transport cuttings to the surface via an annulus 17 between the tubular string 58 and the wellbore 15.

The returned mud can be directed to the mud pit 88 from a rotating control device 66, through the flow line 81, to the shaker 80. A fluid treatment 82 can inject additives as desired to the mud to condition the mud appropriately for the current well activities and possibly future well activities as the mud is being pumped to the mud pit 88. Pump 84 can pull mud from the mud pit 88 and drive it to the top drive 18, via standpipe 86, to continue circulation of the mud through the tubular string 58.

The tubular string 58 can extend into the wellbore 15, with the wellbore 15 extending through the surface 6 into the subterranean formation 8. With a segmented tubular string 58, when tripping the tubular string 58 into the wellbore 15, tubulars 54 are sequentially added to the tubular string 58, e.g., via a top drive 18 and slips 92 (at well center 24) that corporate together to extend the length of the tubular string 58 into the subterranean formation 8. When the tubular string 58 is a wireline or coiled tubing, the tubular string 58 can be uncoiled from a spool and extended into the wellbore 15. With a segmented tubular string 58, when tripping the tubular string 58 out of the wellbore 15, tubulars 54 are sequentially removed from the tubular string 58 to reduce the length of the tubular string 58 extending into the subterranean formation 8. With a wireline or coiled tubing, the tubular string 58 can be coiled onto a spool when being pulled out of the wellbore 15.

The wellbore 15 can have a casing string 76 installed in the wellbore 15 and extending down to a casing shoe 78. The portion of the wellbore 15 with the casing string 76 installed, can be referred to as a cased wellbore. The portion of the wellbore 15 below the shoe 78, without casing, can be referred to as an “uncased” or “open hole” wellbore. The wellbore 15 can be extended by rotating the drill bit 68 and cutting into the earthen formation 8. The rate at which the drill bit 68 progresses into the subterranean formation 8 can be referred to as a rate of penetration (ROP). Many factors affect the ROP of the drill bit 68 and these factors can be adjusted to control ROP.

A rig controller 150 can be used to control rig operations including controlling various rig equipment, such as a pipe handler, the top drive 18, an iron roughneck, fingerboard equipment, imaging systems, various other robots on the rig 10 (e.g., a drill floor robot), or rig power systems 158. The rig controller 150 can control the rig equipment autonomously (e.g., without periodic operator interaction,), semi-autonomously (e.g., with limited operator interaction such as initiating a subterranean operation, adjusting parameters during the operation, etc.), or manually (e.g., with the operator interactively controlling the rig equipment via remote control interfaces to perform the subterranean operation).

The rig controller 150 can include one or more processors with one or more of the processors distributed about the rig 10, such as in an operator's control hut, in a pipe handler, in an iron roughneck, in a vertical storage area, in the imaging systems, in various other robots, in the top drive 18, at various locations on the rig floor 16 or the derrick 14 or the platform 12, at a remote location off of the rig 10, at downhole locations, etc. It should be understood that any of these processors can perform control or calculations locally or can communicate to a remotely located processor for performing the control or calculations. Each of the processors can be communicatively coupled to a non-transitory memory, which can include instructions for the respective processor to read and execute to implement the desired control functions or other methods described in this disclosure. These processors can be coupled via a wired or wireless network.

The rig controller 150 can collect data from various data sources around the rig and downhole (e.g., sensor data via mud pulse telemetry, EM telemetry, etc.) and from remote data sources (e.g., suppliers, manufacturers, transporters, company men, remote rig reports, etc.) to monitor and facilitate the execution of the subterranean operation and control ROP during drilling operations.

During subterranean operations, such as drilling, various logging operations are generally performed to collect and store sensor data for later processing to provide visualization of parameters and characteristics of the wellbore and its surroundings. The processing can be performed by the rig controller 150 during the subterranean operation or after the subterranean operation is complete. A tool 110 can be included in the BHA 60 (or otherwise included in the tubular string 58) for performing logging or measuring operations at various times during the operation, or during the operation. Tool 110 can have a longitudinal center axis, which can correspond to the longitudinal center axis 50 of an internal bore of the BHA 60 (or tubular 54). Some of the logging/measuring operations can be to collect downhole sensor data of the wellbore 15 while the tubular string 58 is being rotated (such as for drilling, reaming, etc.). The downhole sensor data can be communicated to the surface via various telemetry methods that can be detected at the surface and decoded to retrieve the sensor data.

FIG. 3 is a representative partial cross-section view of a wellbore 15 being drilled using a bottom hole assembly (BHA) 60, in accordance with certain embodiments. A tubular string 58 can be used to further extend the wellbore 15 by rotating the drill bit 68, which can be done by either driving the mud motor 64 without rotating the tubular string 58, rotating the tubular string 58 without driving the mud motor 64, or rotating both the mud motor 64 and the tubular string 58. When rotating the drill bit 68 (arrows 90), the tubular string 58 can be lowered to engage the drill bit 68 with the bottom 74 of the wellbore 15 and to increase weight on bit (WOB).

Drilling fluid can flow down through the tubular string 58 to exit the drill bit 68 and travel back to the surface via the annulus 17. As a desired WOB is applied to the drill bit 68 and the drill bit 68 is rotated (with drilling fluid flowing from the tubular string 58 into the annulus 17), the drill bit 68 can progress along a path at a rate (e.g., distance/time).

The rate that the drill bit progresses along the path can be referred to as a rate of penetration (ROP) of the drill bit 68. The ROP represents the rate of progression of the drill bit 68 along the path that extends the wellbore 15 further into the subterranean formation 8. ROP can be used to determine an estimated amount of time the rig 10 may remain at the rig site 11 to drill the wellbore 15 to a desired target depth (TD).

For example, with a desired WOB, a desired RPM of the drill bit 68, and a desired flow rate of the drilling fluid, the drill bit 68 can advance from a bottom 74 of the wellbore 15 to a new bottom 74′ of the wellbore 15, where the drill bit 68 travels along a distance L2 in a time period T. Therefore, the ROP can be calculated as the distance L2 divided by the time period T (ROP=L2/T). Calculating the actual ROP of the wellbore 15 can provide valuable feedback to well planning for future wellbores or the remainder of the current wellbore 15. The drill bit RPM can be determined by adding the surface RPM (or rotational speed of the tubular string 58) to a calculated drill bit RPM that indicates the rotation of the drill bit 68 relative to the tubular string 58, such as via a mud motor 64. The calculated drill bit RPM can be determined by the flow rate of fluid into the tubular string 58 and a differential pressure across the mud motor 64, which can be determined from surface (or near surface) sensors 70 or downhole sensors 70.

It may be desirable to predict a future ROP of the drill bit 68 (or rig 10) and optimize the ROP, for example, by maximizing performance while maintaining optimal drilling health. Real time ROP predictions can be based on actual operating parameters such as WOB, calculated drill bit RPM, drilling fluid flow rates, differential pressure across the mud motor 64, and a calculated (or simulated) Equivalent Confined Compressive Rock Strength (ECCRS) or an estimated Confined Compressive Rock Strength (CCRS). A physics-based model (e.g., an unsteady-state physics model or a fast running time domain analysis model), can predict ROP while providing insight into dysfunctions like vibrations, stick-slip, whirl, factors that may affect MSE (e.g., RPM, WOB, or wellbore friction of the tubular string 58, fluid pressure, etc.), bit stall, etc. While an ROP optimizer (e.g., the physics-based model) simulates drilling the wellbore 15 through the subterranean formation, the simulation can detect when some of these dysfunctions occur in the simulation. This information can be used to adjust various drilling parameters to minimize (or eliminate) the dysfunctions. When the best recipe of parameters are determined that minimizes dysfunctions and maximizes ROP, the recipe of parameters can then be used by the rig to advance the wellbore 15 further into the subterranean formation 8. The real time ROP predictions and associated parameters can be provided to an operator of the rig 10 or to the rig controller 150 for control of the rig 10 (e.g., automated control, semi-automated control, or manual control of the rig 10).

FIG. 4 is a representative functional block diagram of a rig controller 150 that can control rig equipment of the rig 10 and perform methods of the current disclosure (e.g., ROP optimization), in accordance with certain embodiments. The rig controller 150 can include one or more local or remote processing units 160 that can be locally or remotely positioned relative to the rig 10 or downhole. Each processing unit 160 can include one or more processors 162 (e.g., microprocessors, programmable logic arrays, programmable logic devices, etc.), non-transitory memory storage devices 164, peripheral interface 166, human machine interface (HMI) device(s) 168, and possibly a remote telemetry interface 165 for internet communication or satellite network communication. The HMI devices 168 can include a touchscreen, a laptop, a desktop computer, a workstation, or wearables (e.g., smart phone, smart watch, tablet, etc.). These components of the rig controller 150 can be communicatively coupled together via one or more networks 154, which can be wired or wireless networks.

The processors 162 can be configured to read instructions from one or more non-transitory memory storage devices 164 and execute those instructions to perform any of the operations described in this disclosure. A peripheral interface 166 can be used by the rig controller 150 to receive sensor data from around the rig 10 or downhole which can collect data on the rig operations being performed. The peripheral interface 166 can also be used by the rig controller 150 to send commands to personnel or rig equipment to control rig operations during a subterranean operation. The rig controller 150 can receive a well plan 163 via the network 154 (or peripheral interface 166) and can determine a rig state based on the well plan 163 and data from the sensors 70 and from parameter information from the HMI devices 168 (such as WOB, etc.).

The rig controller 150 can include a rock strength database 169 that can store historical rock strength data from previously drilled wellbores. The historical rock strength data can include the condensed compressed rock strength (CCRS) values as a function of depth for previously drilled offset wellbores that are similar to the subterranean formation 8 through which the future wellbore 15 is planned to be drilled or is being drilled. The historical data can also include the rig equipment and recipes used to drill the offset wellbores, the actual ROP as a function of depth of the offset wellbore, and the drilling parameters used to drill the offset wellbore.

This historical rock strength data can be used by a rock strength simulator 172 (e.g., a statistical model, a real-time simulator, a physics-based real-time simulator, etc.) of the rig controller 150 to determine an equivalent confined compressive rock strength (ECCRS) profile for the future wellbore 15 (see FIG. 5). The ECCRS can be stored in one or more non-transitory memory storage devices 164 for retrieval as needed during operations. An ROP optimizer 170 of the rig controller 150 can use the ECCRS profile and various characteristics of the drilling operation to predict a real-time ROP of the drill bit 68 before or during drilling operations (see FIG. 6).

With the ECCRS and the estimated drilling parameters (e.g., differential pressure, WOB, hook load, top drive RPM, depth, drill bit properties, fluid flow rates, etc.), the ROP optimizer 170 can calculate (or simulate) an expected ROP as a function of depth for at least a portion of the future wellbore 15. This expected ROP can be updated as portions of the future wellbore 15 are drilled and the actual ROP for those portions is known, which can then be used to update parameters of the rock strength simulator 172 and the ROP optimizer 170 to align the results of these simulators 172, 170 with the actual values.

The rock strength simulator 172 can determine the ECCRS from the historical rock strength data from offset wellbores (e.g., historical rock strength data stored in the rock strength database 169). This can be done using a statistical model to collect information from offset wellbores that are similar to the rock layer configuration of the portion of the subterranean formation 8 through which the future wellbore 15 is to be drilled or is being drilled and then calculate the ECCRS profile for the future wellbore 15. The ECCRS profile can be adjusted as actual drilling data is collected during drilling of the future wellbore 15.

Alternatively, or in addition to, the rock strength simulator 172 can determine the ECCRS from real-time parameter data (e.g., sensor data from sensors 70, drilling parameters from the HMI devices 168, actual ROP, etc.). When using historical data, the simulator has the luxury of time to calibrate, edit, update, and process the historical data to determine the ECCRS. However, for real-time simulations based on real-time data from the rig or other data sources, there is limited time to make decisions on the data and to filter out anomalies.

For the real-time simulations to determine ECCRS for a portion of the future wellbore 15, the rock strength simulator 172 can receive parameter data from the data sources (e.g., the rig, the rig equipment, the sensors 70, the HMI devices, vendor data, etc.) from a previously drilled portion of the future wellbore 15 to calculated ECCRS for a portion of the future wellbore 15 to be drilled. The rock strength simulator 172 can use standard minimization techniques (e.g., least squares approach or linear regression approach) to minimize errors in the real-time data. The rock strength simulator 172 can then determine the ECCRS for at least a portion of the future wellbore 15 to be drilled.

As described in this disclosure, the ROP optimizer 170 can use the ECCRS for determining an estimated ROP as a function of depth for drilling a future portion of the future wellbore 15. Also, with the ECCRS established for the future portion, the ROP optimizer 170 can run a plurality of ROP simulations to determine the sensitivity of the ROP to various parameters (e.g., WOB, hook load, top drive RPM, differential pressure, etc.) and determine the best recipe of parameters to be used for the drilling operation for the future portion to provide an optimum ROP.

The rock strength simulator 172 can, based on real-time parameter data received for the current a drilling operation, determine the ECCRS in real-time using the following equation (1):

ECCRS
⁡
(
realtime
)

=

2
⁢
W
⁢
O
⁢
B

D
b

(

D
⁢
O
⁢
C
*
z

+

L
f

)

Eq
.

(
1
)

Where ECCRS (realtime) is the real-time results from the rock strength simulator 172 based on the real-time data, WOB refers to weight on bit, Db refers to a drill bit diameter, DOC refers to depth of cut of the drill bit 68, “z” refers to a zeta parameter and Lf refers to a flat length parameter which are constraints dependent on geometries of the drill bit 68. This equation can be used to determine ECCRS in real-time, without having historical rock strength data from offset wellbores to validate the ECCRS.

However, the rock strength simulator 172 can also use historical rock strength data to validate real-time data and identify errors in the real-time data during the real-time simulations for determining ECCRS. The historical rock strength data from one or more offset wellbores (e.g., from the historical rock strength database 169) can be used to compare with predicted ECCRS values as a function of depth to identify any potential errors in the real-time parameter data as well as unexpected changes in the rock formations the rig 10 can be drilling through. With the historical rock strength data, the rock strength simulator 172 can continue to validate and update the estimated ECCRS.

The condensed compressive rock strength (CCRS) for an offset wellbore can be determined using historical parameter data from the offset wellbore by solving Equation (2) below for “x”.

f
⁡
(
x
)

=

A
⁡
(

a
⁢
x

+
b

)

⁢

e

-
β

⁢
x

+

B
⁢
x

+
C

=
0

Eq
.

(
2
)

Where “A,” “B,” and “C” are defined by the following equations (3), (4), (5).

A
=

α
.

a
0

⁢

R
⁢
P
⁢

M
.
W

⁢
O
⁢
B

D
b

.
ROP

Eq
.

(
3
)

B
=

a
.
W

⁢
O
⁢
B

A
B

Eq
.

(
4
)

C
=

b
.
W

⁢
O
⁢
B

A
b

Eq
.

(
5
)

Where, “x” represents the CCRS, “ROP” represents a rate of penetration of the drill bit 68, “RPM” represents an angular velocity of the drill bit 68, “WOB” represents weight on the drill bit 68, “Ab” represents cross-section wellbore area, “Db” represents a diameter of the drill bit 68, “p” represents drilling mud density, “d_cut” represents a diameter of the cuttings, and the remaining variables and coefficients are defined below in equations (6).

a
0

=

1
⁢

3
.
3

⁢

3
/

(

10
⁢
π

)

Eq
.

(
6
)

λ
=

-

1
.
0

⁢
144
⁢

ln
⁢

ρ

+

8
.
1

⁢
386

a
=

(

1
.
3

⁢
7
⁢
7
⁢
9
⁢
E

-
9

)

⁢
λ

b
=

0.
1132
⁢
λ

β
=

1.
1
⁢
6
⁢
0
⁢
3
⁢
E

-
9

α
=

0.
9
⁢
4
⁢
0
⁢
2
⁢

(

-

0
.
8

⁢
876
⁢

ln
⁢

ρ

+

7
.
2

⁢
4
⁢
6
⁢
1

)

⁢

(

1
⁢

7
.
7

⁢

d
cut

+

0
.
6

⁢
6
⁢
3
⁢
7

)

The calculated CCRS can be used to validate and verify the estimated ECCRS values from the rock strength simulator 172.

For example, if the estimated ECCRS values for a certain depth are unacceptably different from the historical rock strength values for the same depth, then the rock strength simulator 172 can flag the estimated ECCRS values as being suspect and can run various simulations with various adjusted parameters to recreate substantially equal values to the historical rock strength values. Rock strength simulator 172 can log actual ECCRS values as a function of depth as well as the deviations of the estimated ECCRS values from the actual ECCRS values.

The ROP optimizer can simulate the interaction of the drill bit 68 with the rock of the subterranean formation 8 having the estimated rock strength properties (i.e., ECCRS) to determine an estimated ROP. By adjusting drilling parameters (e.g., differential pressure, WOB, hook load, top drive RPM, depth, drill bit properties, fluid flow rates, etc.) the simulated interaction of the drill bit with the rock can be changed to improve or optimize the estimated ROP. By simulating, via the ROP optimizer 170, the interaction of the drill bit with the subterranean formation 8, the ROP optimizer can detect dysfunctions caused by the drill bit interaction (e.g., vibrations, stick-slip, whirl, stall, bit bounce, etc.). Therefore, the ROP optimizer 170 can run several iterations of simulations for predicting ROP for a portion of the future wellbore 15 to determine which drilling parameters minimize dysfunctions and maximize ROP.

A ranking engine 174 can be used to rank (or score) the results of each of a plurality of ROP simulations performed by the ROP optimizer 170 (either run in parallel or serially) to establish a ranking for each of the plurality of the ROP simulations relative to each other. The ROP optimizer can use this ranking to select the optimum ROP for the rig 10. When the optimum ROP is identified (or selected) by the ROP optimizer 170, the ROP optimizer 170 can communicate the desired drilling parameters to the rig 10 or rig controller 150, which can use the desired drilling parameters to drill the portion of the future wellbore 15. The ROP optimizer 170 can compare the estimated ROP to the actual ROP for the portion of the future wellbore 15 and adjust the drilling parameters if the comparison indicates an unacceptable amount of deviation of the actual ROP from the estimated ROP.

FIG. 5 is a representative flow diagram of a method 200 for determining an equivalent confined compressive rock strength (ECCRS) profile of a future wellbore 15, in accordance with certain embodiments. The method 200 can begin at operation 202, where the rig controller 150 (or a module of the rig controller 150) begins the process of determining an estimated confined compressive rock strength (ECCRS) for the roadmap of a future wellbore 15 to be drilled by the rig 10. The confined compressive rock strength is a parameter that can be used to calculate or predict an ROP for the rig 10 extending a wellbore 15 through the subterranean formation 8, because it can be used to simulate and predict the interaction of a drill bit with the rock in the subterranean formation 8. The roadmap (or planned wellbore trajectory defined by a well plan) of the future wellbore 15 can indicate a strata of the subterranean formation 8 with one or more layers of material (or rock) through which the wellbore 15 is to be extended. The confined compressive rock strength can be used to model an interaction of the drill bit 68 with the subterranean formation 8 and determine a predicted ROP value for each type of material (or rock) in the strata based on the confined compressive rock strength and various other drilling parameters.

In operation 204, the rig controller 150 can sort through the historical rock strength data from previously drilled wellbores that can be stored in the rock strength database 169. The rig controller 150 can identify the material or rock type at each depth of the future wellbore 15 based on the well plan 163 and develop a rock type profile for the future wellbore 15 based on neighborhood wellbores with similarities to the future (or new) wellbore 15, as in operation 206.

A rock strength simulator 172 can be used to identify the neighborhood wellbores and associated rock strength data from the database 169, if historical rock strength data offset wellbore data is available. However, it is not required that historical rock strength data be available to determine ECCRS for portions of the future wellbore 15. As described above, the rock strength simulator 172 can determine an ECCRS profile without historical rock strength data. The rock strength simulator 172 can also use the historical rock strength data to validate the ECCRS profile values.

In operation 208, with the rock strength simulator 172 can determine the ECCRS profile based on real-time data from rig data sources, the rock strength simulator 172 can query the rock strength database 169 to determine appropriate rock strength values for the strata through which the future wellbore 15 will be drilled and calculate an equivalent confined compressive rock strength (ECCRS) for the material in the strata.

In the case where there is little to no historical rock strength data available from offset wellbores, the rock strength simulator 172 can calculate the ECCRS as a function of depth based on real-time parameter data received from the data sources of the rig 10. If historical rock strength data is available, then the rock strength simulator 172 can use the historical data to validate the ECCRS values determined from the real-time rock strength simulations. The real-time simulations of the rock strength simulator 172 is described in more detail above with regard to FIG. 4.

In operation 210, the ECCRS values can be verified or validated to filter out anomalies or errors detected when comparing to the historical data and ensure that the values are viable when used in the ROP optimizer 170. In operation 212, once the values are validated, the rock strength simulator 172 can develop a profile of ECCRS values versus depth of the future wellbore 15 or at least a portion of the future wellbore 15. In operation 214, the ECCRS can be provided to the ROP optimizer 170 (e.g., a physics-based ROP model) for performing a physics-based model simulation to predict ROP along at least a portion of the future wellbore 15.

The ECCRS profile can be modified during real-time ROP optimization by the ROP optimizer 170, as needed (e.g., drill bit 68 enters a rock layer earlier than expected, the drill bit exits a rock layer earlier than expected, a different rock layer is encountered than expected, etc.), but usually the ECCRS profile remains generally unchanged after the rock strength simulator 172 provides it to the ROP optimizer 170. However, with the real-time simulations of the rock strength simulator 172, the ECCRS values can change in real-time as desired while the future wellbore 15 is being drilled.

FIG. 6 is a representative flow diagram of a method 300 for predicting a real-time optimized ROP for a rig 10 (or drill bit 68) drilling a future wellbore 15 (or at least a future portion of a current wellbore 15), in accordance with certain embodiments.

The ROP optimizer is a physics-based model and does not need to be taught like a machine learning model. When using a machine learning model, to provide meaningful results, a training dataset is used to train the machine learning model. After training, the machine learning module can provide results based on the inputs provided. However, a physics-based model does not require training to interpret the data inputs. The physics-based model (or ROP optimizer 170) simulates the interaction of the drill bit 68 with the strata based on physical parameters of the system. The ROP optimizer 170 can also adjust various physical parameters to detect the sensitivity of the ROP predictions based on the physical parameters.

In the ROP optimizer 170 (e.g., physics-based model, or transient dynamics model, or time domain models, etc.) the BHA can be discretized coarsely as rigid and flexible beam elements interconnected via viscoelastic connections. Any beam element will theoretically undergo an arbitrary rigid body motion and a small elastic deformation. Modeling identifies active contact forces such as between the BHA 60 and wellbore 15 and the drill bit 68 and the rock of the strata. This enables the realistic evaluation of BHA 60 dynamics, critical deformations and failure modes. The interaction is modeled with discrete contact, normally and tangentially, accounting for geometry variation. The dynamic effects of fluids on the string are reduced to buoyancy forces modeled as additional masses and frequency-dependent external damping.

Flexible beams can be used for modeling the BHA 60 sections of uniform geometry and density (uniform sections). Equations of motions of beams can be generated on the basis of analytical solutions. The uniform sections are connected in the assembly with viscous-elastic force elements of high stiffness.

As long as the flexibility and damping of the pipes are considered with flexible beam models, the values of coupling element parameters (e.g., stiffness constants for three linear and angular directions, and corresponding damping parameters) can be theoretically infinite. The finite values of the parameters are optimized to provide acceptable results with minimal calculation time.

In operation 310, the ROP optimizer 170 (e.g., physics-based model) can receive a well plan 163 from operation 302, the ECCRS profile from operation 304 (e.g., the ECCRS profile from the method 200, FIG. 5), characteristics of the BHA 60 from operation 306, and parameter data from various sensors 70 around the rig 10 or the HMI devices 168 (such as WOB, hook load, etc.) from operation 308. A state of the rig 10 can be determined by the rig controller 150 based on the parameter data from operation 308. This allows the rig controller 150 to understand progression of the rig 10 through the well plan 163. Prior to drilling the wellbore 15, the ROP optimizer 170 can determine an estimated ROP profile of the wellbore 15 based on the well plan 163, the ECCRS profile, and the physical characteristics of the BHA 60. The estimated ROP profile can be updated in real time as the wellbore 15 is being drilled based on the well plan 163, the ECCRS profile, the physical characteristics of the BHA 60, and the parameter data from one or more sensors 70 or the HMI devices 168.

The ROP optimizer 170 can also run many ROP simulations simultaneously with each simulation altering one or more parameters of the simulation to determine a particular sensitivity of ROP to the one or more parameters. For example, in operation 312, the ROP optimizer 170 can run an ROP simulation while modifying the WOB to determine the sensitivity of the ROP to the changing WOB parameter. Alternatively, or in addition to, in operation 314, the ROP optimizer 170 can run an ROP simulation while modifying the drill bit RPM to determine a sensitivity of the ROP to the changing RPM parameter. Alternatively, or in addition to, in operation 316, the ROP optimizer 170 can run an ROP simulation while modifying a differential pressure (DP) or flow rate of the drilling fluid to determine a sensitivity of the ROP or to the changing DP or flow rate parameters.

In operation 318, a ranking engine 174 can evaluate each of the multiple ROP simulations (such as in operations 312, 314, 316) and determine an optimum ROP and the associated drilling parameters. The optimum ROP can be the simulated ROP from the multiple ROP simulations with the highest ranking which can be established by the ranking engine 174. The simulated ROP with the highest ranking does not necessarily mean that the simulated ROP achieves the highest ROP, just that the simulated ROP best satisfies an acceptable trade-off between the highest ROP and an overall health of the rig 10 (and possibly personnel, as well).

The ROP optimizer 170 can run an ROP simulation based on the selected optimum drilling parameters and determine a resulting ROP. In operation 320, the ROP optimizer 170 can detect dysfunctions (e.g., vibrations, stick-slip, whirl, stall, bit bounce, etc.) predicted by the ROP simulation. The level of predicted dysfunctions can cause the ROP optimizer 170 to modify the drilling parameters to reduce the predicted dysfunctions to more acceptable levels. The resulting drilling parameters can be seen as optimum drilling parameters that should produce an optimum ROP.

In operation 322, the optimum drilling parameters (and the optimum ROP) can be sent to an operator or the rig controller 150 as recommendations for controlling the drilling operations of the rig 10. The operations 310 through 322 can be repeated as needed in real-time to provide real-time ROP adjustments for maintaining an optimum ROP as the wellbore 15 is extended into the subterranean formation 8.

The optimum ROP can be at least periodically compared to the actual ROP of the rig 10 as the future wellbore 15 is being drilled. Based on the comparison, the rig controller 150 or an operator can detect anomalies during drilling and the detection can be used to cause more detailed analysis as to the cause of the deviation from the estimated ROP (e.g., premature bit wear, unexpected rock type, pump degradation or failure, unacceptable cuttings build-up, unexpected friction in the wellbore, etc.).

Various Embodiments

Embodiment 1. A method of optimizing a rate of penetration (ROP) in real-time in a subterranean operation, the method comprising:

- determining, via a rock strength simulator, an equivalent confined compressive rock strength (ECCRS) profile along a future wellbore;
- receiving the ECCRS profile at an ROP optimizer;
- receiving physical parameters of a bottom hole assembly (BHA) at the ROP optimizer; and
- simulating in real-time, via the ROP optimizer, a simulated ROP of a drill bit of the BHA through a portion of a subterranean formation based on the ECCRS profile, the physical parameters of the BHA, and drilling parameters of a rig.

Embodiment 2. The method of embodiment 1, wherein the ROP optimizer is a physics-based model.

Embodiment 3. The method of embodiment 2, wherein the physics-based model is a fast running time domain mechanics model.

Embodiment 4. The method of embodiment 2, wherein the physics-based model simulates the BHA as a discretized BHA with rigid and flexible beam elements interconnected via viscoelastic connections.

Embodiment 5. The method of embodiment 1, further comprising:

- receiving a well plan at an ROP optimizer, wherein the future wellbore is defined by the well plan.

Embodiment 6. The method of embodiment 1, wherein further comprising:

- varying the simulated ROP of the drill bit by adjusting one or more of the drilling parameters; and
- determining an optimum simulated ROP by comparing various simulated ROPs.

Embodiment 7. The method of embodiment 6, further comprising predicting, via the ROP optimizer, dysfunctions of the optimum simulated ROP.

Embodiment 8. The method of embodiment 7, wherein the dysfunctions comprise at least one of:

- vibrations;
- stick-slip;
- whirl;
- stall;
- bit bounce;
- factors that affect mechanical specific energy (MSE); or
- combinations thereof.

Embodiment 9. The method of embodiment 1, selecting, via the rock strength simulator, one or more previously drilled wellbores from a rock strength database.

Embodiment 10. The method of embodiment 9, wherein one or more characteristics of the one or more previously drilled wellbores are similar to one or more characteristics of the future wellbore.

Embodiment 11. The method of embodiment 10, wherein at least one of the one or more characteristics of the one or more previously drilled wellbores is rock strength.

Embodiment 12. The method of embodiment 9, wherein determining the ECCRS profile comprises:

- retrieving, via the rock strength simulator, historical rock strength properties associated with the one or more previously drilled wellbores.

Embodiment 13. The method of embodiment 1, wherein simulating the simulated ROP comprises:

- simulating a plurality of ROP simulations;
- ranking, via a ranking engine, each of the plurality of ROP simulations; and
- selecting, via the ROP optimizer, from the plurality of ROP simulations the simulated ROP with a highest ranking from the ranking engine.

Embodiment 14. The method of embodiment 13, further comprising:

- simulating the plurality of ROP simulations while the rig is drilling along a roadmap of the future wellbore defined by a well plan.

Embodiment 15. The method of embodiment 13, wherein the plurality of ROP simulations comprise:

- at least one of:
  - simulating sensitivity of ROP to weight on bit (WOB);
- simulating sensitivity of ROP to revolutions per minute (RPM) of a tubular string;
- simulating sensitivity of ROP to differential pressure (DP) across a mud motor; or combinations thereof.

Embodiment 16. The method of embodiment 13, further comprising:

- determining, via the ROP optimizer, the simulated ROP with the highest ranking; and
- predicting, via the ROP optimizer, dysfunctions of the simulated ROP with the highest ranking.

Embodiment 17. The method of embodiment 16, wherein the dysfunctions comprise at least one of:

- vibrations;
- stick-slip;
- whirl;
- stall;
- bit bounce;
- factors that affect mechanical specific energy (MSE); or
- combinations thereof.

Embodiment 18. The method of embodiment 1, further comprising:

- receiving a well plan for the future wellbore at the ROP optimizer; and
- simulating the simulated ROP based on the well plan.

Embodiment 19. The method of embodiment 18, wherein the well plan comprises a roadmap, which indicates a path, of the future wellbore through the subterranean formation and simulating the simulated ROP predicts ROP along at least a portion of the roadmap.

Embodiment 20. The method of embodiment 19, wherein determining the ECCRS profile comprises determining the ECCRS profile for the roadmap of the future wellbore defined by the well plan.

Embodiment 21. The method of embodiment 19, further comprising:

- simulating, via the ROP optimizer, a plurality of simulated ROPs for the portion of the roadmap;
- selecting one of the plurality of simulated ROPs with associated drilling parameters; and
- recommending the associated drilling parameters for drilling the portion of the roadmap of the future wellbore.

Embodiment 22. The method of embodiment 21, further comprising drilling the portion of the future wellbore through a subterranean formation based on the associated drilling parameters.

Embodiment 23. The method of embodiment 22, further comprising scoring performance of the rig to drill the portion of the future wellbore by comparing the simulated ROP associated with the associated drilling parameters to an actual ROP of the portion of the future wellbore.

Embodiment 24. The method of embodiment 1, further comprising predicting, via the ROP optimizer, an ROP along the future wellbore prior to drilling the future wellbore and during drilling of the future wellbore.

Embodiment 25. A system for predicting ROP for a future wellbore according to this disclosure.

Embodiment 26. A system of optimizing a rate of penetration (ROP) in real-time in a subterranean operation, the system comprising:

- a rig controller configured to perform the methods of embodiments 1 through 24.

Embodiment 27. A system for optimizing a rate of penetration (ROP) in real-time in a subterranean operation, the system comprising:

- a rig;
- a tubular string extending from the rig into a subterranean formation, wherein the tubular string comprises a bottom hole assembly (BHA) with a drill bit; and
- a rig controller configured to:
- determine, via a rock strength simulator, an equivalent confined compressive rock strength (ECCRS) profile along a future wellbore;
- receive the ECCRS profile at an ROP optimizer of the rig controller;
- receive physical parameters of the bottom hole assembly (BHA) at the ROP optimizer; and
- simulate in real-time, via the ROP optimizer, a simulated ROP of the drill bit of the BHA through a portion of the subterranean formation based on the ECCRS profile, the physical parameters of the BHA, and drilling parameters of the rig.

Embodiment 28. The system of embodiment 27, wherein the ROP optimizer simulates the BHA as a discretized BHA with rigid and flexible beam elements interconnected via viscoelastic connections.

Embodiment 29. The system of embodiment 27, wherein the rig controller is further configured to receive a well plan at the ROP optimizer, wherein the future wellbore is defined by the well plan.

Embodiment 30. The system of embodiment 27, wherein the rock strength simulator is a statistical model that is configured to receive historical parameter data from historical wells and determine the ECCRS profile along at least a portion of the future wellbore based on the historical parameter data.

Embodiment 31. The system of embodiment 27, wherein the rock strength simulator is a real time simulator that is configured to receive real-time parameter data from the rig and determine the ECCRS profile along at least a portion of the future wellbore based on the real-time parameter data.

Embodiment 32. The system of embodiment 27, wherein the rock strength simulator is a real time simulator that is configured to receive real-time parameter data from the rig and historical parameter data from historical wells, and wherein the rock strength simulator is further configured to determine the ECCRS profile along at least a portion of the future wellbore based on the real-time parameter data and the historical parameter data.

Embodiment 33. The system of embodiment 27, wherein the rig controller is further configured to:

- vary the simulated ROP of the drill bit by adjusting one or more of the drilling parameters; and
- determine an optimum simulated ROP by comparing various simulated ROPs.

Embodiment 34. The system of embodiment 33, wherein the rig controller is further configured to predict, via the ROP optimizer, dysfunctions of the optimum simulated ROP, and wherein the dysfunctions comprise at least one of vibrations; stick-slip; whirl; stall; bit bounce; factors that affect mechanical specific energy (MSE); or combinations thereof.

Embodiment 35. The system of embodiment 27, wherein the rig controller is further configured to select, via the rock strength simulator, one or more previously drilled wellbores from a rock strength database.

Embodiment 36. The system of embodiment 35, wherein the rig controller is further configured to retrieve, via the rock strength simulator, historical rock strength properties associated with the one or more previously drilled wellbores.

Embodiment 37. The system of embodiment 27, wherein the rig controller is further configured to:

- simulate a plurality of ROP simulations;
- rank each of the plurality of ROP simulations; and
- select from the plurality of ROP simulations the simulated ROP with a highest ranking.

Embodiment 38. The system of embodiment 37, wherein the rig controller is further configured to simulate the plurality of ROP simulations while the rig is drilling along a roadmap of the future wellbore defined by a well plan.

Embodiment 39. The system of embodiment 37, wherein the plurality of ROP simulations comprise:

- at least one of:
  - simulation of sensitivity of ROP to changes in weight on bit (WOB);
  - simulation of sensitivity of ROP to changes in revolutions per minute (RPM) of a
  - simulation of sensitivity of ROP to changes in differential pressure (DP) across a mud motor; or
  - combinations thereof.

Embodiment 40. The system of embodiment 27, wherein the rig controller is further configured to:

- receive a well plan for the future wellbore at the ROP optimizer; and
- simulate the simulated ROP based on the well plan.

Embodiment 41. The system of embodiment 40, wherein the well plan comprises a roadmap of the future wellbore through the subterranean formation and simulation of the simulated ROP predicts ROP along at least a portion of the roadmap.

Embodiment 42. The system of embodiment 41, wherein the rig controller is further configured to determine the ECCRS profile for the roadmap of the future wellbore defined by the well plan.

Embodiment 43. The system of embodiment 41, wherein the rig controller is further configured to:

- simulate, via the ROP optimizer, a plurality of ROP simulations for the portion of the roadmap;
- select one of the plurality of simulated ROPs with associated drilling parameters; and
- recommend the associated drilling parameters for drilling the portion of the roadmap of the future wellbore.

Embodiment 44. The system of embodiment 43, wherein the rig is further configured to drill the portion of the future wellbore through a subterranean formation based on the associated drilling parameters.

Embodiment 45. The system of embodiment 44, wherein the rig controller is further configured to score performance of the rig to drill the portion of the future wellbore by comparing one of the plurality of ROP simulations associated with the associated drilling parameters to an actual ROP of the portion of the future wellbore.

Embodiment 46. The system of embodiment 27, wherein the rig controller is further configured to predict, via the ROP optimizer, an ROP along the future wellbore prior to and during drilling of the future wellbore.

While the present disclosure may be susceptible to various modifications and alternative forms, specific embodiments have been shown by way of example in the drawings and tables and have been described in detail herein. However, it should be understood that the embodiments are not intended to be limited to the particular forms disclosed. Rather, the disclosure is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosure as defined by the following appended claims. Further, although individual embodiments are discussed herein, the disclosure is intended to cover all combinations of these embodiments.