DRILLING PARAMETER RECOMMENDATIONS BASED ON OFFSET WELL DATA

Abstract

A system and method of steering a drill string when forming a wellbore in a subterranean formation. The method includes identifying two or more parameters associated with steering the drill string in a subject well; determining, via a statistical model, individual contributions to a tool yield model by each of the identified parameters; and suggesting, based on the statistical model and on current values of the identified parameters, one or more changes in the identified parameters, the changes sufficient to alter a trajectory of the drill string in the subject well.

Description

BACKGROUND

As part of hydrocarbon recovery operations, a wellbore can be formed in a subterranean formation for extracting produced hydrocarbon material or other suitable material. The wellbore may experience or otherwise encounter one or more wellbore operations such as drilling the wellbore. Drilling, or otherwise forming, the wellbore can involve using a drilling system that can include a drill bit and other suitable tools or components for forming the wellbore. During drilling, the drilling system may change the course (e.g., speed, direction, etc.) of the drill bit to form a wellbore that may not be purely vertical.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure may be better understood by referencing the accompanying drawings.

FIG. 1 is an elevation view in partial cross section of an example well system that supports directional drilling, according to aspects of the present disclosure.

FIG. 2 is a flowchart illustrating a method for suggesting changes to parameters used to steer a drill string, according to aspects of the present disclosure.

FIG. 3 illustrates a system for suggesting changes to steering parameters based on online parameter recommendation logic, according to aspects of the present disclosure.

FIG. 4 illustrates a system 400 for deriving a set of offset wells from a well drilling database, for building a tool yield model and an ROP model based on drilling information associated with the set of offset wells, and for suggesting changes to steering parameters based on the models, according to aspects of the present disclosure.

FIG. 5 is a flowchart illustrating a method used to model tool yield and ROP, according to aspects of the present disclosure.

FIG. 6 is a flowchart illustrating an example method for deriving a set of offset wells from a well drilling database, for building a tool yield model and an ROP model based on drilling information associated with the set of offset wells, and for suggesting changes to steering parameters based on the models, according to aspects of the present disclosure.

FIG. 7 is a flowchart illustrating a method of offset well analysis, according to aspects of the present disclosure.

FIG. 8 is a flowchart illustrating an example method of developing models from the drilling data associated with the offset wells of FIG. 7, according to aspects of the present disclosure.

FIG. 9 is a rules-based method of making parameter recommendations, according to aspects of the present disclosure.

FIG. 10 is an optimization-based method of making parameter recommendations, according to aspects of the present disclosure.

Like reference numbers and designations in the various drawings indicate like elements.

DETAILED DESCRIPTION

The description that follows includes example systems, methods, techniques, and program flows that embody embodiments of the disclosure. Unless otherwise specified, use of the terms “connect,” “engage,” “couple,” “attach,” or any other like term describing an interaction between elements is not meant to limit the interaction to a direct interaction between the elements and may also include an indirect interaction between the elements described. Unless otherwise specified, use of the terms “up,” “upper,” “upward,” “uphole,” “upstream,” or other like terms shall be construed as generally away from the bottom, terminal end of a well; likewise, use of the terms “down,” “lower,” “downward,” “downhole,” or other like terms shall be construed as generally toward the bottom, terminal end of the well, regardless of the wellbore orientation. Use of any one or more of the foregoing terms shall not be construed as denoting positions along a perfectly vertical axis. In some instances, a part near the end of the well can be horizontal or even slightly directed upwards. Unless otherwise specified, use of the term “subterranean formation” shall be construed as encompassing both areas below exposed earth and areas below earth covered by water such as ocean or fresh water.

As noted above, during drilling, drilling operations may introduce a change in the operation (e.g., speed, direction, etc.) of the drill bit to change the trajectory of the drill string, forming a wellbore that may not be purely vertical. Doglegs are sections of a borehole where the trajectory changes rapidly. They are an unescapable fact in hydrocarbon recovery operations. Thoughtfully planned and drilled, doglegs are part of an optimized borchole, avoiding problematic formations and maintaining the right drilling angle to reach a desired zone. Many factors, however, influence whether the dogleg location and curvature are appropriate or undesirable.

Operating parameters such as weight on bit (WOB), rotations per minute (RPM) of the bit, and flowrate may be adjusted in real time to steer a drill string. For example, the operating parameters may be adjusted to increase or decrease the dogleg capability of the drill string. At the same time, however, operating parameters (such as WOB, RPM, and flowrate) may be adjusted to maximize the rate of drilling, to manage a safe operating envelope and for telemetry and data transmission.

The mechanism by which parameters such as WOB, RPM, and flowrate individually impact the steering action is not well understood. In addition, there is no comprehensive physics-based model that relates the influence of these controllable drilling parameters to dogleg severity (DLS). Instead, current practice often relies on the intuition and experience of the directional drillers to drive the change in these parameters for steering direction and efficiency.

A new method of controlling directional steering uses drilling parameters such as WOB, RPM and flowrate to control the steering. The new method may use offset well data to arrive at drilling parameter recommendations in real time, as described below.

Certain aspects and features of the present disclosure relate to a bottom hole assembly (BHA) having a steering mechanism connected to a drill bit through a tool string, the drill bit for drilling into a subterranean formation to form a wellbore for extracting produced hydrocarbons. The steering mechanism may include a rotary steering system (RSS) including a steering collar and one or more pad actuators. In some examples, the steering collar may be a frame of the tool string, stiffening the tool string. In some examples, the pad actuators may be mounted on the steering collar to exert force on the side of a wellbore to change the direction of drilling while forming the wellbore.

This disclosure includes illustrative examples used to introduce the reader to the general subject matter discussed herein; the examples are not intended to limit the scope of the disclosed concepts. The following sections describe various additional features and examples with reference to the drawings in which like numerals indicate like elements, and directional descriptions are used to describe the illustrative aspects, but, like the illustrative aspects, should not be used to limit the present disclosure.

Example Well System

FIG. 1 is an elevation view in partial cross section of an example well system that supports directional drilling, according to aspects of the present disclosure. In the example shown in FIG. 1, the well system 100 directs a drill bit 114 in drilling a wellbore 118 through a subterranean formation 102, such as a subsea well or a land well. Example embodiments are not limited to only drilling an oil well. Some implementations may also encompass natural gas wellbores, other hydrocarbon wellbores, or wellbores in general. Further, some implementations may be used for the exploration and formation of geothermal wellbores intended to provide a source of heat energy instead of hydrocarbons.

In the example shown in FIG. 1, well system 100 includes a drill string 106 attached to a derrick 108 and a bottom hole assembly (BHA) 104; the BHA 104 may be positioned or otherwise arranged at the bottom of the drill string 106. The derrick 108 may be located at the surface 110 and may, in some example approaches, include a kelly 112 connected to drill string 106; the kelly 112 may be used, for instance, to lower and raise the drill string 106.

The BHA 104 may include a drill bit 114, a rotary steerable system 109, other suitable components, or a combination thereof. The drill bit 114 may, in some examples, be operatively coupled to a tool string 116, with the tool string 116 attached to the drill string 106 such that the drill bit 114 may be moved axially within drilled wellbore 118. During operation, the drill bit 114 can penetrate the subterranean formation 102 to extend the wellbore 118.

The BHA 104 may control the drill bit 114 as the drill bit 114 advances into the subterranean formation 102. For example, the BHA 104 may use the rotary steerable system 109 to change a direction of drilling by applying a steering pressure or other suitable force to a wall of the wellbore 118.

In the example shown in FIG. 1, fluid such as a drilling mud may be pumped downhole from a mud tank 120 using a mud pump 122 that may be powered by an adjacent power source, such as a prime mover (or motor) 124. The mud may be pumped from the mud tank 120, through a stand pipe 126, which feeds the mud through the drill string 106 to the rotary steerable system 109, or other suitable components of the well system 100, and on to the drill bit 114. The mud may, in some examples, exit one or more nozzles (not shown) arranged in the drill bit 114 and may thereby cool the drill bit 114. Additionally or alternatively, the mud may be directed (e.g., as pressurized mud) into the rotary steerable system 109 for adjusting a direction of the drill bit 114, as discussed in further detail below.

After exiting the drill bit 114 or other suitable component, the mud may circulate back to the surface 110 via an annulus defined between the wellbore 118 and the drill string 106. The returning mud transports cuttings from the wellbore 118 into the mud tank 120 and aids in maintaining the integrity of the wellbore 118. For example, cuttings and mud mixture passed from the annulus through the flow line 128 may be processed such that a cleaned mud is returned down hole through the stand pipe 126.

In some examples, the rotary steerable system 109 may include a steering collar, one or more actuation cylinders, and a radial seal for each cylinder. The steering collar may be designed to provide a rigid frame for the rotary steerable system 109. In one example approach, each actuation cylinder is mounted in a pocket of the steering collar, with a radial seal installed between each actuation cylinder and the steering collar; the radial seal forms a pressure seal or other suitable type of seal for each actuation cylinder in the rotary steerable system 109. In one such example approach, the radial seal allows the rotary steerable system 109 to receive pressure (e.g., via pressurized mud) used to apply the steering force without incurring damage, obstruction, excessive wear, or other related undesirable effects from the pressure. In one example approach, a piston positioned in each actuation cylinder may be used to apply the steering pressure or other suitable forces to the wall of the wellbore.

The tool string 116 may include one or more logging while drilling (LWD) or measurement-while-drilling (MWD) tools that collect data and measurements relating to various borehole and formation properties as well as the position of the drill bit 114 and various other drilling conditions as the drill bit 114 extends the wellbore 118 through the formations 102. The LWD/MWD tools may include a device for measuring formation resistivity, a gamma ray device for measuring formation gamma ray intensity, devices for measuring the inclination and azimuth of the tool string 116, pressure sensors for measuring drilling fluid pressure, temperature sensors for measuring borehole temperature, etc.

In the example shown in FIG. 1, RSS 109 is configured to change the direction of the tool string 116 and/or the drill bit 114, such as based on information indicative of tool orientation and a desired drilling direction received from a drilling application. In one or more embodiments, the RSS 109 is coupled to the drill bit 114 and may drive rotation of the drill bit 114. Specifically, the RSS 109 may rotate in tandem with the drill bit 114 or may rotate at a fraction of the rate of drill bit 114. In some implementations, the rotary steerable tool 109 may be a point-the-bit system or a push-the-bit system.

FIG. 2 is a flowchart illustrating a method for suggesting changes to parameters used to steer a drill string, according to aspects of the present disclosure. In the example approach of FIG. 2, the method includes identifying (200) two or more parameters associated with steering a drill string in a subject well., determining (202), via statistical model, individual contributions to a tool yield model by each of the identified steering parameters, and suggesting (204) based on the statistical model, a change in one or more of the identified steering parameters, the change sufficient to alter a trajectory of the drill string in the subject well.

In one such example approach, the method uses drilling information from similar wells located close to the subject well to model the effects of changes in drilling parameters on drill string performance such as ROP and DLS/Tool Yield in wells like the subject well. In operation. the model provides suggested changes in drilling parameters to the drilling operator or to automated drilling controllers in real time.

In one such example, the solution includes offline model development and online parameter recommendation logic. FIG. 3 illustrates a system for suggesting changes to steering parameters based on online parameter recommendation logic, according to aspects of the present disclosure. In the system of FIG. 3, a processor 302 receives steering parameters such as ROP, WOB, RPM, Flowrate, inclination, and Formation Information which may be obtained from the rock strength properties or Mechanical Specific Energy (MSE), retrieves the well plan and the steering model derived from the offset wells from memory 304 and uses the steering parameters, the well plan and the steering model to suggest changes to one or more of WOB, RPM and Flowrate. Additional safety considerations may also be implemented to enhance the recommendation (such as tool face control for the Mud motor 122, differential pressure limit to prevent the mud motor stall and limits on the input parameters). The limits of the input parameters may be obtained from the maximum allowable limits of the various tools and processes used in the drilling operation.

FIG. 4 illustrates a system 400 for deriving a set of offset wells from a well drilling database, for building a tool yield model and an ROP model based on drilling information associated with the set of offset wells, and for suggesting changes to steering parameters based on the models, according to aspects of the present disclosure. In the system of FIG. 4, a processor 402 is connected to a database of well drilling data 404 and to memory 406. Processor 402 derives a set of offset wells from the well drilling database 404 based on equipment information (such as BHA, tool type and design, size and location of stabilizers, bit type and design), well information (such as location and outer diameter) and offset well parameters such as distance from the subject well (Radius). In one example approach, processor 402 filters the wells received from database 404 to obtain wells that fall within a specified distance of the subject well and that have the same bit type and size, the same tool type and size and the same BHA makeup. The wells that remain are screened for similarity and wells that are similar enough are saved as offset wells.

Processor 402 determines a tool yield model and an ROP model based on drilling information associated with the set of offset wells and uses the models to derive a mathematical model for each input/output pair using regression. In the example shown in FIG. 4, processor 402 makes suggestions for changes in WOB, RPM and flowrate based on the models and inputs such as the current values of WOB, ROP, RPM, Flowrate and inclination. Additional safety considerations may also be implemented to enhance the recommendation (such as tool face control for the Mud motor 122, differential pressure limit to prevent the mud motor stall and limits on the input parameters).

FIG. 5 is a flowchart illustrating a method used to model tool yield and ROP, according to aspects of the present disclosure. In the example shown in FIG. 5, offset well learning based on drilling data obtained for similar tools in similar formations improves steering performance in a subject well. As part of the offline model development, a processor queries (500) a database 404 to obtain drilling data for wells located near to the subject well and then filters (502) the data based on parameters such as the distance to the subject well, the BHA type and Size, and the Bit Type, design and Size, tool type and design, size and location of stabilizers.

In one example approach, the processor filters for wells with similar BHA and Bit design and performs (504) a similarity analysis on the wells using, for example, a distance-based similarity method such as Dynamic Time Warping. The group of most similar wells are the offset wells used for further analysis.

In one example approach, the processor extracts (506) independent input features from each offset well and uses the data to build (508) a data-driven model based on, for instance, a Neural Network Technique or a Random Forest Method, to define the relationship between the input and output. In one example approach, the result is a black box model in which the output is the maximum Yield Capacity of the drill string at 100% Duty cycle. The inputs are the parameters that influence the DLS capability of the tool.

The processor then performs (510) a statistical analysis on the black box model to obtain a set of mathematical models that describes the relationship of each individual input with the output. The models provide partial dependence data for each input feature on the output. The processor performs (512) symbolic regression or other data modeling techniques on the partial dependence data to obtain a data-driven partial model.

In one example approach, the processor develops a mathematical model based on Mechanical Specific Energy to describe the ROP relationship. The processor then applies the chain rule to the Specific Mechanical Energy equation to find the effect of each individual input on the ROP. The ROP model and the tool yield model may then be used to derive the drilling parameter recommendation logic. In another approach, a data driven ROP model may be developed using statistical modeling on the inputs that affect the ROP. The inputs may be and not limited to WOB, depth of cut (DOC) which is defined as ROP/RPM, and formation properties like Rock Strength or MSE.

In one example approach, the processor runs an optimization method on the ROP model and the tool yield model that provides a window of WOB, RPM, and Flowrate that would give a required DLS capability of the drill string. Additional safety considerations may also be implemented to enhance the recommendation (such as tool face control for the Mud motor, Differential Pressure Limits, and limits on the input parameters). The limits of the input parameters may be obtained from the maximum allowable limits of the various tools and processes used in the drilling operation.

The approach described provides valuable information that may be used to improve steering performance. The approach improves steering efficiency using appropriate and optimized drilling parameters which lead to improvement in drilling efficiency, increasing the value of the steering tool and operation. Furthermore, carly indication (in pre-job and in real-time) in scenarios where the required DLS may not be achievable allows for exploration in drilling parameter space.

FIG. 6 is a flowchart illustrating an example method for deriving a set of offset wells from a well drilling database, for building a tool yield model and an ROP model based on drilling information associated with the set of offset wells, and for suggesting changes to steering parameters based on the models, according to aspects of the present disclosure. In the example of FIG. 6, the method queries (600) a database 404 of well drilling data to obtain drilling information on particular wells and then builds (604) a list of offset wells based on the parameters expressed in input 604.

Key operating parameters like WOB, flowrate, DLS and ROP may be extracted (606) as features from the drilling information associated with the offset wells. The features may include but are not limited to operating parameters like WOB, Flowrate, DLS, ROP, and RPM. Parameters for the new well may be estimated by calculating the average for each feature from the offset well data. The expected parameter values may also be calculated for different sections in the well (such as by horizontal section, by vertical section, by curved section, or by, for example, formation). The calculated expectations may be used for well planning and design of services (DOS).

The method develops (608) a tool yield and an ROP model based on the data from the offset wells and applies (610) a statistical analysis of individual contributions by parameter to the tool yield model. The tool yield model and the ROP model are then used to generate suggestion logic that suggests (612) changes, if any, needed to one or more parameters to obtain a desired change in, for instance, DSL. The suggested changes may be supplied to an operator (616) for manual control of the well parameters or may be provided (614) to a machine control system for automatic application to the steering parameters. In one example approach, after the changes are applied, feedback may be gathered on the change in DLS and new parameter changes suggested based on the feedback.

Example Operations

FIG. 7 is a flowchart illustrating a method of offset well analysis, according to aspects of the present disclosure. In the example of FIG. 7, offset well analysis includes identifying a list of offset wells and their historical drilling data by querying a database of drilling data and filtering the results of the query on parameters such as BHA information, RSS type and design, Size and design of stabilizers, Bit type and design, and Trajectory information like Depth, inclination, and TVD obtained from the well plan.

In one example approach, offset well analysis includes application programming interfaces (API) that connect to different databases to extract the available drilling data. In one such example approach, the data for each well is identified via a unique identifier for each well and may include but is not limited to information obtained from survey, well planning, surface and downhole sensors sampled during the drilling operation, well information, BHA information, data obtained from different manual processes during operation such as Mud report, information regarding the type of operation (such as, for example, Drilling, Trip In and Trip Out). The data may be organized within a single database or in many databases.

In one example approach, such as shown in FIG. 7, a processor connects (700) to one or more databases (702) to access the drilling information for each well. The processor receives as input (706) the BHA information about the current well, the current well location, and the current well plan. The well plan may include trajectory details such as the Measured Depth (MD), Inclination, and True Vertical Depth (TVD) of the current well. The BHA information input includes but is not limited to Tool type, Size and design, and Bit type, Size and design. In addition, additional components of the BHA may include the number, location, and size of stabilizers and other components. Based on this information, the processor filters all the drilling data and receives in response to its query only the wells matching the inputs. In one example approach, the processor filters (704) for similar wells within a radius, R, of the current well drilling location. In one such example approach, the radius is an input provided by the user and has a default value.

Features are extracted (708) for similarity analysis and the wells obtained from filtering (704) are processed through the similarity analysis to find a set of the most similar wells to the target well. The most similar wells obtained after similarity analysis are the “offset wells.” In one example approach, a distance-based similarity measure called the Dynamic Time Warping method (DTW) is used for similarity analysis. In one such example approach, a multivariate form of DTW is used.

In one example approach, data is synchronized with measured depth (710) and, in some such example approaches, data is subsampled with constant sampling frequency of MD. In one example approach, the DTW algorithm finds an optimal matching between the two multivariate signals and calculates total minimum cost for that optimal matching. The inputs for the DTW method are the inclination and TVD. In some forms of similarity measurement, similarity of the operating parameters may be used. In that case, the operating parameters like WOB, Flowrate, and ROP may also be used for calculating the similarity score.

In one example approach, the input parameters for calculating the DTW similarity score are normalized before the multivariate form of DTW is applied (712). In addition, the inputs are constrained to have the same starting and ending MD. All the inputs may be synchronized in depths and sampled at equidistance depth. Furthermore, the constraints may be placed on the DTW algorithm on admissible warping paths. Such constraints will speed up the DTW algorithm as well as prevent pathological warping paths. One constraint may be the depth window or an adjustment window on in which the algorithm can look for a matching path. A DTW score is calculated for all combinations of the target well with the filtered wells. The DTW scores are normalized in depth.

In one example approach, all the wells that fall within the threshold normalized DTW score are identified (714) as the offset wells

$D_{i,j}=❘x_i-y_j❘+\min \left\{D_{i-1,j},D_{i-1,j-1},D_{i,j-1}\right\}❘i-j❘\le r$

Where, r is the warping window.

• • G⊂D_(i,j), where i,j belongs to the warping path with minimum costG=[set of cost in Di,j along the path of minimum cost]

$g=\frac{{\Sigma }_k{G}_k}{N\times \mathrm{Td}}$

Where, g is the normalized score, N is the number of sample points, and Td is the sampling frequency of Depth. The offset wells are then saved (718) to the offset well list while wells that are not sufficiently similar are discarded (716). A check is made to determine if this is the last of the filtered wells and if not, another well is analyzed (714). If, however, this is the last of the filtered wells (720), output the list of offset wells (722).

FIG. 8 is a flowchart illustrating an example method of developing models from the drilling data associated with the offset wells of FIG. 7, according to aspects of the present disclosure. In the example shown in FIG. 8, the method obtains the relationship and identifies the trend between key operating parameters like WOB, Flowrate, ROP, and DLS/Build rate. In some such example approaches, offset wells 722 may be identified automatically as explained with respect to FIG. 7 or may be manually input into the system.

In some example approaches, the method extracts (802) relevant features (such as WOB, RPM, DLS, inclination, ROP, Flowrate, and Formation Information) from the drilling information. In some such example approaches, the features are augmented to calculate pad force, MSE, and tool yield.

In one example approach, Tool Yield is estimated from the DLS and is equal to the DLS at 100% steering input or Duty cycle. Alternatively, Tool Yield may be estimated from BR or rate of Turn at their corresponding value at 100% Build command and Turn command.

$\mathrm{Tool}\mathrm{Yield}=\frac{\mathrm{DLS}}{\mathrm{Duty}\mathrm{Cycle}\left(u\right)}=\frac{\mathrm{Build}\mathrm{Rate}\left(\mathrm{BR}\right)}{\mathrm{Build}\mathrm{Command}\left(u\right)}=\frac{\mathrm{Turn}\mathrm{Rate}\left(\mathrm{TR}\right)}{\mathrm{Turn}\mathrm{Command}\left(u\right)}\mathrm{Constaint}:❘u❘>x$

Here, a constraint, x, on the steering input, u, is provided for when u approaches a very low steering input. This method of Tool Yield estimation ignores the drilling dynamics and assumes that the effect of the steering input on DLS is immediate. In addition, the method assumes a linear relationship between the Duty cycle and DLS. Alternatively, model-based estimation methods like Kalman Filter or other Bayesian estimation methods or statistical methods may be used to include the effect of drilling dynamics in the estimation of the Tool Yield and obtain a more accurate value.

In one example approach, input features that are used for the model development include WOB, RPM at Bit, Inclination, ROP, and Flowrate. Additional derived parameters may also be used for the model development which may be Pad Force estimated using Flowrate and Differential pressure for Push the Bit RSS, Mechanical Specific Energy (MSE), which can be used as a proxy for the formation strength during drilling. Rock strength values may also be used as input if available. Other sensor values and derived parameters may include the effect of vibration and other effects on tool yield.

In one example approach, as noted above, model building is a two-part process. The first part involves using different statistical and machine learning techniques such as tree-based optimization method like Random Forest or neural network techniques for building a black box model. Such techniques are very sophisticated and can learn the patterns and trends in data during the optimization process while building a model. In one example approach, data is prepared by selecting the data for specific sections of the wells that will need to be studied or optimized in real time. Generally, the section will be a curved section of the well, as one objective is to optimize the Tool Yield or DLS while building the curve in the new well. The same process may be applied, however, to build models for any section of the well, or for more than one section of the well, applying the section logic as needed will drilling the new well. Once the features are extracted from the offset wells for specific sections, the data for each feature for all the offset wells is combined. The combined set of features is then preprocessed (804) to normalize the input features, and to perform filtering, outlier removal, and feature augmentation.

In one example approach, a machine learning regression modeling is applied (806) using, for instance, a tree-based or a neural network-based method with hyperparameter tuning. Each dataset and model may require a different set of hyperparameters. One way to determine these is through multiple experiments, where one picks a set of hyperparameters and then runs them through the model. This is called hyperparameter tuning. In essence, training the model sequentially with different sets of hyperparameters. This process may be manual, or may use one of several automated hyperparameter tuning methods, but typically will require some form of statistical analysis, such as the loss function, to determine which set of hyperparameters gives the best result.

In one example approach, the combined dataset from offset well is divided into a training set and a testing set. The training set is used to build the model and the testing set is used to test the performance of the model. Based on the performance of the model during testing, the hyperparameters used for model building and optimization are tuned (808) to obtain the best performance. In one such example approach, the process of hyperparameter tuning may be automated by defining a search space of hyperparameters and iteratively testing the performance of the model by random or some statistics-based combination of the hyperparameters within the search space. After N number of iterations, the best performing set of hyperparameters is used for model building. This process gives a black box model that will predict the Tool Yield or DLS based on the input set of features. In another example approach, Neural Network methods, which use a window of data to predict the output (like a Recurrent Neural Network), are used for this model building process.

Once the black box model is obtained, statistical analysis on the black box model is performed (810) to obtain the relationship between each input feature with the output. In one example approach, this can be done by calculating the contribution of the feature I on the prediction of Tool Yield or DLS. A simple method for this estimation is by calculating the partial dependence.

In one example approach, partial dependence is calculated using the Monte Carlo Method given by:

$\left(x_S\right)=\frac{1}{n}\sum _{i=1}^n\hat{f}\left(x_s,x_c^{\left(i\right)}\right)$

Where f_xs is the partial dependence of the feature x_s and x_c are the other features used in the model. Here, for each unique value in x_s, the marginal contribution of the value of x_s is computed using the constant value of x_s, for all values of x_c. This process may be repeated for each unique value in x_s to get a set of input/output pairs with marginal contributions. This method of calculation of the marginal contribution of each feature does, however, assume that the input features are independent, which is not necessarily true.

In an alternate example approach, a game theory-based method for calculating the marginal contribution (such as Shapley Additive explanation (SHAP)) may be used to calculate the marginal contributions. This method is based on the idea of fairness in contribution and should be consistent with the two ideas; Additivity and Consistency. Additivity refers to the concept that that the sum of the contribution of each feature to the change in output features should be equal to the total change in output features. Consistency refers to the idea that the feature with largest contribution should have largest SHAP value. For SHAP calculation, average expected marginal contribution is calculated by using Game Theory:

$\begin{array}{c}\mathrm{shapely}\mathrm{value}\mathrm{of}\mathrm{feature}i\\ \mathrm{contribution}\mathrm{of}\mathrm{feature}i\mathrm{to}\mathrm{prediction}f\left(x\right)\end{array}=\begin{array}{c}\mathrm{Average}\mathrm{over}\mathrm{all}\\ \mathrm{feature}\text{'}s\mathrm{subset}\\ S\subseteq M/\left\{i\right\}\end{array}\left[\begin{array}{c}\mathrm{Marginal}\mathrm{Contribution}\\ f\left(S\bigcup \left\{i\right\}\right)-f\left(S\right)\end{array}\right]$

Marginal contributions may be calculated by other techniques as well.

Once the marginal contribution is obtained, a set of input output datasets for each independent feature is obtained. For additive feature contribution,

${\varnothing }_0+\sum _{j=1}^m{\varnothing }_i^j\left(x_i\right)=f\left(x_i\right)$

Here, f(x_i) is the predictive model associated with (X, Y), x_i is the single observation of X, j is the feature, and ∅_i^j(x_i) is the contribution of each feature:

$\mathrm{Yield}=\int \frac{\partial f}{\partial \mathrm{WOB}}+\int \frac{\partial f}{\partial \mathrm{RPM}}\mathrm{dRPM}+\int \frac{\partial f}{\partial \theta }d\theta +\int \frac{\partial f}{\partial F_p}{\mathrm{dF}}_p+\int \frac{\partial f}{\partial \mathrm{MSE}}\mathrm{dMSE}$

Where, θ is the inclination, F_p is the pad force, and MSE is Mechanical Specific Energy. In the presence of additional input features, the equation may be modified to include the presence of the added features or may be reduced to reflect the absence of features.

In one example approach, each integral in the above equation is obtained (812) by fitting a simple nonlinear model using regression on the marginal contribution dataset for each feature obtained in the previous step. While fitting a model, linear/nonlinear combination of multiple features may be affecting a contribution of a single feature on Tool Yield/DLS. For example, in the relationship of WOB contribution on Tool Yield/DLS, RPM might be having a secondary affect on how WOB effects the Tool Yield/DLS. For Instance, at Higher RPM, the contribution of WOB to Tool Yield/DLS may be higher while at lower RPM the opposite takes place. This kind of relationship can be obtained by using symbolic regression. Alternatively, other regression or data modeling techniques may be utilized to build this relationship.

In one example approach, the result (814) of the process is a linear or nonlinear model from regression for each input describing the contribution of the input on the output at an average value of the other features. Using these models and the user input of the input features, the trend of Tool Yield with the change in the input features can be predicted. For example, with the model of dWOB on dYield/dDLS, which direction WOB needs to change to increase Yield/DLS can be predicted, and such information can be transmitted to the operator in real time.

Realtime usage of the models will be described next. In one example approach, the goal is to identify, in real time, parameters such as WOB, Flowrate, RPM, and to provide a recommendation for changes in one or more parameters of the model sufficient to result in a change in trajectory of the drill string.

FIG. 9 is a rules-based method of making parameter recommendations, according to aspects of the present disclosure. In one example approach, as described in FIG. 9, rules are defined for calculating the changes in one or more parameters needed to achieve a desired DLS in real time. In the example shown in FIG. 9, the method calculates (902) the DLS capability required based on the inputs 900. In some such example approaches, the input (900) includes the well plan, the models and the current values of RPM, WOB, ROP, Flowrate, and inclination.

In one example approach, the model for the change in Tool Yield/DLS with respect to the change in operating parameters is used for online parameter recommendation. The model takes (902) input 900 for the input features and Well plan. Using the input inclination, real time DLS may be calculated. Using the calculation of the current DLS and the current trajectory offset from the Well plan, the method makes an estimate of the current DLS and determines (904) if the current Tool yield is sufficient to meet the well plan. If the current Tool Yield is not sufficient, the method calculates the amount of Tool Yield that needs to be increased and determines (904) if the new Tool yield is sufficient to meet the well plan. In one such example approach, a safety margin is added to the amount of Tool Yield that needs to be increased.

Using the model, the method determines (906) an amount of parameter change (in WOB, RPM, Flowrate, or ROP) that will result in the required change of Tool Yield and supplied the value to the operator or control system for control. In one such example approach, a priority is assigned to the order in which parameters change to change Tool Yield and the priority is used by the method to determine the parameter to change (908) to achieve the desired DLS.

In one example approach, the priority for the change for the parameters may be set initially and the limits for the parameters may also be used as a constraint on which parameter to change. For example, operators can set the priority as WOB/ROP as first parameter to change, then RPM, and flowrate as the last parameter. This priority can be different based on requirement.

In one example approach, each parameter further includes a limit on how much the parameter may change. Based on that limit, a recommendation for WOB/ROP, RPM, and Flowrate may be provided.

FIG. 10 is an optimization-based method of making parameter recommendations, according to aspects of the present disclosure. There are alternate methods for determining parameter change needed for a desired change in Tool Yield. For example, as illustrated in the flowchart of FIG. 10, optimization is used to select parameters to change for a desired change in tool yield. In the example shown in FIG. 10, the method calculates (1002) the DLS capability required based on the inputs 1000. In some such example approaches, the input (1000) includes the well plan, the models and the current values of RPM, WOB, ROP, Flowrate, and inclination.

In one example approach, the model for the change in Tool Yield/DLS with respect to the change in operating parameters is used for online parameter recommendation. The model takes (1002) input 1000 for the input features and Well plan. Using the input inclination, real time DLS may be calculated. Using the calculation of the current DLS and the current trajectory offset from the Well plan, the method makes an estimate of the current DLS and determines (1004) if the current Tool yield is sufficient to meet the well plan. If the current Tool Yield is not sufficient, the method calculates the amount of Tool Yield that needs to be increased and determines (1004) if the new Tool yield is sufficient to meet the well plan. In one such example approach, a safety margin is added to the amount of Tool Yield that needs to be increased.

In one example approach, the method sets up (1006) an optimization problem using ROP model and Tool Yield/DLS model, with the objective to get required DLS with ROP maximization in the presence of constraints. In addition, ROP can be a constraint to the objective function where the main objective is to gain required tool yield. The method runs (1008) the optimization with, in one example approach, the goal of calculating the range of each parameter that would provide the required DLS with ROP maximization. The method then recommends (1010) the change in one or more parameters based on the output of the optimization function.

In one such example approach, a simplistic model of ROP may be used to model the effect of changes in ROP. For example, using an MSE equation and calculating a derivative of it,

$\mathrm{dROP}=\frac{2\pi \times \mathrm{Torque}}{\mathrm{Area}\times \mathrm{MSE}-\mathrm{WOB}}\mathrm{dRPM}+\frac{2\pi \times \mathrm{RPM}\times \mathrm{Torque}}{{\left(\mathrm{Area}\times \mathrm{MSE}-\mathrm{WOB}\right)}^2}\left(-\mathrm{dWOB}\right)+\frac{2\pi \times \mathrm{RPM}}{\mathrm{Area}\times \mathrm{MSE}-\mathrm{WOB}}\mathrm{dTorque}$

An optimization algorithm may be run to calculate the range of RPM, WOB, and Flowrate that would give a required change in Tool Yield without change in ROP. Alternatively, the method may also obtain a range of parameters that will give the required Tool Yield and the best ROP. Given below is an example of the objective function which may be used in any other form. This may be used in both ROP control or WOB control mode of drilling.

• • Objective function:

${\min \left(\Delta \mathrm{TY}-\leftarrow {\mathrm{\Delta TY}}_{\mathrm{required}}\right)}^2\max \Delta {\mathrm{ROP}}^2\mathrm{or}\min -\Delta \mathrm{ROP}❘\Delta \mathrm{ROP}❘\mathrm{Bounds}\mathrm{WOB\_min}<\mathrm{WOB}<\mathrm{WOB\_max}\mathrm{RPM\_max}<\mathrm{RPM}<\mathrm{RPOM\_min}\mathrm{Flow\_max}<\mathrm{Flow}<\mathrm{Flow\_min}$

In one example approach, each parameter further includes a limit on how much the parameter may change. Based on that limit, a recommendation for WOB/ROP, RPM, and Flowrate may be provided.

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

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

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

EXAMPLE EMBODIMENTS

Aspects disclosed herein include:

Embodiment #1: A method of steering a drill string when forming a wellbore in a subterranean formation, the method comprising identifying two or more parameters associated with steering the drill string in a subject well; determining, via a statistical model, individual contributions to a tool yield model by each of the identified parameters; and suggesting, based on the statistical model and on current values of the identified parameters, one or more changes in the identified parameters, the changes sufficient to alter a trajectory of the drill string in the subject well.

Embodiment #2: The method of Embodiment #1, wherein determining individual contributions includes obtaining the tool yield model, wherein the tool yield model is a regression model of drilling information from similar wells; performing statistical modeling of the tool yield model to identify independent contributions to output as a linear combination of the independent contributions to output of each identified parameter; and performing regression analysis of each parameter/output pair.

Embodiment #3: The method of any one of Embodiments #1 and 2, wherein the tool yield model is a regression model of drilling information for curved sections of boreholes of similar wells, the regression model including hyperparameter tuning.

Embodiment #4: The method of any one of Embodiments #1-3, wherein determining individual contributions to a tool yield model by each of the identified parameters includes retrieving drilling information obtained from offset wells.

Embodiment #5: The method of Embodiment #4, wherein retrieving drilling information obtained from offset wells includes identifying, as offset wells, wells with characteristics like the subject well that are within a radius, R, of the subject well.

Embodiment #6: The method of Embodiment #5, wherein identifying wells with characteristics like the subject well includes calculating a similarity score for each well and, if the similarity score is less than a threshold value, identifying the well as an offset well.

Embodiment #7: The method of Embodiment #5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; and filtering the drilling information to identify wells that used a similar bit type, size, and design as the subject well.

Embodiment #8: The method of Embodiment #5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; and filtering the drilling information to identify wells that used a similar tool size, type, and design as the subject well.

Embodiment #9: The method of Embodiment #5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; and filtering the drilling information to identify wells that used a similar borchole apparatus (BHA) as the subject well.

Embodiment #10: The method of Embodiment #1, wherein the tool yield model is a regression model of drilling information of similar wells and wherein identifying wells like the subject well includes: querying a database to obtain the drilling information associated with different wells; filtering the drilling information to identify wells that are within a radius R of the subject well and that used: a similar bit type, size, and design as the subject well; a similar tool size, type, and design as the subject well; and a similar borehole apparatus (BHA) as the subject well; calculating a similarity score for each identified well; and, if the similarity score is less than a threshold value, labeling the well as an offset well.

Embodiment #11: The method of Embodiment #10, wherein the method further comprises applying a regression model to the drilling information of sections of the offset well that curve to determine the tool yield model.

Embodiment #12: The method of any one of Embodiments #1-3, 10 and 11, wherein suggesting a change in one of the identified parameters includes: calculating a dogleg severity (DLS) required to meet a well plan for the subject well; calculating a current DLS; and if the current DLS is less than the required DLS, applying current parameter values, limits and the statistical model to calculate a direction and amount by with the parameters need to change to obtain the required DLS.

Embodiment #13: The method of any one of Embodiments #1-3, 10 and 11, wherein suggesting one or more changes in the identified parameters includes: calculating a dogleg severity (DLS) required to meet a well plan for the subject well; calculating a current DLS; and if the current DLS is less than the required DLS, determining changes in the parameters that maximize rate of penetration (ROP) or achieves a ROP within certain constrained limits at the required DLS.

Embodiment #14: The method of Embodiment #13, wherein determining changes in the parameters that maximize rate of penetration (ROP) at the required DLS includes solving an optimization problem using an ROP model and the tool yield model

Embodiment #15: The method of any one of Embodiments #1-3, 10 and 11, wherein the method further comprises incorporating the suggested changes in the identified parameters in the drilling system of the subject well; receiving feedback from the drilling system after incorporating the suggested changes, wherein the feedback includes new values for one or more of the identified parameters; updating the current values to reflect the new values; and suggesting, based on the statistical model and on the updated current values of the identified parameters, one or more changes in the identified parameters.

Embodiment #16. A nonvolatile computer readable medium having instructions that, when executed by a processor: identify two or more parameters associated with steering a drill string in a subject well; determine, via a statistical model, individual contributions to a tool yield model by each of the identified parameters; and suggest, based on the statistical model and on current values of the identified parameters, one or more changes in the identified parameters, the changes sufficient to alter a trajectory of the drill string in the subject well.

Embodiment #17. The computer readable medium of Embodiment #16, wherein the instructions that, when executed by the processor, suggest one or more changes in the identified parameters include instructions that, when executed by the processor: calculate a dogleg severity (DLS) required to meet a well plan for the subject well; determine a current DLS; and if the current DLS is less than the required DLS, determine changes in the identified parameters needed to obtain the required DLS.

Embodiment #18. A method of determining tool yield as a function of dogleg severity (DLS) for a drill string in a subject well, the method comprising: querying a database to obtain drilling information associated with different wells; filtering the drilling information to identify wells from the database that are similar to the subject well and that are within a radius R of the subject well; calculating a similarity score for each identified well; if the similarity score is less than a threshold value, labeling the well as an offset well; and applying a regression model with hyperparameter tuning to the drilling information of sections of the offset well that curve.

Embodiment #19. The method of claim Embodiment #18, wherein filtering the drilling information to identify wells from the database that are like the subject well includes filtering the identified wells to find wells that have one or more of: a similar bit type, size, and design as the subject well; a similar tool size, type, and design as the subject well; a similar borehole apparatus (BHA) as the subject well; a similar rotary steering system (RSS) as the subject well; a similar inclination as the planned inclination with respect to measured depth of the drill string; a similar true vertical depth (TVD) as the planned TVD with respect to measured depth of the subject well.

Embodiment #20. The method of any one of Embodiments #18 and 19, wherein the regression model includes hyperparameter tuning.

Claims

1. A method of steering a drill string when forming a wellbore in a subterranean formation, the method comprising: identifying two or more parameters associated with steering the drill string in a subject well;determining, via a statistical model, individual contributions to a tool yield model by each of the identified parameters; andsuggesting, based on the statistical model and on current values of the identified parameters, one or more changes in the identified parameters, the changes sufficient to alter a trajectory of the drill string in the subject well.

2. The method of claim 1, wherein determining individual contributions includes: obtaining the tool yield model, wherein the tool yield model is a regression model of drilling information from similar wells;performing statistical modeling of the tool yield model to identify independent contributions to output as a linear combination of the independent contributions to output of each identified parameter; andperforming regression analysis of each parameter/output pair.

3. The method of claim 1, wherein the tool yield model is a regression model of drilling information for curved sections of boreholes of similar wells, the regression model including hyperparameter tuning.

4. The method of claim 1, wherein determining individual contributions to a tool yield model by each of the identified parameters includes retrieving drilling information obtained from offset wells.

5. The method of claim 4, wherein retrieving drilling information obtained from offset wells includes identifying, as offset wells, wells with characteristics like the subject well that are within a radius, R, of the subject well.

6. The method of claim 5, wherein identifying wells with characteristics like the subject well includes calculating a similarity score for each well and, if the similarity score is less than a threshold value, identifying the well as an offset well.

7. The method of claim 5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; andfiltering the drilling information to identify wells that used a similar bit type, size, and design as the subject well.

8. The method of claim 5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; andfiltering the drilling information to identify wells that used a similar tool size, type, and design as the subject well.

9. The method of claim 5, wherein identifying wells with characteristics like the subject well includes: querying a database to obtain drilling information associated with different wells; andfiltering the drilling information to identify wells that used a similar borehole apparatus (BHA) as the subject well.

10. The method of claim 1, wherein the tool yield model is a regression model of drilling information of similar wells and wherein identifying wells like the subject well includes: querying a database to obtain the drilling information associated with different wells;filtering the drilling information to identify wells that are within a radius R of the subject well and that used: a similar bit type, size, and design as the subject well;a similar tool size, type, and design as the subject well; anda similar borehole apparatus (BHA) as the subject well;calculating a similarity score for each identified well; andif the similarity score is less than a threshold value, labeling the well as an offset well.

11. The method of claim 10, wherein the method further comprises: applying a regression model to the drilling information of sections of the offset well that curve to determine the tool yield model.

12. The method of claim 1, wherein suggesting a change in one of the identified parameters includes: calculating a dogleg severity (DLS) required to meet a well plan for the subject well;calculating a current DLS; andif the current DLS is less than the required DLS, applying current parameter values, limits and the statistical model to calculate a direction and amount by with the parameters need to change to obtain the required DLS.

13. The method of claim 1, wherein suggesting one or more changes in the identified parameters includes: calculating a dogleg severity (DLS) required to meet a well plan for the subject well;calculating a current DLS; andif the current DLS is less than the required DLS, determining changes in the parameters that maximize rate of penetration (ROP) or achieves a ROP within certain constrained limits at the required DLS.

14. The method of claim 13, wherein determining changes in the parameters that maximize rate of penetration (ROP) at the required DLS includes solving an optimization problem using an ROP model and the tool yield model.

15. The method of claim 1, wherein the method further comprises: incorporating the suggested changes in the identified parameters in the drilling system of the subject well;receiving feedback from the drilling system after incorporating the suggested changes, wherein the feedback includes new values for one or more of the identified parameters;updating the current values to reflect the new values; andsuggesting, based on the statistical model and on the updated current values of the identified parameters, one or more changes in the identified parameters.

16. A nonvolatile computer readable medium having instructions that, when executed by a processor: identify two or more parameters associated with steering a drill string in a subject well;determine, via a statistical model, individual contributions to a tool yield model by each of the identified parameters; andsuggest, based on the statistical model and on current values of the identified parameters, one or more changes in the identified parameters, the changes sufficient to alter a trajectory of the drill string in the subject well.

17. The computer readable medium of claim 16, wherein the instructions that, when executed by the processor, suggest one or more changes in the identified parameters include instructions that, when executed by the processor: calculate a dogleg severity (DLS) required to meet a well plan for the subject well;determine a current DLS; andif the current DLS is less than the required DLS, determine changes in the identified parameters needed to obtain the required DLS.

18. A method of determining tool yield as a function of dogleg severity (DLS) for a drill string in a subject well, the method comprising: querying a database to obtain drilling information associated with different wells;filtering the drilling information to identify wells from the database that are similar to the subject well and that are within a radius R of the subject well;calculating a similarity score for each identified well;if the similarity score is less than a threshold value, labeling the well as an offset well; andapplying a regression model with hyperparameter tuning to the drilling information of sections of the offset well that curve.

19. The method of claim 18, wherein filtering the drilling information to identify wells from the database that are like the subject well includes filtering the identified wells to find wells that have one or more of: a similar bit type, size, and design as the subject well;a similar tool size, type, and design as the subject well;a similar borehole apparatus (BHA) as the subject well;a similar rotary steering system (RSS) as the subject well;a similar inclination as the planned inclination with respect to measured depth of the drill string; anda similar true vertical depth (TVD) as the planned TVD with respect to measured depth of the subject well.

20. The method of claim 18. wherein the regression model includes hyperparameter tuning.