FORMATION BREAKDOWN PRESSURE NEAR WELLBORES

Among other things, methods and systems are described for calculating formation breakdown pressures. A method involves determining, during hydraulic fracturing operations, a pore pressure for a wellbore; determining a poroelastic stress for the wellbore using a poroelastic stress equation and based on the pore pressure; determining, during the hydraulic fracturing operations, a breakdown pressure upper bound for the wellbore; applying, during the hydraulic fracturing operations, a stress correction on the breakdown pressure upper bound based on whether the wellbore is an open hole wellbore or a cemented liner wellbore; and determining, during the hydraulic fracturing operations, a breakdown pressure for the wellbore based on the stress-corrected upper bound breakdown pressure for the wellbore.

TECHNICAL FIELD

The present disclosure describes systems and methods for determining formation breakdown pressure near wellbores.

BACKGROUND

Well stimulation is a well intervention technique in which several operations are performed on a well to increase the well's hydrocarbon production. Hydraulic fracturing is an example well stimulation technique in which the bedrock formation is fractured by injecting highly pressurized fluids. In this technique, different drilling fluids are pumped into targeted completion zones to stimulate the well. The success of a hydraulic fracturing operation depends on an accurate estimation of the formation breakdown pressure prior to the actual stimulation job being performed.

Among other things, an accurate estimation of the breakdown pressure value is important for determining how much horsepower is required on-site for creating adequate fracture geometry and successful placement of stimulation materials into the created fracture. Overstimulation can lead to an inappropriate selection of the well completion type and expenditure loss, while under-stimulation can result in operational failures. Accurately calculating breakdown pressure value is one of the significant challenges in hydraulic fracturing operations, especially for deviated and horizontal wells in tight sandstone formations and compressional in-situ stress regimes.

SUMMARY

Existing techniques for accurately calculating the formation breakdown pressure are deficient or limited, especially for deviated and horizontal wellbores.

This disclosure describes systems and methods for implementing a workflow for accurately calculating formation breakdown pressures, e.g., for deviated and horizontal wellbores. The workflow considers a generalized stress model for an arbitrary wellbore orientation and azimuth. The workflow employs the theory of poroelasticity to compute pore pressures and poroelastic stresses numerically. The workflow then uses the computed pore pressures and poroelastic stresses to accurately calculate the breakdown pressure.

As described in more detail below, the calculated breakdown pressure takes into account the underlying fluid (e.g., hydrocarbon) and solid (e.g., rock formation) physical parameters when computing the breakdown pressure at a particular depth and wellbore orientation. The underlying flow and mechanics parameters include an initial wellbore pressure, fracturing fluid compressibility and viscosity, in-situ stresses in the formation, formation strength, permeability of the rock formation, porosity of the rock formation, minimum and maximum horizontal stresses, inclination and azimuth angles of the wellbore orientation, the tensile strength of the formation rock, a poroelastic parameter, the Poisson ratio of the rock formation, and the wellbore radius.

One aspect of the subject matter described in this specification may be embodied in a method that involves receiving input parameters for computing a breakdown pressure for a wellbore in a formation, the input parameters comprising an inclination angle of the wellbore from a vertical axis, and an azimuth angle of the wellbore relative to a maximum horizontal stress direction, at a particular depth; determining, during hydraulic fracturing operations, a pore pressure for the wellbore based on a time duration, an injection fluid compressibility, and a poroelastic parameter; determining a poroelastic stress for the wellbore using a poroelastic stress equation and based on the pore pressure determined for the wellbore, an empirical parameter, a pore pressure, the poroelastic parameter, a tensile strength of rock, and a Poisson ratio; determining, during the hydraulic fracturing operations, a breakdown pressure upper bound for the wellbore based on a minimum horizontal stress and a maximum horizontal stress for the wellbore, an overburden vertical stress for the wellbore, the inclination angle of the wellbore, the azimuth angle of the wellbore, and a wellbore circumferential angle; applying, during the hydraulic fracturing operations, a stress correction on the breakdown pressure upper bound for the wellbore based on whether the wellbore is an open hole wellbore or a cemented liner wellbore; and determining, during the hydraulic fracturing operations, a breakdown pressure for the wellbore based on the stress-corrected upper bound breakdown pressure for the wellbore, the poroelastic stress for the wellbore, and the pore pressure for the wellbore.

The previously described implementation is implementable using a computer-implemented method; a non-transitory, computer-readable medium storing computer-readable instructions to perform the computer-implemented method; and a computer system including a computer memory interoperably coupled with a hardware processor configured to perform the computer-implemented method or the instructions stored on the non-transitory, computer-readable medium. These and other embodiments may each optionally include one or more of the following features.

In some implementations, the method further involves determining, based at least on the breakdown pressure, a horsepower level needed for creating a fracture geometry used in the hydraulic fracturing operations; determining a successful placement of stimulation materials for the hydraulic fracturing operations; determining, based at least on the breakdown pressure, a pressure rating of tubulars required for fracturing treatment; and completing the hydraulic fracturing operations using the horsepower level, the successful placement of the stimulation materials, and one or more tubulars having the determined pressure rating of the tubulars required for the fracturing treatment.

In some implementations, determining the pore pressure for the wellbore involves determining the pore pressure for the wellbore using a Stehfest method equation that is a function of the time duration, a distance from the wellbore in a radial direction, the injection fluid compressibility, and the poroelastic parameter.

In some implementations, the Stehfest method equation is further a function of a modified Bessel function of a second kind of order0.

In some implementations, the poroelastic stress is further based on a Composite Simpson's Rule for numerical integration.

In some implementations, the input parameters further include an initial wellbore pressure, a rock permeability, a rock porosity, an injection fluid compressibility, an injection fluid viscosity, a Poisson ratio, a wellbore radius, and a distance from the wellbore in a radial direction, at a particular depth.

In some implementations, an initial value for the distance from the wellbore in a radial direction is two and a half the wellbore radius.

In some implementations, the wellbore is one of: (i) a deviated and horizontal wellbore, or (ii) a vertical wellbore.

In some implementations, an initial value for the time duration is a time at which the formation is expected to break after a slurry injection.

In some implementations, an initial value for the time duration is 1000 seconds.

In some implementations, the wellbore is either open hole or cement lined.

Existing techniques for calculating breakdown pressure either compute the breakdown pressure using approximations to analytical solutions (which do not take into account the underlying physical parameters), or use pure numerical solutions (e.g., the Finite Element Method and the Distinct Element Method). Thus, the existing techniques for computing breakdown pressure can be categorized into two main methods or approaches: (i) a first approach that relies on crude approximations of analytical solutions, and (ii) a second approach that relies on pure numerical solutions.

One of the disadvantages of the first approach is that it does not take into account the effects of key physical parameters, such as, rock porosity and permeability, and fracturing fluid compressibility and viscosity. These are key physical parameters that can significantly affect the breakdown pressure. In addition, these parameters can vary (even within the same wellbore), which makes such approximations not reliable. Moreover, the first approach cannot take into account the orientation of the wellbore in an arbitrary setting. Further, approximations to analytical solutions rely heavily on empirical parameters that require extensive resources to calculate (e.g., to be calibrated).

The second approach relies merely on numerical solutions, such as the use of the Distinct Element Method and the Finite Element Method. This approach is computationally expensive and requires both the flow and mechanics problems to be solved in a coupled manner. Therefore, this approach can only provide approximate solutions to the underlying physical equations. Additionally, this approach is still not fully developed. For example, only recently have phase field methods been proposed to simulate hydraulic fracture initiation and propagation. These methods are computationally expensive and rely on simplified models of the actual physical problem.

The disclosed workflow is a hybrid approach that combines the advantages of analytical solutions and numerical techniques and avoids the dependence on any empirical parameters, and theoretically derives an expression of the breakdown pressure. Further, the disclosed workflow works for any arbitrary wellbore orientation by taking into account the corresponding inclination and azimuth angles of the wellbore. Furthermore, eliminating empirical parameters from the workflow removes the need to calibrate these parameters, which adds to the practically of the workflow since parameter calibration is not always possible due to the lack of data. In addition, the disclosed workflow employs numerical techniques that can overcome numerical instability issues when implementing analytical solutions. For example, the disclosed workflow utilizes a Laplace Transform solution to solve for pore pressure and does not invert the Laplace Transform analytically. Rather, the workflow does so numerically to avoid numerical instability issues. In particular, the disclosed workflow solves the underlying partial differential equation analytically using the Laplace Transform, then inverts the obtained solution (in the Laplace Transform domain) numerically using the Stehfest Method. Thus, the workflow computes the breakdown pressure using a rigorously derived theoretical expression.

The disclosed workflow also eliminates the dependence on empirical parameters, which are often associated with approximations to analytical solutions. Removing empirical parameters from the workflow eliminates the need to calibrate these parameters. Doing so adds to the robustness, accuracy, and efficiency (e.g., computing and processing efficiency) of the workflow. Also, the disclosed workflow computes breakdown pressure as a function of underlying physical parameters. This approach results in a more accurate estimate of the breakdown pressure compared to existing techniques. Moreover, incorporating the physical parameters into the workflow is done using a hybrid analytical and numerical approach, which enhances the accuracy and computational efficiency of the disclosed workflow.

DETAILED DESCRIPTION

This disclosure describes systems and methods for implementing a formation breakdown pressure calculation workflow. The workflow considers an arbitrary wellbore orientation and azimuth, uses a generalized stress model, and calculates the formation breakdown pressure as a function of the underlying flow and mechanics parameters. Additionally, this disclosure describes actions that can be performed based on the calculated breakdown pressure.

The disclosed workflow is an extension of a workflow described in U.S. Patent. No. 11,675,106, entitled “Predicting formation breakdown pressure for hydrocarbon recovery applications,” which is incorporated herein by reference. The workflow described in U.S. Patent. No. 11,675,106 considers vertical wells only. This disclosure first describes the workflow for calculating the breakdown pressure for a vertical wellbore. The disclosure then adapts the vertical wellbore workflow to a generalized workflow for all other types of wells, e.g., deviated and horizontal wells.

FIG.1illustrates a cross-sectional view of an example of a vertical borehole100subject to in-situ stresses and an induced fracture102during hydraulic fracturing, according to some implementations. As shown inFIG.1, the in-situ stresses include a minimum horizontal stress Shand a maximum horizontal stress SH, where |SH|>|Sh|.

A breakdown pressure (Pf) is the pressure at which fracture initiation occurs. Mathematically, the breakdown pressure can be defined as the pressure at which the maximum tensile stress reaches the tensile strength of the rock (σf) at the wellbore. This is expressed in Equation (1) as:

In Equation (1), for the vertical well case, Sθ(1)is a circumferential stress induced by tectonic stresses (e.g., the two horizontal stresses Shand SH), Sθ(2)is the stress induced by a borehole pressure Pw, and Sθ(3)is the stress induced by the fluid permeation into the formation, which is known as the poroelastic stress. Poroelastic stress is a function of the pore pressure Ppand other underlying physical parameters.

A two-dimensional (2D) cylindrical coordinate system (r, θ) is assumed when solving Equation (1) around the vertical wellbore100. At r=a, which is the wellbore radius, if Equation (1) is satisfied, then it can be assumed that Pf=Pw. In terms of the minimum and maximum horizontal stress Shand SH, Sθ(1)and Sθ(2)can be calculated using Equations (2) and (3), respectively:

The 2D (r, θ) coordinate system can be rotated such that the r-axis is aligned with the orientation of the maximum horizonal stress SH. In this case, Sθ(1)has a maximum value when θ=0, π, which reduces Equation (2) to:

Since the breakdown pressure is being calculated at the wellbore radius, r=a, the expression for Sθ(1)is further reduced to:

Equations (1)-(6) can be used to derive an expression for a breakdown pressure upper bound in the vertical well case. Note that in the upper bound case, Pp=0. Thus, the upper bound breakdown pressure is calculated as:

The breakdown pressure lower bound can be computed as:

In Equation (8), a is the Biot poroelastic coefficient and v is the Poisson ratio. Note that tensile strength of the rock (σf) has a predetermined value.

The breakdown pressure can be calculated as a function of the pore pressure, Pp, and the poroelastic stress, Sθ(3). Specifically, the pore pressure Ppcan be computed using Equation (9) as:

In Equation (9), P0is the initial wellbore pressure, t is the time at which the fracture opens, a is the wellbore radius, r is the radial distance away from the wellbore, and K0(x) is a modified Bessel function of the second kind of order0. The parameter cican be calculated using Equation (10) as:

Further, the parameter c can be calculated using Equation (11) as:

In Equation (11), Ø is the rock porosity, cfis the injection fluid compressibility, K is the rock permeability, and μ is the injection fluid viscosity.

Once the pore pressure Ppis determined, the poroelastic stress can be calculated as:

Then, the breakdown pressure can be calculated as:

In some implementations, Equation (13) can be extended to a generalized stress model to cover the case of deviated and horizontal wells. Specifically, for an arbitrary borehole, a generalized stress model is used to determine the principal stresses affecting the wellbore.

FIG.2illustrates a schematic200of stress transformation for a deviated and horizontal well, according to some implementations. As shown inFIG.2, Shand SHare the minimum and maximum horizontal stresses (|SH|>|Sh|), Svis the vertical (overburden) stress, abis the inclination angle of the well (from the vertical axis), β is the azimuth angle of the well relative to the SHdirection, and θ is the wellbore circumferential angle.

In some implementations, the stress distribution (in polar coordinates) at the wellbore wall is given by Equation set (14):

where

In Equation Sets (14) and (16), σxx, σyy, σzz, σxy, σyz, and σxzare the in-situ stress components of the transformed Cartesian local coordinate system. Further, σr, σθ, σz, σθz, σrθ, and σrθrepresent the stress distribution at the wellbore wall in polar coordinates (r, θ, z) obtained by linear superposition. In particular, σr, σθ, and σzare the radial, hoop, and axial stress components, and σθz, σrθ, and σrzare shear stress components respectively. Moreover, pwis the wellbore pressure (pressure inside the well), ppis the pore pressure (pressure outside the well), a is the Biot poroelastic coefficient, v is the Poisson ratio, ϕ is the porosity, and δ is the wellbore permeability coefficient.

In some implementations, to compute the upper bound for the breakdown pressure, the wellbore permeability coefficient is set to 0 (δ=0) to obtain Equation Set (17):

To compute the upper bound in these generalized settings, the maximum principal stress component acting on the θz-plane is found and balanced with the tensile strength of the rock. To find the principal stresses on the θz-plane, a 2D plane stress problem in which σr=σrθ=σrz=0 is solved. To do so, the 2D stress tensor on the θz-plane is written as:

To compute the principal stress acting on the θz-plane, the eigenvalues of σ are found. To do so, the eigenvalues (λ) are calculated such that

By replacing the 2D stress tensor in Equation (19) with the Matrix (18), Equation (19) translates to:

Then, Equation (21) results from expanding the determinant in Equation (20):

Equation (21) can be solved such that either λ=0 (which corresponds to the principal stress acting on the r-direction, recall that σr=σrθ=σrz=0), or ((σθ−λ)(σz−λ)−σθz2)=0. Thus, Equation (21) can be written as a Quadratic Equation (22):

The unknown variable in Quadratic Equation (22) is λ, which admits the following general solution:

Equation (23) gives the two eigenvalues of the stress tensor σ. Now, the maximum eigenvalue is the maximum principal stress σ2acting on the θz-plane. The maximum principal stress σ2is represented in Equation (24) as

In some implementations, to calculate the upper bound of the breakdown pressure, pwis calculated such that σ2=−σf, where (σf) is the tensile strength of the rock. This translates Equation (24) into:

Equation (25) can be rewritten as:

Both sides of the equation are then squared:

Then, both sides of the equation are expanded:

Solving the above equations leads to Equation (28):

Equation (28) can be simplified to:

Using Equation (29), the upper bound for the breakdown pressure is then calculated as:

FIG.3illustrates an example breakdown pressure calculation workflow300, according to some implementations. The workflow300can be used to calculate the formation breakdown pressure near a wellbore. The wellbore can be a vertical wellbore, a horizontal and deviated wellbore, or any other type of wellbore of any orientation. The workflow300can be performed by a computer system having one or more computers located in one or more locations and programmed appropriately in accordance with this specification. An example of the computer system is the computing system600illustrated inFIG.6and described below.

At step302, the computing system obtains input parameters for the workflow300. Obtaining the input parameters can include receiving input parameter values from other devices or systems, determining predetermined values for input parameters, and/or setting values for input parameters. In some examples, the input parameters include, but are not limited to, initial wellbore pressure P0, rock permeability K, rock porosity Ø, injection fluid compressibility cf, injection fluid viscosity μ, minimum and maximum horizontal stresses Shand SH, overburden vertical stress Sv, tensile strength of the formation rock σf, Biot poroelastic parameter a, Poisson Ratio v, inclination angle of the well ab, azimuth angle of the well relative to the SHdirection β, wellbore radius a, at a particular depth.

At step304, the computer system sets the time, t, to 1000 seconds and sets r to 2.5 a. The time “t” is the time at which the fracture will initiate (e.g., the formation will break) after pumping the drilling fluid at a very high pressure to hydraulically frack/break the formation. In one example, the time, t, is set to 1000 seconds (around 16.6 minutes) for the formation to frack after starting the hydraulic fracturing job.

At step306, the computer system computes the pore pressure p(t,r) using Equations (9), (10), and (11). For the purposes of this workflow, Equations (9), (10), and (11) are reproduced below as Equations (31), (32), and (33), respectively.

In some examples, the computer system sets n=8, but other values are possible.

At step308, the computer system calculates the poroelastic stress using Equation (12), which is reproduced below as Equation (34):

In some examples, the computer system evaluates the integral in Equation (34) using the Composite Simpson's Rule for numerical integration. The steps for evaluating the integral in Equation (34) using the Composite Simpson's Rule for numerical integration is depicted in Table (1) below.

At step310, the computer system calculates the breakdown pressure upper bound using Equation (30), which is reproduced below as Equation (35):

At step312, the computer system applies an effective stress correction to the breakdown pressure upper bound. In some examples, the effective stress correction is based on whether the wellbore is an open hole wellbore or a cemented liner wellbore. More specifically, if the wellbore is open hole, the computer system applies the correction of Equation (36):

And if the wellbore is a cemented liner wellbore, the computer system applies the correction of Equation (37):

At step314, the computer system calculates the breakdown pressure Pfusing Equation (38):

FIGS.4A and4Billustrate the results of measured breakdown pressure and the computed breakdown pressure in deviated wells with open hole and cement liner completions, respectively. The workflow300ofFIG.3was implemented and tested in Matlab against two deviated wells (one well is with an open hole completion, and the other a cemented liner). The results for the open hole well are shown inFIG.4A, along with the upper and lower bounds. The results for the cemented liner are shown inFIG.4B.FIGS.4A and4Bshow a very close match between the measured (actual) breakdown pressure, and the computed breakdown pressure (by workflow300) in both cases.

More specifically,FIG.4Aillustrates the results of measured (actual) breakdown pressure, and the computed breakdown pressure (by workflow300) in an open hole deviated well. The plot on the left shows the formation permeability values (in log scale), and the plot on the right shows the corresponding breakdown pressure values computed in three different ways: the blue curve uses the lower bound formula (Equation (8)), the yellow curve uses the upper bound formula (Equation (7)), and the orange curve uses workflow300. The actual (measured) breakdown pressure values are shown in black dots and match the orange curve (workflow300) very closely.

FIG.4Billustrates the results of measured (actual) breakdown pressure, and the computed breakdown pressure (by workflow300) in a cemented liner deviated well. The plot on the left shows the formation permeability values (in log scale), and the plot on the right shows the corresponding breakdown pressure values computed in three different ways: the blue curve uses the lower bound formula (Equation (8)), and the yellow curve uses the upper bound formula (Equation (7)), and the orange curve uses workflow300. The actual (measured) breakdown pressure values are shown in black dots and match the orange curve (workflow300) very closely.

FIG.5illustrates a flowchart of an example method500, according to some implementations. For clarity of presentation, the description that follows generally describes method500in the context of the other figures in this description. For example, method500can be performed by computer system600ofFIG.6. It will be understood that method500can be performed, for example, by any suitable system, environment, software, hardware, or a combination of systems, environments, software, and hardware, as appropriate. In some implementations, various steps of method500can be run in parallel, in combination, in loops, or in any order.

At step502, method500involves receiving input parameters for computing a breakdown pressure for a wellbore in a formation. The input parameters include an inclination angle of the wellbore from a vertical axis, and an azimuth angle of the wellbore relative to a maximum horizontal stress direction, at a particular depth.

At step504, method500involves determining, during hydraulic fracturing operations, a pore pressure for the wellbore based on a time duration, an injection fluid compressibility, and a poroelastic parameter.

At step506, method500involves determining a poroelastic stress for the wellbore using a poroelastic stress equation and based on the pore pressure determined for the wellbore, an empirical parameter, a pore pressure, the poroelastic parameter, a tensile strength of rock, and a Poisson ratio.

At step508, method500involves determining, during the hydraulic fracturing operations, a breakdown pressure upper bound for the wellbore based on a minimum horizontal stress for the wellbore and the maximum horizontal stress for the wellbore, an overburden vertical stress for the well, the inclination angle of the wellbore, the azimuth angle of the wellbore, and a wellbore circumferential angle.

At step510, method500involves applying, during the hydraulic fracturing operations, a stress correction on the breakdown pressure upper bound for the wellbore based on whether the wellbore is an open hole wellbore or a cemented liner wellbore.

At step512, method500involves determining, during the hydraulic fracturing operations, a breakdown pressure for the wellbore based on the stress-corrected upper bound breakdown pressure for the wellbore, the poroelastic stress for the wellbore, and the pore pressure for the wellbore.

In some implementations, the method further involves determining, based at least on the breakdown pressure, a horsepower level needed for creating a fracture geometry used in the hydraulic fracturing operations; determining a successful placement of stimulation materials for the hydraulic fracturing operations; determining, based at least on the breakdown pressure, a pressure rating of tubulars required for fracturing treatment; and completing the hydraulic fracturing operations using the horsepower level, the successful placement of the stimulation materials, and one or more tubulars having the determined pressure rating of the tubulars required for the fracturing treatment.

A prior estimation/prediction of the formation breakdown pressure is needed to determine the technical and operational specifications of the multistage well completion system required on site. These operational specifications include the pressure rating (e.g., is a 10,000 psi-rated multistage completion system or a 15,000 psi-rated multistage completion system to be used). Higher pressure ratings of the well completion will require higher horsepower levels, and vice versa. More specifically, if the predicted breakdown pressure is higher than 15,000 psi, then a 10,000 psi-rated well completion system is inadequate to successfully frack the formation. On the other hand, if the predicted breakdown pressure is less than 15,000 psi, then a 15,000 psi-rated well completion system might not be needed which will save unnecessary costs due to over-design of completion and surface equipment.

During the hydraulic fracturing process, a fluid is pumped into the well at a very high pressure (in some cases it can reach up to 15,000 psi). Water-based fluids (slick-water) are the most commonly used fluids during this well stimulation activity (i.e., hydraulic fracturing). If the predicted breakdown pressure is high, then other chemical additives (such as special chemical-based viscoelastic surfactants) can be added/combined with the fracturing fluid to increase its density and improve its efficiency, and therefore, reduce the horsepower level of the surface equipment to meet the formation breakdown pressure requirements. Therefore, knowing the breakdown pressure in advance (in addition to the completion type) can also help selecting the type of stimulation materials that should be added to the fracturing fluid.

In some implementations, determining the pore pressure for the wellbore involves determining the pore pressure for the wellbore using a Stehfest method equation that is a function of the time duration, a distance from the wellbore in a radial direction, the injection fluid compressibility, and the poroelastic parameter.

In some implementations, the Stehfest method equation is further a function of a modified Bessel function of a second kind of order0.

In some implementations, the poroelastic stress is further based on a Composite Simpson's Rule for numerical integration.

In some implementations, the input parameters further include an initial wellbore pressure, a rock permeability, a rock porosity, an injection fluid compressibility, an injection fluid viscosity, a Poisson ratio of the formation rock, a wellbore radius, and a distance from the wellbore in a radial direction, at a particular depth.

In some implementations, an initial value for the distance from the wellbore in a radial direction is two and a half the wellbore radius.

In some implementations, the wellbore is one of: (i) a deviated and horizontal wellbore, or (ii) a vertical wellbore.

In some implementations, an initial value for the time duration is a time at which the formation is expected to break after a slurry injection.

In some implementations, an initial value for the time duration is 1000 seconds.

In some implementations, the wellbore includes either open hole completions or cement liners.

FIG.6is a block diagram of an example computer system600that can be used to provide computational functionalities associated with described algorithms, methods, functions, processes, flows, and procedures, according to some implementations of the present disclosure.

The illustrated computer602is intended to encompass any computing device such as a server, a desktop computer, an embedded computer, a laptop/notebook computer, a wireless data port, a smart phone, a personal data assistant (PDA), a tablet computing device, or one or more processors within these devices, including physical instances, virtual instances, or both. The computer602can include input devices such as keypads, keyboards, and touch screens that can accept user information. Also, the computer602can include output devices that can convey information associated with the operation of the computer602. The information can include digital data, visual data, audio information, or a combination of information.

The information can be presented in a graphical user interface (UI) (or GUI). In some implementations, the inputs and outputs include display ports (such as DVI-I+2x display ports), USB 3.0, GbE ports, isolated DI/O, SATA-III (6.0 Gb/s) ports, mPCle slots, a combination of these, or other ports. In instances of an edge gateway, the computer602can include a Smart Embedded Management Agent (SEMA), such as a built-in ADLINK SEMA 2.2, and a video sync technology, such as Quick Sync Video technology supported by ADLINK MSDK+. In some examples, the computer602can include the MXE-5400 Series processor-based fanless embedded computer by ADLINK, though the computer602can take other forms or include other components.

The computer602can serve in a role as a client, a network component, a server, a database, a persistency, or components of a computer system for performing the subject matter described in the present disclosure. The illustrated computer602is communicably coupled with a network630. In some implementations, one or more components of the computer602can be configured to operate within different environments, including cloud-computing-based environments, local environments, global environments, and combinations of environments.

At a high level, the computer602is an electronic computing device operable to receive, transmit, process, store, and manage data and information associated with the described subject matter. According to some implementations, the computer602can also include, or be communicably coupled with, an application server, an email server, a web server, a caching server, a streaming data server, or a combination of servers.

The computer602can receive requests over network630from a client application (for example, executing on another computer602). The computer602can respond to the received requests by processing the received requests using software applications. Requests can also be sent to the computer602from internal users (for example, from a command console), external (or third) parties, automated applications, entities, individuals, systems, and computers.

Each of the components of the computer602can communicate using a system bus603. In some implementations, any or all of the components of the computer602, including hardware or software components, can interface with each other or the interface604(or a combination of both), over the system bus. Interfaces can use an application programming interface (API)612, a service layer613, or a combination of the API612and service layer613. The API612can include specifications for routines, data structures, and object classes. The API612can be either computer-language independent or dependent. The API612can refer to a complete interface, a single function, or a set of APIs612.

The service layer613can provide software services to the computer602and other components (whether illustrated or not) that are communicably coupled to the computer602. The functionality of the computer602can be accessible for all service consumers using this service layer613. Software services, such as those provided by the service layer613, can provide reusable, defined functionalities through a defined interface. For example, the interface can be software written in JAVA, C++, or a language providing data in extensible markup language (XML) format. While illustrated as an integrated component of the computer602, in alternative implementations, the API612or the service layer613can be stand-alone components in relation to other components of the computer602and other components communicably coupled to the computer602. Moreover, any or all parts of the API612or the service layer613can be implemented as child or sub-modules of another software module, enterprise application, or hardware module without departing from the scope of the present disclosure.

The computer602can include an interface604. Although illustrated as a single interface604inFIG.6, two or more interfaces604can be used according to particular needs, desires, or particular implementations of the computer602and the described functionality. The interface604can be used by the computer602for communicating with other systems that are connected to the network630(whether illustrated or not) in a distributed environment. Generally, the interface604can include, or be implemented using, logic encoded in software or hardware (or a combination of software and hardware) operable to communicate with the network630. More specifically, the interface604can include software supporting one or more communication protocols associated with communications. As such, the network630or the interface's hardware can be operable to communicate physical signals within and outside of the illustrated computer602.

The computer602includes a processor605. Although illustrated as a single processor605inFIG.6, two or more processors605can be used according to particular needs, desires, or particular implementations of the computer602and the described functionality. Generally, the processor605can execute instructions and manipulate data to perform the operations of the computer602, including operations using algorithms, methods, functions, processes, flows, and procedures as described in the present disclosure.

The computer602can also include a database606that can hold data for the computer602and other components connected to the network630(whether illustrated or not). For example, database606can be an in-memory, conventional, or a database storing data consistent with the present disclosure. In some implementations, the database606can be a combination of two or more different database types (for example, hybrid in-memory and conventional databases) according to particular needs, desires, or particular implementations of the computer602and the described functionality. Although illustrated as a single database606inFIG.6, two or more databases (of the same, different, or combination of types) can be used according to particular needs, desires, or particular implementations of the computer602and the described functionality. While database606is illustrated as an internal component of the computer602, in alternative implementations, database606can be external to the computer602.

The computer602also includes a memory607that can hold data for the computer602or a combination of components connected to the network630(whether illustrated or not). Memory607can store any data consistent with the present disclosure. In some implementations, memory607can be a combination of two or more different types of memory (for example, a combination of semiconductor and magnetic storage) according to particular needs, desires, or particular implementations of the computer602and the described functionality. Although illustrated as a single memory607inFIG.6, two or more memories607(of the same, different, or combination of types) can be used according to particular needs, desires, or particular implementations of the computer602and the described functionality. While memory607is illustrated as an internal component of the computer602, in alternative implementations, memory607can be external to the computer602.

An application608can be an algorithmic software engine providing functionality according to particular needs, desires, or particular implementations of the computer602and the described functionality. For example, an application608can serve as one or more components, modules, or applications608. Multiple applications608can be implemented on the computer602. Each application608can be internal or external to the computer602.

The computer602can also include a power supply614. The power supply614can include a rechargeable or non-rechargeable battery that can be configured to be either user- or non-user-replaceable. In some implementations, the power supply614can include power-conversion and management circuits, including recharging, standby, and power management functionalities. In some implementations, the power-supply614can include a power plug to allow the computer602to be plugged into a wall socket or a power source to, for example, power the computer602or recharge a rechargeable battery.

There can be any number of computers602associated with, or external to, a computer system including computer602, with each computer602communicating over network630. Further, the terms “client,” “user,” and other appropriate terminology can be used interchangeably without departing from the scope of the present disclosure. Moreover, the present disclosure contemplates that many users can use one computer602and one user can use multiple computers602.

FIG.7illustrates hydrocarbon production operations700that include both one or more field operations710and one or more computational operations712, which exchange information and control exploration for the production of hydrocarbons. In some implementations, outputs of techniques of the present disclosure can be performed before, during, or in combination with the hydrocarbon production operations700, specifically, for example, either as field operations710or computational operations712, or both.

Examples of field operations710include forming/drilling a wellbore, hydraulic fracturing, producing through the wellbore, injecting fluids (such as water) through the wellbore, to name a few. In some implementations, methods of the present disclosure can trigger or control the field operations710. For example, the methods of the present disclosure can generate data from hardware/software including sensors and physical data gathering equipment (e.g., seismic sensors, well logging tools, flow meters, and temperature and pressure sensors). The methods of the present disclosure can include transmitting the data from the hardware/software to the field operations710and responsively triggering the field operations710including, for example, generating plans and signals that provide feedback to and control physical components of the field operations710. Alternatively or in addition, the field operations710can trigger the methods of the present disclosure. For example, implementing physical components (including, for example, hardware, such as sensors) deployed in the field operations710can generate plans and signals that can be provided as input or feedback (or both) to the methods of the present disclosure.

Examples of computational operations712include one or more computer systems720that include one or more processors and computer-readable media (e.g., non-transitory computer- readable media) operatively coupled to the one or more processors to execute computer operations to perform the methods of the present disclosure. The computational operations712can be implemented using one or more databases718, which store data received from the field operations710and/or generated internally within the computational operations712(e.g., by implementing the methods of the present disclosure) or both. For example, the one or more computer systems720process inputs from the field operations710to assess conditions in the physical world, the outputs of which are stored in the databases718. For example, seismic sensors of the field operations710can be used to perform a seismic survey to map subterranean features, such as facies and faults. In performing a seismic survey, seismic sources (e.g., seismic vibrators or explosions) generate seismic waves that propagate in the earth and seismic receivers (e.g., geophones) measure reflections generated as the seismic waves interact with boundaries between layers of a subsurface formation. The source and received signals are provided to the computational operations712where they are stored in the databases718and analyzed by the one or more computer systems720.

In some implementations, one or more outputs722generated by the one or more computer systems720can be provided as feedback/input to the field operations710(either as direct input or stored in the databases718). The field operations710can use the feedback/input to control physical components used to perform the field operations710in the real world.

For example, the computational operations712can process the seismic data to generate three-dimensional (3D) maps of the subsurface formation. The computational operations712can use these 3D maps to provide plans for locating and drilling exploratory wells. In some operations, the exploratory wells are drilled using logging-while-drilling (LWD) techniques which incorporate logging tools into the drill string. LWD techniques can enable the computational operations712to process new information about the formation and control the drilling to adjust to the observed conditions in real-time.

The one or more computer systems720can update the3D maps of the subsurface formation as information from one exploration well is received and the computational operations712can adjust the location of the next exploration well based on the updated3D maps. Similarly, the data received from production operations can be used by the computational operations712to control components of the production operations. For example, production well and pipeline data can be analyzed to predict slugging in pipelines leading to a refinery and the computational operations712can control machine operated valves upstream of the refinery to reduce the likelihood of plant disruptions that run the risk of taking the plant offline.

In some implementations of the computational operations712, customized user interfaces can present intermediate or final results of the above-described processes to a user. Information can be presented in one or more textual, tabular, or graphical formats, such as through a dashboard. The information can be presented at one or more on-site locations (such as at an oil well or other facility), on the Internet (such as on a webpage), on a mobile application (or app), or at a central processing facility.

The presented information can include feedback, such as changes in parameters or processing inputs, that the user can select to improve a production environment, such as in the exploration, production, and/or testing of petrochemical processes or facilities. For example, the feedback can include parameters that, when selected by the user, can cause a change to, or an improvement in, drilling parameters (including drill bit speed and direction) or overall production of a gas or oil well. The feedback, when implemented by the user, can improve the speed and accuracy of calculations, streamline processes, improve models, and solve problems related to efficiency, performance, safety, reliability, costs, downtime, and the need for human interaction.

In some implementations, the feedback can be implemented in real-time, such as to provide an immediate or near-immediate change in operations or in a model. The term real-time (or similar terms as understood by one of ordinary skill in the art) means that an action and a response are temporally proximate such that an individual perceives the action and the response occurring substantially simultaneously. For example, the time difference for a response to display (or for an initiation of a display) of data following the individual's action to access the data can be less than 1 millisecond (ms), less than 1 second(s), or less than 5 s. While the requested data need not be displayed (or initiated for display) instantaneously, it is displayed (or initiated for display) without any intentional delay, taking into account processing limitations of a described computing system and time required to, for example, gather, accurately measure, analyze, process, store, or transmit the data.

Events can include readings or measurements captured by downhole equipment such as sensors, pumps, bottom hole assemblies, or other equipment. The readings or measurements can be analyzed at the surface, such as by using applications that can include modeling applications and machine learning. The analysis can be used to generate changes to settings of downhole equipment, such as drilling equipment. In some implementations, values of parameters or other variables that are determined can be used automatically (such as through using rules) to implement changes in oil or gas well exploration, production/drilling, or testing. For example, outputs of the present disclosure can be used as inputs to other equipment and/or systems at a facility. This can be especially useful for systems or various pieces of equipment that are located several meters or several miles apart, or are located in different countries or other jurisdictions.

Moreover, the separation or integration of various system modules and components in the previously described implementations should not be understood as requiring such separation or integration in all implementations; and the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

The nomenclature used in this disclosure is listed in Table 2:

TABLE 2NomenclaturePf= Formation Breakdown Pressure (psi)σf= The Tensile Strength of the Rock (psi)Sθ(1)= The Circumferential Stress (Stress due to Tetonic Stresses) (psi)Sθ(2)= Stress Induced by Borehole Pressure (psi)Sθ(3)= Poroelastic Stress (psi)Pp= Pore Pressure (psi)Pw= Borehole Pressure (psi)P0= Initial Wellbore Pressure (psi)Sh= Minimum Horizontal Stress (psi)SH= Maximum Horizontal Stress (psi)r = Distance from Wellbore in Radial Direction (ft)a = Wellbore Radius (ft)p(t, r) = Pore Pressure (psi) as a Function of time (seconds), and Distance from Wellbore (ft)K = Rock Permeability (md)Ø = Rock Porosity (Dimensionless)cf=Injection⁢Fluid⁢Compressiblity(1p⁢s⁢i)μ = Injection Fluid Viscosity (cp)t = Time (seconds)K0(x) = Modifed Bessel Function of the Second Kind of Order 0β = Empirical Parameter (Dimensionless)α = Biot Poroelastic Paramter (Dimensionless)v = Poisson Ratio (Dimensionless).