WO2025117441A1

WO2025117441A1 - Determination of operating spaces for control of a subterranean operation

Info

Publication number: WO2025117441A1
Application number: PCT/US2024/057274
Authority: WO
Inventors: Pedro ARÉVALO; Alexander Starostin
Original assignee: Baker Hughes Oilfield Operations LLC
Current assignee: Baker Hughes Oilfield Operations LLC
Priority date: 2023-11-29
Filing date: 2024-11-25
Publication date: 2025-06-05
Anticipated expiration: 2026-05-29

Abstract

A method of performing a subterranean operation includes flowing a fluid through a borehole in a subterranean formation, providing a pressure limit, providing a downhole formation pressure constraint, simulating fluid pressure in the borehole using a mathematical model, and determining a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm. The optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint. The method also includes performing the subterranean operation using the determined boundaries.

Description

DETERMINATION OF OPERATING SPACES FOR CONTROL OF A SUBTERRANEAN

OPERATION

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Application No. 63/603,885, filed on November 29, 2023, which is incorporated herein by reference in its entirety.

BACKGROUND

[0001] Exploration and production of hydrocarbons require a number of diverse activities to be performed in a borehole penetrating a resource bearing formation. Such activities include drilling, performing downhole measurements, casing perforation, hydraulic fracturing, formation evaluation, and pressure pumping. Some activities, such as drilling and production, involve controlling the pressure and flow rate of fluid circulated through a borehole and/or entering a borehole from a formation.

SUMMARY

[0002] An embodiment of a method of performing a subterranean operation includes flowing a fluid through a borehole in a subterranean formation, providing a pressure limit, providing a downhole formation pressure constraint, simulating fluid pressure in the borehole using a mathematical model, and determining a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm. The optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint. The method also includes performing the subterranean operation using the determined boundaries.

[0003] An embodiment of a system for performing a subterranean operation includes a processor configured to perform the subterranean operation using a borehole system disposed in a borehole in a subterranean formation, the borehole system including a borehole string. The processor is configured to flow a fluid through the borehole, acquire a pressure limit, acquire a downhole formation pressure constraint, simulate fluid pressure in the borehole using a mathematical model, and determine a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm. The optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint. The processor is also configured to perform the subterranean operation using the determined boundaries.

BRIEF DESCRIPTION OF THE DRAWINGS

[0004] The following descriptions should not be considered limiting in any way. With reference to the accompanying drawings, like elements are numbered alike:

[0005] Figure 1 is a cross-sectional view of an embodiment of a system for performing subterranean operations;

[0006] Figure 2A depicts aspects of an example of fluid pressure simulations using a hydraulics model of a borehole system;

[0007] Figure 2B depicts aspects of an example of effective circulating density simulations using a hydraulics model of a borehole system;

[0008] Figure 3 depicts an example of an operating space in the form of a two- dimensional array, the operating space indicating operating boundaries for a combination of mud weight and surface flow rate;

[0009] Figure 4 depicts an example of projections of operating spaces during a drilling operation for estimation of operational limits and pressure windows ahead of a drill bit along a projected drilling path; and

[0010] Figure 5 is a flow chart depicting an embodiment of a method of controlling a subterranean operation.

DETAILED DESCRIPTION

[0011] Systems and methods for monitoring and controlling subterranean operations are described herein. Embodiments of a method include determining operational boundaries related to circulation of fluid through a borehole and a system (through pumps and fluid tanks). The operational boundaries are used to control operational parameters of a subterranean operation, such as surface pressure and flow rate, mud weight, composition of injected fluids, and others.

[0012] An embodiment of a method includes generating an operating space that prescribes boundaries for operational parameters related to control of fluid flow and mud weight (fluid composition) in a borehole. An embodiment of an operating space (“safe operating space”) is a multi-dimensional (e.g., two-dimensional or three-dimensional) space or matrix having dimensions defined by a combination of hydraulic boundaries. For example, the safe operating space is a two-dimensional space defined by two hydraulic boundaries. In an embodiment, the hydraulic boundaries include a surface flow rate boundary and a mud weight boundary.

[0013] The hydraulic boundaries may be determined based on simulation of a borehole system or portions thereof. For example, determination of the operating space is performed based on a mathematical model of fluid flow through a subterranean system (“hydraulics model”), a borehole string model or other information related to geometric and material properties of a borehole string, limitations of surface equipment (e.g., pump pressure and flow rate limits) and earth formation properties, such as earth formation constraints (pore pressure, fracture pressure). The safe operating space may be determined using an optimization procedure that runs the hydraulics model in iterations with different input parameters until boundaries for current operational parameters are found.

[0014] In an embodiment, control of operational parameters, such as flow rate and mud weight, can be realized automatically and in real time using the safe operating space. For example, a processing device calculates the safe operating space, and sends boundaries to a control device or system that controls a subterranean operation based on the boundaries. The safe operating space includes the boundaries. For example, a rig control system controls mud weight (e.g., by controlling solids content in injected fluid) and surface flow rate to stay within the boundaries corresponding to the safe operating space. Embodiments may also include generating predictions or projections of the safe operating space and optimal parameters, which are parameters within the boundaries of the predicted or projected safe operating space. A prediction or projection generated at a given time refers to a greater subterranean depth of the borehole (greater measured depth (MD), or greater true vertical depth (TVD)), than a current MD or TVD at the given time.

[0015] Embodiments described herein present a number of advantages. The embodiments allow for effective real time control of drilling and other operations in an automated manner to maintain operational parameters within certain boundaries so as to avoid damage to equipment or an earth formation, and to optimize such parameters. The safe operating space can be used to calculate set points or updated set points for automated systems. Examples of damage to equipment that can be avoided include damage of a fluid pump (mud pump) and damage of a drilling system pipe system (e.g. standpipe). Examples of damage to the earth formation that can be avoided include flow of formation fluids into the borehole (a kick) and the fracturing of the earth formation,

[0016] Referring to Figure 1, a system for performing subterranean operations (e.g., drilling, logging, stimulation, production, etc.) includes a borehole string 12 disposed in a wellbore or borehole 14 that penetrates at least one earth formation 16 during a drilling operation. As described herein, a “borehole” or “wellbore” refers to a single hole that makes up all or part of a drilled well. As described herein, “earth formation” refer to the various features and materials that may be encountered in a subsurface environment and surround the borehole.

[0017] In an embodiment, the borehole string 12 is configured as a drill string 12. However, the system 10 and the borehole string 12 are not so limited. For example, the borehole string 12 can be a production string (e.g., including coiled tubing or pipe) or other type of string that can be disposed in the borehole 14.

[0018] In an embodiment, the system 10 includes a derrick 18 that supports a rotary table 20 that is rotated at a desired rotational speed (revolutions per minute (RPM)). The drill string 12 includes one or more drill pipe sections that extend from the rotary table and are connected to a drilling assembly 22 that includes a drill bit 24. Drilling fluid or drilling mud (also referred to as “injected fluid”) is pumped through the drill string 12 and/or the borehole 14. The drilling assembly 22 and/or other components of the drill string 12 (or components connected to the drill string 12) may be configured as at least part of a bottomhole assembly (BHA) 26.

[0019] The drilling assembly 22 may be rotated from the surface as discussed above, using the rotary table 20 or a top drive, or may be rotated in another manner. For example, a drill motor or mud motor 28 can be coupled to the drilling assembly 22 to rotate the drilling assembly 22.

[0020] The drilling assembly 22 may include a steering assembly 30 connected to the drill bit 24. The steering assembly 30 may be a bent sub steering assembly, a rotary steering assembly or other suitable device or system. The steering assembly 30 can be utilized to steer the drill bit 24 and the borehole string 12 through the formation 16.

[0021] The system 10 includes any number of downhole tools 32 for various processes including formation drilling, geosteering, and formation evaluation (FE) for measuring versus depth and/or time one or more physical quantities in or around a borehole (e.g., formation properties, drilling mud properties, and/or borehole properties). The tools 32 may be included in or embodied as a BHA, drill string component or other suitable carrier. The tools may include a measurement while drilling tool including sensors for directional measurement (e.g., inclination and azimuth). The tools may further include a power generator providing electrical power to the tools in the BHA or drill string. [0022] The system 10 also includes surface components, devices and/or systems for controlling circulation of fluid through the borehole 14. For example, a pumping device 34 is connected to a mud tank 36 (fluid tank) or other fluid source, and pumps fluid such as drilling mud into the borehole string 12 via a flow line 38 (injected fluid). Properties of the drilling mud (e.g., density, viscosity, mud weight, etc.) may be controlled or adjusted via a mud mixer 40. The drilling mud is injected into the borehole string via a standpipe (not shown) and returns through an annulus of the borehole 14 to the surface and to a return line 42. The annulus is defined by an outer diameter of the borehole string 12 and a diameter of the borehole 14.

[0023] One or more downhole components, such as the drill string 12, the downhole tool 32, the drilling assembly 22 and the drill bit 24, include one or more sensors configured to measure various parameters of fluid, surface equipment, the borehole string, the formation and/or borehole. For example, one or more fluid flow sensing devices 44 may be disposed at one or more locations on the borehole string 12 along a length of the borehole 14, e.g., the open hole section. Each fluid flow sensing device 44 includes one or more sensors for measuring parameters of fluid in the borehole, such as pressure and density.

[0024] The system 10 also includes sensors for measuring parameters at the surface. For example, sensors 46 may be placed at the flow line 38 and/or the return line 42 for measuring parameters such as pressure, flow rate, density, rheology, viscosity, cuttings content, fluid content (e.g., oil, water and/or gas), and temperature. Other sensors such as a pump monitoring device 48 may be included to measure operational parameters of the pumping device 34. String operation sensors, such as sensor 49, may be included to monitor string related parameters, such as rate of penetration (ROP), weight on bit (WOB), revolutions per minute (RPM), and/or torque. Such surface parameter measurements may be performed in real time during an operation.

[0025] Various other sensors may be incorporated into the system 10. For example, the borehole string 12 includes one or more sensors for formation evaluation measurements and/or other parameters of interest relating to the formation, borehole, geophysical characteristics, and borehole fluids. Such sensors may include formation evaluation sensors (e.g., resistivity, dielectric constant, water saturation, porosity, density and/or permeability), sensors for measuring borehole parameters (e.g., borehole size), and sensors for measuring aspects of the borehole string and/or components therein (e.g., bending moment, temperature and/or vibrations). [0026] Generally during drilling, operators monitor fluid properties such as pressure, flow rate and/or density and control operational parameters to maintain borehole fluid pressures within desired boundary conditions. Such boundary conditions depend on formation constraints, such as formation pore pressure and formation fracture pressure. Fluid properties are monitored and operational parameters adjusted as needed to maintain borehole fluid pressure within the boundary conditions and between the pore pressure and the fracture pressure.

[0027] For example, an operator controls fluid density at the surface so as to prevent an underbalanced condition in the borehole 14 and to avoid flow in from the formation (pressure in the borehole is lower than the pore pressure in the formation). On the other hand, an operator controls fluid density at the surface so as to prevent an overbalanced condition in the borehole 14 and to avoid fracturing the formation (pressure in the borehole is greater than the formation pressure; drilling mud penetrates into the formation). The properties of the borehole fluid (such as density and/or viscosity) and the fluid flow rate largely determine the effectiveness of the fluid to carry cuttings to the surface.

[0028] In an embodiment, the system 10 includes a processing device configured to perform functions related to determining safe operating spaces, limiting operational parameters of a drilling or other subterranean operation, and/or controlling such parameters. The processing device can transmit boundaries of control parameters such as pressure, flow rate and drilling mud parameters (e.g. mud weight) to appropriate control devices and systems. Such parameters are controlled as described herein based on a combination of boundaries related to fluid flow rate and fluid density (mud weight). As discussed further herein, in an embodiment, the processing device is configured to calculate combinations of fluid parameters that stay within selected boundaries to ensure proper operation of surface equipment and effective circulation of fluid. Such combinations are referred to herein as “safe operating spaces.”

[0029] As shown in Figure 1, the processing device may be part of a surface and/or downhole processing device that can perform calculations, simulations and modelling, acquire measurement data, calculate safe operating spaces and/or control operational parameters. Calculation of safe operating spaces and/or control of operational parameters may be performed automatically by the processing device and in real time during an operation and without an interaction or interference of a human being. In an embodiment, the processing device is disposed at a surface location (e.g., at a rig site or remotely located and in communication with a rig site), and acquires surface and downhole information used to generate and/or update models of a borehole.

[0030] For example, the system 10 includes a surface processing unit 50 and/or downhole processor 52. The downhole processor 52 may perform functions such as acquiring information from downhole tools (e.g., sensor data), and transmitting such information to the surface processing unit 50 via a telemetry system, such as mud pulse telemetry, electromagnetic telemetry, acoustic telemetry, or wired pipe telemetry.

[0031] The surface processing unit 50 (and/or the downhole processor 52) may be configured to perform functions such as determining safe operating spaces, and providing the safe operating space and/or operational parameter boundaries to one or more control devices or systems that control operational parameters. Examples of operational parameters include drilling and steering parameters, the flow rate and pressure of borehole fluid, drilling mud properties and others. For example, the surface processing unit 50 sends a safe operating space, or boundaries of operational parameters, to a rig control system. In some embodiments, the surface processing unit 50 directly controls one or more operational parameters in an automated fashion without the interaction of a human being.

[0032] The surface processing unit 50 may perform other functions, such as transmitting and receiving data, processing measurement data, simulating fluid properties, calibrating or adjusting models, modeling hydraulic conditions inside the borehole, and/or monitoring operations of the system 10. The surface processing unit 50 includes an input/output (I/O) device 54, a processor 56, and a data storage device 58 (e.g., memory, computer-readable media, etc.) for storing data, models and/or computer programs or software that cause the surface processing unit 50 to perform aspects of methods and processes described herein.

[0033] The surface processing unit 50 (or other suitable processor or combination of processors) is configured to limit operational parameters automatically and in real time based on a safe operating space that provides boundaries related to fluid properties and flow parameters. In an embodiment, the safe operating space is calculated based one or more mathematical models that simulate fluid parameters such as pressure and flow rate, and/or simulate fluid composition. The mathematical model receives inputs from sensors and from a borehole string model that simulates the borehole string and its components. The sensor inputs used by the mathematical model are either only surface sensor inputs (e.g. surface flow rate, surface mud weight/density, surface mud temperature, surface RPM, surface ROP and/or surface WOB), or only downhole sensor inputs (e.g. downhole flow rate, downhole mud weight/density, downhole mud temperature, downhole RPM, downhole ROP and/or downhole WOB), or both surface sensor and downhole sensor inputs.

[0034] Operational parameters such as flow rate and mud weight are limited by properties of a subterranean region or formation being drilled (formation constraints), as well as the capacity of surface and downhole equipment (e.g., flow rate and pressure limits), such as the pressure limit of the surface pumps (mechanical or equipment limits). In an embodiment, both operational and mechanical limits are used to define a safe operating space and the boundaries defined by the safe operating space. In an embodiment, the pressure limits included the pressure limits of the drill string, the pressure limits of the BHA, or the pressure limit of each of one or more components in the drill string or the BHA.

[0035] For example, operational limits include limits to downhole fluid pressure and fluid density of fluid flowing through an annulus of a borehole. The downhole fluid pressure and fluid density limits can be translated into pressure and density at the surface (pressure and density in a standpipe), which are monitored by surface sensors.

[0036] Mechanical limits represent the mechanical or physical capacity of the surface equipment (e.g., mud pump) to deliver certain flow rates and to maintain certain pressures in the standpipe where the fluid is injected. Mechanical limits also include limitations regarding flow rates and fluid pressure that the borehole string can withstand.

[0037] Determination of a safe operating space is based on both mechanical limits of surface (e.g. pump pressure limit) and downhole components (e.g. drill string or BHA pressure limit) and constraints of the formation. The safe operating space can be used in real time by an automated control system to maintain operational parameters, such as surface flow rate and injected fluid properties (e.g., mud weight/density), within safe limits (safe operating boundaries) to avoid damage to equipment and a formation around a borehole. Another operational parameter that can be controlled by the automated control system is an amount of solids added to an injected fluid.

[0038] The amount of solids to be added to an injected fluid can be determined using the safe operating space (e.g., the safe operating space defines a boundary or boundaries of the mud weight, the mud weight boundary defines a limit of solids that can be added to the injected fluid to remain within the boundary or boundaries of the mud weight). Based on the boundary or boundaries of the mud weight in the safe operating space, the amount of solids that are to be added or that can be added to the injected fluid to remain within the boundaries of the safe operating space for the mud weight can be determined. The amount of solids added to the injected fluid to achieve a specific density (mud weight) of the injected fluid can be calculated using a compositional model of the injected fluid. In this manner the boundary or boundaries in the safe operating space for the mud weight also define the boundary or boundaries of the amount of solids added to the injected fluid.

[0039] The safe operating space may be initially determined based on equipment limits (mechanical constraints), expected operational parameters (e.g., planned flow rate, planned mud weight) and expected formation properties (formation constraints). During an operation, the safe operating space may be updated periodically and provided to the processing device for real time operational parameter control.

[0040] In an embodiment, the safe operating space is determined based on one or more mathematical models of a borehole system. The mathematical model(s) include a hydraulics model of a borehole, such as the borehole 14. A borehole string model and/or a surface equipment model provide input data to the hydraulics model. Equipment limits related to surface equipment, such as the pumping device 34, can be acquired from manufacturer information and/or data from previous operations. Formation constraints can be acquired based on offset well information, earth model simulations, and/or from downhole calibration operations (e.g. pressure while drilling measurements, such as a leak-off test).

[0041] During an operation, parameters such as surface flow rate and surface fluid pressure, and surface mud weight, can be controlled automatically and in real time by acquiring real time measurements and applying the real time measurements to update the mathematical model(s). In an embodiment, optimal combinations of operational parameters for the safe operating space are determined during the operation by performing an optimization procedure (optimization algorithm).

[0042] Figure 2 depicts an example of results calculated by a hydraulics model generated based on geometric properties (e.g., drill string diameter along the borehole, borehole diameter along the borehole, length of the borehole, and/or orientation of the borehole (inclination, azimuth)), formation properties (e.g. rock type, porosity, and/or permeability), and operational parameters (e.g., density and viscosity of drilling mud, flow rate and/or pressure, ROP, RPM, and/or temperature). The model may be initially generated prior to an operation, and subsequently updated using real time sensor measurements during the operation (e.g., running the hydraulics model in real time).

[0043] The hydraulics model accounts for both surface and downhole conditions, to facilitate determination of a safe operating space and operational parameter boundaries. The optimization procedure allows for optimizing operational parameters by considering both surface and downhole conditions simultaneously (such as pump pressure limit, or BHA pressure limit, and formation constraints). That is, the optimization procedure, using the hydraulics model, optimizes fluid flow rate and mud weight simultaneously based on a surface limit (e.g. pump pressure limit) and a downhole constraint(s), such as the formation constraints (pore pressure and fracture pressure). Simultaneous optimization refers to optimizing multiple parameters, such as the fluid flow rate and the fluid density, at the same time. Both parameters are determined by one optimization algorithm. The optimization algorithm allows determination of boundaries for both of the two parameters considering the effect of a variation of one of the two parameters on the respective other of the two parameters. At least the determination of an at least 2-dimensional safe operating space that provides boundaries to the flow rate and boundaries to the mud weight considering the pump pressure limit and the formation constraints as disclosed herein is new. The determined boundaries of the safe operating space relate to the surface flow rate and the surface mud weight.

[0044] Figure 2A shows fluid pressure (in bar) simulated by using the hydraulics model. A graph 70a shows fluid pressures as a function of measured depth in meters (m) along a borehole. The simulated fluid pressures include pressures at the surface (measured depth = 0 m), as well as pressures at different measured depths along the borehole to the bottom of the borehole at 5000 m.

[0045] The graph 70a includes curves representing fluid pressures in a borehole string (string pressure, e.g., the borehole string 12 of FIG. 1) as a function of measured depth. At depth = 0 meters, the string pressure equals the standpipe pressure, e.g. the pressure the pump has to provide. The simulated string pressure is calculated based on the hydraulics model based on a measured or assumed surface fluid pressure or based on a measured or assumed downhole fluid pressure.

[0046] The string pressure as a function of depth is shown for various flow rates. Curve 72a represents string pressure vs measured depth for a flow rate of 2500 liters/minute (1/min), curve 74a represents string pressure vs measured depth for a flow rate of 2750 1/min, and curve 76a represents string pressure vs measured depth for a flow rate of 3000 1/min. Curves 78a and 80a represent string pressure vs measured depth for flow rates of 3250 1/min and 3500 1/min, respectively. The mud weight at the surface is the same for all displayed curves and equals to 1.230 kg/m³.

[0047] Figure 2B shows effective circulating density (ECD) in specific gravity units (SG) simulated by using the hydraulics model. ECD depends on mud density and is the effective density of the fluid circulating in the borehole resulting from the sum of the hydrostatic pressure imposed by the static fluid column and the friction pressure. A graph 70b shows ECD as a function of measured depth along the borehole. The graph 70b includes curves of the simulated ECD along the borehole reaching from the surface (measured depth = 0 m) to the bottom of the borehole at 5000 m. At measured depth = 0 m, the ECD relates to the mud density at the surface or at the mud pump (mud density in the standpipe).

[0048] The ECD as a function of depth is shown for various flow rates. Curve 72b represents ECD vs measured depth for a flow rate of 2500 liters/minute (1/min), curve 74b represents ECD vs measured depth for a flow rate of 2750 1/min, and curve 76b represents ECD vs measured depth for a flow rate of 3000 1/min. Curves 78b and 80b represent ECD vs measured depth for flow rates of 3250 1/min and 3500 1/min, respectively. The mud weight at the surface is the same for all displayed curves and equals to 1.230 kg/m³.

[0049] Figure 2A includes, beside the simulation results of the hydraulics model for the pressure along the borehole, the pump pressure limit 86 (equipment limit). Figure 2B includes, beside the simulation results of the hydraulics model for the ECD along the borehole, the formation pore pressure 82 and the formation fracture pressure 84 displayed in SG units (operational constraints). The pore pressure 82 and the fracture pressure 84 vary along the length of the borehole in the open hole section.

[0050] The hydraulics model is iterated by applying different flow rates and comparing calculated pressure with parameters related to the pressure limit of the pump and the formation constraints at the corresponding depth. As a result, a maximum flow rate is determined. The maximum flow rate is compared to surface equipment limits (e.g., pump flow rate limits), or flow rate limits for the borehole string (i.e., limit to flow rate within the string), or flow rate limits in the annulus. The highest flow rate that neither damages the formation nor damages the surface and downhole equipment is selected as the maximum flow rate limit for the flow rate at the surface. As described further herein, the maximum flow rate can be determined using an optimization procedure that employs, for example, a bisectional search algorithm or other search algorithm using the hydraulics model simulation results.

[0051 ] The maximum mud weight is similarly determined using the optimization procedure. The maximum mud weight may be used to calculate a maximum amount of solids to be added to injected fluid under a given set of conditions to increase density without damaging the formation and surface equipment integrity.

[0052] In an embodiment, the hydraulics model is iterated to estimate, using the optimization procedure, a maximum mud weight that satisfies limits on pressure in the system (operational limits and constraints). A composition of the injected fluid (e.g., drilling mud) is determined, for example, from the compositional model. The compositional model provides mud density based on fluid composition, such as oil content, water content, Calcium Chloride content and/or solid components. The compositional model and the maximum mud weight are then used to calculate a maximum solids concentration. The maximum concentration of solids that is the amount of solids that can be added to the mud weight to increase its density (or ECD) under current operational conditions without damaging the formation.

[0053] The maximum mud weight is defined as the highest mud weight that neither damages the formation nor damages the surface equipment. The maximum solids concentration and/or maximum mud weight is sent to automated mud mixing equipment.

[0054] The surface maximum flow rate and the maximum mud weight are used to construct the safe operating space, which specifies combinations of mud weight and flow rate that can be applied without causing damage. These combinations make up the safe operating space.

[0055] In an embodiment, the safe operating space is defined for combinations based on the previous estimation of maximum flow rate and maximum mud weight. In this embodiment, the solution assumes one parameter is constant (e.g., mud weight) while the other is changing (e.g., flow rate).

[0056] In another embodiment, the safe operating space is defined by combining both the maximum mud weight and the maximum flow rate (or another combination of variables) as hydraulic variables (neither is assumed to be constant) into a single search algorithm (combined optimization of flow rate and mud weight) to determine a limiting function, rather than a limiting value. The function defines a boundary for multiple combinations of mud weight and flow rate. The boundaries for the flow rate and the mud weight to use under current drilling conditions can be derived from the function by using a current flow rate and mud weight, measured in real time by a sensor, applying the hydraulics model, iterating the hydraulics model within the optimization procedure (using the single search algorithm) and determining the maximum values for the flow rate and the mud weight simultaneously in one single procedure (not separately and not sequentially) by varying the model parameters to find the optimal combination of maximum flow rate and maximum mud weight considering the surface pump pressure limit and the downhole formation constraints at the same time. The maximum values for the flow rate and the mud weight are used to define the safe operating space. [0057] Referring to Figures 2A and 2B, Figure 2B shows that a flow rate of 2500 1/min (curve 72b), 2750 1/min (curve 74b) and 3000 1/min (76b) are keeping the ECD (corresponds to mud weight) within the formation constraints 82 (pore pressure) and 84 (fracture pressure). Figure 2A shows that flow rates of 2500 1/min (curve 72a) and 2750 1/min (curve 74a) keep the fluid pressure below the pump pressure limit 86. However, a flow rate of 3000 1/min (curve 76a), which would combine with the formation constraints (Figure 2B), does not conform with the pump pressure limit, because it requires a pump pressure that is beyond the pump pressure limit. The optimization procedure iterating the hydraulics model determines the maximum flow rate accounting for the maximum mud weight at the same time and vice versa, providing boundaries for the flow rate and the mud weight and the safe operating space.

[0058] The safe operating space may be determined by using a suitable search algorithm within the optimization procedure. The search algorithm is used to find the maximum surface flow rate, the maximum mud weight and/or other hydraulic or operational limits, which are used to define the safe operating space. The following description of search algorithms are described in conjunction with determining a maximum flow rate (maximum surface flow rate); it is understood that the algorithms can be used to find limits associated with other parameters, such as mud weight limits.

[0059] For example, a bisectional search algorithm can be employed to find the operational limits. A bisectional search algorithm involves defining a function of an operational parameter as a continuous function, and finding the root of the function. The algorithm may include multiple iterations, where each iteration includes bisecting the defined function and calculating a midpoint. Iterations are performed until a root or zero value is found.

[0060] For example, a continuous function is defined by determining a first function of pressure values for high flow rates (i.e., flow rates at or above a selected flow rate threshold), and determining a second function of pressure values for low flow rates (i.e., flow rates below the flow rate threshold). The first function is assigned positive values, and the second function is assigned negative values. The first and second functions are combined to create the defined function, and iterations are performed until the root is found.

[0061] Other search algorithms can be used to find a limit using a defined function, such as a gradient search using a derivative of the defined function. If the defined function is not continuous, the limit may be determined by a Monte Carlo search algorithm. [0062] Figure 3 shows an example of a safe operating space represented within a table 120 (a two-dimensional array or matrix) of flow rate values (in gallons/minute or gpm) and mud weight values (in kilograms per square meter or kg/m³). The table 120 was constructed by iterating the hydraulics model. An optimal combination of flow rate and mud weight, as well as other combinations that stay within the mud weight and flow rate limits, are included within the safe operating space.

[0063] The columns of the table 120 represent mud weight (MW) values. Specifically, Columns A, B, C, D and E include MW values of 1107 kg/m³, 1168.5 kg/m³, 1230 kg/m³, 1291.5 kg/m³ and 1353 kg/m³, respectively.

[0064] The rows of the table 120 represent flow rate (FW) values. Rows 1, 2, 3, 4, and 5 include values of 480 gpm, 540 gpm, 600 gpm, 660 gpm and 720 gpm, respectively.

[0065] During an operation, a processing device (e.g., the surface processing unit) uses the table 120 to set values of flow rate and mud weight at the surface. For example, cells B2, B3, C2, C3, and C4 represent “safe” combinations (the safe operating space, field with very light grey color code), or combinations that do not cause any damage, neither to the equipment, nor to the formation. The currently monitored value of the flow rate and mud weight is represented by the “Real Time” value. The safe operating space provides information on whether or not specific deviations from the currently measured real time values will be within the safe operating space. The currently measured real time value of the flow rate and the mud weight each represent 100% (flow rate = 600 gpm, mud weight = 1230 kg/m³). The field C3 indicates the current selection of flow rate and mud weight is within the safe operating space, indicated by the very light grey color code and the encircled tick or check symbol.

[0066] The field B2, for example, represents a reduction by -10% (down to 90%) of the flow rate and a reduction of -5% (down to 95%) of the mud weight. Such a change would keep the flow rate and the mud weight within the safe operating space.

[0067] The field D4, for example, represents an increase of the flow rate by 10% (up to 110%) and an increase of the mud weight by 5% (up to 105%). Such a change would cause the operation to leave the safe operating space as indicated by the dark gray color code and the encircled cross or “x” symbol.

[0068] The field B4, for example, represents an increase of the flow rate by 10% (up to 110%) and a decrease of the mud weight by -5% (down to 95%). Such a change would cause the operation to be in a critical condition indicated by the triangular alert symbol. [0069] The processing device may further refine the safe operating space to determine an optimal or preferred combination of values. This can be accomplished by using the optimization algorithm iterating the hydraulic model(s) under current conditions to find an optimal combination that will result in optimal downhole conditions. The current condition is monitored by sensors. In an embodiment, the current condition is monitored by only surface sensors monitoring surface operational parameters. In another embodiment, the current condition is monitored by surface sensors monitoring surface operational parameters and downhole sensors monitoring downhole operational parameters.

[0070] In addition to updating the model(s) and updating or generating a safe operating space for current conditions, the model(s) may be used to generate predictions or projections regarding safe operating spaces.

[0071 ] Figure 4 depicts an example in which current operational parameters are controlled in real time using a current safe operating space, such as the table 120 and safe combinations as discussed above. In addition, the model(s) are used in conjunction with a projected drilling path and planned operational parameters to provide projected safe operating spaces. In this example, a first projected operating space is defined in a table 122 for 30 meters ahead of the drill bit, and a second projected operating space is defined in a table 124 for 100 meters ahead of the bit.

[0072] Although the above embodiments include determine safe operating spaces using optimization techniques, the embodiments are not so limited. For example, a safe operating space can be determined by combine batch calculation to run a matrix of simulations instead of a single batch. Each matrix would combine mud weight and flowrate as input parameters. The operational and mechanical limitations imposed for both flow rate and mud weight are combined to assess integrity of each combination of parameters. In another example, pressure waves generated when changing flow rates can be used to determine not only the maximum operational flow rate, but also maximum step-size to change the flow rate without damaging a formation and/or borehole system.

[0073] Figure 5 shows a method 130 of estimating fluid properties during a downhole operation. The method 130 includes one or more of stages 131-135 described herein, at least portions of which may be performed by a processor (e.g., the surface processing unit 50 and/or downhole processor 52). In one embodiment, the method includes the execution of all of stages 131-135 in the order described. However, certain stages 131-135 may be omitted, stages may be added, or the order of the stages changed. [0074] The method 130 is discussed in relation to the system 10 of Figure 1 and in conjunction with a drilling operation. It is noted that the method 130 is not so limited and can be used in conjunction with any suitable downhole or energy industry operation that includes flowing fluid through a borehole.

[0075] In the first stage 131, pre-job modelling is performed to generate initial model(s) of the borehole system, hydraulics parameters and fluid composition (hydraulics model(s)). As discussed above, the models are initially generated based on planned operational parameters and expected downhole conditions. The initial model(s) may be used to calculate an initial safe operating space.

[0076] In the second stage 132, a borehole string (e.g., the borehole string 12) is deployed into a borehole during a drilling or other operation, and automatically controls suitable operational parameters based on the initial safe operating space. For example, the borehole string is configured as a drill string and is deployed as part of a drilling, directional drilling and/or measurement operation. The borehole string includes at least one fluid property sensor, such as a fluid density sensor, pressure sensor, flow rate sensor, or combination of sensors at a given location or depth.

[0077] Surface equipment, such as drill rig, includes one or fluid property sensors, such as flow rate sensors. Examples include the fluid flow sensors 46 shown in FIG. 1.

[0078] In the third stage 133, surface and downhole sensor data is acquired in real time during the operation. For example, downhole fluid flow parameters (e.g., flow rate, density), operational parameters such as rate of penetration, revolutions per minute, and equipment operating settings (e.g., pump pressure and flow rate) are acquired and input to the model(s).

[0079] In the fourth stage 134, the sensor data is input to the model(s) and the model(s) are updated and are used to adjust or generate a new safe operating space. In an embodiment, the safe operating space is adjusted by iterating the model(s) and determining optimized flow rate and mud weight parameters using an optimization procedure, as described herein. For example, a bisectional search algorithm is performed by the optimization procedure to determine limits, which are used as boundaries of the updated safe operating space.

[0080] In the fourth stage 135, operational parameters are adjusted in real time, and automatically, using a control system to maintain flow rate and mud weight within the boundaries prescribed by the updated safe operating space. [0081] For example, real time sensor data is input to the model(s), and an optimization procedure is performed to determine the maximum flow rate that can be applied. The optimization procedure includes inputting a flow rate value and a mud weight value, calculating associated operational parameters using the model(s) and comparing to the limits and constraints. If the calculated parameters are at or within a selected range of the limits, the optimization procedure ends and the inputted flow rate and mud weight are used. If the calculated parameters are outside of the selected range, further iterations are performed using successively larger flow rates and mud weights until a maximum allowable flow rate and maximum allowable mud weight is found. In this manner, the limits for the flow rate and the mud weight can be determined simultaneously by considering the surface operational limit(s) and the downhole constraints at the same time. The same process can be performed to determine minimum flow rate and minimum mud weight.

[0082] The optimization procedure in step 134 may be performed periodically during the real time operation, such as every minute, every 5 minutes, 10 minutes, 20 minutes or every 30 minutes. In an alternative embodiment the optimization procedure may be triggered by sensor measurements of one or more sensors reaching predetermined measurement ranges, values, or value combinations.

[0083] It is noted that one or more of the above stages may be performed in real time or near real time. For example, direct measurements taken downhole by the pressure sensor and/or other sensors, generation or updating of the model(s), and/or analysis of direct measurements and model adjustments can be performed in real time as an operation progresses and/or as measurement data is acquired. In addition, actions performed based on the corrected fluid property distribution may be performed in real time. For example, operational parameters such as the density, fluid composition, flow rate and/or pressure of drilling mud (or other fluid) injected into the borehole can be adjusted in real time to maintain downhole fluid pressure within boundary conditions (e.g., pore pressure and fracture pressure) and maintain surface and downhole component integrity.

[0084] Set forth below are some embodiments of the foregoing disclosure:

[0085] Embodiment 1: A method (130) of performing a subterranean operation, characterized by: flowing a fluid through a borehole (14) in a subterranean formation (16); providing a pressure limit; providing a downhole formation pressure constraint; simulating fluid pressure in the borehole (14) using a mathematical model; determining a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm, wherein the optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint; and performing the subterranean operation using the determined boundaries.

[0086] Embodiment 2: The method (130) of any prior embodiment, wherein the formation pressure constraint includes at least one of a formation pore pressure and a formation fracture pressure.

[0087] Embodiment 3: The method (130) of any prior embodiment, wherein the mathematical model includes a hydraulics model.

[0088] Embodiment 4: The method (130) of any prior embodiment, wherein determining the boundary for the fluid flow rate and the boundary for the fluid density is performed in real time during the subterranean operation.

[0089] Embodiment 5: The method (130) of any prior embodiment, further characterized by selecting at least one of a fluid flow rate and a fluid density based on the determined boundary for the fluid flow rate and the determined boundary for the fluid density in an automated way without interference of a human being.

[0090] Embodiment 6: The method (130) of any prior embodiment, wherein the optimization algorithm includes a bisectional search algorithm.

[0091] Embodiment 7: The method (130) of any prior embodiment, further characterized by using the determined boundary for the fluid density to calculate an amount of solids to be added to the fluid, and adding the calculated amount of solids to the fluid in an automated way without interference of a human being.

[0092] Embodiment 8: The method (130) of any prior embodiment, wherein the calculation of the amount of solids includes using a fluid compositional model.

[0093] Embodiment 9: The method (130) of any prior embodiment, wherein the mathematical model uses sensor measurements, and the sensor measurements include at least one of rate of penetration, revolutions per minute, fluid density, and fluid flow rate.

[0094] Embodiment 10: The method (130) of any prior embodiment, wherein using the optimization algorithm is triggered by a predetermined sensor measurement value.

[0095] Embodiment 11: The method (130) of any prior embodiment, wherein using the optimization algorithm includes using a weighting function.

[0096] Embodiment 12: The method (130) of any prior embodiment, further characterized by defining a safe operating space using the determined boundaries.

[0097] Embodiment 13: The method (130) of any prior embodiment, wherein the safe operating space is a 2-D space. [0098] Embodiment 14: The method (130) of any prior embodiment, wherein the fluid flow rate is a surface fluid flow rate and the fluid density is a surface fluid density.

[0099] Embodiment 15: The method (130) of any prior embodiment, wherein using the optimization algorithm includes iterating the mathematical model to determine the boundaries.

[0100] Embodiment 16: The method (130) of any prior embodiment, wherein the pressure limit includes a surface pump pressure limit.

[0101] Embodiment 17: A system (10) for performing a subterranean operation, characterized by: a processor (50,56) configured to perform the subterranean operation using a borehole system disposed in a borehole (14) in a subterranean formation (16), the borehole system including a borehole string (12), the processor (50,56) configured to: flow a fluid through the borehole (14); acquire a pressure limit; acquire a downhole formation pressure constraint; simulate fluid pressure in the borehole (14) using a mathematical model; determine a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm, wherein the optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint; and perform the subterranean operation using the determined boundaries.

[0102] Embodiment 18: The system (10) of any prior embodiment, wherein the formation pressure constraint includes at least one of a formation pore pressure and a formation fracture pressure.

[0103] Embodiment 19: The system (10) of any prior embodiment, wherein the mathematical model includes a hydraulics model.

[0104] Embodiment 20: The system (10) of any prior embodiment, wherein the pressure limit includes a surface pump pressure limit.

[0105] The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) are to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. Further, it should be noted that the terms “first,” “second,” and the like herein do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The terms “about”, “substantially” and “generally” are intended to include the degree of error associated with measurement of the particular quantity based upon the equipment available at the time of filing the application. For example, “about” and/or “substantially” and/or “generally” can include a range of ± 8% of a given value.

[0106] The teachings of the present disclosure may be used in a variety of well operations. These operations may involve using one or more treatment agents to treat a formation, the fluids resident in a formation, a borehole, and I or equipment in the borehole, such as production tubing. The treatment agents may be in the form of liquids, gases, solids, semi-solids, and mixtures thereof. Illustrative treatment agents include, but are not limited to, fracturing fluids, acids, steam, water, brine, anti-corrosion agents, cement, permeability modifiers, drilling muds, emulsifiers, demulsifiers, tracers, flow improvers etc. Illustrative well operations include, but are not limited to, hydraulic fracturing, stimulation, tracer injection, cleaning, acidizing, steam injection, water flooding, cementing, etc.

[0107] While the invention has been described with reference to an exemplary embodiment or embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the claims. Also, in the drawings and the description, there have been disclosed exemplary embodiments of the invention and, although specific terms may have been employed, they are unless otherwise stated used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention therefore not being so limited.

Claims

CLAIMS What is claimed is:

1. A method (130) of performing a subterranean operation, characterized by: flowing a fluid through a borehole (14) in a subterranean formation (16); providing a pressure limit; providing a downhole formation pressure constraint; simulating fluid pressure in the borehole (14) using a mathematical model; determining a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm, wherein the optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint; and performing the subterranean operation using the determined boundaries.

2. The method (130) of claim 1, wherein the formation pressure constraint includes at least one of a formation pore pressure and a formation fracture pressure.

3. The method (130) of claim 1 or claim 2, wherein the mathematical model includes a hydraulics model.

4. The method (130) of any one of claims 1 to 3, wherein determining the boundary for the fluid flow rate and the boundary for the fluid density is performed in real time during the subterranean operation.

5. The method (130) of any one of claims 1 to 4, further characterized by selecting at least one of a fluid flow rate and a fluid density based on the determined boundary for the fluid flow rate and the determined boundary for the fluid density in an automated way without interference of a human being.

6. The method (130) of any one of claims 1 to 5, wherein the optimization algorithm includes a bisectional search algorithm.

7. The method (130) of any one of claims 1 to 6, further characterized by using the determined boundary for the fluid density to calculate an amount of solids to be added to the fluid, and adding the calculated amount of solids to the fluid in an automated way without interference of a human being.

8. The method (130) of claim 7, wherein the calculation of the amount of solids includes using a fluid compositional model.

9. The method (130) of any one of claims 1 to 8, wherein the mathematical model uses sensor measurements, and the sensor measurements include at least one of rate of penetration, revolutions per minute, fluid density, and fluid flow rate.

10. The method (130) of claim 9, wherein using the optimization algorithm is triggered by a predetermined sensor measurement value.

11. The method (130) of any one of claims 1 to 10, wherein using the optimization algorithm includes using a weighting function.

12. The method (130) of any one of claims 1 to 11, further characterized by defining a safe operating space using the determined boundaries.

13. The method (130) of claim 12, wherein the safe operating space is a 2-D space.

14. The method (130) of any one of claim 1 to 13, wherein the fluid flow rate is a surface fluid flow rate and the fluid density is a surface fluid density.

15. The method (130) of any one of claims 1 to 14, wherein using the optimization algorithm includes iterating the mathematical model to determine the boundaries.

16. The method (130) of any one of claims 1 to 15, wherein the pressure limit includes a surface pump pressure limit.

17. A system (10) for performing a subterranean operation, characterized by: a processor (50,56) configured to perform the subterranean operation using a borehole system disposed in a borehole (14) in a subterranean formation (16), the borehole system including a borehole string (12), the processor (50,56) configured to: flow a fluid through the borehole (14); acquire a pressure limit; acquire a downhole formation pressure constraint; simulate fluid pressure in the borehole (14) using a mathematical model; determine a boundary for a fluid flow rate and a boundary for a fluid density using an optimization algorithm, wherein the optimization algorithm determines the boundary for the fluid flow rate and the boundary for the fluid density simultaneously using the pressure limit and the downhole formation constraint; and perform the subterranean operation using the determined boundaries.

18. The system (10) of claim 17, wherein the formation pressure constraint includes at least one of a formation pore pressure and a formation fracture pressure.

19. The system (10) of claim 17 or claim 18, wherein the mathematical model includes a hydraulics model.

20. The system (10) of any one of claims 17 to 19, wherein the pressure limit includes a surface pump pressure limit.