Modeling Pressure Response of In-Situ Diverting Acid Flow

Embodiments described herein relate generally to downhole exploration and production efforts in the resource recovery industry, and more particularly, to techniques for modeling pressure response of in-situ diverting acid flow. Embodiments described herein relate to a mechanistic model for modeling the pressure response of in-situ diverting acid flow (also referred to herein as self-diverting acid flow) in carbonate formations.

Stimulation of hydrocarbon production increases production by improving the flow of hydrocarbons into a borehole from a reservoir. Various techniques may be employed to stimulate hydrocarbon production. For example, acid stimulation may be performed, in which an acid is flowed downhole within a tubular disposed in a borehole and released into the borehole to treat the formation and stimulate fluid flow into or from the formation. After release of the acid from the tubular, hydrocarbons are received by the tubular.

In one embodiment, a method for modeling pressure response of acid flow of an acid in a formation is provided. The method includes receiving data associated with acid stimulation of a formation. The method includes modeling the pressure response of the acid flow in the formation, wherein modeling the pressure response is based on a model which divides a domain into multiple zones, and modeling the pressure response includes modeling a length of a disturbance zone included in the multiple zones based on a function of: reaction kinetics associated with the acid and rock included in the formation; and an injection rate of the acid, a velocity of the acid, or both. The method includes determining whether the pressure response satisfies a pressure response threshold. The method includes performing the acid stimulation based on a stimulation parameter associated with the data and the acid stimulation or a modified stimulation parameter, responsive to determining whether the pressure response satisfies the pressure response threshold.

In another embodiment, a system for modeling pressure response of acid flow of an acid in a formation is provided which includes a processing system for executing computer readable instructions, the computer readable instructions controlling the processing system to perform operations. The operations include receiving data associated with acid stimulation of a formation. The operations include modeling the pressure response of the acid flow in the formation, wherein modeling the pressure response is based on a model which divides a domain into multiple zones, and modeling the pressure response includes modeling a length of a disturbance zone included in the multiple zones based on a function of: reaction kinetics associated with the acid and rock included in the formation; and an injection rate of the acid, a velocity of the acid, or both. The operations include determining whether the pressure response satisfies a pressure response threshold. The operations include performing the acid stimulation based on a stimulation parameter associated with the data and the acid stimulation or a modified stimulation parameter, responsive to determining whether the pressure response satisfies the pressure response threshold.

Other embodiments of the present invention implement features of the above-described method in computer systems and computer program products.

Additional technical features and benefits are realized through the techniques of the present invention. Embodiments and aspects of the invention are described in detail herein and are considered a part of the claimed subject matter. For a better understanding, refer to the detailed description and to the drawings.

Apparatuses, systems and methods are provided for performing, facilitating, and/or modeling stimulation of subterranean formations for, e.g., hydrocarbon production. An example of a stimulation process is acid stimulation.

Referring to, an embodiment of a hydrocarbon production stimulation system, which operates at a wellbore operation, includes a borehole stringconfigured to be disposed in a boreholethat penetrates at least one earth formation. The borehole may be an open hole, a cased hole, or a partially cased hole. In one embodiment, the borehole stringis a production string that includes a tubular, such as a pipe (e.g., multiple pipe segments) or coiled tubing, that extends from a wellheadat a surface location (e.g., at a drill site or offshore stimulation vessel). A “borehole string” as described herein may refer to any structure suitable for being lowered into a wellbore or for connecting a drill or downhole tool to the surface, and is not limited to the structure and configuration described herein. For example, the borehole string may be configured as a wireline tool, coiled tubing, a drillstring, or a logging while drilling (LWD) string.

The hydrocarbon production stimulation systemincludes one or more stimulation assembliesconfigured to control injection of stimulation fluid and direct stimulation fluid into one or more production zones in the formation. Each stimulation assemblyincludes one or more injection or flow control devicesconfigured to direct stimulation fluid from a conduit in the tubularto the borehole. As used herein, the term “fluid” or “fluids” includes liquids, gases, hydrocarbons, multi-phase fluids, mixtures of two of more fluids, water and fluids injected from the surface, such as water or stimulation fluids. Stimulation fluids may include any suitable fluid used to reduce or eliminate an impediment to fluid production. A fluid sourcemay be coupled to the wellheadand injected into the borehole string.

In one embodiment, the stimulation fluid is an acid stimulation fluid. Examples of acid stimulation fluids include acids such as, but not limited to, hydrochloric acid (HCl), hydrofluoric acid, acetic acid, formic acid, sulfamic acid, chloracetic acid, carboxylic acids, organic acids and chelating agents, retarded acids, any other acid capable of dissolving the subterranean formation, and any combination thereof. Examples of chelating agents that may be suitable for use in accordance with one or more embodiments described herein include, but are not limited to, ethylenediaminetetraacetic acid (“EDTA”), glutamic acid N,N-diacetic acid (“GLDA”), and any combination thereof. Acid stimulation is useful for, e.g., removing the skin on the borehole wall that can form when a wellbore is formed in a formation, such as a carbonate formation or another suitable type of formation. In accordance with one or more embodiments of the present disclosure, the acid stimulation fluid may include self-diverting acids. In some embodiments, the acid stimulation fluid may include viscoelastic surfactant (VES) based self-diverting acids.

The flow control devicesmay be any suitable structure or configuration capable of injecting or flowing stimulation fluid from the borehole stringand/or tubularto the borehole. Examples flow control devices include flow apertures, flow input or jet valves, injection nozzles, sliding sleeves and perforations. In one embodiment, acid stimulation fluid is injected from the surface fluid sourcethrough the tubularto a sliding sleeve interface configured to provide fluid communication between the tubularand a borehole annulus. The acid stimulation fluid can be injected into an annulus formed between the tubularand the borehole wall and/or from an end of the tubular, e.g., from a coiled tubing.

Various sensors or sensing assemblies may be disposed in the system to measure downhole parameters and conditions. For example, pressure and/or temperature sensors may be disposed at the production string at one or more locations (e.g., at or near injection devices). Other types of sensors can also be implemented. Such sensors may be configured as discrete sensors such as pressure/temperature sensors or distributed sensors. An example distributed sensor is a Distributed Temperature Sensor (DTS) assemblythat is disposed along a selected length of the borehole string. The DTS assemblyextends, for example, along the entire length of the stringbetween the surface and the end of the string (e.g., a toe end) or extends along selected length(s) corresponding to injection devicesand/or production zones. According to an embodiment, the DTS assemblyis configured to measure temperature continuously or intermittently along a selected length of the stringand includes at least one optical fiber that extends along the string(e.g., on an outside surface of the string or the tubular). Temperature measurements collected via the DTS assemblycan be used in a model to estimate fluid flow parameters in the stringand the borehole(e.g., to estimate acid distribution in the formationand/or production zones).

It is understood that one or more embodiments described herein are capable of being implemented in conjunction with any suitable type of computing environment now known or later developed. In one embodiment, the DTS assembly, the injection assemblies, and/or other components are in communication with one or more processing systems, such as a surface processing unitand/or a downhole electronics unit. The communication incorporates any of various transmission media and connections, such as wired connections, fiber optic connections, and wireless connections. The surface processing unit, the downhole electronics unit, and/or the DTS assemblycan include components to provide for processing, storing, and/or transmitting data collected from various sensors associated therewith.

Examples of components include, without limitation, at least one processor, storage, memory, input devices, output devices, and the like. For example, the surface processing unitincludes a processorincluding a memoryand configured to execute software for processing measurements and generating a model as described below. As examples, one or more of the embodiments described herein can be implemented as instructions stored on a computer-readable storage medium, as hardware modules, as special-purpose hardware (e.g., application specific hardware, application specific integrated circuits (ASICs), application specific special processors (ASSPs), field programmable gate arrays (FPGAs), as embedded controllers, hardwired circuitry, etc.), or as some combination or combinations of these. According to aspects of the present disclosure, the features and functionality described herein can be a combination of hardware and programming. The programming can be processor executable instructions stored on a tangible memory, and the hardware can include the processorfor executing those instructions. Thus a system memory (e.g., the memory) can store program instructions that when executed by the processorimplement the features and functionality described herein.

depicts a block diagram of the surface processing unitof, which can be used for implementing the techniques described herein. In examples, the surface processing unithas one or more central processing units,,, etc. (collectively or generically referred to as processor(s)and/or as processing device(s)). In aspects of the present disclosure, each processorcan include a reduced instruction set computer (RISC) microprocessor. Processorsare coupled to system memory (e.g., random access memory (RAM)) and various other components via a system bus. Read only memory (ROM)is coupled to system busand can include a basic input/output system (BIOS), which controls certain basic functions of surface processing unit.

Further illustrated are an input/output (I/O) adapterand a network adaptercoupled to system bus. I/O adaptercan be a small computer system interface (SCSI) adapter that communicates with a memory, such as a hard diskand/or a tape storage deviceor any other similar component. I/O adapterand memory, such as hard diskand tape storage deviceare collectively referred to herein as mass storage. Operating systemfor execution on the surface processing unitcan be stored in mass storage. The network adapterinterconnects system buswith an outside networkenabling the surface processing unitto communicate with other systems.

A display(e.g., a display monitor) is connected to system busby display adaptor, which can include a graphics adapter to improve the performance of graphics intensive applications and a video controller. In one aspect of the present disclosure, adapters,, and/orcan be connected to one or more I/O busses that are connected to system busvia an intermediate bus bridge (not shown). Suitable I/O buses for connecting peripheral devices such as hard disk controllers, network adapters, and graphics adapters typically include common protocols, such as the Peripheral Component Interconnect (PCI). Additional input/output devices are shown as connected to system busvia user interface adapterand display adapter. A keyboard, mouse, and speakercan be interconnected to system busvia user interface adapter, which can include, for example, a Super I/O chip integrating multiple device adapters into a single integrated circuit.

In some aspects of the present disclosure, the surface processing unitincludes a graphics processing unit. Graphics processing unitis a specialized electronic circuit designed to manipulate and alter memory to accelerate the creation of images in a frame buffer intended for output to a display. In general, graphics processing unitis very efficient at manipulating computer graphics and image processing and has a highly parallel structure that makes it more effective than general-purpose CPUs for algorithms where processing of large blocks of data is done in parallel.

Thus, as configured herein, the surface processing unitincludes processing capability in the form of processors, storage capability including system memory (e.g., RAMand/or mass storage), input means such as keyboardand mouse, and output capability including speakerand display. In some aspects of the present disclosure, a portion of system memory (e.g., RAMand mass storage) collectively store the operating systemto coordinate the functions of the various components shown in the surface processing unit.

One or more embodiments described herein provide for modeling pressure response in association with in-situ diverting acid flow in a formationduring matrix acidizing. Matrix acidizing is a stimulation process wherein acid is injected into a wellbore to penetrate rock pores. Matrix acidizing is a technique applied for removing formation damage from pore plugging caused by mineral deposition. The acids, usually inorganic acids, such as, for example, fluoridic (HF) and or cloridic (HCl) acids, are pumped into the formation at or below the formation fracturing pressure in order to dissolve the mineral particles by chemical reactions. The acids create high-permeability, high productivity flow channels called wormholes and bypasses the near-wellbore damage. The operation time may depend on parameters such as, for example, the length of the wellbore, the rock type, severity of the damage, acid pumping rate, downhole conditions and other factors. It may be desirable to predict formation properties in order to improve hydrocarbon recovery.

Aspects of models supported by embodiments of the present disclosure are described herein with reference to.

depicts a conceptual diagramof acid flow in linear geometry according to one or more embodiments described herein. The diagramshows a wormholeextending from a core inletpenetrating through the rock sample (e.g., rock sample included in formation). Zones (also referred to herein as regions of formation), including wormhole zone, disturbance zone, and virgin zone, extend outward (away) from the core inlet. Fluid, such as a stimulation fluid (e.g., self-diverting acid), is directed through the core inletand into the wormholeusing, for example, one or more stimulation assemblies. Virgin zonerepresents the end of wormhole growth. For example, virgin zonerepresents a portion of the formationwhich is unaffected by pressure due to acid stimulation. Example embodiments of the present disclosure include basing the linear model on linear laboratory data, not field data.

depicts a conceptual diagramof acid flow in radial geometry according to one or more embodiments described herein. As illustrated at, wormhole zone, disturbance zone, and virgin zoneextend radially outward (away) from the core inlet. The diagramshows wormholesextending from the core inletpenetrating through the earth formation. Fluid, such as stimulation fluid (e.g., self-diverting acid), is directed through the core inletand into the wormholes. Virgin zonerepresents the end of wormhole growth. Example embodiments of the present disclosure include basing the radial model on linear laboratory data, not field data.

In general, with reference to, at the start of the injection of a self-diverting acid as described herein (wormhole zone), the acid flows linearly away from the core inlet(near the core inlet). In general, with reference to, at the start of the injection of a self-diverting acid as described herein (wormhole zone), the acid flows radially outward away from the core inlet(near the core inlet). The acid accesses pores within the formation; wormhole velocity decreases with acid invasion depth (away from the core inlet). As the acid travels farther (i.e., deeper) into the formation(disturbance zone) relative to the core inlet, the acid generates pathways (e.g., wormholes). The start, the end, and the length of disturbance zonemay be based on the fluid velocity, acid concentration, acid type, formation temperature, and formation properties.

One or more embodiments of the present disclosure provide a mechanistic model for modeling the pressure response of self-diverting acid flow in carbonate formations. As will be described herein, the mechanistic model is capable of generating and providing the full pressure curve shape of self-diverting acid flow in linear flow and radial flow. In some aspects, the model accounts for acid consumption (e.g., change in concentration) in a wormholeand porous media. In some embodiments, the model is capable of tracking changes in pH until a high viscosity associated with the acid is generated. The model is capable of modeling a disturbance zonebetween a tipof the wormholeand a high viscosity barrier(e.g., pH=2 for in-situ gelled acids, pH=1 for viscoelastic surfactant (VES) based acids).

In accordance with one or more embodiments of the present disclosure, a strength of the model implemented herein is the capability of the model for simulating the full pressure response of self-diverting acids. That is, for example, aspects of the model support modeling how the flow of self-diverting acids affects pressure response. According to one or more embodiments described herein, the fundamental core dimensions of the model may be scaled to cores of differing lengths (e.g., to relatively long cores) and/or diameters. In some aspects, examples described herein support upscaling of the model (a linear model) to a radial model with relatively minimum or no adjustments to the model. As will be described herein, aspects of the model support bridging the gap between lab experimental data and field treatment of diverting acids.

Aspects of the model described herein provide improvements over other modeling techniques for modeling pressure. For example, other modeling techniques fail to model or consider pressure curve shape. In some cases, such other modeling techniques may utilize empirical equations for modeling pressure and are incapable of modeling pressure curve shape as provided by the modeling techniques according to example embodiments of the present disclosure.

Aspects of a linear model (also referred to herein as a linear pressure response model) in accordance with one or more embodiments of the present disclosure are described herein with reference to. Aspects of the linear model are expressed by the following equation:

where dpis total pressure drop, dpis pressure drop associated with the wormhole zone, dpis pressure drop associated with the disturbance zone, and dpis pressure drop associated with the virgin zone.

Aspects of the linear model support calculating Cand dpassociated with the wormhole zonebased on the following equations:

where Cis acid concentration at the tipof the wormhole, Cis initial acid concentration at the core inlet, Iis the length of the wormhole(e.g., from the core inletto the tipof the wormhole), ν is velocity of the acid in the wormhole, and Kis effective reaction rate in the wormhole.

Kis mass transfer rate, and Kis surface reaction rate.

Dis diffusion coefficient, T is temperature, Cis initial acid concentration at the core inlet, b1 is a constant based on acid type.

Kis surface reaction rate coefficient, ais interfacial area, Eis activation energy, R is universal gas constant.

K, K, and Kare included in acid-rock reaction kinetics described herein.

q is injection rate, and dis diameter of the wormholein the wormhole zone(e.g., width of the wormhole).

In an example, dp≈0.

Aspects of the linear model support calculating C, l, and dpassociated with the disturbance zonebased on the following equations:

where Cis acid concentration at high viscosity, lis length of the disturbance (e.g., length of the disturbance zone), μ is fluid viscosity of the injected acid, νis velocity of the acid in the disturbance zone, ν is velocity of the acid in the wormhole, φ is porosity of the formation, k is permeability, β is the non-Darcy coefficient (also referred to herein as the Forchheimer coefficient or non-Darcy flow coefficient), and βνis non-Darcy losses due to flow disturbance. As seen in the example with reference to Equation (12), example embodiments of the present disclosure include calculating dpusing the Forchheimer-like equation.

Aspects of the linear model support calculating dpassociated with the virgin zonebased on the following equations:

where lis virgin zone length (from high viscosity barrierto core outlet), lis core length (wormhole zone+disturbance zone+virgin zone) In some aspects, the linear model supports calculating disturbance zonereach to the core outlet, where dp=dp=0. For example, the core is a piece of rock into which acid is injected. Acid is injected from one side (e.g., inlet), and the acid flow goes through the core to the other side (e.g., outlet) of the core.

In the equations described herein with reference to the linear model, a, a, aand aare constants based on acid type and rock mineralogy, and embodiments of the present disclosure support deriving and/or modifying the constants using laboratory experiments, numerical models, and/or field data.

Aspects of a radial model (also referred to herein as a radial pressure response model) in accordance with one or more embodiments of the present disclosure are described herein with reference to. Aspects of the radial model may include aspects of the linear model described herein, and repeated descriptions of like elements are omitted for brevity. For example, aspects of the radial model support calculating dpbased on Equation (1), and further, calculating other parameters as described herein.

Aspects of the radial model support calculating Cand dpassociated with the wormhole zonein association with a wormholebased on the following equations:

where Cis acid concentration at the tipof a wormhole, ris length of the wormhole, and ν is velocity of the acid inside the wormhole. In an example, dp≈0.