US20250305401A1

US20250305401A1 - Modeling pressure response of in-situ diverting acid flow

Info

Publication number: US20250305401A1
Application number: US18/621,448
Authority: US
Inventors: Mahmoud ALI
Original assignee: Baker Hughes Oilfield Operations LLC
Current assignee: Baker Hughes Oilfield Operations LLC
Priority date: 2024-03-29
Filing date: 2024-03-29
Publication date: 2025-10-02
Also published as: WO2025207908A1

Abstract

Examples described herein provide for modeling pressure response of acid flow of an acid in a formation. An example method includes receiving data associated with acid stimulation of a formation and modeling the pressure response of the acid flow in the formation. 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 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.

Description

BACKGROUND

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.

SUMMARY

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.

BRIEF DESCRIPTION OF THE DRAWINGS

Referring now to the drawings wherein like elements are numbered alike in the several figures:

FIG. 1 depicts block diagram of a system for well production and/or stimulation according to one or more embodiments described herein.

FIG. 2 depicts a block diagram of the surface processing unit of FIG. 1 , which can be used for implementing the techniques according to one or more embodiments described herein.

FIG. 3 depicts a conceptual diagram of in-situ diverting acid flow in linear geometry according to one or more embodiments described herein.

FIG. 4 depicts a flow diagram of a method for modeling in-situ diverting acid flow in radial geometry according to one or more embodiments described herein.

FIG. 5 depicts an example flowchart of a method in accordance with one or more embodiments of the present disclosure.

FIGS. 6 through 15 depict graphs according to one or more embodiments described herein.

DETAILED DESCRIPTION

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 FIG. 1 , an embodiment of a hydrocarbon production stimulation system 10, which operates at a wellbore operation, includes a borehole string 12 configured to be disposed in a borehole 14 that penetrates at least one earth formation 16. The borehole may be an open hole, a cased hole, or a partially cased hole. In one embodiment, the borehole string 12 is a production string that includes a tubular 18, such as a pipe (e.g., multiple pipe segments) or coiled tubing, that extends from a wellhead 20 at 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 system 10 includes one or more stimulation assemblies 22 configured to control injection of stimulation fluid and direct stimulation fluid into one or more production zones in the formation 16. Each stimulation assembly 22 includes one or more injection or flow control devices 24 configured to direct stimulation fluid from a conduit in the tubular 18 to the borehole 14. 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 source 26 may be coupled to the wellhead 20 and injected into the borehole string 12.
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 devices 24 may be any suitable structure or configuration capable of injecting or flowing stimulation fluid from the borehole string 12 and/or tubular 18 to 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 source 26 through the tubular 18 to a sliding sleeve interface configured to provide fluid communication between the tubular 18 and a borehole annulus. The acid stimulation fluid can be injected into an annulus formed between the tubular 18 and 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 24). 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) assembly 28 that is disposed along a selected length of the borehole string 12. The DTS assembly 28 extends, for example, along the entire length of the string 12 between the surface and the end of the string (e.g., a toe end) or extends along selected length(s) corresponding to injection devices 24 and/or production zones. According to an embodiment, the DTS assembly 28 is configured to measure temperature continuously or intermittently along a selected length of the string 12 and includes at least one optical fiber that extends along the string 12 (e.g., on an outside surface of the string or the tubular 18). Temperature measurements collected via the DTS assembly 28 can be used in a model to estimate fluid flow parameters in the string 12 and the borehole 14 (e.g., to estimate acid distribution in the formation 16 and/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 28, the injection assemblies 24, and/or other components are in communication with one or more processing systems, such as a surface processing unit 30 and/or a downhole electronics unit 32. The communication incorporates any of various transmission media and connections, such as wired connections, fiber optic connections, and wireless connections. The surface processing unit 30, the downhole electronics unit 32, and/or the DTS assembly 28 can 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 unit 30 includes a processor 34 including a memory 36 and 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 processor 34 for executing those instructions. Thus a system memory (e.g., the memory 36) can store program instructions that when executed by the processor 34 implement the features and functionality described herein.
FIG. 2 depicts a block diagram of the surface processing unit 30 of FIG. 1 , which can be used for implementing the techniques described herein. In examples, the surface processing unit 30 has one or more central processing units 221 a, 221 b, 221 c, etc. (collectively or generically referred to as processor(s) 221 and/or as processing device(s) 221). In aspects of the present disclosure, each processor 221 can include a reduced instruction set computer (RISC) microprocessor. Processors 221 are coupled to system memory (e.g., random access memory (RAM) 224) and various other components via a system bus 233. Read only memory (ROM) 222 is coupled to system bus 233 and can include a basic input/output system (BIOS), which controls certain basic functions of surface processing unit 30.
Further illustrated are an input/output (I/O) adapter 227 and a network adapter 226 coupled to system bus 233. I/O adapter 227 can be a small computer system interface (SCSI) adapter that communicates with a memory, such as a hard disk 223 and/or a tape storage device 225 or any other similar component. I/O adapter 227 and memory, such as hard disk 223 and tape storage device 225 are collectively referred to herein as mass storage 234. Operating system 240 for execution on the surface processing unit 30 can be stored in mass storage 234. The network adapter 226 interconnects system bus 233 with an outside network 236 enabling the surface processing unit 30 to communicate with other systems.
A display 235 (e.g., a display monitor) is connected to system bus 233 by display adaptor 232, 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 226, 227, and/or 232 can be connected to one or more I/O busses that are connected to system bus 233 via 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 bus 233 via user interface adapter 228 and display adapter 232. A keyboard 229, mouse 230, and speaker 231 can be interconnected to system bus 233 via user interface adapter 228, 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 unit 30 includes a graphics processing unit 237. Graphics processing unit 237 is 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 unit 237 is 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 unit 30 includes processing capability in the form of processors 221, storage capability including system memory (e.g., RAM 224 and/or mass storage 234), input means such as keyboard 229 and mouse 230, and output capability including speaker 231 and display 235. In some aspects of the present disclosure, a portion of system memory (e.g., RAM 224 and mass storage 234) collectively store the operating system 240 to coordinate the functions of the various components shown in the surface processing unit 30.
One or more embodiments described herein provide for modeling pressure response in association with in-situ diverting acid flow in a formation 16 during 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 FIGS. 3 and 4 .
FIG. 3 depicts a conceptual diagram 300 of acid flow in linear geometry according to one or more embodiments described herein. The diagram 300 shows a wormhole 310 extending from a core inlet 305 penetrating through the rock sample (e.g., rock sample included in formation 16). Zones (also referred to herein as regions of formation 16), including wormhole zone 315, disturbance zone 320, and virgin zone 325, extend outward (away) from the core inlet 305. Fluid, such as a stimulation fluid (e.g., self-diverting acid), is directed through the core inlet 305 and into the wormhole 310 using, for example, one or more stimulation assemblies 22. Virgin zone 325 represents the end of wormhole growth. For example, virgin zone 325 represents a portion of the formation 16 which 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.
FIG. 4 depicts a conceptual diagram 400 of acid flow in radial geometry according to one or more embodiments described herein. As illustrated at FIG. 4 , wormhole zone 315, disturbance zone 320, and virgin zone 325 extend radially outward (away) from the core inlet 305. The diagram 400 shows wormholes 310 extending from the core inlet 305 penetrating through the earth formation 16. Fluid, such as stimulation fluid (e.g., self-diverting acid), is directed through the core inlet 305 and into the wormholes 310. Virgin zone 325 represents 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 FIG. 3 , at the start of the injection of a self-diverting acid as described herein (wormhole zone 315), the acid flows linearly away from the core inlet 305 (near the core inlet 305). In general, with reference to FIG. 4 , at the start of the injection of a self-diverting acid as described herein (wormhole zone 315), the acid flows radially outward away from the core inlet 305 (near the core inlet 305). The acid accesses pores within the formation 16; wormhole velocity decreases with acid invasion depth (away from the core inlet 305). As the acid travels farther (i.e., deeper) into the formation 16 (disturbance zone 320) relative to the core inlet 305, the acid generates pathways (e.g., wormholes). The start, the end, and the length of disturbance zone 320 may 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 wormhole 310 and 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 zone 320 between a tip 311 of the wormhole 310 and a high viscosity barrier 312 (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 FIG. 3 . Aspects of the linear model are expressed by the following equation:
$\begin{matrix} {dp}_{t} = {dp}_{wz} + {dp}_{dz} + {dp}_{vz} & (1) \end{matrix}$
where dp_tis total pressure drop, dp_wzis pressure drop associated with the wormhole zone 315, dp_dzis pressure drop associated with the disturbance zone 320, and dp_vzis pressure drop associated with the virgin zone 325.
Aspects of the linear model support calculating C_Awtand dp_wzassociated with the wormhole zone 315 based on the following equations:
$\begin{matrix} C_{Awt} = C_{Ao} e^{- \frac{K_{eff 1} l_{wh}}{v}} & (2) \end{matrix}$ $\begin{matrix} K_{eff 1} = \frac{K_{m} K_{S}}{K_{m} + K_{S}} & (3) \end{matrix}$ $\begin{matrix} K_{m} = a_{1} D_{m} & (4) \end{matrix}$ $\begin{matrix} D_{m} = e^{(- \frac{1621.411}{T} + 1.326 * C_{Ao} - b 1)} & (5) \end{matrix}$ $\begin{matrix} K_{S} = K_{So} a_{v} e^{- \frac{E_{A}}{RT}} & (6) \end{matrix}$ $\begin{matrix} v = \frac{4 q}{π d_{wh}^{2}} & (7) \end{matrix}$
where C_Awtis acid concentration at the tip 311 of the wormhole 310, C_Aois initial acid concentration at the core inlet, I_whis the length of the wormhole 310 (e.g., from the core inlet 305 to the tip 311 of the wormhole 310), ν is velocity of the acid in the wormhole, and K_eff1is effective reaction rate in the wormhole 310.
K_mis mass transfer rate, and K_Sis surface reaction rate.
D_mis diffusion coefficient, T is temperature, C_Aois initial acid concentration at the core inlet 305, b1 is a constant based on acid type.
K_Sois surface reaction rate coefficient, a_νis interfacial area, E_Ais activation energy, R is universal gas constant.
K_eff1, K_S, and K_Soare included in acid-rock reaction kinetics described herein.
q is injection rate, and d_whis diameter of the wormhole 310 in the wormhole zone 315 (e.g., width of the wormhole 310).
In an example, dp_wz≈0.
Aspects of the linear model support calculating C_Ahv, l_d, and dp_dzassociated with the disturbance zone 320 based on the following equations:
$\begin{matrix} C_{Ahv} = 10^{- pH} & (8) \end{matrix}$ $\begin{matrix} l_{d} = - \frac{\ln \frac{C_{Ahv}}{C_{Awt}} v_{i}}{K_{eff 2}} & (9) \end{matrix}$ $\begin{matrix} v_{i} = \frac{v}{φ} & (10) \end{matrix}$ $\begin{matrix} K_{eff 2} = a_{2} K_{eff 1} & (11) \end{matrix}$ $\begin{matrix} {dp}_{dz} = \frac{μ {vl}_{d}}{k} + β v_{i}^{2} & (12) \end{matrix}$ $\begin{matrix} v = \frac{4 q}{π d_{c}^{2}} & (13) \end{matrix}$ $\begin{matrix} β = a_{3} (\frac{Acid volume injected}{{PV}_{disturbance zone}}) k^{- 0.2} & (14) \end{matrix}$
where C_Ahvis acid concentration at high viscosity, l_dis length of the disturbance (e.g., length of the disturbance zone 320), μ is fluid viscosity of the injected acid, ν_iis velocity of the acid in the disturbance zone 320, ν is velocity of the acid in the wormhole 310, φ is porosity of the formation 16, k is permeability, β is the non-Darcy coefficient (also referred to herein as the Forchheimer coefficient or non-Darcy flow coefficient), and βν_i ²is 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 dp_dzusing the Forchheimer-like equation.
Aspects of the linear model support calculating dp_vzassociated with the virgin zone 325 based on the following equations:
$\begin{matrix} {dp}_{vz} = \frac{μ {Vl}_{v}}{K} & (15) \end{matrix}$ $\begin{matrix} {dp}_{dz} = \frac{μ {Vl}_{d}}{k} + β v_{i}^{2} & (12) \end{matrix}$ $\begin{matrix} β = a_{3} (\frac{Acid volume injected}{{PV}_{disturbance zone}}) {k^{- 0.2} (\frac{l_{c} - l_{wh}}{l_{d}})}^{a_{4}} & (16) \end{matrix}$
where l_νis virgin zone length (from high viscosity barrier 312 to core outlet), l_cis core length (wormhole zone 315+disturbance zone 320+virgin zone 325) In some aspects, the linear model supports calculating disturbance zone 320 reach to the core outlet 305, where dp_wz=dp_vz=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, a₁, a₂, a₃and a₄are 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 FIG. 4 . 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 dp_tbased on Equation (1), and further, calculating other parameters as described herein.
Aspects of the radial model support calculating C_Awtand dp_wzassociated with the wormhole zone 315 in association with a wormhole 310 based on the following equations:
$\begin{matrix} C_{Awt} = C_{Ao} e^{- \frac{K_{eff 1} l_{wh}}{v}} & (2) \end{matrix}$ $\begin{matrix} v = \frac{q}{A_{o}} (b_{2} - \frac{b_{3}}{1 + {(\frac{r_{wh}}{b_{4}})}^{b_{3}}}) & (17) \end{matrix}$
where C_Awtis acid concentration at the tip 311 of a wormhole 310, r_whis length of the wormhole 310, and ν is velocity of the acid inside the wormhole 310. In an example, dp_wz≈0.
Aspects of the radial model support calculating C_Ahv, l_d, and dp_dzassociated with the disturbance zone 320 in association with a wormhole 310 based on the following equations:
$\begin{matrix} C_{Ahv} = 10^{- pH} & (8) \end{matrix}$ $\begin{matrix} l_{d} = - \frac{\ln \frac{C_{Ahv}}{C_{Awt}} v_{i}}{K_{eff 2}} & (9) \end{matrix}$ $\begin{matrix} v_{i} = \frac{v}{φ} & (10) \end{matrix}$ $\begin{matrix} K_{eff 2} = a_{2} K_{eff 1} & (11) \end{matrix}$ $\begin{matrix} {dp}_{dz} = \frac{μ q \ln (\frac{r_{wh} + l_{d}}{r_{wh}})}{kh} + β v_{i}^{2} & (18) \end{matrix}$ $\begin{matrix} β = a_{3} (\frac{Acid volume injected}{{PV}_{disturbance zone}^{a_{5}}}) k^{- 0.2} & (19) \end{matrix}$
where C_Ahvis acid concentration at high viscosity, l_dis length of the disturbance, μ is fluid viscosity of the injected acid, ν_iis interstitial velocity of the acid in the disturbance zone 320, ν is velocity of the acid in the wormhole zone 315, k is permeability, β is the non-Darcy coefficient (also referred to herein as the Forchheimer coefficient or non-Darcy flow coefficient), and βν_i ²is 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 dp_dzusing the Forchheimer-like equation.
Aspects of the radial model support calculating dp_vzassociated with the virgin zone 325 based on the following equation:
$\begin{matrix} {dp}_{vz} = \frac{μ q \ln (\frac{r_{e}}{r_{wh} + l_{d}})}{kh} & (20) \end{matrix}$
In the equations described herein with reference to the radial model, a₁, a₂, a₃and a₅are constants based on acid type and rock mineralogy, and embodiments of the present disclosure support deriving and/or modifying the constantsusing laboratory experiments, numerical models, and/or field data.
An example method according to one or more embodiments of the present disclosure is described herein. The method may include calculating pore volume to breakthrough (PVBT) of the in-situ diverting acid system from experimental data or using a carbonate acidizing model described herein. In some aspects, the method may include applying the volume of diverter in association with creating a wormhole 310 along the linear core. According to one or more embodiments described herein, the method may include calculating PVBT using the following equation:
$\begin{matrix} PVBT = \frac{Acid Volume to Breakthrough}{Pore Volume} & (21) \end{matrix}$
In an example of calculating PVBT, the method may include applying a linear model (linear pressure response model) described herein. In some aspects, the method may include adjusting parameters a₃and a₄in association with matching the calculated PVBT to experimental pressure response (e.g., pressure response acquired from experimental data).
The method may include applying the adjusted parameters a₃and a₄to a radial model (radial pressure response model) described herein and designing field treatments based on outputs provided by the radial model. In some aspects, the method may include using the full pressure curve from linear experiments to improve field design.
The models described herein capture the effect of core dimensions and wellbore diameter on pressure response. The models described herein support modeling which considers the effect of rock mineralogy, temperature, acid concentration, acid type, and additives. Aspects of the models described herein provide advantages in that predictability of the models has increased reliability and accuracy compared to other models. For example, as described herein, predictions by the models may be based on fundamental flow and chemical engineering equations. These and other advantages will be apparent as further described herein.
FIG. 5 illustrates an example flowchart of a method 500 supportive of modeling a pressure response of acid flow of an acid in a formation in accordance with one or more embodiments of the present disclosure. The method 500 may be implemented by any suitable processing system downhole or on surface (e.g., the surface processing unit 30, the surface processing unit 30, a downhole electronics unit 32, a cloud computing node of a cloud computing environment, etc.), any suitable processing device (e.g., the processor 34, one of the processors 21), and/or combinations thereof or another suitable system or device.
In the descriptions of the flowcharts herein, the operations may be performed in a different order than the order shown, or the operations may be performed in different orders or at different times. Certain operations may also be left out of the flowcharts, one or more operations may be repeated, or other operations may be added to the flowcharts.
At 505, the method 500 includes receiving (e.g., by the surface processing unit 30) data associated with acid stimulation of a formation.
According to an embodiment, the data is linear core flow data. The data can be laboratory data, field data, and/or combinations thereof. According to one or more embodiments described herein, receiving the data can include collecting the data, such as in a laboratory environment, at a wellbore operation (e.g., in the field), and/or the like. For example, one or more sensors (e.g., temperature sensors, pressure sensors, etc.) can be used to collect the data.
At 510, the method 500 includes modeling the pressure response of the acid flow in the formation, where 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.
At 515, the method 500 includes determining whether the pressure response satisfies a pressure response threshold.
At 520, the method 500 includes, responsive to determining that the pressure response fails to satisfy the pressure response threshold, modifying a stimulation parameter in association with adjusting the pressure response.
Non-limiting examples of the stimulation parameter include a type of acid, an acid formulation, an acid concentration, and the like.
At 525, the method 500 includes performing the acid stimulation based at least in part on a stimulation parameter associated with the acid stimulation or the modified stimulation parameter, responsive to determining whether the pressure response satisfies the pressure response threshold.
For example, the method 500 may include (not illustrated), responsive to determining (at 515) that the pressure satisfies the pressure response threshold, refraining from modifying the stimulation parameter. Accordingly, for example, at 525, the method 500 may include performing the acid stimulation based at least in part on the stimulation parameter (e.g., without modifying the stimulation parameter).
In an example, at 525, performing the acid stimulation may include (e.g., by hydrocarbon production stimulation system 10), using one or more of the stimulation assemblies 22, controlling injection of stimulation fluid (e.g., acid stimulation fluid) and directing the stimulation fluid into one or more production zones in the formation 16.
In some aspects, the acid includes a self-diverting acid.
In some aspects, modeling the pressure response is based on a function of a consecutive series of flow disturbances in the disturbance zone causing pressure build up.
In some aspects, the pressure response is a function of an injected volume of the acid, a pore volume of the disturbance zone, and the velocity of the acid.
In some aspects, the pressure response includes at least one of: first pressure response associated with a first zone of the multiple zones, the first zone including a wormhole formed in the formation in association with the acid stimulation; second pressure response associated with a second zone of the multiple zones, where the second zone is adjacent the first zone; and third pressure response associated with a third zone of the multiple zones, where the third zone is adjacent the second zone.
In some aspects, the method 500 may include determining an acid concentration of the acid associated with the acid stimulation, where the acid concentration is associated with an end portion of a wormhole formed in association with the acid stimulation, where modeling the pressure response (at 510) is based on the acid concentration.
In some aspects, the method 500 may include determining a second acid concentration of the acid, where the second acid concentration is associated with a location in the formation at which a viscosity level of the acid satisfies a threshold viscosity, where modeling the pressure response (at 510) is based on the second acid concentration.
In some aspects, modeling the pressure response includes determining, by applying the data associated with the acid stimulation to the model, a pore volume to breakthrough value associated with the formation, where setting or modifying the stimulation parameter is based on the pore volume to breakthrough value.
In some aspects, modeling the pressure response is based on one or more dimensions of a wormhole formed in the formation in association with the acid stimulation.
In some aspects, modeling the pressure response is based on temperature information associated with the formation.
In some aspects, the model includes a linear model.
In some aspects, the model includes a radial model.
In some aspects, the data associated with the acid stimulation includes: laboratory data; and field data associated with one or more wellbore operations.
Various tuning and implementation aspects of a carbonite acidizing model in accordance with one or more embodiments of the present disclosure are now described with reference to FIGS. 6 through 15 .
FIGS. 6 through 9 illustrate example plots 600 through 900 of change in pressure (delta P (psi)) with respect to pore volume (PV) of an injected in-situ gelled acid, in which the acid (at a temperature of 250 degrees Fahrenheit) is injected into limestone. The solid line represents experimental data and the dashed line represents pressure predictions generated by a model described herein. Results associated with plots 600 through 900 respectively correspond to injection rates of the acid of 1cc/minute, 4 cc/minute, 6 cc/minute, and 10 cc/minute.
FIG. 10 illustrates an example plot 1000 of change in pressure (delta P (psi)) with respect to pore volume (PV) of an injected in-situ gelled acid, in which the acid (at a temperature of 250 degrees Fahrenheit) is injected into dolomite according to an injection rate of 6 cc/minute. The solid line represents experimental data and the dashed line represents pressure predictions generated by a model described herein.
FIG. 11 illustrates an example plot 1100 of change in pressure (delta P (psi)) with respect to pore volume (PV) of an injected 15% HCl VES based acid, in which the acid (at a temperature of 175 degrees Fahrenheit) is injected into limestone according to an injection rate of 0.5 cc/minute. The solid line represents delta P and the dotted line represents pressure predictions generated by a model described herein.
FIG. 12 illustrates an example plot 1200 of change in pressure (delta P (psi)) with respect to pore volume (PV) of an injected 15% HCl VES based acid, in which the acid (at a temperature of 175 degrees Fahrenheit) is injected into dolomite according to an injection rate of 1 cc/minute. The solid line represents delta P and the dotted line represents pressure predictions generated by a model described herein.
FIG. 13 illustrates an example plot 1300 of change in pressure (delta P (psi)) with respect to time (minutes) for an injected HCl VES based acid, in which the acid (at a temperature of 150 degrees Fahrenheit) is injected. Plot 1300 illustrates results associated with a model for experimental data 1 (solid line), a model for experimental data 2 (dashed line), and model generated data (triangles) in accordance with one or more embodiments of the present disclosure.
FIG. 14 illustrates an example plot 1400 of formation face pressure. Plot 1400 illustrates radial pressure response (psi)) with respect to volume (gal/ft) of an injected in-situ gelled acid under radial flow, in which the acid (at a temperature of 250 degrees Fahrenheit) is injected according to injection rates 0.1 gal/(ft.min) (dash-dotted line), 0.5 gal/(ft.min) (dashed line), and 1 gal/(ft.min) (solid line).
FIG. 15 illustrates an example plot 1500 of formation face pressure. Plot 1400 illustrates radial pressure response (psi)) with respect to volume (gal/ft) of an injected in-situ gelled acid under radial flow, in which the acid is injected according to an injection rate of 1 gal/(ft.min) and temperatures of 250 degrees Fahrenheit (dash-dotted line), 200 degrees Fahrenheit (dashed line), and 150 degrees Fahrenheit (solid line).
According to one or more embodiments described herein, the models described herein can be tuned for different parameters (e.g., acid concentrations, different flow rates, different temperatures, and the like).
Example embodiments of the disclosure include or yield various technical features, technical effects, and/or improvements to technology. Example embodiments of the disclosure provide technical solutions for modeling pressure response in a formation. The techniques described herein represent an improvement to conventional acidizing models as described herein. Accordingly, stimulation decisions can be made more accurately and faster, thus improving stimulation efficiency, reducing non-production time, improving hydrocarbon recovery, and the like. This increases hydrocarbon recovery from a hydrocarbon reservoir compared to conventional techniques.
Set forth below are some embodiments of the foregoing disclosure:
Embodiment 1. A method for modeling pressure response of acid flow of an acid in a formation, the method comprising: receiving data associated with acid stimulation of a formation; 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 comprises modeling a length of a disturbance zone comprised in the multiple zones based on a function of: reaction kinetics associated with the acid and rock comprised in the formation; and an injection rate of the acid, a velocity of the acid, or both. The method comprises determining whether the pressure response satisfies a pressure response threshold; and performing the acid stimulation based at least in part 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.
Embodiment 2. A method according to any prior embodiment, further including: responsive to determining that the pressure response fails to satisfy the pressure response threshold, modifying the stimulation parameter in association with adjusting the pressure response; and performing the acid stimulation based at least in part on the modified stimulation parameter.
Embodiment 3. A method according to any prior embodiment, wherein the acid comprises a self-diverting acid.
Embodiment 4. A method according to any prior embodiment, wherein modeling the pressure response is based on a function of a consecutive series of flow disturbances in the disturbance zone causing pressure build up.
Embodiment 5. A method according to any prior embodiment, wherein the pressure response is a function of an injected volume of the acid, a pore volume of the disturbance zone, and the velocity of the acid.
Embodiment 6. A method according to any prior embodiment, wherein the pressure response comprises at least one of: first pressure response associated with a first zone of the multiple zones, the first zone comprising a wormhole formed in the formation in association with the acid stimulation; second pressure response associated with a second zone of the multiple zones, wherein the second zone is adjacent the first zone; and third pressure response associated with a third zone of the multiple zones, wherein the third zone is adjacent the second zone.
Embodiment 7. A method according to any prior embodiment, further comprising: determining an acid concentration of the acid associated with the acid stimulation, wherein the acid concentration is associated with an end portion of a wormhole formed in association with the acid stimulation, wherein modeling the pressure response is based at least in part on the acid concentration.
Embodiment 8. A method according to any prior embodiment, further comprising: determining a second acid concentration of the acid, wherein the second acid concentration is associated with a location in the formation at which a viscosity level of the acid satisfies a threshold viscosity, wherein modeling the pressure response is based at least in part on the second acid concentration.
Embodiment 9. A method according to any prior embodiment, wherein modeling the pressure response comprises: determining, by applying the data associated with the acid stimulation to the model, a pore volume to breakthrough value associated with the formation, wherein setting or modifying the stimulation parameter is based on the pore volume to breakthrough value.
Embodiment 10. A method according to any prior embodiment, wherein modeling the pressure response is based at least in part on one or more dimensions of a wormhole formed in the formation in association with the acid stimulation.
Embodiment 11. A method according to any prior embodiment, wherein modeling the pressure response is based at least in part on temperature information associated with the formation.
Embodiment 12. A method according to any prior embodiment, wherein the model comprises a linear model.
Embodiment 13. A method according to any prior embodiment, wherein the model comprises a radial model.
Embodiment 14. A method according to any prior embodiment, wherein the data associated with the acid stimulation comprises: laboratory data; and field data associated with one or more wellbore operations.
Embodiment 15. A system for modeling pressure response of acid flow of an acid in a formation, the system comprising: a processing system configured to execute computer readable instructions, the computer readable instructions controlling the processing system to perform operations comprising: receiving data associated with acid stimulation of a formation; 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 comprises modeling a length of a disturbance zone comprised in the multiple zones based on a function of: reaction kinetics associated with the acid and rock comprised in the formation; and an injection rate of the acid, a velocity of the acid, or both. The operations comprise determining whether the pressure response satisfies a pressure response threshold; responsive to determining that the pressure response fails to satisfy the pressure response threshold, modifying a stimulation parameter in association with adjusting the pressure response; and performing the acid stimulation based at least in part on the modified stimulation parameter.
Embodiment 16. A system according to any prior embodiment, wherein the computer readable instructions control the processing system to perform further operations comprising: responsive to determining that the pressure response fails to satisfy the pressure response threshold, modifying the stimulation parameter in association with adjusting the pressure response; and performing the acid stimulation based at least in part on the modified stimulation parameter.
Embodiment 17. A system according to any prior embodiment, wherein the acid comprises a self-diverting acid.
Embodiment 18. A system according to any prior embodiment, wherein modeling the pressure response is based on a function of a consecutive series of flow disturbances in the disturbance zone causing pressure build up.
Embodiment 19. A system according to any prior embodiment, wherein the pressure response is a function of an injected volume of the acid, a pore volume of the disturbance zone, and the velocity of the acid.
Embodiment 20. A system according to any prior embodiment, wherein the pressure response comprises at least one of: first pressure response associated with a first zone of the multiple zones, the first zone comprising a wormhole formed in the formation in association with the acid stimulation; second pressure response associated with a second zone of the multiple zones, wherein the second zone is adjacent the first zone; and third pressure response associated with a third zone of the multiple zones, wherein the third zone is adjacent the second zone.
The use of the terms “a” and “an” and “the” and similar referents in the context of describing the present disclosure (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 further 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 modifier “about” used in connection with a quantity is inclusive of the stated value and has the meaning dictated by the context (e.g., it includes the degree of error associated with measurement of the particular quantity).
The teachings of the present disclosure can be used in a variety of well operations. These operations can involve using one or more treatment agents to treat a formation, the fluids resident in a formation, a wellbore, and/or equipment in the wellbore, such as production tubing. The treatment agents can 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.
While the present disclosure has been described with reference to an embodiment or embodiments, it will be understood by those skilled in the art that various changes can be made and equivalents can be substituted for elements thereof without departing from the scope of the present disclosure. In addition, many modifications can be made to adapt a particular situation or material to the teachings of the present disclosure without departing from the essential scope thereof. Therefore, it is intended that the present disclosure not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this present disclosure, but that the present disclosure will include all embodiments falling within the scope of the claims. Also, in the drawings and the description, there have been disclosed embodiments of the present disclosure and, although specific terms can 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 present disclosure therefore not being so limited.

Claims

What is claimed is:

1. A method for modeling pressure response of acid flow of an acid in a formation, the method comprising:

receiving data associated with acid stimulation of a formation;

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 comprises modeling a length of a disturbance zone comprised in the multiple zones based on a function of:

reaction kinetics associated with the acid and rock comprised in the formation; and

an injection rate of the acid, a velocity of the acid, or both;

determining whether the pressure response satisfies a pressure response threshold; and

performing the acid stimulation based at least in part 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.

2. The method of claim 1, further comprising:

responsive to determining that the pressure response fails to satisfy the pressure response threshold, modifying the stimulation parameter in association with adjusting the pressure response; and

performing the acid stimulation based at least in part on the modified stimulation parameter.

3. The method of claim 1, wherein the acid comprises a self-diverting acid.

4. The method of claim 1, wherein modeling the pressure response is based on a function of a consecutive series of flow disturbances in the disturbance zone causing pressure build up.

5. The method of claim 1, wherein the pressure response is a function of an injected volume of the acid, a pore volume of the disturbance zone, and the velocity of the acid.

6. The method of claim 1, wherein the pressure response comprises at least one of:

first pressure response associated with a first zone of the multiple zones, the first zone comprising a wormhole formed in the formation in association with the acid stimulation;

second pressure response associated with a second zone of the multiple zones, wherein the second zone is adjacent the first zone; and

third pressure response associated with a third zone of the multiple zones, wherein the third zone is adjacent the second zone.

7. The method of claim 1, further comprising:

determining an acid concentration of the acid associated with the acid stimulation, wherein the acid concentration is associated with an end portion of a wormhole formed in association with the acid stimulation,

wherein modeling the pressure response is based at least in part on the acid concentration.

8. The method of claim 7, further comprising:

determining a second acid concentration of the acid, wherein the second acid concentration is associated with a location in the formation at which a viscosity level of the acid satisfies a threshold viscosity,

wherein modeling the pressure response is based at least in part on the second acid concentration.

9. The method of claim 1, wherein modeling the pressure response comprises:

determining, by applying the data associated with the acid stimulation to the model, a pore volume to breakthrough value associated with the formation,

wherein setting or modifying the stimulation parameter is based on the pore volume to breakthrough value.

10. The method of claim 1, wherein modeling the pressure response is based at least in part on one or more dimensions of a wormhole formed in the formation in association with the acid stimulation.

11. The method of claim 1, wherein modeling the pressure response is based at least in part on temperature information associated with the formation.

12. The method of claim 1, wherein the model comprises a linear model.

13. The method of claim 1, wherein the model comprises a radial model.

14. The method of claim 1, wherein the data associated with the acid stimulation comprises:

laboratory data; and

field data associated with one or more wellbore operations.

2. A system for modeling pressure response of acid flow of an acid in a formation, the system comprising:

a processing system configured to execute computer readable instructions, the computer readable instructions controlling the processing system to perform operations comprising:

receiving data associated with acid stimulation of a formation;

an injection rate of the acid, a velocity of the acid, or both;

16. The system of claim 15, wherein the computer readable instructions control the processing system to perform further operations comprising:

17. The system of claim 15, wherein the acid comprises a self-diverting acid.

18. The system of claim 15, wherein modeling the pressure response is based on a function of a consecutive series of flow disturbances in the disturbance zone causing pressure build up.

19. The system of claim 15, wherein the pressure response is a function of an injected volume of the acid, a pore volume of the disturbance zone, and the velocity of the acid.

20. The system of claim 15, wherein the pressure response comprises at least one of: