A solution method for carbonate karst at the pore scale

Abstract

This invention provides a solution method for carbonate rock karstification at the pore scale, comprising: constructing the kinetic equations for the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process; determining the ion concentration change transport model; determining the time and space variation of the solid volume fraction in the solid phase region during carbonate rock karstification and establishing the volume control equations; determining the ion reaction source term equations at the fluid-solid two-phase interface; updating the main population ion concentration and the auxiliary population ion concentration; and extending the model using the time scale coordination principle to ensure that the time scale of karstification is consistent with the time scale of flow, thereby obtaining a solution model for the solid precipitation karstification process. This invention uses chemical kinetic equilibrium theory and the time scale coordination principle to describe the problem of carbonate rock karstification, constructing an efficient, complete, and reliable numerical model.

Description

Technical Field

[0001] This invention relates to the field of carbonate rock karst solution technology, and more specifically, to a method for solving carbonate rock karst at the pore scale. Background Technology

[0002] Carbonate reservoirs are characterized by complex spatial pore structures and strong heterogeneity due to the combined influence of original lithology, structure, and karst. Acidification is a primary means of geological modification of carbonate reservoirs. It is a highly complex physicochemical process involving the mass transfer of hydrogen ions from the pore fluid to the carbonate surface under the macroscopic movement (convection) and concentration gradient (diffusion) of the acid, thereby altering the formation porosity. Traditional macroscopic numerical simulation techniques, by establishing mathematical models and studying the macroscopic acidification process of carbonates, can reveal the development and expansion patterns of macroscopic acid-etched vermiformes, which is of great significance for the study of vermiforme formation and fracture network development. However, macroscopic methods focus on the dissolution process and cannot describe the thermal factors, diffusion, reaction, and flow behavior of different ions during the reaction process.

[0003] To address the problems of existing technologies, this invention provides a method for solving carbonate rock karst at the pore scale. Summary of the Invention

[0004] To address the problems in the prior art, this invention provides a method for solving carbonate rock karst at the pore scale, the method comprising the following steps:

[0005] S1. Construct the dynamic equations for the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process, and apply additional stress corrections to the solid phase region.

[0006] S2. Analyze the comprehensive chemical reactions that occur during the karstification of carbonate rocks, and determine the ion concentration change transmission model by the relationship between the main population ions and the auxiliary population ions.

[0007] S3. Determine the changes in the solid volume fraction of the solid phase region with time and space during the karstification process of carbonate rocks, and establish the volume control equation;

[0008] S4. Determine the ion reaction source term equation at the fluid-solid interface based on ionic forces and the activity coefficients of the main population ions.

[0009] S5. Based on the ion concentration change transport model, the volume control equation, and the ion reaction source term equation, update the main population ion concentration and update the auxiliary population ion concentration.

[0010] S6. Extend the solution model by using the time scale coordination principle to make the time scale of dissolution consistent with the time scale of flow, and obtain the solution model of solid precipitation dissolution process.

[0011] According to an embodiment of the present invention, step S1 includes:

[0012] The design architecture is based on the single-phase flow process theory in fluid mechanics. At the same time, the Navier-Stokes equation with volume fraction mixing average is used to describe the two-phase motion process, and the dynamic equation of fluid-solid two-phase motion is constructed.

[0013] Considering the concentration transfer of ions generated after the dissolution of solid precipitates in the two-phase flow system of carbonate rock karstification, an equation for the transfer of ion concentration in solution is constructed.

[0014] Based on the dynamic equations of fluid-solid two-phase motion, the kinematic equations of the solid region are modified, and a modified stress source term is added to the source term calculation of the momentum equation of the solid region.

[0015] According to an embodiment of the present invention, step S2 includes:

[0016] The comprehensive chemical reactions that occur during the karstification of carbonate rocks were analyzed. Hydrogen ions, calcium ions, and bicarbonate ions were taken as the main population ions, hydroxide ions were taken as the auxiliary population ions, and chloride ions were taken as the unreacted population ions. The main chemical reactions that occur during the physicochemical process of carbonate rock karstification were determined.

[0017] Considering the additional water ionization reactions that occur during the dissolution process, determine the additional ionic chemical reactions in the physicochemical process of carbonate rock dissolution;

[0018] There are ion source terms generated by chemical reaction and dissolution at the fluid-solid interface. Based on the reaction coefficients of each substance in the main chemical reaction and the additional ion chemical reaction, the ion concentration change transport equation and the concentration change source term equation of the main population ion are determined.

[0019] Based on the changing trends of the main population ions, the equations for tracking and calculating hydrogen ions, calcium ions, and bicarbonate ions were obtained.

[0020] According to an embodiment of the present invention, step S3 includes:

[0021] To ensure the continuity and non-negativity of the source term at the fluid-solid interface, a derived function of the hyperbolic tangent function is constructed to calculate the area of ​​the phase interface per unit volume within the grid cell.

[0022] Based on the area of ​​the phase interface per unit volume within the grid cell, the governing equations for the variation of solid volume fraction at the fluid-solid interface with time and space during carbonate karstification are determined.

[0023] Based on the governing equations of the solid volume fraction at the fluid-solid interface as a function of time and space, the volume governing equations of the solid region during the carbonate rock dissolution process are determined.

[0024] According to an embodiment of the present invention, step S4 includes:

[0025] The activity product of the reactant ions in the main chemical reaction is determined based on the ionic forces and the activity coefficients of the main population ions.

[0026] Based on the activity product of the reacting ions, the chemical reaction rate of the main chemical reaction, and the ionic reaction equilibrium constant of the main chemical reaction, the ionic reaction source term equation at the fluid-solid interface is obtained.

[0027] According to an embodiment of the present invention, step S5 includes:

[0028] The auxiliary population ion concentration is updated based on the updated main population ion concentration, the types of auxiliary population ions, the activity coefficients of auxiliary population ions, the activity coefficients of the main population ions, and the ion reaction equilibrium constant.

[0029] According to an embodiment of the present invention, step S6 includes:

[0030] Step a: Set the calculation time step according to the flow time scale. When the flow iteration calculation reaches convergence, freeze the flow field, assuming that the converged flow field remains unchanged before the shape of the solid region changes.

[0031] Step b: Under the condition that the solution ion concentration field reaches steady-state convergence with the flow field, as long as the solid phase region does not change, the source term of ion concentration change at the interface at each moment is a constant. Multiply the dissolution time scale by the ion concentration source term under convergence conditions to obtain the overall dissolution source term within the dissolution time scale. The calculation time is also increased by a dissolution time scale, so as to achieve consistency with the flow time scale.

[0032] Step c: Update the ion concentration in the solution using the ion concentration source term and the ion concentration change transmission equation, and update the volume fraction of the solid region using the solid dissolution source term and the volume control equation, thereby updating the velocity field in the post-dissolution computational domain.

[0033] Step d: After obtaining the new concentration field and velocity field, repeat the above process and iterate repeatedly until the convergence condition is met.

[0034] According to one embodiment of the present invention, the solution model is tested using square and circular carbonate rocks respectively, and the solution model is updated based on the test results.

[0035] According to another aspect of the invention, a storage medium is also provided, which includes a series of instructions for performing the steps of the method described in any of the preceding claims.

[0036] According to another aspect of the invention, a solution apparatus for carbonate karst at the pore scale is also provided, performing the method as described in any of the preceding claims, the apparatus comprising:

[0037] The correction module is used to construct the dynamic equations of the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process, and to apply additional stress corrections to the solid phase region.

[0038] The concentration field module is used to analyze the comprehensive chemical reactions that occur during the karstification of carbonate rocks. By determining the ion concentration change transmission model through the relationship between the main population ions and the auxiliary population ions;

[0039] The velocity field module is used to determine the changes in the solid volume fraction of the solid phase region with time and space during the karstification of carbonate rocks, and to establish the volume control equation.

[0040] The ion reaction source term module is used to determine the ion reaction source term equation at the fluid-solid interface based on the ion force and the activity coefficient of the main population ions.

[0041] The concentration update module is used to update the main population ion concentration and the auxiliary population ion concentration based on the ion concentration change transport model, the volume control equation, and the ion reaction source term equation.

[0042] The iterative module is used to extend the solution using the timescale coordination principle, so that the timescale of dissolution is consistent with the timescale of flow, thus obtaining a solution model for the solid precipitation dissolution process.

[0043] This invention provides a solution method for carbonate karst at the pore scale. Compared with existing technologies, its significant advantages are as follows: 1. It uses numerical simulation to reproduce the two-phase flow process, performs mathematical analysis on the physical processes of carbonate karst, and solves a system of mathematical equations for multiple coupled and interacting physical phenomena simultaneously. 2. It employs chemical kinetic equilibrium theory and the principle of time-scale coordination to describe the problem of carbonate karst, thereby constructing an efficient, complete, and reliable numerical model. This provides a more comprehensive system for the study of multiphase physical-chemical processes within pores and further provides technical support for the improvement of acid fracturing processes.

[0044] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the description, claims, and drawings. Attached Figure Description

[0045] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with the embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0046] Figure 1 A flowchart illustrating a solution method for carbonate rock karstification at the pore scale according to an embodiment of the present invention is shown.

[0047] Figure 2 A flowchart illustrating a solution method for carbonate rock karstification at the pore scale according to another embodiment of the present invention is shown.

[0048] Figures 3(a) and 3(b) show the initial fluid-solid two-phase distribution of square and circular carbonate rocks according to an embodiment of the present invention;

[0049] Figures 4(a)-4(f) A visualization of the dissolution of a square carbonate solid precipitate at different times according to an embodiment of the present invention is shown.

[0050] Figures 5(a)-5(f) A visualization of the dissolution of circular carbonate solid precipitates at different times according to an embodiment of the present invention is shown;

[0051] Figures 6(a)-6(f) The graph shows the variation of H ion concentration during the karstification of a square carbonate rock at different times according to an embodiment of the present invention;

[0052] Figures 7(a)-7(f) The graph shows the variation of H ion concentration at different times during the karstification of a circular carbonate rock according to an embodiment of the present invention.

[0053] In the accompanying drawings, the same parts use the same reference numerals. Also, the drawings are not drawn to scale. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0055] In existing technologies, dissolution is carried out based on experimental and numerical simulation techniques. Due to the high resource consumption and poor controllability of formation physical parameters required by experimental methods, current research mostly adopts numerical simulation techniques. The development of acidification mathematical models has gone through a process from one-dimensional models (steady state), two-dimensional models (steady state and non-steady state) to three-dimensional models (steady state and non-steady state). Among them, the three-dimensional model uses geostatistical methods to construct three-dimensional hydraulic fracture morphology considering the heterogeneity of minerals and permeability. It uses the finite volume method to directly solve the N-S equations and convection-diffusion equations, and obtains the acid concentration distribution on the three-dimensional rough fracture surface and the fracture width distribution after acid etching. For example, existing technologies (CN202010770011.3), (CN201910526917.8), and (numerical simulation of large-scale acidification of fractured carbonate reservoirs based on step-by-step algorithm, Acta Petrolei Sinica, 2020, 41(03):102-116+125.).

[0056] Existing numerical simulation techniques only study the flow processes within fracture networks. While they can reveal the macroscopic expansion patterns of fracture networks, which is significant for macroscopic fracture propagation research, this macroscopic approach often overemphasizes the motion of the fluid itself and the physical processes of solid dissolution. It fails to directly and effectively reflect microscopic mechanisms occurring within these processes (such as the kinetics of ion reactions, transport, and diffusion in chemical reactions, and temperature changes). Particularly during dissolution, the physical phenomena occurring at the interface between two phases can only be studied from a microscopic perspective to establish a basic framework for the study of acidification problems.

[0057] Therefore, this invention conducts an in-depth investigation into the physicochemical coupling effect of carbonate rock karstification at the pore scale, clarifies the intrinsic triggering mechanism of macroscopic phenomena during acid fracturing, and supplements the macroscopic research system proposed by predecessors by exploring the multiphase physicochemical processes in the micropores, thus constructing a more comprehensive system for the study of carbonate rock karstification mechanism, so as to further promote the improvement and enhancement of acid fracturing technology.

[0058] Figure 1 A flowchart illustrating a solution method for carbonate rock dissolution at the pore scale according to an embodiment of the present invention is shown. The present invention derives a solution model for the carbonate rock precipitation and dissolution process through chemical kinetic equilibrium theory and the principle of time scale coordination.

[0059] like Figure 1 As shown, in step S1, the dynamic equations of the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process are constructed, and additional stress corrections are applied to the solid phase region.

[0060] In one embodiment, step S1 includes: designing an architecture based on the single-phase flow process theory in fluid mechanics, and using the Navier-Stokes equations with volume fraction mixing average to describe the two-phase motion process, thereby constructing the dynamic equations for the fluid-solid two-phase motion.

[0061] The mathematical description of the flow phenomena in the carbonate karst corrosion process discussed in this invention adopts the single-phase flow process theory in fluid mechanics for its design framework. Simultaneously, it uses the Navier-Stokes equations with volume fraction mixing average to describe the two-phase motion process. The continuity equation and momentum equation in the mathematical model are as follows, i.e., the dynamic equations of the fluid-solid two-phase motion are:

[0062]

[0063]

[0064] Where u is the velocity value at the center of the fluid region grid cell / m·s -1 ρ is the weighted average density of the fluid-solid two phases (kg·m³). -3 μ is the weighted average dynamic viscosity coefficient of the fluid-solid two phases (Pa·s); p is the pressure value at the center of the fluid region grid cell (Pa); g is the gravitational acceleration (m·s). -2 ;F τ F represents the circumferential (or tangential) stress at the interface between two phases, represented by the Marangoni force, in N / N. σ The radial (or normal) stress at the interface between two phases, represented by surface tension, is expressed in N.

[0065] In one embodiment, step S1 includes: considering the concentration transfer of ions generated after the dissolution of solid precipitates in a fluid-solid two-phase flow system of carbonate rock karstification, and constructing an equation for the transfer of ion concentration in the solution.

[0066] In the fluid-solid two-phase flow system of carbonate rock dissolution, there is a concentration transfer of ions generated after the carbonate rock dissolves into the solution. Therefore, the equation for the ion concentration transfer in the solution is:

[0067]

[0068] Where C is the concentration value at the center of the computational domain grid cell (mol·m). -3 ;D C S is the weighted average mass transfer coefficient of the fluid-solid two phases; C For the source term in the process of mass or concentration transfer.

[0069] The equation for heat exchange, or energy transfer, of ions in solution after the solid precipitate dissolves is:

[0070]

[0071] In the formula: c p S is the weighted average specific heat capacity of the fluid-solid two phases; T is the temperature value at the center of the computational domain grid cell in K; k is the weighted average heat transfer coefficient of the fluid-solid two phases; S Q It is the source term in the energy transfer process.

[0072] In one embodiment, step S1 includes: modifying the kinematic equations of the solid region based on the dynamic equations of the fluid-solid two-phase motion, and adding a modified stress source term in the source term calculation of the momentum equation of the solid region.

[0073] Specifically, a kinematic description of carbonate karst erosion in the solid region is performed, and additional force corrections are applied to the solid region. Since the solid region is treated as a fluid region in the solution of the fluid region equations, kinematic equation corrections are needed for the solid region. A modified stress source term, Lamd, is added to the source term calculation in the momentum (NS) equation of the solid region. The specific calculation form of this added modified stress source term is as follows:

[0074]

[0075] Where Lamd is the modified stress source term in the solid region; u ba Auxiliary velocity values ​​for calculating additional stress in the solid region / m·s -1 ; Δt is the computation time step used in numerical calculation / s; α is the volume fraction of the main phase (solid phase) in the grid cell.

[0076] like Figure 1 As shown, in step S2, the comprehensive chemical reactions that exist during carbonate rock karstification are analyzed, and the ion concentration change transport model is determined by the relationship between the main population ions and the auxiliary population ions.

[0077] In one embodiment, step S2 includes: analyzing the comprehensive chemical reactions present during carbonate rock karstification, using hydrogen ions, calcium ions, and bicarbonate ions as the main population ions, hydroxide ions as the secondary population ions, and chloride ions as the unreacted population ions, to determine the main chemical reactions occurring in the physicochemical process of carbonate rock karstification.

[0078] The analysis of the complex chemical reactions occurring during carbonate rock karstification simplifies the types of ions in the solution by ignoring HCO3, which is not present in the original solution. — And substances such as H2CO3(aq) can convert hydrogen ions into H+. + Calcium ions (Ca) 2+ and bicarbonate ions HCO3 — As the dominant population ion, the hydroxide ion OH-— As a secondary population ion, chloride ions Cl... — As non-reactive population ions, the main chemical reactions that occur during the physicochemical process of carbonate rock dissolution are generally considered to be:

[0079]

[0080] In one embodiment, step S2 includes: considering some additional water ionization reactions that occur during the dissolution process, and identifying additional ionic chemical reactions in the physicochemical process of carbonate rock dissolution.

[0081] During the dissolution process, some additional hydrolysis and ionization reactions also occur. Under the simplified ion classification method, this mainly refers to the ionization reaction of water. The additional ion chemical reaction equations are as follows:

[0082]

[0083] In one embodiment, step S2 includes: having an ion source term generated by chemical reaction dissolution at the fluid-solid interface, and determining the ion concentration change transport equation and the main population ion concentration change source term equation based on the reaction coefficients of each substance in the main chemical reaction and the additional ion chemical reaction.

[0084] At the fluid-solid interface, due to the dissolution caused by chemical reactions, the ion source term can generally be considered, based on the reaction coefficients of each substance in the chemical reaction equations, as follows: The transport equation for the concentration of ions in the solution and the calculation formula for the source term are:

[0085]

[0086]

[0087] In the formula: ψ j The calculated auxiliary summation concentration of the main population ions is given; D is the mass transfer diffusion coefficient of the ions in the solution, which is set to 5.02 × 10⁻⁵ / m. 2 ·s -1 ;υ jm denoted by , where is the coefficient of the ion in the chemical reaction equation; , where n is the normal vector at the fluid-solid interface; I m This is the source term for the concentration change of the main population ions during the dissolution calculation process.

[0088] In one embodiment, step S2 includes: obtaining the tracking calculation process equations for hydrogen ions, calcium ions, and bicarbonate ions based on the changing trends of the main population ion reactions.

[0089] The tracking and calculation processes for hydrogen ions, calcium ions, and bicarbonate ions based on the changing trends of the main population ion reactions are as follows:

[0090]

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] In the formula: To assist in calculating the total concentration of hydrogen ions; To assist in the calculation of calcium ion concentration; This is used to calculate the total concentration of bicarbonate ions.

[0097] like Figure 1 As shown, in step S3, the change of solid volume fraction in the solid phase region with time and space during the carbonate rock karstification process is determined, and a volume control equation is established.

[0098] In one embodiment, step S3 includes: in order to ensure the continuity and non-negativity of the source terms on the fluid-solid interface, constructing a derived function of the hyperbolic tangent function to calculate the area of ​​the phase interface per unit volume within the grid cell.

[0099] In existing technology, the equation for calculating the area of ​​the interface between two phases per unit volume within a mesh cell is:

[0100]

[0101] In this invention, to ensure the continuity and non-negativity of the source terms at the interface, a derived function of the hyperbolic tangent function is constructed to approximate the area calculation equation for the unit volume phase interface within the grid cell in the prior art. The specific calculation function form is as follows:

[0102] S cc =1-(tanh(2×(V)) m -0.5))) 2 (17)

[0103] In the formula: S cc The mass transfer area at the fluid-solid interface is expressed as the gradient of the solid volume fraction per m³. -1 V m This represents the volume fraction of the solid region.

[0104] In one embodiment, step S3 includes: determining the governing equations for the change of solid volume fraction at the fluid-solid interface with time and space during carbonate karstification based on the area of ​​the unit volume phase interface within the grid cell.

[0105] During the dissolution of carbonate rocks, the solid volume fraction at the fluid-solid interface continuously decreases, and its governing equations for time and space variation are as follows:

[0106]

[0107] In the formula: V m This represents the volume fraction of the solid region. Let be the molar volume of the carbonate solid precipitate, set to 3.747 × 10⁻⁶. -5 / m 3 ·mol -1 S cc The mass transfer area at the fluid-solid interface is expressed as the gradient of the solid volume fraction per m³. -1 .

[0108] In one embodiment, step S3 includes: determining the volume control equation of the solid region during the carbonate rock dissolution process based on the control equation of the solid volume fraction at the fluid-solid interface as a function of time and space.

[0109] The volume control equation for the solid region during the dissolution process is:

[0110]

[0111] In the formula: δt is the time step in numerical calculation.

[0112] like Figure 1 As shown, in step S4, the ion reaction source term equation at the fluid-solid interface is determined based on the ionic force and the activity coefficient of the main population ions.

[0113] In one embodiment, step S4 includes: determining the activity product of the reactant ions of the main chemical reaction based on the ionic forces and the activity coefficients of the main population ions.

[0114] The specific form of ionic force is:

[0115]

[0116] The reactive ion activity product Q in the source term calculation of the ion transport equation m for:

[0117]

[0118] In the formula: Q m The reaction ion activity product of the main chemical reaction; Nc The number of ions involved in the main chemical reaction; γ j The activity coefficient of the ion that is the dominant population ion. A is a constant with a value of 1.171; a is a constant with a value of 3.5 × 10⁻⁶. -10 B is a constant with a value of 3.282 × 10⁻⁶. 9 ;z i The oxidation state of the ion; C j Volume concentration of dominant population ions / mol·m -3 .

[0119] In one embodiment, step S4 includes: obtaining the ionic reaction source term equation at the fluid-solid interface based on the reactive ion activity product, the chemical reaction rate of the main chemical reaction, and the ionic reaction equilibrium constant of the main chemical reaction.

[0120] The ionic reaction source term equation at the fluid-solid interface is:

[0121]

[0122] In the formula: k m The chemical reaction rate of the main chemical reaction; K m The chemical equilibrium constant of the main chemical reaction; Q m It is the activity product of the reactant ions in the main chemical reaction.

[0123] like Figure 1 As shown, in step S5, based on the ion concentration change transport model, volume control equation, and ion reaction source term equation, the main population ion concentration is updated, and the auxiliary population ion concentration is also updated.

[0124] In one embodiment, step S5 includes: updating the auxiliary population ion concentration based on the updated main population ion concentration, the types of auxiliary population ions, the activity coefficients of auxiliary population ions, the activity coefficients of main population ions, and the ion reaction equilibrium constant.

[0125] The auxiliary population ion concentration equation is:

[0126]

[0127] In the formula: C i Volume concentration of secondary population ions / mol·m -3 ;γ i The activity coefficient of ions in the secondary population; K i γ is the equilibrium constant for ionic reactions; j The activity coefficient of the dominant population ion; C j Volume concentration of dominant population ions / mol·m -3 ;v jidenoted as the coefficient of the main population ion in the ionic reaction equation.

[0128] Furthermore, since the secondary population ions consist only of hydroxide ions, its concentration update equation is as follows:

[0129]

[0130] In the formula: It can be considered a constant with a value of 10. -14 .

[0131] like Figure 1 As shown, in step S6, the time scale coordination principle is used to extend the model, ensuring that the time scale of dissolution is consistent with the time scale of flow, thus obtaining a solution model for the solid precipitation dissolution process. This invention utilizes the time scale coordination principle to extend the model, ensuring that the time scale of dissolution is consistent with the time scale of flow, which enhances the model's efficiency.

[0132] In one embodiment, step S6 includes step a, setting the time step of the calculation according to the time scale of the flow, and freezing the flow field after the flow iteration calculation reaches convergence, assuming that the converged flow field remains unchanged before the shape of the solid region changes.

[0133] In one embodiment, step S6 includes step b, where, under the condition that the solution ion concentration field converges to a steady state with the flow field, as long as the solid phase region does not change, the ion concentration change source term at the interface at each moment is a constant. The dissolution time scale is multiplied by the ion concentration source term under the convergence condition to obtain the overall dissolution source term within the dissolution time scale. The calculation time is also increased by a dissolution time scale, thereby achieving consistency with the flow time scale.

[0134] In one embodiment, step S6 includes step c, updating the ion concentration in the solution through the ion concentration source term and the ion concentration change transport equation, and updating the volume fraction of the solid region through the solid dissolution source term and the volume control equation, thereby updating the velocity field in the post-dissolution computational domain.

[0135] In one embodiment, step S6 includes step d, which involves re-executing the above process after obtaining the new concentration field and velocity field, iteratively calculating repeatedly until the convergence condition is met.

[0136] In one embodiment, a method for solving carbonate rock dissolution at the pore scale further includes: testing the solution model using square and circular carbonate rocks respectively, and updating the solution model based on the test results. Specifically, after the carbonate rock dissolution model is implemented in program form, two different shapes of carbonate rocks are used as test examples: one is square carbonate rock, and the other is circular carbonate rock. Numerical simulation and qualitative analysis of the shape evolution process of the two different shapes of carbonate rocks during the dissolution process are performed. The simulation results show that the solution model proposed in this application accurately reflects the real physical phenomenon of carbonate rock dissolution.

[0137] Figure 2 A flowchart illustrating a solution method for carbonate rock karstification at the pore scale according to another embodiment of the present invention is shown.

[0138] like Figure 2 As shown, a method for solving carbonate rock karst at the pore scale comprises four main steps:

[0139] The first key step is to construct the kinetic equations for the fluid-solid two-phase motion and the ion concentration transfer equations. Specifically, numerical simulations are used to construct these equations to reproduce the two-phase flow process. For the kinetic equations, since the solid volume shape changes continuously over time during the dissolution process, a Lamd stress source term needs to be added to the solid region for correction; that is, the kinetic equations for the two-phase flow are constructed by adding the Lamd stress source term.

[0140] The second key step involves considering the velocity field to determine the variation of the solid volume fraction in the solid phase region with time and space during the dissolution of carbonate rocks, and to establish the volume control equations. To ensure the continuity and non-negativity of the source terms at the interface, a derived function of the hyperbolic tangent function is constructed to approximate the area of ​​the phase interface per unit volume within the grid cell.

[0141] The third key step involves considering the concentration field and constructing concentration transport equations for the main and auxiliary ion populations. This is primarily achieved by analyzing the comprehensive chemical reactions during the dissolution process and the coefficient relationships between the main and auxiliary ion populations during the coupled reactions. Furthermore, based on the initial volume molar concentration field of the main ion population, relevant parameters such as the ion mass molar concentration field, ionic force, and ion activity coefficient are calculated. Then, based on the calculated ion activity coefficients, the ion reaction activity product is solved to derive the ion reaction source term and the dissolution source term in the solid phase region.

[0142] The fourth key step is to extend the model using the timescale coordination principle to ensure consistency between the timescale of dissolution and that of flow. This is because in the computational model of carbonate rock dissolution, the timescale of dissolution is much larger than that of flow, leading to a computational inconsistency between the two phenomena. During the calculation process, the numerical calculation of the flow phenomenon has already reached the convergence criterion, initiating a large number of invalid calculations, consuming computational time and resources, and reducing the efficiency of the dissolution numerical model. Therefore, the timescale coordination principle is used to ensure consistency between the timescale of dissolution and flow. Specifically, the ion concentration in the solution is updated using the ion concentration source term and the ion concentration change transport equation, and the volume fraction of the solid phase region is updated using the solid dissolution source term and the volume control equation, thereby updating the velocity field in the post-dissolution computational domain. After obtaining the new concentration field and velocity field, the above process is repeated iteratively until the iteration termination condition is met.

[0143] The present invention provides a method for solving carbonate karst at the pore scale, which can also be used in conjunction with a computer-readable storage medium storing a computer program. Executing the computer program runs the method for solving carbonate karst at the pore scale. The computer program can execute computer instructions, which include computer program code. The computer program code can be in the form of source code, object code, executable file, or some intermediate form.

[0144] Computer-readable storage media can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0145] It should be noted that the contents of computer-readable storage media may be appropriately added to or subtracted from the contents according to the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable storage media may not include electrical carrier signals and telecommunication signals.

[0146] In addition, the present invention also provides a solution device for carbonate karst at the pore scale, which implements a solution method for carbonate karst at the pore scale, comprising: a correction module, a concentration field module, a velocity field module, an ion reaction source term module, a concentration update module, and an iteration module.

[0147] The correction module is used to construct the kinetic equations for the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process, and to apply additional stress corrections to the solid phase region. The concentration field module is used to analyze the comprehensive chemical reactions present during carbonate rock dissolution, and to determine the ion concentration change transmission model through the relationship between the main population ions and the auxiliary population ions. The velocity field module is used to determine the changes in the solid volume fraction of the solid phase region with time and space during carbonate rock dissolution, and to establish the volume control equations. The ion reaction source term module is used to determine the ion reaction source term equations at the fluid-solid two-phase interface based on the ion force and the activity coefficients of the main population ions. The concentration update module is used to update the main population ion concentration and the auxiliary population ion concentration based on the ion concentration change transmission model, the volume control equations, and the ion reaction source term equations. The iteration module is used to extend the solution using the time scale coordination principle to keep the time scale of dissolution consistent with the time scale of flow, and to obtain the solution model for the solid precipitation dissolution process.

[0148] This invention uses two different shapes of carbonate rocks as test examples: a square carbonate rock and a circular carbonate rock. Numerical simulations and qualitative analyses were performed on the shape evolution of these two different shaped carbonate solids during the dissolution process. In the computational domain, acid was injected from the left boundary of the physical model, filling the domain with acidic fluid. The solid phase regions of the two carbonate shapes were located in the center of the computational domain. The construction of the geometric model and the processing of the calculation results in this invention utilize the Linux-based post-processing software Paraview to visualize the pre-processing and calculation results. The geometric model and mesh drawing format of this example are shown in Figures 3(a) and 3(b).

[0149] The geometric model is a rectangular computational domain of 0.05m × 0.025m, with a mesh density of 50 × 25. A fluid-solid two-phase system is distributed within the computational domain. The square solid phase region is a gray-white area, a rectangular region with geometric parameters of 0.01m × 0.009m, located at the very center of the overall computational domain. The other regions are fluid regions. For this test case, the gravitational acceleration is set to 9.8 m / s². -2 The initial pressure field, velocity field, and ion volume concentration fields for various reactions are all zero. Simultaneously containing 0.001 mol·m -3 An acidic solution with a hydrogen ion concentration of 0.01 m·s⁻¹ enters from the entrance on the left side of the geometric region. -1The injection velocity of the fluid into the computational domain causes dynamic changes in the velocity field, pressure field, and hydrogen ion concentration field. When the acidic fluid flows over the surface of the solid region, it comes into contact with it and undergoes ionic chemical reactions. Furthermore, the fluid flow and diffusion along the concentration gradient lead to changes in the ion concentration within the fluid region of the computational domain. In the numerical calculation, the finite volume method is used to discretize the tracking equations for various physical quantities. The Euler method is used for discretizing the unsteady-state terms, while Gaussian linear schemes are used for discretizing the fluid phase and diffusion. The source term is solved using implicit discretization. The algebraic equation solvers for the pressure equation and concentration tracking equation use a preconditioned biconjugate gradient solver (PBiCG), while the algebraic equation solver for the velocity equation uses a smooth solver. After setting these conditions, the time step corresponding to the grid scale is set according to the Courant number, and the calculation of the example can then be performed.

[0150] The calculation results of the square carbonate solid dissolution test example are as follows: Figures 4(a)-4(f) As shown, the carbonate solid in this model completely dissolves at approximately 23,000 s. Figures 4(a), 4(b), 4(c), 4(d), 4(e), and 4(f) respectively show the shape contour maps of the solid phase region at 0 s, 5,000 s, 10,000 s, 15,000 s, 20,000 s, and 25,000 s during the dissolution process. As can be seen from the figures, the square carbonate solid precipitate continuously deforms during the dissolution process, tending to become elliptical. The first half of the solid phase region undergoes deformation first because it comes into contact with the faster-flowing acidic fluid, while the dissolution rate of the solid precipitate located downstream of the flow direction is slower. This is consistent with our common sense of physics. Therefore, the numerical model of dissolution (the solution model of the solid precipitate dissolution process) constructed in this invention can reflect the real physical phenomenon.

[0151] The calculation results of the dissolution test example of circular carbonate solid precipitates are as follows: Figures 5(a)-5(f) As shown, the carbonate solid precipitate in this example was completely dissolved after approximately 21,000 s of calculation. Figures 5(a), 5(b), 5(c), 5(d), 5(e), and 5(f) show the solid phase region shape contour maps at 0 s, 5000 s, 10000 s, 15000 s, 20000 s, and 25000 s, respectively, during the dissolution process. As can be seen from the figures, the circular solid precipitate underwent continuous deformation during dissolution, and like the square solid, it also tended to become elliptical. In addition, by comparing the dissolution time of the two shapes of solids, it can be seen that the dissolution rate of the circular solid is faster than that of the square solid, because its surface area is larger and the contact area with the acid is also larger.

[0152] The visualization results of the H ion concentration change during the dissolution of square carbonates are as follows: Figures 6(a)-6(f) As shown in Figures 6(a), 6(b), 6(c), 6(d), 6(e), and 6(f), the hydrogen ion concentration distribution cloud maps at times 0s, 5000s, 10000s, 15000s, 20000s, and 25000s during the dissolution process, respectively. As can be seen from the figures, as time progresses, the carbonate rock gradually dissolves, the concentration of hydrogen ions participating in the carbonate rock reaction gradually decreases, and the change in the hydrogen ion concentration gradient continuously decreases.

[0153] Visualization results of H ion concentration changes during the dissolution of circular carbonates are as follows: Figures 7(a)-7(f) As shown in Figures 7(a), 7(b), 7(c), 7(d), 7(e), and 7(f), the hydrogen ion concentration distribution cloud maps at times 0s, 5000s, 10000s, 15000s, 20000s, and 25000s during the dissolution process, respectively. As time changes, the circular carbonate rock dissolution deformation gradually decreases, resulting in a continuous increase in the number of unreacted hydrogen ions, and the hydrogen ion concentration continuously increases in the area far from the entrance.

[0154] In summary, this invention provides a solution method for carbonate rock karstification at the pore scale. Compared with existing technologies, its significant advantages are as follows: 1. It uses numerical simulation to reproduce the two-phase flow process, performs mathematical analysis on the physical processes of carbonate rock karstification, and solves a system of mathematical equations for multiple coupled and interacting physical phenomena simultaneously. 2. It employs chemical kinetic equilibrium theory and the principle of time-scale coordination to describe the problem of carbonate rock karstification, thereby constructing an efficient, complete, and reliable numerical model. This provides a more comprehensive system for the study of multiphase physical-chemical processes within pores and further provides technical support for the improvement of acid fracturing processes.

[0155] It should be understood that the embodiments disclosed herein are not limited to the specific structures, processing steps, or materials disclosed herein, but should be extended to equivalent substitutions of these features as understood by those skilled in the art. It should also be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting.

[0156] In the description of this invention, unless otherwise stated, "a plurality of" means two or more; the terms "upper," "lower," "left," "right," "inner," "outer," "front end," "rear end," "head," "tail," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0157] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "connected" and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0158] The phrase "an embodiment" or "an embodiment" used in this specification means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. Therefore, the phrase "an embodiment" or "an embodiment" appearing in various places throughout the specification does not necessarily refer to the same embodiment.

[0159] The embodiments of the present invention are given for illustrative and descriptive purposes only, and are not intended to be exhaustive or to limit the invention to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art. The embodiments were chosen and described in order to better illustrate the principles and practical application of the invention, and to enable those skilled in the art to understand the invention and to design various embodiments with various modifications suitable for a particular purpose.

[0160] While the embodiments disclosed in this invention are as described above, the content is merely for the purpose of facilitating understanding of the invention and is not intended to limit the invention. Any person skilled in the art to which this invention pertains may make any modifications and variations in form and detail of the implementation without departing from the spirit and scope disclosed herein; however, the scope of patent protection for this invention shall still be determined by the scope defined in the appended claims.

Claims

1. A method for solving carbonate rock karst at the pore scale, characterized in that, The method includes the following steps: S1. Construct the dynamic equations for the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process, and apply additional stress corrections to the solid phase region. S2. Analyze the comprehensive chemical reactions that occur during the karstification of carbonate rocks, and determine the ion concentration change transmission model by the relationship between the main population ions and the auxiliary population ions. S3. Determine the changes in the solid volume fraction of the solid phase region with time and space during the karstification process of carbonate rocks, and establish the volume control equation; S4. Determine the ion reaction source term equation at the fluid-solid interface based on ionic forces and the activity coefficients of the main population ions. S5. Based on the ion concentration change transport model, the volume control equation, and the ion reaction source term equation, update the main population ion concentration and update the auxiliary population ion concentration. S6. Extend the solution model by using the time scale coordination principle to make the time scale of dissolution consistent with the time scale of flow, and obtain the solution model of solid precipitation dissolution process. Step S1 includes: designing a framework based on the single-phase flow process theory in fluid mechanics, and using the Navier-Stokes equation with volume fraction mixing average to describe the two-phase motion process, thus constructing the dynamic equation for the fluid-solid two-phase motion; considering the concentration transfer of ions generated after the solid precipitate dissolves in the fluid-solid two-phase flow system of carbonate rock karstification, thus constructing the equation for the transfer of ion concentration in the solution. Based on the dynamic equations of fluid-solid two-phase motion, the kinematic equations of the solid region are modified, and a modified stress source term is added to the source term calculation of the momentum equation of the solid region. Step S2 includes: analyzing the comprehensive chemical reactions present during carbonate rock dissolution, using hydrogen ions, calcium ions, and bicarbonate ions as the main population ions, hydroxide ions as the secondary population ions, and chloride ions as the unreacted population ions to determine the main chemical reactions occurring in the physicochemical process of carbonate rock dissolution; considering the additional water ionization reactions that occur during dissolution, determining the additional ionic chemical reactions in the physicochemical process of carbonate rock dissolution; recognizing the ion source terms generated by chemical reactions at the fluid-solid interface, and determining the ion concentration change transmission equation and the main population ion concentration change source term equation based on the reaction coefficients of each substance in the main chemical reactions and the additional ionic chemical reactions; and obtaining the tracking calculation process equations for hydrogen ions, calcium ions, and bicarbonate ions based on the reaction change trends of the main population ions. Step S6 includes: Step a) Setting the calculation time step according to the flow time scale. After the flow iteration calculation reaches convergence, the flow field is frozen, assuming that the converged flow field remains unchanged before the shape of the solid region changes; Step b) Under the condition that the solution ion concentration field reaches steady-state convergence with the flow field, as long as the solid region does not change, the ion concentration change source term at the interface at each moment is a constant. The dissolution time scale is multiplied by the ion concentration source term under convergence to obtain the overall dissolution source term within the dissolution time scale. The calculation time is also increased by a dissolution time scale to achieve consistency with the flow time scale; Step c) Updating the ion concentration in the solution through the ion concentration source term and the ion concentration change transmission equation, and updating the solid region volume fraction through the solid dissolution source term and the volume control equation, thereby updating the velocity field in the calculation domain after dissolution; Step d) After obtaining the new concentration field and velocity field, re-execute steps a to c, iteratively calculating until the convergence condition is met.

2. The method for solving carbonate karst at the pore scale as described in claim 1, characterized in that, Step S3 includes: To ensure the continuity and non-negativity of the source term at the fluid-solid interface, a derived function of the hyperbolic tangent function is constructed to calculate the area of ​​the phase interface per unit volume within the grid cell. Based on the area of ​​the phase interface per unit volume within the grid cell, the governing equations for the variation of solid volume fraction at the fluid-solid interface with time and space during carbonate karstification are determined. Based on the governing equations of the solid volume fraction at the fluid-solid interface as a function of time and space, the volume governing equations of the solid region during the carbonate rock dissolution process are determined.

3. The method for solving carbonate karst at the pore scale as described in claim 1, characterized in that, Step S4 includes: The activity product of the reactant ions in the main chemical reaction is determined based on the ionic forces and the activity coefficients of the main population ions. Based on the activity product of the reacting ions, the chemical reaction rate of the main chemical reaction, and the ionic reaction equilibrium constant of the main chemical reaction, the ionic reaction source term equation at the fluid-solid interface is obtained.

4. The method for solving carbonate karst at the pore scale as described in claim 1, characterized in that, Step S5 includes: The auxiliary population ion concentration is updated based on the updated main population ion concentration, the types of auxiliary population ions, the activity coefficients of auxiliary population ions, the activity coefficients of the main population ions, and the ion reaction equilibrium constant.

5. A method for solving carbonate karst at the pore scale as described in any one of claims 1-4, characterized in that, The solution model was tested using square and circular carbonate rocks respectively, and the solution model was updated based on the test results.

6. A storage medium, characterized in that, It contains a series of instructions for performing a solution method for carbonate karst at the pore scale as described in any one of claims 1-5.

7. A solution apparatus for carbonate rock karst at the pore scale, characterized in that, The apparatus for implementing the solution method for carbonate karst at the pore scale as described in any one of claims 1-5 comprises: The correction module is used to construct the dynamic equations of the fluid-solid two-phase motion and the ion concentration transfer equations during the flow process, and to apply additional stress corrections to the solid phase region. The concentration field module is used to analyze the comprehensive chemical reactions that occur during the karstification of carbonate rocks. By determining the ion concentration change transmission model through the relationship between the main population ions and the auxiliary population ions; The velocity field module is used to determine the changes in the solid volume fraction of the solid phase region with time and space during the karstification of carbonate rocks, and to establish the volume control equation. The ion reaction source term module is used to determine the ion reaction source term equation at the fluid-solid interface based on the ion force and the activity coefficient of the main population ions. The concentration update module is used to update the main population ion concentration and the auxiliary population ion concentration based on the ion concentration change transport model, the volume control equation, and the ion reaction source term equation. The iterative module is used to extend the solution using the timescale coordination principle, so that the timescale of dissolution is consistent with the timescale of flow, thus obtaining a solution model for the solid precipitation dissolution process.

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