Method for establishing self-diverting acid viscosity equation for reservoir acidification numerical simulation

Abstract

The application discloses a self-diverting acid viscosity equation establishment method for reservoir acidification numerical simulation, and steps are as follows: selecting a viscoelastic surfactant; based on the viscoelastic surfactant, adding CaCl2 and HCl solution with a proportion determined according to the stoichiometric number of HCl and CaCO3 reaction, and determining the viscosity of the mixed system; adding H + and Ca 2+ concentration into equivalent pH value C pH , fitting the change of the self-diverting acid viscosity with C pH into a linear combination of exponential function and error function, and establishing the self-diverting acid viscosity equation; listing the self-diverting acid acidification numerical simulation model; setting the model condition, and simulating the acidification effects of the conventional acid and the self-diverting acid. The self-diverting acid viscosity equation considers the synergistic effect of H + and Ca 2+ concentration on the viscosity, converts the binary influence of pH value and Ca 2+ into the unary influence of C pH , and when used for numerical simulation, the difference between the self-diverting acid and the conventional acid acidification effects can be accurately simulated.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas reservoir production enhancement technology, specifically a method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization. Background Technology

[0002] During acidizing carbonate reservoirs, the acid preferentially enters the high-permeability layer, dissolving minerals and creating high-conductivity channels. This further increases the permeability of the high-permeability layer, while the low-permeability layer remains untreated, resulting in unsatisfactory acidizing effects. Therefore, diversion techniques are often used to redirect the acid to the low-permeability layer. Currently, the main diversion techniques developed are mechanical diversion and chemical diversion. Among them, viscoelastic surfactant-based self-diverting acids are widely used due to their excellent diversion performance and ease of operation. When self-diverting acids are injected into carbonate reservoirs, the system viscosity is very low; as the acid-rock reaction proceeds, the H... + Concentration decreases while Ca 2+ Increased concentration alters the aggregation morphology of viscoelastic surfactants, increasing the apparent viscosity of the system and the resistance to acid flow. This forces subsequent acid to enter the low-permeability layer, achieving acid diversion. Before self-diverting acidification, the diversion effect needs to be simulated. Common simulation methods include physical simulation and numerical simulation. Physical simulation is fundamental for understanding experimental laws but has certain limitations; numerical simulation is usually based on experimental results and offers high simulation efficiency.

[0003] The reversing effect of self-reversing acids depends on the viscosity-increasing ability of the system. The main factors affecting the viscosity-increasing ability of self-reversing acids are: the concentration of viscoelastic surfactant, the pH value of the system, and Ca2+. 2+ Concentration, etc. Current methods for establishing viscosity equations mostly rely on experimental fitting, first adjusting pH and Ca... 2+ The effects of factors such as concentration are fitted individually as functional equations. Then, a simple multiplication operation is performed on the fitted functions to establish an equation for the self-adjusting acid viscosity change under the influence of multiple factors. When conducting physical experiments to study the effect of pH on viscosity, CaCO3 is often used to adjust the pH of the system. As the pH of the system increases, the CaCO3 concentration also increases. 2+ The concentration also increased, while Ca 2+ Increased concentration can also cause changes in the system's viscosity, which means that the measured viscosity change is not entirely due to H+. + The concentration is also affected by Ca 2+ Concentration interference introduces errors into the fitted functional equations. Therefore, currently reported methods for establishing viscosity equations cannot accurately reflect the viscosity changes of self-sustaining acids in carbonate reservoirs. Consequently, the reliability of the self-sustaining acid reversal effect derived from numerical simulations needs further verification. Accurately predicting viscosity changes is crucial for assessing the reversal effect; therefore, establishing a method considering H... + and Ca 2+The viscosity equation for the concentration synergistic effect is of great significance. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for establishing a self-directing acid viscosity equation in numerical simulation of reservoir acidization. In the physical simulation experiment, this application considers the simultaneous presence of H₂ in the system. + and Ca 2+ In this case, the influence of ion concentration changes on the viscosity of the system was investigated, an accurate viscosity equation was established, and the viscosity equation was substituted into the self-directing acid dual-scale continuous model. The redirection effect of self-directing acid in carbonate reservoirs was simulated by numerical simulation method.

[0005] The present invention is achieved by the following technical solution.

[0006] A method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization includes the following steps:

[0007] S1. Select a viscoelastic surfactant;

[0008] S2. Based on the viscoelastic surfactant from step S1, prepare systems containing different concentrations of viscoelastic surfactant, CaCl2, and hydrochloric acid, and determine the viscosity of the mixed system; the ratio of CaCl2 to HCl is determined according to the stoichiometric coefficients of the chemical reaction formula between HCl and CaCO3.

[0009] S3. H + and Ca 2+ Concentration converted to equivalent pH value C pH The viscosity of the acid will change with C. pH The change is fitted to a linear combination of an exponential function and an error function, and a self-directing acid viscosity equation is established.

[0010] S4. List the numerical simulation models of self-directing acidification;

[0011] S5. Set model conditions to simulate the acidification effects of conventional acids and self-reversing acids.

[0012] Furthermore, after self-directed acid injection into carbonate reservoirs, their viscosity mainly changes with H. + and Ca 2+ H changes with concentration + and Ca 2+ All concentrations are converted to equivalent pH values ​​C. pH The viscosity of self-adjusting acid varies with H + and Ca 2+ The complex changes in concentration are converted into changes with C. pH Univariate change.

[0013] Furthermore, unknown H during the formation acid rock reaction process. +and Ca 2+ Concentration distribution is replaced by the coefficient relationship of chemical equations, and viscosity is simulated by physical experiments. + and Ca 2+ The effect of concentration is used to fit the viscosity change to C. pH The function.

[0014] Furthermore, the viscosity equation cannot be simply fitted to a single function or the product of multiple functions, but should be fitted to a linear combination of an exponential function and an error function. The self-adjusting acid viscosity equation includes the initial viscosity of the system, the viscosity increase factor, the equivalent pH value, and the fitting coefficient.

[0015] Furthermore, when the viscosity equation is applied to the numerical simulation of acidification, the penetration depth in the low-permeability layer is 2 to 3 times that of conventional acid when the initial viscosity of the acid is 10 mPa·s and the viscosity increase factor is 20.

[0016] Specifically, a method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization includes the following steps:

[0017] S1: Select a viscoelastic surfactant and evaluate its performance from three aspects: thickening ability, shear resistance, and temperature resistance. Select a viscoelastic surfactant that meets the performance requirements.

[0018] S2: Based on the viscoelastic surfactant selected in step S1, prepare viscoelastic surfactant + CaCl2 + hydrochloric acid systems of different concentrations, and measure the viscosity after standing for 2 hours; wherein, the ratio of CaCl2 + HCl is determined according to the stoichiometric coefficient of the chemical reaction formula of HCl and CaCO3; that is, assuming that the carbonate reservoir is composed of only calcite mineral, and not considering small concentration changes such as convection and diffusion, theoretically, for every 1 mol of HCl consumed in the acid solution, 0.5 mol of CaCl2 will be generated; the chemical reaction formula of HCl and CaCO3 is:

[0019] 2HCl+CaCO3=CaCl2+H2O+CO2 (1);

[0020] S3: H + and Ca 2+ Concentration converted to equivalent pH value C pH This includes two situations: one is when the concentration of hydrochloric acid in the system changes from C... H,0 Reduced to 0, while Ca 2+ Concentration increased from 0 to C Ca,m One is that the system changes from fresh acid to residual acid; the other is that the concentration of hydrochloric acid in the system is 0, and Ca... 2+ Concentration from C Ca,m The increase begins, meaning that in the residual acid region, the hydrogen ion concentration is very low and can be ignored, Ca... 2+Due to the cumulative effects of convection and diffusion, the equation is:

[0021]

[0022] In the formula, C H,0 The initial concentration of hydrochloric acid in the system is %, C. Ca,m The initial concentration is C H,0 The maximum concentration of CaCl2 produced by the complete reaction of HCl and CaCO3, %; M H C is the relative molecular mass of HCl; Ca M represents the concentration of CaCl2 in the system, in %; Ca ρ is the relative molecular mass of CaCl2. L The density of the system is expressed in g·cm³. -3 ;

[0023] With C pH With H as the independent variable and viscosity as the dependent variable, the curve is fitted as a linear combination of an exponential function and an error function, establishing a method that considers H... + and Ca 2+ The self-directing acid viscosity equation of the synergistic effect:

[0024]

[0025] In the formula, μ eff Let μ0 be the viscosity of the system, in Pa·s; μ0 be the initial viscosity of the acid system, i.e., the viscosity when the system contains no Ca. 2+ The viscosity at that time is comparable to that of conventional acids, Pa·s; μ m (C pH ) represents the viscosity-increasing factor, i.e., the ratio of maximum viscosity to initial viscosity; C pH is the equivalent pH value corresponding to the maximum viscosity of the system; c is a coefficient obtained from the fitting; W2 and W3 are coefficients obtained from the fitting.

[0026] To avoid situations where the calculated viscosity equation results in a viscosity lower than the initial acid viscosity, it is stipulated that when the calculated viscosity is lower than the initial viscosity, the calculated viscosity will be assigned the initial viscosity.

[0027]

[0028] In the formula, μ0 is the initial viscosity of the acid solution, Pa·s;

[0029] S4: Obtain formation parameters, list a mathematical model for the acidization shift of carbonate reservoirs, and substitute it to consider H. + and Ca 2+ The viscosity equation for the synergistic effect is used to simulate the diversion effect of self-diverting acid in carbonate reservoirs; the mathematical model for diversion acidification in carbonate reservoirs includes the flow equation of self-diverting acid in the formation, the mass conservation equation of the fluid, and H...+ Convection-diffusion equations, Ca 2 + The convection-diffusion equation and the reaction-dissolution equation between self-directing acid and carbonate rock:

[0030]

[0031] In the formula, u is the self-directing acid flow rate, m·s -1 K represents the formation permeability, in meters. 2 μ is the viscosity of the self-directing acid, Pa·s; P is the flow pressure of the self-directing acid in the formation, Pa; Formation porosity, decimal; t, reaction time, seconds; C H H in porous media + Concentration, mol·m -3 ;D eH For H + Diffusion coefficient, m 2 ·s -1 ;k c For H + Mass transfer coefficient, m·s -1 ;a v Pore ​​surface area, i.e., the pore area per unit volume of rock, m 2 ·m -3 C s The concentration of acid at the rock surface is expressed in mol·m⁻¹. -3 ;D eCa For Ca 2+ Diffusion coefficient, m 2 ·s -1 α represents the mass of rock that can be dissolved by one mole of acid, expressed in kg·mol⁻¹. -1 ;ρ s Density of rock, g·cm³ -3 ;

[0032] S5: Establish a geometric model of a two-layer carbonate reservoir. To avoid computational complexity, the following assumptions are made: ① Based on the difference in interlayer permeability, the carbonate reservoir is divided into high-permeability and low-permeability layers. High and low permeability represent relative values, not the high and low permeability classifications of the reservoir; ② Except for the initial permeability, the other parameters of the two strata are the same; ③ There is no barrier between the high-permeability and low-permeability layers; ④ The influence of fractures and caverns in the reservoir is not considered.

[0033] The initial and boundary conditions of the formation model are set. The initial conditions include porosity distribution, pressure, and acid concentration. There are three types of boundary conditions: inlet conditions (injection rate, acid concentration), outlet conditions (outlet boundary pressure), and no-flux boundary conditions (zero flux). The model described in S4 is solved using the finite element method by changing the permeability gradient k. rSimulate the acidification redirection effect of self-directing acid under different formation conditions;

[0034] The formula for calculating the permeability gradient is:

[0035]

[0036] k high For high permeability of the layer, k low The permeability of the low-permeability layer is low.

[0037] The present invention has the following beneficial effects:

[0038] 1. The self-directing acid viscosity equation establishment method proposed in this invention takes into account H + and Ca 2+ The synergistic effect of concentration will reveal unknown H+ during the formation acid rock reaction process. + and Ca 2+ The concentration relationship was replaced by a stoichiometric relationship, and the viscosity of the self-adaptive acid was studied through indoor experiments. + and Ca 2+ The synergistic effect of concentration can accurately simulate the influence of changes in acid composition caused by acid reaction in the formation on the viscosity of the system;

[0039] 2. This invention proposes an equivalent pH value (C). pH The concept of H + and Ca 2+ The effect of concentration on the viscosity of the system is converted to C pH The effect of H will cause the viscosity of the system to change. + and Ca 2+ The complex changes in concentration are converted into changes with C. pH The univariate change simplifies the computational complexity. Attached Figure Description

[0040] Figure 1 For the present invention H + and Ca 2+ The effect of concentration synergistic effect on the viscosity of the self-suspension acid system;

[0041] Figure 2 This is a diagram showing the division of the stratigraphic geometry model of the present invention;

[0042] Figure 3 These are diagrams illustrating the effects of conventional acid modification in different formations using the present invention.

[0043] Figure 4 The diagram shows the effect of the self-directing acid in different formations. Detailed Implementation

[0044] To enable those skilled in the art to better understand the present invention, the present invention will be further described below through embodiments and in conjunction with the accompanying drawings.

[0045] Example 1

[0046] A method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization is implemented according to the following steps:

[0047] S1: Screen three commonly used viscoelastic surfactants for self-adaptive acidification, namely EHSB, EAB-40, and LD-VES. Evaluate the performance of the viscoelastic surfactants from three aspects: thickening ability, shear resistance, and temperature resistance. Select the viscoelastic surfactant LD-VES that meets the performance requirements.

[0048] S2: Based on the viscoelastic surfactant selected in step S1, prepare LD-VES+CaCl2+hydrochloric acid systems of different concentrations according to the ratio of hydrochloric acid and CaCl2 powder in Table 1, and measure the viscosity after standing for 2 hours. The ratio of CaCl2 to HCl is determined according to the stoichiometric coefficients of the chemical reaction between HCl and CaCO3. That is, assuming the carbonate reservoir consists only of calcite, and neglecting small concentration changes such as convection and diffusion, theoretically, for every 1 mol of HCl consumed in the acid solution, 0.5 mol of CaCl2 will be generated. The chemical reaction between HCl and CaCO3 is as follows:

[0049] 2HCl+CaCO3=CaCl2+H2O+CO2(1);

[0050] Table 1. Experimental Drug Proportioning Table

[0051]

[0052]

[0053] Taking the 6% LD-VES + 11% CaCl2 + 7.5% HCl system as an example, the experimental steps are as follows: ① Weigh 12g of the LD-VES system into a beaker and dissolve it with an appropriate amount of deionized water; ② Weigh 22g of CaCl2 powder into a beaker and dissolve it with an appropriate amount of deionized water; ③ Weigh 40g of hydrochloric acid into a beaker and dissolve it with an appropriate amount of deionized water; ④ Quickly pour the diluted hydrochloric acid and CaCl2 solution into the beaker containing the LD-VES solution, and continue to add deionized water until the total volume is 200mL; ⑤ Incubate the prepared system at 600r·min -1Stir the mixture with a magnetic stirrer for 5 minutes at a certain speed to ensure thorough mixing of the CaCl2 solution and LD-VES; ⑥ Heat the mixed system in a 60℃ water bath for 20 minutes to remove air bubbles generated during preparation; ⑦ Let the mixture stand at room temperature for 2 hours, and then measure the viscosity of the system using an SNB-2 rotational viscometer, selecting rotor No. 3 and a rotation speed of 50 r·min. -1 .

[0054] Table 2 shows the viscosity measured when hydrochloric acid and CaCl2 powder were added simultaneously to LD-VES systems with concentrations of 2%, 4%, and 6%.

[0055] Table 2. Experimental Drug Proportioning Table

[0056]

[0057] S3: H + and Ca 2+ Concentration converted to equivalent pH value C pH This includes two situations: one is that the concentration of hydrochloric acid in the system changes from C... H,0 Reduced to 0, while Ca 2+ Concentration increased from 0 to C Ca,m One is that the system changes from fresh acid to residual acid; the other is that the concentration of hydrochloric acid in the system is 0, and Ca... 2+ Concentration from C Ca,m The increase begins, meaning that in the residual acid region, the hydrogen ion concentration is very low and can be ignored, Ca... 2+ Due to the accumulation of effects such as convection and diffusion.

[0058]

[0059] In the formula, C H,0 The initial concentration of hydrochloric acid is %, C. Ca,m The initial concentration is C H,0 The maximum concentration of CaCl2 produced by the complete reaction of HCl and CaCO3 is experimentally determined to be 22%; M H M is the relative molecular mass of HCl. Ca ρ is the relative molecular mass of CaCl2. L The density of the system is expressed in g·cm³. -3 .

[0060] Figure 1 When the LD-VES concentration in the system is 2%, 4%, and 6%, H + and Ca 2+ Concentration converted to equivalent pH value C pH At that time, the viscosity of the system increases with C. pH Change. (Based on C) pH With H as the independent variable and viscosity as the dependent variable, the curve is fitted as a linear combination of an exponential function and an error function, establishing a model considering H...+ and Ca 2+ The self-directing acid viscosity equation of the synergistic effect.

[0061]

[0062] In the formula, μ eff Let μ be the viscosity of the system, Pa·s; μ0 is the initial viscosity of the system, i.e., the system without Ca. 2+ The viscosity at that time is comparable to that of conventional acids, Pa·s; μ m (C pH ) represents the viscosity-increasing factor, i.e., the ratio of maximum viscosity to initial viscosity. When μ m (C pH When ) is 1, the viscosity is the initial value μ0; C pHmax is the equivalent pH value corresponding to the maximum viscosity of the system, which is 0.01 according to the experiment; c is a coefficient, which is 0.45 obtained by fitting; W2 and W3 are the fitted coefficients, which are 0.8947 and 0.3765 respectively.

[0063] To avoid situations where the calculated viscosity is less than the initial viscosity in the fitted viscosity equation, it is stipulated that when the calculated viscosity is less than the initial viscosity, the calculated viscosity will be assigned the initial viscosity.

[0064]

[0065] S4: Obtain formation parameters, list a mathematical model for the acidization shift of carbonate reservoirs, and substitute it to consider H. + and Ca 2+ A viscosity equation for the synergistic effect is used to simulate the diversion effect of self-diverting acid in carbonate reservoirs. The mathematical model for acid diversion in carbonate reservoirs includes the flow equation of self-diverting acid in the formation, the mass conservation equation of the fluid, and H... + Convection-diffusion equations, Ca 2 + The convection-diffusion equation and the reaction-dissolution equation between self-directing acid and carbonate rock:

[0066]

[0067] In the formula, u is the self-directing acid flow rate, m·s -1 K represents the formation permeability, in meters. 2 μ is the viscosity of the self-directing acid, given by SO4, in Pa·s; P is the flow pressure of the self-directing acid in the formation, in Pa. Formation porosity, decimal; t, reaction time, seconds; C H H in porous media + Concentration, mol·m -3 ;D eH For H +Diffusion coefficient, m 2 ·s -1 ;k c For H + Mass transfer coefficient, m·s -1 ;a v Pore ​​surface area, i.e., the pore area per unit volume of rock, m 2 ·m -3 C s The concentration of acid at the rock surface is expressed in mol·m⁻¹. -3 ;D eCa For Ca 2+ Diffusion coefficient, m 2 ·s -1 α represents the mass of rock that can be dissolved by one mole of acid, expressed in kg·mol⁻¹. -1 ;ρ s Density of rock, g·cm³ -3 .

[0068] S5: Establish a geometric model of a two-layer carbonate reservoir. To avoid computational complexity, the following assumptions are made: ① Based on the difference in interlayer permeability, the carbonate reservoir is divided into high-permeability and low-permeability layers. High permeability and low permeability are relative values, not the high permeability and low permeability of the oil reservoir concept; ② Except for the difference in initial permeability, the other parameters of the two strata are the same; ③ There is no barrier between the high-permeability and low-permeability layers; ④ The influence of fractures and caverns is not considered.

[0069] Table 3 Model Parameter Table

[0070]

[0071] The formula for calculating the permeability gradient is:

[0072] k high For high permeability of the layer, k low The permeability of the low-permeability layer is low.

[0073] In this embodiment, the permeability difference k r =2.

[0074] The initial and boundary conditions of the model are set as follows:

[0075] Initial conditions: P = P0, C H =0,

[0076] Boundary condition: When x = 0, When x = L, P = P0. When y = 0 or W, -n·u = 0.

[0077] The model described in S04 was solved using the finite element method to simulate the acidizing and redirection effects of conventional acid and self-redirecting acid under formation conditions.

[0078] Figure 3 The acidification effect of conventional acid with a viscosity of 10 mPa·s in carbonate reservoirs is shown. In low-permeability layers, the amount of acid introduced is small, the wormhole penetration depth is shallow, and the stimulation effect is poor.

[0079] Figure 4 To demonstrate the acidification effect of self-directing acid in carbonate reservoirs, the acid ingress rate in low-permeability layers increased significantly, and the wormhole penetration depth was approximately 60% of that in high-permeability layers. This indicates that self-directing acid has a better modification effect in low-permeability layers, which is 2 to 3 times that of conventional acid modification.

Claims

1. A method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization, characterized in that, Includes the following steps: S1. Select a viscoelastic surfactant; S2. Based on the viscoelastic surfactant from step S1, prepare systems containing different concentrations of viscoelastic surfactant, CaCl2, and hydrochloric acid, and determine the viscosity of the mixed system; the ratio of CaCl2 to HCl is determined according to the stoichiometric coefficients of the chemical reaction formula between HCl and CaCO3. S3. H + and Ca 2+ Concentration converted to equivalent pH value C pH This includes two situations: one is when the concentration of hydrochloric acid in the system changes from C... H,0 Reduced to 0, while Ca 2+ Concentration increased from 0 to C Ca,m Another scenario is where the hydrochloric acid concentration in the system is 0, and Ca... 2+ Concentration from C Ca,m Start increasing; the equation is as follows: （2）； In the formula, C H,0 The initial concentration of hydrochloric acid in the system is % (%). C Ca,m The initial concentration is C H,0 The maximum concentration of CaCl2 produced by the complete reaction of HCl and CaCO3, % , M H This represents the relative molecular mass of HCl. C Ca The concentration of CaCl2 in the system is %; M Ca Here is the relative molecular mass of CaCl2; ρ L The density of the system is expressed in g·cm³. -3 ; by C pH With H as the independent variable and viscosity as the dependent variable, the curve is fitted as a linear combination of an exponential function and an error function, establishing a model considering H... + and Ca 2+ The self-directing acid viscosity equation of the synergistic effect: （3）； In the formula, μ eff Let be the viscosity of the system, Pa·s; μ 0 represents the initial viscosity of the acid system, in Pa·s; μ m ( C pH () represents the viscosity-increasing factor; C pH is the equivalent pH value corresponding to the maximum viscosity of the system; c is a coefficient obtained from the fitting. W 2 and W 3 is a coefficient, obtained from the fitting; S4. Obtain formation parameters, list a mathematical model for the acidization shift of carbonate reservoirs, and substitute it into the model considering H. + and Ca 2+ The viscosity equation for the synergistic effect is used to simulate the diversion effect of self-diverting acid in carbonate reservoirs; the mathematical model for diversion acidification in carbonate reservoirs includes the flow equation of self-diverting acid in the formation, the mass conservation equation of the fluid, and H... + Convection-diffusion equations, Ca 2+ The convection-diffusion equation and the reaction-dissolution equation between self-directing acid and carbonate rock: （5）； In the formula, u is the self-directing acid flow rate, m·s -1 ; K m is the formation permeability. 2 ; μ The viscosity of the acid is the self-adaptive viscosity, Pa·s; P The flow pressure of the self-directing acid in the formation, Pa; Formation porosity, decimal; t The reaction time is in seconds. C H H in porous media + Concentration, mol·m -3 ; D eH For H + Diffusion coefficient, m 2 ·s -1 ; k c For H + Mass transfer coefficient, m·s -1 ; For comparison, m 2 ·m -3 ; C s The concentration of acid at the rock surface is expressed in mol·m⁻¹. -3 ; D eCa For Ca 2+ Diffusion coefficient, m 2 ·s -1 ; α The mass of rock that can be dissolved by one mole of acid, expressed in kg·mol⁻¹ -1 ; ρ s Density of rock, g·cm³ -3 ; S5. Establish a geometric model of the two-layer carbonate reservoir, and set the initial and boundary conditions of the formation model. The initial conditions include porosity distribution, pressure, and acid concentration; the boundary conditions include inlet conditions, outlet conditions, and no-flow boundary conditions; solve the model described in step S4 using the finite element method, by changing the permeability gradient. k r The acidizing diversion effect of self-diverting acid under different formation conditions was simulated; the formula for calculating the permeability gradient is: （6）； k high For high permeability of the layer, k low The permeability of the low-permeability layer is low.

2. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, In step S1, the method for selecting a viscoelastic surfactant is to evaluate the performance of the viscoelastic surfactant from three aspects: thickening ability, shear resistance, and temperature resistance, and select a viscoelastic surfactant that meets the performance requirements.

3. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, In step S3, to avoid the case where the viscosity of the fitted viscosity equation is less than the initial acid viscosity, it is stipulated that when the calculated viscosity is less than the initial viscosity, the calculated viscosity will be assigned to the initial viscosity. （4）； In the formula, μ 0 represents the initial viscosity of the acid solution, in Pa·s.

4. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, In step S5, a geometric model of a two-layer carbonate reservoir is established. To avoid computational complexity, the following assumptions are made: ① Based on the difference in interlayer permeability, the carbonate reservoir is divided into high-permeability and low-permeability layers. High permeability and low permeability represent relative values, not the high-permeability and low-permeability classifications of the reservoir; ② Except for the difference in initial permeability, the other parameters of the two strata are the same; ③ There is no barrier between the high-permeability and low-permeability layers; ④ The influence of fractures and caverns in the reservoir is not considered.

5. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, After self-directed acid injection into carbonate reservoirs, the viscosity mainly changes with H. + and Ca 2+ H changes with concentration + and Ca 2+ Concentrations are all converted to equivalent pH values C pH The viscosity of self-adjusting acid varies with H + and Ca 2+ Complex changes in concentration are converted into variations with... C pH Univariate change.

6. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, Unknown H during the reaction of acid rocks in the formation + and Ca 2+ Concentration distribution is replaced by the coefficient relationship of chemical equations, and viscosity is simulated by physical experiments. + and Ca 2+ The effect of concentration is used to fit the viscosity change as C pH The function.

7. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, The viscosity equation is fitted as a linear combination of an exponential function and an error function. The self-adapting acid viscosity equation includes the initial viscosity of the system, the viscosity increase factor, the equivalent pH value, and the fitting coefficient.

8. The method for establishing a self-directing acid viscosity equation for numerical simulation of reservoir acidization according to claim 1, characterized in that, The viscosity equation was applied to the numerical simulation of acidification. When the initial viscosity of the acid was 10 mPa·s and the viscosity increase factor was 20, the penetration depth in the low-permeability layer was 2 to 3 times that of the conventional acid.

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