Calculation method of carbonate rock rough slit acid liquid mass transfer coefficient

Abstract

A carbonate rock rough slit acid liquid mass transfer coefficient calculation method comprises the following steps: 1) setting conditions based on carbonate rock rough morphology, and constructing a diffusion boundary layer thickness equation under the rough morphology conditions; and 2) solving to obtain the thickness of the diffusion boundary layer, and calculating the mass transfer coefficient according to the relational expression between the thickness of the diffusion boundary layer and the mass transfer coefficient. The carbonate rock rough slit acid liquid mass transfer coefficient calculation method is provided by considering rough morphology influence, no slippage of the acid liquid and filtration loss, and compared with a plane assumption condition in the prior art, the method is more consistent with a real condition, and the coincidence degree with an experimental test result is higher.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development, and in particular to a method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks. Background Technology

[0002] Carbonate oil and gas fields are an important part of the global oil and gas industry, accounting for about 60% of the world's conventional oil and gas reserves and about 50% of its production. Due to the complex pore structure and poor reservoir permeability of carbonate rocks, oil and gas production often faces problems such as poor fluidity and low recovery rate, leading to development difficulties. Acid fracturing technology is an important means of economically and effectively developing such reservoirs.

[0003] Acid fracturing simulation, as a crucial technique in acid fracturing technology, significantly impacts the effectiveness of carbonate reservoir stimulation. In acid fracturing simulation calculations, H... + Reaction rate and H + Mass transfer rates collectively characterize the acid-rock reaction boundary and affect the accuracy of simulations. The overall rate of the limestone-HCl reaction is primarily controlled by the mass transfer process; therefore, it is necessary to study the H+... + Research on mass transfer coefficients is being conducted.

[0004] Existing methods for calculating mass transfer coefficients are applicable to acid-rock reactions under plate conditions. + The mass transfer coefficient, H, of the rough crack is calculated using existing methods. + The calculated mass transfer coefficient differs significantly from experimentally measured data, thus failing to accurately characterize the mass transfer coefficient under rough fracture surface conditions. Therefore, research is urgently needed on methods for calculating the mass transfer coefficient on rough fracture surfaces of carbonate rocks. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the mass transfer coefficient of acid in rough fractures of carbonate rocks, based on the calculation of the mass transfer coefficient under rough fracture conditions. The specific technical solution of the embodiments of the present invention is as follows:

[0006] A method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks includes the following steps:

[0007] 1) Based on the condition of rough morphology of carbonate rocks, construct the equation for the thickness of diffusion boundary layer under the condition of rough morphology;

[0008] 2) Solve to obtain the diffusion boundary layer thickness, and calculate the mass transfer coefficient according to the relationship between the diffusion boundary layer thickness and the mass transfer coefficient.

[0009] Furthermore, in step 1), the acid flow conditions are no slippage and there is filtration loss.

[0010] Furthermore, the equation for the diffusion boundary layer thickness in step 1) is:

[0011]

[0012] Where δ is the thickness of the diffusion boundary layer; T is time; The unit tangent vector is along the tangent direction of the surface. It is a unit normal vector, pointing towards the inside of the fluid; It is the tangent vector; It is the normal vector; is the filtration velocity vector, and its direction is the normal direction; D is the material diffusion coefficient; E and F are equation coefficients, which are dimensionless.

[0013] Furthermore, the relationship described in step 2) is:

[0014]

[0015] Where, k g ρ is the mass transfer coefficient, in m / s.

[0016] Furthermore, the mass transfer coefficient was obtained by experimental testing under rough morphology conditions, and the experimental test results were compared with the theoretical calculation results.

[0017] Furthermore, when the surface roughness coefficient of the crack is greater than or equal to a set threshold, a curvature correction coefficient is introduced to correct the diffusion boundary layer thickness equation, where the roughness coefficient = d / R. min Where d is the distance between the center of the first computational unit and the interface, and R min Let be the radius of the circle with the smallest curvature that exists in the surface.

[0018] Furthermore, the threshold is set to 0.05.

[0019] Furthermore, the revised equation for the diffusion boundary layer thickness is as follows:

[0020]

[0021] On the other hand, the present invention provides hardware for implementing a method for calculating the mass transfer coefficient of acid in a rough slit in carbonate rocks, comprising: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of the method for calculating the mass transfer coefficient of acid in a rough slit in carbonate rocks as described in any one of the above claims.

[0022] On the other hand, the present invention provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program, which is executed by a processor to implement the method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks as described in any one of the above claims.

[0023] This invention fully considers the influence of rough morphology, the absence of acid slippage, and the existence of filtration loss, and provides a method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks. Compared with the planar assumption in the prior art, this method is more consistent with the actual situation and has a higher degree of agreement with experimental test results. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0026] Figure 2 This is a comparison chart of theoretical calculations and experimental results for the mass transfer coefficient in existing technologies.

[0027] Figure 3 This is a schematic diagram of the preparation of a simulated three-dimensional rough rock slab.

[0028] Figure 4 This is a comparison chart of the calculated mass transfer coefficient results and experimental results using the method of this invention. Detailed Implementation

[0029] The details of the present invention can be more clearly understood by referring to the accompanying drawings and the description of specific embodiments. However, the specific embodiments of the present invention described herein are for illustrative purposes only and should not be construed as limiting the invention in any way. Under the teachings of this invention, those skilled in the art can conceive of any possible modifications based on the invention, and these should all be considered to fall within the scope of the invention.

[0030] In acid fracturing model calculations, H + Reaction rate and H + Mass transfer rates characterize the acid-rock reaction boundary and affect the accuracy of the simulation. The overall rate of the limestone-HCl reaction is primarily controlled by mass transfer; therefore, it is necessary to study the H+ ion transfer rate. + Mass transfer coefficient k g Conduct relevant research.

[0031] In existing technologies, theoretical calculation methods are based on flat plate conditions to calculate the mass transfer coefficient. The theoretical calculation method for the mass transfer coefficient is as follows:

[0032]

[0033] In the formula: k g D is the mass transfer coefficient, in m / s;e m is the effective diffusion coefficient of the substance. 2 / s;N sh is the Sherwood number, which is the ratio of convective mass transfer to diffusion mass transfer and is dimensionless; w is the slit width, in meters.

[0034] In the calculation formula (1), the effective diffusion coefficient D e Furthermore, the seam width w is usually known, and the only parameter that needs to be determined is the Sherwood number N. sh Its value needs to be determined based on the Reynolds number N. Re The magnitude is used to determine the flow regime, and then N is selected under the corresponding flow regime. sh The calculation formula is as follows:

[0035]

[0036] Where: N Re N is the Reynolds number, characterized by the ratio of inertial forces to viscous forces in a fluid, and is dimensionless. Sc N is the Schmidt number, characterized by the ratio of kinematic viscosity to diffusion coefficient, and is dimensionless. Pe is the Petrette number, which is the ratio of convection rate to diffusion rate and is dimensionless.

[0037] In the experimental determination, the mass transfer coefficient is mainly determined by the average acid-rock reaction rate. In the experimental determination, the experimental rock slab is first divided into grids of a certain size (e.g., 1 mm) with a length, width, and height, and the center line of the rock slab is taken as the reference line. The dissolution height of each grid on the reference line at different acid injection times is statistically analyzed. In order to reduce the influence of changes in the surface morphology of the rock slab on the flow rate and mass transfer, the time is divided into different stages according to a certain time. For example, 20 min can be selected as the calculation time unit. The dissolution height of 20 min and 40 min is subtracted from the experimental time of 40 min and 60 min respectively to obtain the dissolution height of 20-40 min and 40-60 min. 0-20 min, 20-40 min, and 40-60 min are defined as the first, second, and third stages respectively. Then, the average acid-rock reaction rate J is calculated according to equation (3), and the average mass transfer coefficient is further obtained according to equation (4).

[0038]

[0039] k g =J / C (4)

[0040] Where: J represents the average acid-rock reaction rate, kg / (m³). 2 ·s); △h is the dissolution height, m; ρ s Density of rock; kg / m³ 3φ is porosity; t is time, s; β is the solubility of the acid in the rock minerals, kg / kg; M is the molar mass of the rock, kg / mol.

[0041] Figure 2 This section compares the theoretical results of mass transfer coefficient using existing technology with experimental measurements. The results show the mass transfer coefficients for the upper and lower rock plates under a specific experimental condition. A significant difference in magnitude between the two values ​​is evident. Experimental measurements show that k... g The flow field differences caused by surface roughness at different lengths of the rock slab have a significant impact on the mass transfer coefficient, leading to variations in k measured at different locations in experiments. g The difference is even greater. This is because the theoretical calculation of the mass transfer coefficient in existing technologies is based on the assumption of a flat plate, which differs significantly from the actual morphology of the rough surface of carbonate rocks. Therefore, in order to more accurately determine the H during acid fracturing... + Regarding the mass transfer rate, this application provides a method for calculating the mass transfer coefficient of acid in a rough slit of carbonate rock, comprising the following steps:

[0042] 1) Based on the condition of rough morphology of carbonate rocks, construct the equation for the thickness of diffusion boundary layer under the condition of rough morphology;

[0043] 2) Solve to obtain the diffusion boundary layer thickness, and calculate the mass transfer coefficient according to the relationship between the diffusion boundary layer thickness and the mass transfer coefficient.

[0044] In step 1), the two-dimensional convection-diffusion equation for the acid solution is first established. Assuming the amount of reactants produced is negligible compared to the main concentration, and axial diffusion is less than normal diffusion, the simplified expression for the two-dimensional convection-diffusion equation is:

[0045]

[0046] In the formula: c is the concentration of the substance, kg / m³ 3 x and z represent the axial and normal directions, respectively, in meters (m); u and w represent the velocities along the x and z directions, respectively, in meters per second (m / s); t is time, in seconds (s); D is the diffusion coefficient, in meters (m). 2 / s.

[0047] Use dimensionless concentration Replacing equation (5) with the actual concentration distribution, we get:

[0048]

[0049] After the concentration is replaced, the boundary conditions become:

[0050]

[0051] In the formula: c0 is the concentration at position z = 0, kg / m³ 3 c ∞ The concentration at position z = ∞, kg / m³ 3 δ represents the mass transfer boundary layer;

[0052] The dimensionless boundary conditions are:

[0053]

[0054] By integrating the boundary layer in equation (6) and applying the solution, a weak solution to the equation can be obtained:

[0055]

[0056] Applying Leibniz's rule to process the two integrals on the left side of equation (9), and directly integrating the two integrals on the right side, we obtain:

[0057]

[0058] Combine the following definitions and continuity equations:

[0059]

[0060] Substituting into equation (10), we get:

[0061]

[0062] Assuming the flow is locally linear, the vertical velocity at δ can be approximated as:

[0063]

[0064] Substitute into equation (12), and express the equation as δ 2 The equation yields:

[0065]

[0066] Combine the following conditions:

[0067]

[0068] Substituting into equation (14) and introducing coefficients, we get:

[0069]

[0070] in:

[0071]

[0072] In one embodiment, it is assumed that the velocity distribution in space and time is known and fixed; implicitly, it is assumed that the diffusion boundary layer is completely located within the hydrodynamic boundary layer, and that all velocities are constant along the surface direction. Based on the four limiting cases of mass transfer (unsteady diffusion, no convection; steady-state flow surface with no shear and no strain; steady-state flow with constant shear; steady-state flow with constant strain, u0 is not zero), the equations are verified and the exact values ​​of the coefficients E and F in the first differential equation are derived, where E = 0.735 and F = π, and equation (16) becomes:

[0073]

[0074] Considering the rough morphology of the cracks, the absence of acid slippage, and the presence of filtration loss during cleaning, the plate setting condition in equation (16) is modified to obtain the equation for the thickness of the diffusion boundary layer with rough morphology:

[0075]

[0076] Where δ is the thickness of the diffusion boundary layer; T is time; The unit tangent vector is along the tangent direction of the surface. It is a unit normal vector, pointing towards the inside of the fluid; It is the tangent vector; is the filtration velocity vector, and its direction is the normal direction; D is the material diffusion coefficient.

[0077] In step 2), the diffusion boundary layer thickness is obtained by solving the diffusion boundary layer thickness equation established in step 1). Then, the mass transfer coefficient is calculated based on the relationship between the mass transfer coefficient and the boundary layer thickness. The relationship is as follows:

[0078]

[0079] The above process allows for the calculation of the mass transfer coefficient under the condition of rough morphology.

[0080] In a preferred embodiment of the present invention, when the roughness coefficient of the crack surface is greater than a set threshold, a curvature correction coefficient is introduced to correct the diffusion boundary layer thickness equation, wherein the roughness coefficient = d / R min The corrected equation for the diffusion boundary layer thickness is as follows:

[0081]

[0082] Where d is the distance between the center of the first computational unit and the interface, and R min Let R be the radius of the minimum curvature circle existing in the surface, and R be the radius of the curvature circle in the surface.

[0083] In a preferred embodiment of the present invention, the threshold value is set to 0.05, i.e., the roughness coefficient. When this is done, a 1 / R term is introduced into the principal curvature direction of the diffusion boundary layer thickness equation to correct it, and the accuracy of the local plane is higher.

[0084] In a specific embodiment of this invention, theoretical calculations and experimental measurements were performed to verify and compare the differences between the proposed mass transfer coefficient calculation method and the experimental results. First, the values ​​of the basic parameters were determined, as shown in Table 1. Then, as... Figure 3 As shown, a pseudo-three-dimensional rough plate (178 mm in length and 36 mm in width) was prepared using laser engraving technology according to the set experimental parameters. Acid etching experiments were then conducted to obtain experimental data and determine the H... + Mass transfer coefficient.

[0085] Table 1 Momentum equation and H + Parameter values ​​for mass transfer coefficient calculation

[0086]

[0087] The mass transfer coefficient calculated by the method provided in this invention is compared with the mass transfer coefficient obtained based on experimental measurements, and the results are as follows: Figure 4 As shown in the figure, the error between the two is less than 5%, indicating that the mass transfer coefficient calculation method provided by the present invention has high accuracy and is more consistent with the actual situation.

[0088] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the mass transfer coefficient of acid in a rough slit of carbonate rock, comprising the following steps: 1) Based on the condition of rough morphology of carbonate rocks, construct the equation for the thickness of diffusion boundary layer under the condition of rough morphology; 2) Solve to obtain the diffusion boundary layer thickness, and calculate the mass transfer coefficient according to the relationship between the diffusion boundary layer thickness and the mass transfer coefficient.

2. According to the method for calculating the mass transfer coefficient of acid in a rough slit of carbonate rock as described in claim 1, the acid flow conditions in step 1) are no slippage and filtration loss.

3. According to the method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks as described in claim 1, the equation for the thickness of the diffusion boundary layer in step 1) is: in, δ is the thickness of the diffusion boundary layer; T is time; The unit tangent vector is along the tangent direction of the surface. It is a unit normal vector, pointing towards the inside of the fluid; It is the tangent vector; It is the normal vector; is the filtration velocity vector, and its direction is the normal direction; D is the material diffusion coefficient; E and F are equation coefficients, which are dimensionless.

4. The method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks according to claim 1, wherein the relationship in step 2) is: in, k g ρ is the mass transfer coefficient, in m / s.

5. The method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks according to claim 1 further includes obtaining the mass transfer coefficient by experimental testing under rough morphology conditions, and comparing the experimental test results with the theoretical calculation results.

6. The method for calculating the mass transfer coefficient of acid in rough fractures of carbonate rocks according to claim 1, wherein when the roughness coefficient of the fracture surface is greater than or equal to a set threshold, a curvature correction coefficient is introduced to correct the diffusion boundary layer thickness equation, wherein the roughness coefficient = d / R min , where d is the distance between the center of the first computational unit and the interface, and R min Let be the radius of the circle with the smallest curvature that exists in the surface.

7. The method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks according to claim 1, wherein the threshold value is set to 0.

05.

8. According to the method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks as described in claim 1, the modified expression for the diffusion boundary layer thickness equation is as follows:

9. Hardware for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks, comprising: Memory, used to store computer programs; A processor is configured to execute the computer program to implement the steps of the method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks according to any one of claims 1-8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, which is executed by a processor to implement the method for calculating the mass transfer coefficient of acid in rough slits of carbonate rocks according to any one of claims 1-8.

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