Carbonate rock rough slit H + mass transfer coefficient calculation method based on power law acid liquor

Abstract

The invention discloses a carbonate rock rough slit H + mass transfer coefficient calculation method based on a power law acid solution. The method comprises the following steps: 1) deriving a mass transfer coefficient calculation method based on a boundary layer theory and a two-dimensional convective diffusion differential equation; and 2) considering and correcting the power law characteristics of the acid liquor, and constructing the H + mass transfer coefficient calculation method.Compared with the prior art, the H + mass transfer coefficient calculation method provided by the invention considers the power law characteristics of the acid liquor, and is more suitable for the actual situation of a field non-Newtonian acid liquor system.

Description

Technical Field

[0001] This invention relates to the field of oil and gas field development, and particularly to a method for H-type rough fractures in carbonate rocks based on power-law acid solutions. + Methods for calculating mass transfer coefficient. Background Technology

[0002] Carbonate reservoirs are a key area for global oil and gas exploration and development. Their reservoir spaces are primarily characterized by fractures and pores, and the development and connectivity of these fractures directly determine the reservoir's productivity. Acidizing, a core technology for enhancing the production of carbonate reservoirs, involves injecting acid into the reservoir. The chemical reaction between the acid and the carbonate rock dissolves the fracture walls, widening the fractures and creating non-uniform etching, thereby improving reservoir permeability and conductivity.

[0003] Acid fracturing simulation, as a crucial technical module in acid fracturing technology, significantly impacts the effectiveness of carbonate reservoir stimulation, thereby affecting oil and gas production. In acid fracturing model calculations, H... + Reaction rate and H + Mass transfer rate is a key characteristic of acid-rock reaction boundaries and affects the accuracy of simulations. The overall rate of limestone-HCl reaction is primarily controlled by mass transfer; therefore, relevant acid etching experiments are needed to investigate the H+ ion transfer rate. + Mass transfer coefficient k g Perform the calculation.

[0004] The existing formula for calculating the mass transfer coefficient is applicable to calculating the acid-rock reaction H of a flat plate. + The mass transfer coefficient is not systematically incorporated into the power-law characteristics of the acid. In acidification processes, non-Newtonian acid systems such as gelling acids and thickening acids with added thickeners are widely used. A significant characteristic of these acids is their typical power-law fluid properties, with viscosity decreasing as the shear rate increases.

[0005] Therefore, based on the mass transfer calculation of rough slits, it is urgent to incorporate the power-law characteristics of acid and establish a mass transfer coefficient calculation method that considers the coupling effect of rheological parameters and roughness, so as to meet the application requirements of non-Newtonian acid systems in the field and provide theoretical support for the precise design of acidification modification. Summary of the Invention

[0006] In view of this, the present invention provides a method for addressing rough slits in carbonate rocks based on power-law acid solutions. + A method for calculating the mass transfer coefficient is proposed to fill the gaps in existing technologies.

[0007] A power-law acid-based rough slit H in carbonate rocks + The method for calculating the mass transfer coefficient includes the following steps:

[0008] 1) A method for calculating the mass transfer coefficient is derived based on boundary layer theory and two-dimensional convection-diffusion differential equations;

[0009] 2) Considering and correcting the power-law properties of acid solutions, construct H... + Mass transfer coefficient calculation method;

[0010] Furthermore, the method for calculating the mass transfer coefficient in step 1) is as follows:

[0011] The equation for the thickness of the diffusion boundary layer is:

[0012]

[0013] The relationship between the mass transfer coefficient and the boundary layer thickness is as follows:

[0014]

[0015] in, The mass transfer boundary layer is represented by t; time is represented by x and z, representing the axial directions, respectively; u and w are the velocities along the x and z directions, respectively; D is the mass diffusion coefficient; k g is the mass transfer coefficient.

[0016] Furthermore, step 2) includes:

[0017] 21) Considering the power-law characteristics of acid, construct the acid shear stress equation;

[0018] 22) Substitute the initial conditions and solve for the boundary layer thickness;

[0019] 23) Substitute the boundary layer thickness into the mass transfer coefficient calculation equation in step 1) to obtain the H+ based on the power-law acid solution. + The expression for calculating the mass transfer coefficient.

[0020] Furthermore, the acid shear stress equation in step 21) is:

[0021] (16)

[0022] in, for Wall shear stress at the location; Viscosity; denoted as ρ, representing the mainstream flow velocity; x represents the coordinate.

[0023] Furthermore, the expression for the boundary layer thickness in step 22) is:

[0024] .

[0025] Furthermore, in step 23), the H based on power-law acid solution... + The expression for calculating the mass transfer coefficient is:

[0026]

[0027] Where L is the seam width; The rheological index; ρ is the consistency coefficient; μ is the density; and μ is the viscosity.

[0028] Compared with the prior art, the present invention has the following beneficial technical effects:

[0029] The H provided by this invention + The mass transfer coefficient calculation method takes into account the power-law characteristics of acid solutions, making it more suitable for the actual situation of non-Newtonian acid systems in the field, compared to the H under the assumption of Newtonian fluids. + The mass transfer coefficient calculation method can provide more accurate chemical reaction kinetic parameters between acid and rock. Attached Figure Description

[0030] 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.

[0031] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0032] Figure 2 This is a comparison chart of the mass transfer coefficient calculated by the prior art method in this embodiment of the invention and experimental data;

[0033] Figure 3 This is a comparison chart of the mass transfer coefficient calculated considering the power-law characteristics in this embodiment of the invention and the experimental data. Detailed Implementation

[0034] In the field of oil extraction, acid fluids play a crucial role in reservoir stimulation and other operations. Accurately calculating the H⁺ mass transfer coefficient of acid fluids is essential for evaluating the reaction effect between acid and rock, optimizing acid systems, and determining operational parameters. In actual field operations, non-Newtonian acid systems are widely used. The rheological properties of these acids differ significantly from those of Newtonian fluids. Traditional calculation methods, often based on Newtonian fluid assumptions, cannot accurately reflect the actual mass transfer characteristics of non-Newtonian acid fluids.

[0035] like Figure 1 As shown, this invention provides a method for addressing rough slits in carbonate rocks based on power-law acid solutions. + Mass transfer coefficient calculation method, used to determine the H+ of power-law acid solution flowing in a rough slit. + The transfer coefficient mainly includes the following steps:

[0036] 1) A method for calculating the mass transfer coefficient is derived based on boundary layer theory and two-dimensional convection-diffusion differential equations;

[0037] 2) Considering and correcting the power-law properties of acid solutions, establish H + A new method for calculating the mass transfer coefficient.

[0038] In this embodiment, step 1) specifically refers to:

[0039] Based on boundary layer theory and two-dimensional convection-diffusion equations;

[0040] Assuming the amount of product is negligible compared to the main concentration, and axial diffusion is less than normal diffusion, the equation simplifies to:

[0041] (1)

[0042] 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;

[0043] Use dimensionless concentration Replacing equation (1) with the actual concentration distribution, we get:

[0044] (2)

[0045] After the concentration is replaced, the boundary conditions become:

[0046] (3)

[0047] In the formula: c0 is the concentration at z=0, kg / m³ 3 ; The concentration at z=∞, kg / m³ 3 ; For mass transfer boundary layer;

[0048] The dimensionless boundary conditions are:

[0049] (4)

[0050] By integrating the boundary layer in equation (2) and applying the solution, a weak solution to the equation can be obtained:

[0051] (5)

[0052] Applying Leibniz's rule to process the two integrals on the left side of equation (5), and directly integrating the two integrals on the right side, we obtain:

[0053] (6)

[0054] Combine the following definitions and continuity equations:

[0055] (7)

[0056] Substituting into equation (6), we get:

[0057] (8)

[0058] Assuming the flow is locally linear, The vertical velocity at that point can be approximated as:

[0059] (9)

[0060] Substitute into equation (8), and express the equation as follows: The equation yields:

[0061] (10)

[0062] Combine the following conditions:

[0063] (11)

[0064] Substituting into equation (10) and introducing coefficients, we get:

[0065] (12)

[0066] in:

[0067] (13)

[0068] We assume that the velocity distribution in space and time is known and fixed; implicitly, we assume that the diffusion boundary layer is entirely within the hydrodynamic boundary layer; unless otherwise stated, we always assume 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), we verify the equation and derive the exact values ​​of coefficients E and F. Equation (12) becomes:

[0069] (14)

[0070] The relationship between the mass transfer coefficient and the boundary layer thickness is as follows:

[0071]

[0072] Therefore, the formula for calculating the mass transfer coefficient, derived from boundary layer theory and the two-dimensional convection-diffusion differential equation, is as follows:

[0073] (15)

[0074] Further, step 2) specifically includes:

[0075] Due to the addition of a slow-release agent, the acid solution has a certain viscosity. Therefore, as a viscous fluid, the acid solution exhibits typical power-law rheological characteristics, meaning it maintains a constant velocity at infinity. The flow develops above the flat plate, and its shear stress is:

[0076] (16)

[0077] In the formula: for Wall shear stress at the location, ; Viscosity, ; For the mainstream flow rate, x is the coordinate, m.

[0078] Combining the above equation, substitute the initial conditions. The boundary layer thickness is obtained by solving:

[0079] (17)

[0080] Furthermore:

[0081] (18)

[0082] In the formula: The Reynolds number is dimensionless. It is a Schmitt number.

[0083] Combining equation (15), we get Calculation formula:

[0084] (19)

[0085] The Schmidt number is defined as the ratio of kinematic viscosity to diffusion coefficient.

[0086] (20)

[0087] In the formula: Kinematic viscosity, .

[0088] Reynolds number:

[0089] (twenty one)

[0090] In the formula: L is the seam width, ; The rheological index is dimensionless (0 < 1). <1); This is the consistency coefficient. .

[0091] Mass transfer coefficient:

[0092] (twenty two)

[0093] Calculation Example

[0094] A pseudo-three-dimensional rough rock slab (178 mm in length and 36 mm in width) was prepared for acid etching experiments. Experimental data were then used for H2 etching. + Calculation of mass transfer coefficient;

[0095] Extract the outline of the rough rock slab morphology, perform geometric modeling, and import it into the model;

[0096] Solve the momentum equation and substitute the velocity into the new method for calculating the mass transfer coefficient for analytical calculation to obtain H. + Mass transfer coefficient;

[0097] The values ​​of the relevant parameters are shown in Table 1 for calculating and solving the equation.

[0098] Table 1 Momentum equation and H + Parameter values ​​for mass transfer coefficient calculation

[0099] Initial velocity (m / s) 0.0144 <![CDATA[Acid solution density (kg / m 3 )]]> 1155 Acid viscosity (Pa·s) 0.025 <![CDATA[H + Effective diffusion coefficient (m) 2 / s)]]> <![CDATA[5.8×10 -9 ]]> Rheological index (dimensionless) 0.4 <![CDATA[Consistency coefficient (Pa·s n ).]]> 0.08

[0100] Figure 2 The graph compares the mass transfer coefficient calculated without considering the power-law nature of the acid (using the method disclosed in CN202511213348.3) with the mass transfer coefficient calculated based on experimental data; the error between the two is 4.9%. The graph also compares the calculation results of the method provided in this invention with the mass transfer coefficient results calculated based on experimental data. Figure 3 As shown, it can be seen that H obtained by considering the power-law property of acid solution calculation + The calculated mass transfer coefficient is basically consistent with the result obtained based on experimental data, with an error of only 1.8%. This indicates that the new model, which takes into account the power law of acid, effectively reduces the deviation between the theoretically calculated mass transfer coefficient and the mass transfer coefficient obtained based on experimental data. The solution accuracy is high, and it can provide theoretical guidance for subsequent acid pressure simulation.

[0101] Therefore, the acid solution H provided by the present invention +The method for calculating the mass transfer coefficient closely matches the actual situation of non-Newtonian acid systems on site. By considering the power-law characteristics of the acid, it can more accurately describe the mass transfer process of H⁺ in the acid, thereby providing more precise kinetic parameters for the chemical reaction between the acid and the rock, which is conducive to the scientific optimization of acid formulation and construction process.

Claims

1. A method for rough seam H in carbonate rocks based on power-law acid solutions + The method for calculating the mass transfer coefficient includes the following steps: 1) A method for calculating the mass transfer coefficient is derived based on boundary layer theory and two-dimensional convection-diffusion differential equations; 2) Considering and correcting the power-law properties of acid solutions, construct H... + Methods for calculating mass transfer coefficient.

2. The method for calculating the mass transfer coefficient according to claim 1, wherein the method for calculating the mass transfer coefficient in step 1) is as follows: The equation for the thickness of the diffusion boundary layer is: The relationship between the mass transfer coefficient and the boundary layer thickness is as follows: in, The mass transfer boundary layer is represented by t; time is represented by x and z, representing the axial directions, respectively; u and w are the velocities along the x and z directions, respectively; D is the mass diffusion coefficient; k g is the mass transfer coefficient.

3. The mass transfer coefficient calculation method according to claim 1, step 2) includes: 21) Considering the power-law characteristics of acid, construct the acid shear stress equation; 22) Substitute the initial conditions and solve for the boundary layer thickness; 23) Substitute the boundary layer thickness into the mass transfer coefficient calculation equation in step 1) to obtain the H+ based on the power-law acid solution. + The expression for calculating the mass transfer coefficient.

4. According to the mass transfer coefficient calculation method of claim 3, the acid shear stress equation in step 21) is: （16） in, for Wall shear stress at the location; Viscosity; denoted as ρ, representing the mainstream flow velocity; x represents the coordinate.

5. The mass transfer coefficient calculation method according to claim 3, wherein the boundary layer thickness expression in step 22) is: 。 6. The mass transfer coefficient calculation method according to claim 3, wherein step 23) involves H+ based on power-law acid solution. + The expression for calculating the mass transfer coefficient is: in, L is the seam width; The rheological index; ρ is the consistency coefficient; μ is the density; and μ is the viscosity.

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