A mathematical model-based method for predicting acid-etched wall morphology

Abstract

This provides a method for predicting acid-etched wall morphology based on a mathematical model. [Solution] The method involves using a 3D laser scanner and fluid finite element software to perform 3D modeling on the rock slab fracture surface, obtaining a fracture space model, and then, based on the fracture space model, coupling the pressure field and velocity field of the fracture space model to obtain a solution, thereby obtaining the fluid dynamics parameter distribution within the fracture, inputting this fluid dynamics parameter distribution into a constructed acid-rock reaction mathematical model, obtaining the erosion mass of each wall node, using the erosion mass of each wall node to obtain the erosion depth corresponding to the wall, and then, using the fracture space model, removing the influence of the erosion depth corresponding to the wall to obtain the wall morphology after acid etching, thereby completing the prediction of the acid-etched wall morphology.

Description

[Technical Field]

[0001] The present invention relates to the field of petroleum engineering, and more particularly to a method for predicting the morphology of acid-etched walls based on a mathematical model. [Background technology]

[0002] Currently, the market is moving towards deep-sea development for natural gas from carbonate rocks. Deep-sea carbonate rocks account for approximately 70% of the world's total oil and gas resources. Even now, oil and gas from deep-sea carbonate rocks are an indispensable part of energy supply. However, the depth of the reserves, strong heterogeneity, high ambient temperature, and high closure pressure are universal challenges faced by the development of deep-sea carbonate rock reserves. After acid pressure modification of deep-sea carbonate rock reserves, problems often arise such as weak flow guidance capacity of acid-etched fractures and a short duration of increased production effect. The most important reason for this is that the acid-etched fracture wall morphology can restrict the oil and gas passage after fracture closure, potentially limiting oil and gas flow. Therefore, the acid-etched fracture wall morphology is one of the determinants of the flow guidance capacity of the acid-etched fracture and is also an important parameter for predicting and judging the acid pressure effect.

[0003] Currently, methods for studying acid-etched fracture surface morphology primarily involve obtaining acid-etched rock surfaces using acid flow experiments and digitizing them using laser scanning, thereby enabling research on acid-etched fractures under different conditions. However, due to the strong heterogeneity of carbonate rocks, the initial fracture surfaces obtained from each experimental sample vary considerably. Therefore, conventional research methods have limitations when exploring the etching characteristics of the same fracture wall under different acid injection conditions. [Overview of the Initiative]

[0004] In contrast to the aforementioned shortcomings of the conventional technology, the method for predicting acid-etched wall morphology based on a mathematical model provided by the present invention solves the problem of being unable to conduct etching morphology studies on the same wall surface under different acid injection conditions.

[0005] To achieve the aforementioned objective of the invention, the technical solution employed by the present invention is a method for predicting the morphology of an acid-etched wall surface based on a mathematical model, and includes the following: S1: Using a 3D laser scanner and fluid finite element software, 3D modeling is performed on the rock plate fracture surface to obtain a fracture space model. S2: Based on the pre-defined conditions of the rift space model and the fluid injection parameters, the solution is obtained by coupling the pressure field and velocity field of the rift space model using the finite volume method principle, and the distribution of fluid dynamics parameters within the rift is obtained. S3: Based on the correlation theory of the boundary layer of acid solution in a slit, spontaneous diffusion, and convective mass transfer, we will construct a mathematical model of acid-rock reactions for controlling mass transfer. S4: The fluid dynamics parameter distribution within the crack is input into the acid rock reaction mathematical model to obtain the erosion mass of each wall node. S5: Using the erosion mass of each wall node, the correspondence with the point erosion depth is analyzed to obtain the erosion depth corresponding to the wall. S6: Using the crack space model described above, the influence of the corrosion depth corresponding to the wall surface is removed to obtain the wall surface morphology after acid etching, and the prediction of the acid-etched wall surface morphology is completed.

[0006] The beneficial effects of this invention are as follows: The processor utilizes a fracture space model and an acid-rock reaction mathematical model to predict the erosion depth corresponding to the wall surface, obtain the wall surface morphology after acid etching, and complete the prediction of the acid-etched wall surface morphology. By using a three-dimensional laser scanner to obtain a digital model of the true fracture surface morphology, and by introducing fluid finite element modeling software to obtain the true fracture space model, experimental work is greatly simplified, experimental samples and costs are saved, and the problem of not being able to conduct etching morphology studies on the same wall surface under different acid injection conditions is solved. By utilizing the fracture space model and the acid-rock reaction mathematical model, the accuracy and prediction efficiency of acid-etched wall surface prediction can be further improved.

[0007] Furthermore, S1 includes the following: Using a three-dimensional laser scanner, the rock slabs split by the Brazilian Split test are scanned to obtain 3D point cloud data of the true rock face. Using fluid finite element software, detailed modeling is performed on the 3D point cloud data of the true rock surface to obtain a meshed rift space model.

[0008] Based on theories concerning the acid-liquid boundary layer within a slit, natural diffusion, and convective mass transfer, we established an acid-rock reaction rate calculation model under comprehensive parameter conditions that consider geological temperature, acid viscosity, acid concentration, acid flow velocity, and slit width, thereby significantly improving the accuracy of the model calculation results.

[0009] Furthermore, S3 includes the following: Based on the boundary layer theory of acid solution within a slit, the critical Reynolds number is calculated by utilizing the relationship between acid solution flow velocity, pump discharge rate, and Reynolds number. Based on the theory of natural diffusion of acid solution within a slit, the diffusion coefficient is calculated by utilizing the effects of acid solution concentration, acid solution viscosity, and geological temperature on acid solution diffusion during acid solution flow. Based on the theory of convective mass transport in acidic liquid within a slit, we obtain the convective mass transport coefficient for mid-layer flow in a geological fissure. The critical Reynolds number, the diffusion coefficient, and the convective mass transfer coefficient of laminar flow are used to obtain the effective mass transfer coefficient of acid solution in the fractured rock formation. Based on the effective mass transfer coefficient of acid solution in the aforementioned rock fissure, we construct a mathematical model of acid rock reaction for controlling mass transfer using Fick's first law and the chemical equation for acid rock reaction.

[0010] By considering comprehensive parameters such as geological temperature, acid viscosity, acid flow velocity, and fracture width, the calculation results more closely match the true conditions of the geological layers, and are therefore more accurate.

[0011] Furthermore, the expression for the critical Reynolds number is as follows:

number

Number

Number

[0012] Furthermore, the expression formula of the effective mass transfer coefficient of the acid solution is as follows.

Number

Number

[0013] Construct a realistic fracture space model using a three-dimensional laser scanner and hydrodynamic finite element software, obtain the fluid parameter distribution on the slit surface after numerical simulation, combine it with the acid-rock reaction mathematical model to obtain the erosion mass of a single node on the slit surface, and further refine and specify the analysis of the erosion law on the slit surface.

[0014] Furthermore, the above S4 includes the following. Using a three-dimensional laser scanner and fluid finite element software, the average node coverage area, calcite content, and dolomite content are obtained. The distribution of fluid dynamics parameters within the fracture, the average coverage area of ​​the node, the calcite content, and the dolomite content are input into the acid rock reaction mathematical model to obtain the erosion mass of each wall node.

[0015] By utilizing the finite element mesh division concept, the fracture surface mesh is divided into nodes, the control area of ​​each node is calculated, and subsequent erosion calculations are subdivided into specific nodes, further matching the actual geological conditions.

[0016] Furthermore, the expression for the average coverage area of ​​the node is as follows:

number

[0017] By using the erosion mass calculation formula and the erosion depth calculation formula, the erosion level of each wall node at different time points can be determined, thereby establishing the acid-induced dynamic erosion process within the slit and predicting the acid-etched wall morphology at different time points.

[0018] Furthermore, the expression for the erosion mass of each wall node is as follows:

number

[0019] Furthermore, the expression for the corrosion depth corresponding to the aforementioned wall surface is as follows:

number

[0020] This specification will be further described in aspects of exemplary embodiments, which are illustrated in detail with the accompanying drawings. These embodiments are not limiting, and the same number represents the same structure. [Figure 1] This is an illustrative flowchart of a method for predicting acid-etched wall morphology based on mathematical models, as shown in some examples herein. [Modes for carrying out the invention]

[0021] The following describes specific embodiments of the present invention to facilitate understanding for those skilled in the art. However, it should be made clear that the present invention is not limited to the scope of these specific embodiments, and that all inventions utilizing the concept of the present invention are protected, as will be obvious to those skilled in the art within the spirit and scope of the invention as defined and specified in the claims of the present invention.

[0022] Examples Figure 1 is an illustrative flowchart of a method for predicting acid-etched wall morphology based on mathematical models as shown in some embodiments of this specification. As shown in Figure 1, the flow includes the following steps. In some embodiments, the flow may be performed by a processor. S1: Using a 3D laser scanner and fluid finite element software, 3D modeling is performed on the rock plate fracture surface to obtain a fracture space model. A 3D laser scanner is a device that scans and acquires information about rock surfaces. Fluid finite element software is used to model rock surfaces and obtain fracture space models. A rift space model is a three-dimensional spatial model that reflects rift information on a rock surface. For example, a rift space model may include mesh nodes for dividing a wall surface.

[0023] In some embodiments, the processor uses a 3D laser scanner to scan a rock slab and obtain 3D point cloud data of the true rock surface. Fluid finite element software is used to perform precise modeling on the 3D point cloud data of the true rock surface and obtain a meshed fracture space model.

[0024] The 3D point cloud data of the true rock face reflects the distribution of point clouds on the surface of the true rock slab. For example, the 3D point cloud data of the true rock face can include 3D point cloud data of rock faces divided by the Brazilian split test.

[0025] In some embodiments, the processor can import 3D point cloud data of the actual rock face into 3D inverse modeling software to obtain a 3D wall model.

[0026] A three-dimensional wall model is a three-dimensional model that reflects the actual surface structure of the rock face.

[0027] In some embodiments, the processor performs surface curving and mesh construction on a 3D wall model to obtain a curved 3D wall model. A meshed fracture space model is a three-dimensional spatial model that reflects rock surface fracture information that contains mesh information.

[0028] In some embodiments, the processor utilizes fluid finite element software to process a curved 3D wall model, and then meshes the processed model to obtain a meshed rift space model.

[0029] S2: Based on the pre-defined conditions of the rift space model and the fluid injection parameters, the solution is obtained by coupling the pressure field and velocity field of the rift space model using the finite volume method principle, and the distribution of fluid dynamics parameters within the rift is obtained. Pre-defined conditions are given assumptions that simplify the prediction model. For example, pre-defined conditions include not considering the effect of temperature on each input parameter, not considering the heat of reaction between the acid rock and the wall model and the acid solution, and not considering the filtration loss of the acid solution and the deformation of the wall model. Fluid injection parameters are the initial and boundary conditions required for the predictive model. For example, fluid injection parameters may include initial conditions such as injection time, acid density, acid viscosity, injection velocity, geological temperature, average slit height, pump injection discharge rate, and boundary conditions such as inlet and outlet types.

[0030] In some embodiments, the processor can acquire initial and boundary conditions based on the scanning conditions of the rock slab fracture surface.

[0031] The finite volume method is a method for calculating fluid dynamics values ​​using conservation equations in integral form. The fluid dynamics parameter distribution within the rift reflects the data of the acidic liquid flow velocity distribution at the slit surface using a triaxial coordinate system.

[0032] In some embodiments, the processor utilizes the finite volume method principle to find a solution for the rift space model based on pre-set conditions and fluid injection parameters, thereby obtaining the distribution of fluid dynamics parameters within the rift.

[0033] S3: Based on the correlation theory of the boundary layer of acid solution in a slit, spontaneous diffusion, and convective mass transfer, we will construct a mathematical model of acid-rock reactions for controlling mass transfer. The boundary layer theory for acid solutions in a slit is a theory that reflects situations where the motion of a fluid is affected by viscous forces. The theory of spontaneous diffusion of acid solution within a slit reflects the natural motion and diffusion of the fluid. The convection-based mass transfer theory of acid solution in a slit reflects the mass transfer conditions between the fluid and the solid wall. The mathematical model of acid-rock reaction for controlling mass transfer is a mathematical model that reflects the motion of the acid solution and the reaction conditions between the acid solution and the rock surface.

[0034] In some embodiments, the processor calculates the critical Reynolds number based on the boundary layer theory of the acid solution in the slit, utilizing the relationship between the acid solution flow velocity, pump discharge rate, and Reynolds number. Based on the natural diffusion theory of the acid solution in the slit, the diffusion coefficient is calculated using the effects of acid solution concentration, acid solution viscosity, and the high temperature of the geological formation on acid solution diffusion during acid solution flow. Based on the convective mass transfer theory of the acid solution in the slit, the convective mass transfer coefficient of laminar flow in the geological fracture is obtained. Using the critical Reynolds number, the diffusion coefficient, and the convective mass transfer coefficient of laminar flow, the effective mass transfer coefficient of the acid solution in the geological fracture is obtained. Based on the effective mass transfer coefficient of the acid solution in the geological fracture, a mathematical model of the acid rock reaction for mass transfer control is constructed using Fick's first law and the acid rock reaction chemical equation.

[0035] The critical Reynolds number is a parameter used to determine the state of acid flow. For example, a Reynolds number less than 2300 indicates laminar flow, a Reynolds number between 2300 and 4000 indicates transitional flow, and a Reynolds number greater than 4000 indicates turbulent flow. The fact that the Reynolds number of the acid flow in the crack is all less than 500 explains why the acid flow in the slit is mainly laminar.

[0036] In some embodiments, the expression for the critical Reynolds number can be as follows:

number

[0037] In some embodiments, the expression of the diffusion coefficient can be as follows.

Equation

[0038] In some embodiments, the expression of the convective mass transfer coefficient is as follows.

Equation

[0039] The effective mass transfer coefficient of the acid solution is a parameter that reflects the mass transfer ability of hydrogen ions from the acid solution to the rock surface and determines the rock corrosion rate during the acid fracturing process.

[0040] In some embodiments, the expression of the effective mass transfer coefficient of the acid solution is as follows.

Equation

[0041] Fick's first law is a law that describes the flow rate of diffusing substances passing through a unit cross-sectional area perpendicular to the diffusion direction per unit time.

[0042] The acid-rock reaction chemical equation is a chemical equation that reflects the change of substances due to the acid-salt reaction.

[0043] In some examples, the mathematical model of the acid-rock reaction is expressed as follows:

number

[0044] S4: The fluid dynamics parameter distribution within the crack is input into the acid rock reaction mathematical model to obtain the erosion mass of each wall node. The erosion mass of each wall node reflects the mass data lost after the rock face of the wall node was eroded by the acid.

[0045] In some embodiments, the processor can use a 3D laser scanner and fluid finite element software to obtain the node-average coverage area, calcite content, and dolomite content. The distribution of fluid dynamics parameters within the fracture, the average coverage area of ​​the node, the calcite content, and the dolomite content are input into the acid rock reaction mathematical model to obtain the erosion mass of each wall node. The average node coverage area is data that reflects the average value of the coverage area of ​​each node.

[0046] In some embodiments, the expression for the average node coverage area is:

number

[0047] In some embodiments, the processor can use a 3D laser scanner to scan the rock slab and obtain the calcite and dolomite content corresponding to each node.

[0048] In some embodiments, the expression for the erosion mass of each wall node is as follows:

number

[0049] S5: Using the erosion mass of each wall node, the correspondence with the point erosion depth is analyzed to obtain the erosion depth corresponding to the wall. The corrosion depth corresponding to the wall surface is data that reflects the change in depth after wall corrosion.

[0050] In some examples, the expression for the corrosion depth corresponding to the wall surface is as follows:

number

[0051] S6: Using the crack space model described above, the influence of the erosion depth corresponding to the wall surface is removed to obtain the wall surface morphology after acid etching, thereby completing the prediction of the acid-etched wall surface morphology. The wall morphology after acid etching reflects the wall morphology after the rock slab wall has been dissolved by the acid solution.

[0052] In some embodiments, the processor uses the acquired mesh wall erosion depth to process the corresponding mesh in the crack space model to obtain the wall morphology after acid etching.

[0053] In several embodiments of this specification, the processor utilizes a fracture space model and an acid-rock reaction mathematical model to predict the erosion depth corresponding to the wall surface, obtain the wall surface morphology after acid etching, and complete the prediction of the acid-etched wall surface morphology. This method significantly simplifies the experimental workload, saves experimental samples and costs, and solves the problem of not being able to conduct etching morphology studies on the same wall surface under different acid injection conditions. Utilizing the fracture space model and the acid-rock reaction mathematical model also improves the accuracy and prediction efficiency of the acid-etched wall surface prediction.

Claims

1. A method for predicting the morphology of acid-etched walls based on a mathematical model, S1: Using a 3D laser scanner and fluid finite element software, 3D modeling is performed on the rock plate fracture surface to obtain a fracture space model. S2: Based on the pre-defined conditions of the rift space model and the fluid injection parameters, the solution is obtained by coupling the pressure field and velocity field of the rift space model using the finite volume method principle, and the distribution of fluid dynamics parameters within the rift is obtained. S3: Based on the correlation theory of the boundary layer, spontaneous diffusion, and convective mass transfer of acid solution within a slit, we constructed a mathematical model of the acid-rock reaction for controlling mass transfer. S4: The fluid dynamics parameter distribution within the crack is input into the acid rock reaction mathematical model to obtain the erosion mass of each wall node. S5: Using the erosion mass of each wall node, the correspondence with the point erosion depth is analyzed to obtain the erosion depth corresponding to the wall. S6: A method for predicting the acid-etched wall morphology based on a mathematical model, characterized by including the use of the crack space model, the removal of the influence of the corrosion depth corresponding to the wall surface, obtaining the wall surface morphology after acid etching, and completing the prediction of the acid-etched wall surface morphology.

2. The aforementioned S1 is, Using a 3D laser scanner, the rock slab was scanned to obtain 3D point cloud data of the true rock surface. A method for predicting the acid-etched wall morphology based on a mathematical model according to claim 1, characterized in that it includes performing detailed modeling on the 3D point cloud data of the true rock surface using fluid finite element software to obtain a meshed slit space model.

3. The aforementioned S3 is, Based on the boundary layer theory of acid solution in a slit, the critical Reynolds number is calculated by utilizing the relationship between acid solution flow velocity, pump discharge rate, and Reynolds number. Based on the theory of natural diffusion of acid solution within a slit, the diffusion coefficient is calculated by utilizing the effects of acid solution concentration, acid solution viscosity, and the high temperature of the geological formation on acid solution diffusion during acid solution flow. Based on the theory of convective mass transport in acidic liquid within a slit, we obtained the convective mass transport coefficient for intermediate flow in a geological fissure. Using the aforementioned critical Reynolds number, diffusion coefficient, and laminar convection mass transfer coefficient, the effective mass transfer coefficient of acid solution in the geological fissure is obtained. A method for predicting the morphology of an acid-etched wall surface based on a mathematical model according to claim 1, characterized in that it includes constructing a mathematical model of the acid-rock reaction for controlling mass transfer using Fick's first law and the acid-rock reaction chemical equation, based on the effective mass transfer coefficient of the acid solution in the aforementioned fracture in the rock layer.

4. The expression for the critical Reynolds number is as follows: [Math 1] The expression for the diffusion coefficient is as follows: [Math 2] The expression for the aforementioned convective mass transfer coefficient is as follows: [Math 3] Here, Re represents the critical Reynolds number, Q represents the pump discharge rate, ρ represents the acid solution density, h represents the average slit height, μ represents the acid solution viscosity, D represents the diffusion coefficient, EXP represents the natural constant exponential form, T represents the geological temperature, C represents the acid solution concentration, and k represents the acid solution concentration. L A method for predicting the morphology of an acid-etched wall surface based on a mathematical model according to claim 3, characterized in that represents the convective mass transfer coefficient, w represents the crack width, u represents the acid solution flow velocity, and v represents the kinematic viscosity of the acid solution.

5. The expression for the effective mass transfer coefficient of the aforementioned acid solution is as follows: [Math 4] The expression for the mathematical model of the acid-rock reaction is as follows: [Math 5] Here, D e ρ represents the transfer coefficient of active ingredients in the acid solution, w represents the crack width, u represents the acid solution flow velocity, ρ represents the acid solution density, μ represents the acid solution viscosity, e represents the natural constant, T represents the geological temperature, C represents the acid solution concentration, and J represents the acid solution concentration. R1 The graph shows the calcite erosion rate at the corresponding node, and J R2 A method for predicting the acid etching wall morphology based on the mathematical model according to claim 3, characterized in that indicates the dolomite erosion rate of the corresponding node.

6. The above S4 includes the following: Using a 3D laser scanner and fluid finite element software, the average node coverage area, calcite content, and dolomite content were obtained. A method for predicting the acid-etched wall morphology based on a mathematical model according to claim 1, characterized in that the distribution of fluid dynamics parameters within the fracture, the average covering area of ​​the node, the calcite content, and the dolomite content are input into the acid-rock reaction mathematical model to obtain the erosion mass of each wall node.

7. The expression for the average coverage area of ​​the node is as follows: [Math 6] Here, 【number】 A method for predicting the morphology of an acid-etched wall surface based on a mathematical model according to claim 6, characterized in that represents the average coverage area of ​​the node, S represents the wall surface area, and n represents the number of wall surface mesh nodes.

8. The expression for the erosion mass of each of the aforementioned wall nodes is as follows: [Number 7] Here, m represents the erosion mass of each wall node, and x 1 This indicates the calcite content, J R1 x indicates the calcite erosion rate at the corresponding node, and x 2 This indicates the dolomite content, J R2 The dolomite erosion rate of the corresponding node is shown. 【number】 A method for predicting the morphology of an acid-etched wall surface based on a mathematical model according to claim 6, characterized in that represents the average coverage area of ​​the node and t represents the acid solution flow simulation time.

9. The expression for the corrosion depth corresponding to the aforementioned wall surface is as follows: [Number 8] Here, h represents the corrosion depth corresponding to the wall surface, and m represents the point corrosion mass. 【number】 represents the average covered area of nodes, and ρ R represents the acid solution density, and a method for predicting the acid etching wall surface morphology based on the mathematical model according to claim 1, characterized by this.

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