Crack permeability calculation method considering rough wall surface structure of crack

Abstract

The invention provides a crack permeability calculation method considering a crack rough wall surface structure, and belongs to the technical field of seismic exploration data processing. The method comprises the following steps: determining the physical size of a required rough wall surface crack model, outputting point cloud coordinate data of a crack wall surface, constructing an interpolation function, and creating the crack wall surface; the method comprises the following steps: establishing a cuboid, segmenting the cuboid by using fracture wall surfaces, reserving an area between two fracture wall surfaces after segmentation, namely a fracture calculation domain, performing flow numerical simulation by applying an N-S equation, and simulating to obtain a pressure gradient and a flow rate of fluid flow in a fracture; and fitting a relation curve of the flow and the pressure gradient by using a nonlinear curve, finding a critical point when the linear flow is transited into the nonlinear flow, calculating a critical coefficient and a corresponding critical flow, and calculating the critical permeability of the rough wall surface crack model according to the Darcy law. According to the method, the problems that conventional fracture form characterization is difficult and uncontrollable, and the Darcy law is not suitable for describing nonlinear seepage in the fracture of the rough wall surface are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of seismic exploration data processing, and particularly relates to a crack permeability calculation method considering crack rough wall structure. BACKGROUND

[0002] Natural cracks are widely present in reservoirs and are important oil and gas storage space and seepage channels. The crack seepage characteristics are affected by many factors, among which the rough structure of the crack surface is an important factor affecting seepage, such as surface roughness, opening, fractal dimension and tortuosity. However, the morphology of real cracks is complex and has strong heterogeneity, and it is difficult to directly describe the crack morphology characteristics and study the reservoir seepage characteristics from the perspective of the crack network system. Therefore, the morphological characterization and mechanism research of seepage characteristics of a single crack are the research ideas currently chosen by many scholars. At the same time, with the rapid development of CT scanning technology and computer software simulation, the micro characterization of crack morphology has gradually become a frontier problem in the research of crack seepage. Based on the microstructure of the crack, the influence of the crack morphology characteristics on its physical properties is further explored, and the calculated reservoir permeability has certain theoretical significance and practical application value for the oil and gas development of the fractured reservoir.

[0003] Du Chunyu established a two-dimensional crack model in 2017 to study the influence of fracture density and fracture opening on the permeability of fracture-cavity media and the flow law, but the fluid permeation characteristics in the two-dimensional model are quite different from those in the three-dimensional model, and the influence of the rough structure of the crack wall on the seepage is not considered. Zhang Ping et al. used CT scanning technology to accurately scan the coal samples of Jiaozuo Coal in 2019 to realize the digital characterization of the crack structure, but the cracks constructed by CT scanning are based on actual rock samples and cannot control the morphological parameters of the cracks. Chen Yuangbo established a crack permeability calculation model based on rock physical experiment calibration in 2022, but it cannot be used for permeability calculation of the crack mathematical model. Li Xiongyan et al. calculated the crack permeability based on the rock mineral component content and the Stoneley wave and electrical imaging logging data in 2022, but the calculated crack permeability does not consider the morphological structure of the crack wall. Xu Qing et al. considered the relative protrusion height, fluctuation angle and tortuosity of the crack to modify the cubic law in 2022, but the morphological structure parameters of the crack physical model are difficult to obtain.

[0004] In summary, how to quickly establish a three-dimensional crack model with controllable morphological parameters and calculate the crack permeability is a current problem. SUMMARY

[0005] To solve the problems in the prior art, the present application provides a method for quickly establishing a three-dimensional crack model with controllable morphological parameters and calculating the crack permeability.

[0006] The application provides a crack permeability calculation method considering a crack rough wall structure, and comprises the following steps:

[0007] S1: determining the physical size of a required rough wall crack model, and outputting point cloud coordinate data of a crack wall;

[0008] S2: constructing an interpolation function, parameterizing a curved surface, and creating a crack wall by using the point cloud coordinate data of the crack wall;

[0009] S3: creating a cuboid according to the crack wall size, segmenting the cuboid by using the crack wall, retaining the region between the two crack walls after segmentation as a crack calculation domain, and converting the crack calculation domain into a solid;

[0010] S4: applying the Navier-Stokes equation (N-S equation) to flow numerical simulation based on the crack calculation domain established in step S3, and obtaining a pressure gradient ∇P and a flow rate Q of fluid flow in the crack through simulation;

[0011] S5: fitting the relationship curve of the flow rate Q and the pressure gradient ∇P by using a nonlinear curve, and obtaining a nonlinear curve expression;

[0012] S6: calculating required parameter values according to physical property parameters of the rough wall crack model and the flow rate Q and the pressure gradient ∇P obtained through simulation, finding a critical point at which linear flow transitions to nonlinear flow, calculating a critical coefficient and a corresponding critical flow rate Q c ;

[0013] S7: the critical flow rate Q c corresponds to a critical pressure gradient ∇P c , and a critical permeability k c of the rough wall crack model is calculated according to Darcy's law.

[0014] Preferably, the physical size of the crack model comprises a non-matching length, a standard deviation, an anisotropy factor, a fractal dimension and an opening degree.

[0015] Preferably, in step S1, a three-dimensional crack is generated by using Synfrc software according to the physical size of the required crack model, and point cloud coordinate data of upper and lower crack walls is output.

[0016] Preferably, step S3 comprises the following steps:

[0017] creating a cuboid with a horizontal direction size equal to the crack wall and a vertical direction height greater than the thickness of the crack wall, which can completely cover the crack wall, merging the crack wall and the cuboid, segmenting the cuboid by using the crack wall, retaining the region between the two crack walls after segmentation as a crack calculation domain, and converting the crack calculation domain into a solid.

[0018] Preferably, step S6 specifically comprises the following steps:

[0019] S61: according to the physical property parameters set by the rough wall crack model and the simulated flow rate Q and pressure gradient △P, calculate the Reynolds number Re and the hydraulic resistance coefficient λ;

[0020] S62: draw the lgRe and lgλ correlation curve, find the first data point that does not conform to the linear relationship, regard the data point as the critical point of the transition from linear flow to nonlinear flow, and the Reynolds number Re at the data point is the critical Reynolds number Re c , calculate the critical coefficient C and the critical flow rate Q c of the transition from linear flow to nonlinear flow.

[0021] Preferably, the fitting formula of the nonlinear curve is:

[0022] ▽P = aQ + bQ 2

[0023] In the formula, △P is the pressure gradient, Pa / m; Q is the flow rate, m 3 / s; a and b are fitting coefficients, dimensionless.

[0024] Preferably, the calculation formula of the Reynolds number Re in step S61 is:

[0025]

[0026] In the formula, ρ is the fluid density, kg / m 3 ; μ is the fluid viscosity, Pa·s; w is the crack width, m; d is the crack equivalent opening, m.

[0027] Preferably, the calculation formula of the hydraulic resistance coefficient λ in step S61 is:

[0028]

[0029] In the formula, ρ is the fluid density, kg / m 3 ; w is the crack width, m; d is the crack equivalent opening, m; L is the length of the liquid flow section, m.

[0030] Preferably, the calculation formula of the critical coefficient C in step S62 is:

[0031]

[0032] In the formula, ρ is the fluid density, kg / m 3 ; w is the crack width, m; Re c is the critical Reynolds number; μ is the fluid viscosity, Pa·s.

[0033] Preferably, the critical flow rate Q c is:

[0034]

[0035] Preferably, the critical permeability calculation formula of the rough wall crack model in step S7 is as follows:

[0036]

[0037] In the formula, w is the crack width, m; μ is the fluid viscosity, Pa·s; d is the crack equivalent opening degree, m; L is the liquid flow section length, m, and △P c is the critical pressure gradient.

[0038] Compared with the prior art, the present application has the following beneficial effects:

[0039] (1) The crack model obtained by the present application can be quantitatively characterized by parameters, the relationship between the flow rate and the pressure gradient is fitted by a nonlinear curve, and the calculated critical permeability can well meet the single crack seepage characteristics. The results obtained by considering the influence of the crack wall form parameters are more in line with the actual situation. The present application overcomes the problems of large difficulty and uncontrollability in conventional crack form characterization, and the Darcy law is not applicable to describe the nonlinear seepage in the rough wall crack.

[0040] (2) The present application can be used to calculate the permeability in the crack network system and the fracture-cavity model in addition to the calculation of the equivalent permeability in the single crack, and has wide application value. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is an interpolation function graph constructed based on the crack space coordinate data of an embodiment of the present application;

[0042] Figure 2 is a single crack wall generated by an embodiment of the present application;

[0043] Figure 3 is a crack geometry model graph constructed by an embodiment of the present application;

[0044] Figure 4 is a flow rate-pressure gradient relationship curve graph of an embodiment of the present application;

[0045] Figure 5 is a lgRe and lgλ relationship curve graph of an embodiment of the present application;

[0046] Figure 6 is a rough wall crack model, flat plate model permeability and crack opening degree relationship curve graph of an embodiment of the present application;

[0047] Figure 7 The flow chart of the crack permeability calculation method considering the structure of the rough wall of the crack is an embodiment of the present application. DETAILED DESCRIPTION

[0048] The specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0049] As Figure 7 , the present application provides a crack permeability calculation method considering the structure of the rough wall of the crack, comprising the following steps:

[0050] S1: determining the physical size of the required rough wall crack model, and outputting the point cloud coordinate data of the crack wall;

[0051] S2: constructing an interpolation function, parameterizing a curved surface, and creating a crack wall using the point cloud coordinate data of the crack wall;

[0052] S3: creating a cuboid according to the size of the crack wall, dividing the cuboid with the crack wall, and retaining the area between the two crack walls after the division as the crack calculation domain, and converting the crack calculation domain into a solid;

[0053] S4: based on the crack calculation domain established in step S3, applying the Navier-Stokes equation for flow numerical simulation, and obtaining the pressure gradient ∇P and flow rate Q of fluid flow in the crack through simulation;

[0054] S5: fitting the relationship curve of flow rate Q and pressure gradient ∇P with a nonlinear curve to obtain a nonlinear curve expression;

[0055] S6: calculating the required related parameter values according to the physical property parameters set by the rough wall crack model and the simulated flow rate Q and pressure gradient ∇P, finding the critical point of the transition from linear flow to nonlinear flow, calculating the critical coefficient and the corresponding critical flow rate Q c ;

[0056] S7: the critical flow rate Q c corresponds to the critical pressure gradient ∇P c , and according to Darcy's law, the critical permeability k c of the rough wall crack model is calculated.

[0057] According to a specific embodiment of the present application, the physical size of the crack model includes a non-matching length, a standard deviation, an anisotropy factor, a fractal dimension, and an opening degree.

[0058] According to a specific embodiment of the present application, in step S1, a three-dimensional crack is generated using Synfrc software according to the physical size of the required crack model, and the point cloud coordinate data of the upper and lower crack walls is output.

[0059] According to one specific embodiment of the present application, step S3 comprises the following steps:

[0060] A cuboid is created, which has a horizontal dimension equal to the crack wall surface and a vertical height greater than the thickness of the crack wall surface, and which can completely cover the crack wall surface. The crack wall surface is merged with the cuboid, and the cuboid is divided by the crack wall surface. The region between the two crack wall surfaces after the division is the crack calculation domain, and the crack calculation domain is converted into a solid.

[0061] According to one specific embodiment of the present application, step S6 specifically comprises the following steps:

[0062] S61: According to the physical property parameters set by the rough wall crack model and the simulated flow rate Q and pressure gradient △P, the Reynolds number Re and the hydraulic resistance coefficient λ are calculated.

[0063] S62: A correlation curve of lgRe and lgλ is drawn, and the first data point that does not conform to the linear relationship is found. The data point is regarded as the critical point of the transition from linear flow to nonlinear flow, and the Reynolds number Re at the data point is the critical Reynolds number Re c . The critical coefficient C and the critical flow rate Q c of the transition from linear flow to nonlinear flow are calculated.

[0064] According to one specific embodiment of the present application, the fitting formula of the nonlinear curve is:

[0065] ▽P = aQ + bQ 2

[0066] In the formula, △P is the pressure gradient, Pa / m; Q is the flow rate, m 3 / s; a and b are fitting coefficients, dimensionless.

[0067] According to one specific embodiment of the present application, the calculation formula of the Reynolds number Re in step S61 is:

[0068]

[0069] In the formula, ρ is the fluid density, kg / m 3 ; μ is the fluid viscosity, Pa·s; w is the crack width, m; and d is the equivalent opening of the crack, m.

[0070] According to one specific embodiment of the present application, the calculation formula of the hydraulic resistance coefficient λ in step S61 is:

[0071]

[0072] In the formula, ρ is the fluid density, kg / m 3; w is the fracture width, m; d is the fracture equivalent opening, m; L is the length of the liquid flow section, m.

[0073] According to one specific embodiment of the present application, the formula for calculating the critical coefficient C in step S62 is:

[0074]

[0075] In the formula, p is the fluid density, kg / m 3 ; w is the fracture width, m; Re c is the critical Reynolds number; and m is the fluid viscosity, Pa·s.

[0076] According to one specific embodiment of the present application, the critical flow rate Q c in step S62 is:

[0077]

[0078] According to one specific embodiment of the present application, the formula for calculating the critical permeability of the rough wall fracture model in step S7 is as follows:

[0080]

[0081] In the formula, w is the fracture width, m; m is the fluid viscosity, Pa·s; d is the fracture equivalent opening, m; L is the length of the liquid flow section, m, and P is the critical pressure gradient. c

[0082] Example 1

[0083] According to one specific embodiment of the present application, the method for calculating the fracture permeability considering the rough wall structure of the fracture is described in detail as follows.

[0084] The method for calculating the fracture permeability considering the rough wall structure of the fracture of the present application comprises the following steps:

[0085] First, the morphological parameters of the required fracture model are determined, i.e., the physical dimensions of the required rough wall fracture model are determined. The carbonate rock core is subjected to CT scanning, a digital core model is constructed, the fracture surface is reconstructed using software, and the range values of each morphological parameter of the required fracture model are obtained, and it is determined that the opening value range of the fracture model in the present application is between 4 mm and 2 mm.

[0086] Based on the physical dimensions, the non-matching length, the standard deviation, the anisotropy factor and the fractal dimension of the required fracture model, a fracture numerical model with a fractal dimension D of 2.1 and a fracture opening of 1.6 mm is established using Synfrc software, and point cloud coordinate data of the fracture is obtained.

[0087] ​An interpolation function is constructed with the point cloud coordinate data of the crack space, as shown in Figure 1 A parameterized surface is created for the crack surface, as shown in Figure 2 .

[0088] A cube is created in the geometry module, which has the same length as the crack wall surface in the x and y directions and a height greater than the thickness of the crack wall surface in the z direction, and which can completely cover the crack wall surface. The crack surface is merged with the cube, the cube is divided by the crack wall surface, and the area between the two crack wall surfaces after the division is the crack area. The crack calculation domain is converted into a solid, as shown in Figure 3 .

[0089] Based on the crack calculation domain established in the above steps, the N-S equation (Navier-Stokes equation) is applied for flow numerical simulation, and the parameters are set as follows: the fluid flow state is laminar flow, the fluid is incompressible Newtonian fluid, the reference pressure is 0.1 MPa, and the reference temperature is 293.15 K; the flow medium is water at 4°C, the fluid density is 1000 kg / m 3 , and the dynamic viscosity is 1 mPa·s; the x direction is selected as the fluid migration direction, the left side of the model is the water inlet, and the right side is the water outlet, both of which have a constant pressure boundary condition, and the pressure of the water outlet is constant, and the upper and lower boundaries are set as impermeable boundaries without sliding.

[0090] The volume flow rate Q of the entire crack model is calculated, and a series of pressure, flow rate data values of fluid flow in the crack, and pressure gradient ▽P of fluid flow in the crack are obtained. The flow rate Q is taken as the horizontal coordinate, with the unit of m 3 / s, and the pressure gradient ▽P is taken as the vertical coordinate, with the unit of Pa / m, to draw the flow rate-pressure gradient curve, and obtain the fitting coefficients a and b, as shown in Figure 4 .

[0091] According to the basic physical property parameters, the flow rate Q and the series of pressure gradient ▽P values, the Reynolds number Re and the hydraulic resistance coefficient λ are calculated, and the lgRe-lgλ correlation curve is drawn, as shown in Figure 5 .

[0092] The first data point in the lgRe-lgλ correlation curve that does not conform to the linear relationship is found, which is the critical point of the transition from linear flow to nonlinear flow. The critical Reynolds number Re c is 212.4, the critical coefficient C is 0.101, and the critical flow rate Q c is 1.06×10 -5 m 3 / s.

[0093] The critical pressure gradient ▽P c corresponding to the critical flow rate is 350 Pa / m, and the critical permeability k of the rough wall crack model is calculated according to Darcy's law.c 1.92x10 7 mD.

[0094] Using the same method, four groups of fracture models with different fracture openings are constructed, and the openings are 0.4mm, 0.8mm, 1.2mm and 2mm respectively. The flow numerical simulation is carried out, the corresponding parameters and critical values are calculated, and the critical parameters of the fracture models with different openings are shown in Table 1.

[0095] Table 1 Critical flow and critical pressure gradient of fracture models with different openings

[0096] Crack opening (mm) Critical flow (10 -5 m 3 / s)]]> Critical pressure gradient (Pa / m) 0.4 0.73 16500 0.8 0.98 2600 1.2 1.02 800 1.6 1.06 300 2.0 1.12 190

[0097] The critical permeability of the fracture model with rough wall surface is calculated by using the critical flow and the critical pressure gradient, and is compared with the permeability of the smooth flat plate model, and is shown in Table 2.

[0098] Table 2 Permeability of fracture models with different openings

[0099]

[0100]

[0101] The relationship curves of the permeability of the rough wall fracture model and the flat plate model and the fracture opening are drawn by taking the fracture opening b as the abscissa and the permeability k as the ordinate, and are shown in Table 2. Figure 6

[0102] The above only describes the preferred embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application is included in the protection scope of the present application.​

Claims

1. A method for calculating a fracture permeability taking into account a fracture rough wall surface structure, characterized by, The method comprises the following steps: S1: determining the physical size of a required rough wall fracture model, and outputting point cloud coordinate data of a fracture wall; S2: constructing an interpolation function using the point cloud coordinate data of the fracture wall, parameterizing a curved surface, and creating the fracture wall; S3: creating a cuboid according to the size of the fracture wall, segmenting the cuboid using the fracture wall, retaining the region between the two fracture walls after segmentation as a fracture calculation domain, and converting the fracture calculation domain into a solid; S4: based on the fracture calculation domain established in step S3, applying the Navier-Stokes equation to perform flow numerical simulation, and obtaining a pressure gradient △P and a flow rate Q of fluid flow in the fracture through simulation; S5: fitting a nonlinear curve of the flow rate Q and the pressure gradient △P to obtain a nonlinear curve expression; S6: According to the physical parameters set by the rough wall crack model and the simulated flow Q and pressure gradient▽P, the required related parameter values are calculated, and the critical point of the transition from linear flow to nonlinear flow is found, the critical coefficient and the corresponding critical flow Q are calculated c ; S7: critical flow rate Q c The corresponding pressure gradient is the critical pressure gradient c According to Darcy's law, the critical permeability k c of the rough wall crack model is calculated.

2. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 1, characterized by, The physical size of the fracture model includes a mismatch length, a standard deviation, an anisotropy factor, a fractal dimension, and an opening degree.

3. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 2, characterized by, In step S1, a three-dimensional fracture is generated using Synfrc software according to the physical size of the required fracture model, and point cloud coordinate data of upper and lower fracture walls is output.

4. The method of calculating the fracture permeability considering the structure of the fracture rough wall surface according to any one of claims 1 to 3, characterized in that, Step S3 comprises the following steps: A cuboid with a horizontal size equal to the fracture wall and a vertical height greater than the thickness of the fracture wall is created, which can completely cover the fracture wall, the fracture wall and the cuboid are combined, the fracture wall is used to segment the cuboid, and the region between the two fracture walls after segmentation is the fracture calculation domain, and the fracture calculation domain is converted into a solid.

5. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 1, characterized by, Step S6 specifically comprises the following steps: S61: calculating the Reynolds number Re and the hydraulic resistance coefficient λ according to the physical property parameters set by the rough wall fracture model and the flow rate Q and the pressure gradient △P obtained through simulation; S62: Draw the lgRe and lgλ correlation curve, find the first data point that does not conform to the linear relationship, regard the data point as the critical point of linear flow transition to nonlinear flow, and the Reynolds number Re at the data point is the critical Reynolds number Re c , calculate the critical coefficient C and the critical flow Q of the linear flow transition to the nonlinear flow c .

6. The method for calculating the fracture permeability considering the rough wall structure of the fracture according to claim 5, wherein, The fitting formula of the nonlinear curve is: wherein is the pressure gradient, Pa / m; Q is the flow rate, m 3 / s; a and b are fitting coefficients, dimensionless.

7. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 6, characterized by, The calculation formula of the Reynolds number Re in step S61 is: where p is the fluid density, kg / m 3 ; μ is the fluid viscosity, Pa-s; w is the fracture width, m; d is the fracture equivalent opening, m.

8. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 6, characterized by, The calculation formula of the hydraulic resistance coefficient λ in step S61 is: where p is the fluid density, kg / m 3 ; w is the fracture width, m; d is the fracture equivalent opening, m; L is the length of the liquid flow section, m.

9. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 6, characterized in that, The calculation formula of the critical coefficient C in step S62 is: where p is the fluid density, kg / m 3 ; w is the fracture width, m; Re c is the critical Reynolds number; and m is the fluid viscosity, Pa-s.

10. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 9, characterized in that, The critical flow rate Q in the step S62 is: c Q = 0.5 * (P1 - P2) 11. The method of calculating the fracture permeability considering the fracture roughness wall surface structure according to claim 1, characterized in that, The critical permeability calculation formula of the rough wall fracture model in step S7 is as follows: In the formula, w is the fracture width, m; μ is the fluid viscosity, Pa·s; d is the equivalent opening degree of the fracture, m; L is the length of the liquid flow section, m, is the critical pressure gradient.

Images