A method for calculating the permeability stress-sensitive evolution model based on multi-scale CT images

Abstract

This invention discloses a method for calculating a permeability stress-sensitive evolution model based on multi-scale CT images. This method modifies the traditional exponential dual-medium permeability stress evolution model. Micron-scale CT and nano-scale CT images of fractures and matrix pores in dense sandstone are acquired. Based on digital image processing, and combined with fractal theory, tortuosity calculation, and a pore network model, the fractal dimensions of tortuous fractures and tortuous pores are calculated, establishing a tortuous dual-medium permeability stress-sensitive evolution model. Compared with the traditional model, this method calculates relevant parameters of fractures and matrix pores based on real core images and considers the variation of pore compressibility with effective stress, making it more consistent with reality. Experimental test data validated the predictive performance of the model, showing good fitting results.

Description

Technical Field

[0001] This invention relates to engineering fields related to the evolution of permeability of soil and rock masses, such as petroleum engineering and water conservancy and hydropower. Specifically, it relates to a method for calculating a permeability stress-sensitive evolution model based on multi-scale CT images. Background Technology

[0002] The pore and fracture structures in rocks are the primary sites for fluid storage and flow, and are also major factors influencing rock permeability. Tight sandstone gas reservoirs exhibit strong spatial heterogeneity due to their small pore size, complex pore structure, diverse pore morphologies, and widespread development of microfractures of various shapes and sizes, demonstrating significant multi-scale characteristics. Previous researchers have established empirical formulas for the permeability of tight sandstone as a function of confining pressure based on extensive experimental results. However, these traditional empirical formulas use relatively simple parameters fitted from experimental results and assume the pore compressibility coefficient to be constant, which does not accurately reflect reality. Therefore, this invention discloses a permeability stress-sensitive evolution model calculation method based on multi-scale CT images. This method calculates the evolution parameters of pores and fractures based on real core images and considers the pore compressibility coefficient as a function of effective stress, dynamically changing with confining pressure, providing a new method for permeability stress-sensitive evolution calculation. Summary of the Invention

[0003] The purpose of this invention is to provide a calculation method for a permeability stress-sensitive evolution model of tight sandstone with high prediction accuracy and strong adaptability. To achieve the above objective, this invention assumes that tight sandstone is a dual porous medium model containing tortuous capillaries and tortuous fracture plates, and satisfies the basic assumptions that the distribution of capillary diameter (fracture aperture) and tortuosity can be described by the fractal scaling law; the capillary diameter (fracture aperture) decreases under confining pressure, but the length of the capillary (fracture plate) remains unchanged. A simplified physical model for permeability stress-sensitive evolution calculation is established, and a permeability weighting coefficient is introduced to consider the dynamic change of pore compressibility coefficient with confining pressure. Key parameters such as the tortuous fractal dimension of pores / fractures are calculated based on the original micro / nano CT images of tight sandstone. This invention mainly includes the following steps:

[0004] (i) The pore / fracture system of tight sandstone is simplified to meet the basic assumptions.

[0005] (ii) Based on Hagen-Poiseuille's equation and the cube law, combined with Darcy's law, the effective permeability expressions k for the matrix pore and fracture systems under confining pressure can be obtained respectively. m and k f .

[0006] (iii) By introducing the matrix pore permeability weighting coefficient c, the relationship between permeability and effective stress in the tortuous dual-pore medium model is obtained.

[0007] (iv) Microscopic images of fractures and matrix pores are obtained based on micron-CT and nano-CT respectively. The tortuous fractal dimension of matrix pores and fractures, as well as the permeability ratio of the two, are calculated by combining digital core technology. The calculation results are then substituted into the tortuous dual-pore medium model established above to obtain the evolution curve of permeability with effective stress.

[0008] Traditional permeability stress-sensitive experiments often obtain sample permeability and its evolution under confining pressure by injecting liquid (gas). However, due to the extremely low permeability of dense sandstone, these experiments often suffer from drawbacks such as long testing cycles and susceptibility to environmental factors like temperature / humidity and the mechanical properties of the testing equipment. Compared to traditional experimental methods, the advantages of this invention are:

[0009] This invention can predict rock permeability and its variation with confining pressure using only raw CT images and digital core simulation. It has a shorter testing cycle and lower testing cost. With the improvement of CT imaging resolution, the error of the prediction results is within an acceptable range in engineering. Attached Figure Description

[0010] To more clearly illustrate the implementation process of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and specific implementation steps.

[0011] Figure 1 This is a slice of the original CT image of dense sandstone.

[0012] Figure 2 This is a schematic diagram of a tortuous dual-porosity medium model.

[0013] Figure 3 This is a slice of a binary CT image of a rock sample.

[0014] Figure 4 This is a graph showing the evolution of permeability. Detailed Implementation

[0015] To explain in detail the method, objectives, and effects of this invention, the following description, in conjunction with the accompanying drawings, will further illustrate the invention. It should be noted that the embodiments described below are only some embodiments of the invention, and not all embodiments. All other embodiments obtained by other researchers and technicians in related fields based on the method proposed in this invention without other innovative labor should be within the protection scope of this application.

[0016] Figure 1These are the original CT images of dense sandstone used in this embodiment, showing the fracture and matrix pore structures obtained using micron-CT and nano-CT, respectively. The sample used for nano-CT scanning was drilled from the same core sample as the micron-CT scanning sample. The fractures are marked in blue, and the pores are indicated by the red arrows.

[0017] To establish a dual-medium model for the stress-sensitive evolution of permeability in tight sandstone, the pore-fracture system of tight sandstone needs to be simplified. Pores are simplified to tortuous capillary bundles, and microfractures are simplified to tortuous flat plates, such as... Figure 2 As shown. The simplified model satisfies the following basic assumptions: the distribution of capillary size and tortuosity can be described by the fractal scaling law; under confining pressure, the diameter of the capillary decreases, but the length of the capillary remains unchanged; the distribution of crack aperture and crack tortuosity can be described by the fractal scaling law; under confining pressure, the crack aperture decreases, but the crack length remains unchanged, and the change in crack height can be ignored.

[0018] Based on fundamental assumptions, the change in capillary diameter λ is used to characterize the change in porosity of the capillary bundle model. According to the Hagen-Poiseuille equation, an expression for the flow rate q in a single tortuous capillary is obtained, where the capillary diameter λ is represented by the initial capillary diameter λ0, and the capillary tortuosity length... l T Use capillary tube to judge length l Furthermore, assuming that the initial capillary diameter distribution can be described by the fractal scaling law, the total flow rate Q in the entire tortuous capillary bundle can be obtained by summing the flow rates in a single tortuous capillary, as shown in Formula 1:

[0019] (1)

[0020] Where, λ 0min λ is the minimum initial capillary diameter. 0max D is the maximum initial capillary diameter. Tm D is the fractal dimension of capillary tortuosity. fm Let denot be the fractal dimension of the capillary, Δp be the pressure difference between the two ends of the capillary, and μ be the fluid dynamic viscosity. l C represents the apparent length of the capillary tube (the geometric straight line length of the model). p P is the porosity compressibility coefficient. eff This is the effective stress.

[0021] Given the total flow rate of the capillary bundle, and based on Darcy's law, the expression for the effective permeability (km) of the capillary bundle model under confining pressure can be derived, as shown in Equation 2:

[0022] (2)

[0023] Where k0 is the initial permeability of the capillary model.

[0024] Similarly, based on the basic assumptions, the change in crack aperture can be used to characterize the change in porosity of the crack model. According to the cube law, the expression for the flow rate q in a single crack is obtained, where the deformed crack aperture 'a' is represented by the initial aperture 'a0', and the crack tortuosity length... l Tf Using the apparent length of the crack l f This means that, assuming the initial aperture of the tortuous crack follows the fractal scaling law, the total flow rate Q in the entire tortuous crack plate model is obtained by summing the flow rates in a single tortuous crack plate, as shown in Formula 3.

[0025] (3)

[0026] Among them, a 0min a is the initial minimum aperture of the fracture. 0max D represents the maximum initial crack aperture, where n is the ratio of the initial crack height to the crack aperture. Tf D is the fractal dimension of the crack tortuosity. ff Let fractal dimension be the crack. l f The apparent length of the crack (the geometric straight line length of the flat plate).

[0027] By obtaining the total flow rate of the fracture plate model, and based on Darcy's law, the effective permeability k of the fracture model under confining pressure can be calculated. f The expression is shown in Formula 4:

[0028] (4)

[0029] Wherein, represents the initial permeability of the tortuous cracked plate.

[0030] By introducing a weighting coefficient c for the permeability of the matrix (torsional capillary) pores, the final expression for the permeability of the tortuous dual-pore medium model as a function of effective stress is obtained, as shown in Equation 5:

[0031] (5)

[0032] The value of c ranges from [0, 1]. When c=1, the effect of cracks on the total permeability can be ignored; when c=0, the contribution of matrix pores to the total permeability can be ignored.

[0033] The original CT images of the acquired rock cores were first processed by binarization, such as... Figure 3 As shown, black represents the segmented pores and cracks; the fractal dimensions D of the pores and cracks are calculated based on the box-counting dimension method. Tm and D TfNext, connectivity analysis is performed on pores and fractures separately, and the permeability weighting coefficient c is assigned a value. Combined with confining pressure parameters, a predicted curve of permeability versus confining pressure can be generated. This curve can then be compared with experimental data. Figure 4 As shown, the model prediction results proposed in this invention are in good agreement with the experimental data, verifying the feasibility of the method.

[0034] The embodiments described above, used to illustrate the basic method, objectives, and effects of the present invention, are merely some embodiments of the present invention and do not limit the scope of application of the present invention. Any modifications or alterations made to the above embodiments based on the methods and principles proposed in this invention are within the scope of the technical solution of the present invention.

Claims

1. A method for calculating a permeability stress-sensitive evolution model based on multi-scale CT images, characterized in that, include: Step S1: First, the matrix pores and fractures are replaced by tortuous capillaries and tortuous plates to simplify the matrix pore and fracture structure of dense sandstone and construct a simplified physical model for calculating the permeability stress evolution equation. Step S2: Assuming the confining pressure, the change in rock porosity is characterized by the change in the diameter λ of the tortuous capillary, thus obtaining the relationship between the diameter λ of the tortuous capillary and the initial diameter λ0 of the tortuous capillary. Using the Hagen-Poiseuille equation, the flow rate of a single tortuous capillary can be calculated, and the total flow rate Q in the entire tortuous capillary bundle is obtained by summing the flow rates in each single tortuous capillary. Based on Darcy's law, the effective permeability k of the capillary bundle model under confining pressure is derived. m expression; Step S3: Assuming the confining pressure, the change in crack porosity is characterized by the change in the aperture of the tortuous crack plate, thus obtaining the relationship between the deformed crack aperture a and the initial aperture a0; according to the cube law, the flow rate of a single tortuous crack plate can be calculated, and the total flow rate Q in the entire tortuous crack plate model is obtained by summing the flow rates of the single tortuous crack plate; according to Darcy's law, the permeability k of the tortuous crack plate model under confining pressure is obtained. f expression; Step S4: Introduce the matrix pore permeability weighting coefficient c to evaluate the contribution of matrix pores and fractures to permeability evolution, and obtain the tortuous dual-medium permeability stress-sensitive evolution model.

2. The method for calculating the permeability stress-sensitive evolution model based on multi-scale CT images according to claim 1, characterized in that, In step 1, a simplified physical model for permeability stress-sensitive evolution is constructed by replacing the pore and fracture structure of the dense sandstone matrix with a tortuous capillary bundle model and a tortuous flat plate fracture model, respectively. The model satisfies the basic assumptions that the distribution of capillary diameter (fracture aperture) and tortuosity can be described by the fractal scaling law; the capillary diameter (fracture aperture) decreases under confining pressure, but the length of the capillary (fracture plate) remains unchanged.

3. The method for calculating the permeability stress-sensitive evolution model based on multi-scale CT images according to claim 1, characterized in that, In step 2, under the basic assumptions, the change in model porosity is characterized by the change in capillary diameter λ. The deformed capillary diameter λ can be represented by the initial capillary diameter λ0, and the capillary tortuosity length... l T Length by capillary l According to the Hagen-Poiseuille equation, the expression for the flow rate q in a single tortuous capillary can be calculated. By summing the flow rates in the single tortuous capillary, the total flow rate Q in the entire tortuous capillary bundle can be obtained. Finally, according to Darcy's law, the effective permeability k of the capillary bundle model under confining pressure can be derived. m The expression is used to establish a permeability evolution model for the tortuous capillary model (matrix pores).

4. The method for calculating the permeability stress-sensitive evolution model based on multi-scale CT images according to claim 1, characterized in that, In step 3, under the basic assumptions, the change in crack porosity is characterized by the change in crack aperture. The crack aperture 'a' after deformation can be represented by the initial aperture 'a0'. According to the cube law, the expression for the flow rate 'q' in a single crack is obtained, along with the crack tortuosity length. l Tf Using the apparent length of the crack l f This means that the total flow rate Q in the entire tortuous fractured plate model is obtained by summing the flow rates in a single tortuous fractured plate. Finally, the permeability k of the tortuous fractured plate model under confining pressure is obtained according to Darcy's law. f The expression is used to establish a permeability evolution model for tortuous cracks (flat plates).

5. The method for calculating the permeability stress-sensitive evolution model based on multi-scale CT images according to claim 1, characterized in that, In step 4, a matrix pore permeability weighting coefficient c is introduced (the fracture permeability weighting coefficient is 1-c). The value of the weighting coefficient c is between 0 and 1. The value of the weighting coefficient c is given by the ratio of matrix pore permeability to fracture permeability obtained from numerical simulation based on CT images. If there are no connected pores, c is considered to be 0, and the permeability is mainly controlled by the fracture. The permeability k of the tortuous capillary model is also considered. m The expression for permeability k in the cracked plate model f The expression can be used to obtain the calculation expression for the tortuous dual-medium permeability stress-sensitive evolution model.

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