Method for determining permeability of shale matrix based on pore size distribution

Abstract

The application discloses a shale matrix permeability determination method based on pore size distribution, and comprises the following steps: obtaining shale nitrogen adsorption coefficients by using porosity and nitrogen adsorption test; obtaining scanning electron microscope photos by shooting and splicing; identifying the spliced scanning electron microscope photos, obtaining organic pores and inorganic pores, and obtaining pore areas of shale samples; obtaining equivalent circle radii of shale pores, and establishing a pseudo-continuous shale pore size distribution curve; obtaining shale pore size distribution density functions according to the continuous shale pore size distribution curve; and obtaining shale matrix permeability. The application combines experimental data and theoretical models, solves the influence of fractures on permeability in the shale permeability test process, directly applies the measured sample real pore size distribution to the calculation of shale matrix permeability, considers pore tortuosity, gas adsorption and slip effect, and makes the calculation result more capable of reflecting the shale matrix permeability, and improves the shale matrix permeability test and calculation precision.

Description

Technical Field

[0001] This invention relates to the field of shale gas development technology, and in particular to a method for determining the permeability of shale matrix based on pore size distribution. Background Technology

[0002] Shale reservoirs contain numerous micropores, and these micro- and nano-porous structures cause gas adsorption as fluids flow through these pores. Simultaneously, due to the rapid flow of gas molecules, slippage occurs at the pore walls where they contact the pores. Furthermore, the pore system of real shale is extremely complex, with the flow path of gas molecules much larger than the sample size, leading to reduced gas transport capacity. Currently, methods for testing shale permeability include steady-state and unsteady-state methods. Unsteady-state methods include pore pressure oscillation, degassing, rock complex resistivity, lattice Boltzmann method, mercury porosimetry, nuclear magnetic resonance, and pressure pulse decay. However, these methods directly utilize core samples and do not consider the influence of invisible micro-fractures, pore tortuosity, and gas adsorption and slippage during the testing process on permeability. Additionally, many existing testing methods are fluid injection methods, but because shale is extremely dense, with pores at the micro- and nano-scale, it is difficult to inject experimental fluids into the sample. Forced injection can also damage the pore structure, leading to erroneous test results.

[0003] For example, in the Chinese invention patent "Patent Publication No.: CN109100278A, entitled 'A Method for Calculating Apparent Permeability Considering the Pore Size Distribution Characteristics of Shale'", the method processes the mercury intrusion porosimetry curve, discretizes the pore size, obtains the permeability contribution rate of each pore interval, and then superimposes them to obtain the sample permeability. It also considers various flow regimes in a single capillary, such as continuous flow and slip flow of free gas. However, this method does not directly use the pore size distribution in the calculation process; instead, it utilizes the contribution rate of each pore interval to the permeability.

[0004] For example, in the Chinese invention patent with publication number CN114136862A and title: "A method for calculating the apparent liquid permeability of a double-wetting shale", the organic matter pore size distribution and inorganic matter pore size distribution are obtained by adsorption of nitrogen and carbon dioxide, and then the pore size corresponding to the peak value of the pore size distribution is taken as the radius of the organic matter pores and inorganic matter pores.

[0005] For example, in the Chinese invention patent with publication number CN114609010A and titled "A logging method and device for the relative permeability of oil and water in shale reservoirs", the pore size distribution of shale is determined by low-temperature nitrogen adsorption, and then used for shale pore network structure correction and obtaining the average pore radius of shale.

[0006] Therefore, the existing apparent permeability calculation models do not directly use the changes in pore size (pore size distribution) of the real sample for the calculation of sample permeability. They only add coefficients describing the pore structure or directly use the average pore radius in the calculation process, which cannot truly reflect the pore structure characteristics of the sample, resulting in a large error in the calculation results.

[0007] Therefore, there is an urgent need to propose a logically simple, accurate and reliable method for determining the permeability of shale matrix based on pore size distribution. Summary of the Invention

[0008] To address the shortcomings of existing technologies, the technical problem this invention aims to solve is to overcome the problems of inaccurate shale matrix permeability testing and calculation methods. These methods fail to consider the impact of microfractures in the sample on shale matrix permeability, leading to overestimation of the shale matrix permeability. Furthermore, they do not apply the true pore size distribution of the sample to the permeability calculation. This invention proposes a pore size distribution-based method for determining shale matrix permeability, which can effectively improve the accuracy of shale matrix permeability testing and calculation and directly apply the pore size distribution to the shale permeability calculation process. The technical solution adopted by this invention is as follows:

[0009] A method for determining the permeability of shale matrix based on pore size distribution includes the following steps:

[0010] Highly evolved shale samples from the target area were obtained and dried; the nitrogen adsorption coefficient f of the shale was determined using porosity and nitrogen adsorption tests. a ;

[0011] Shale samples were taken, and scanning electron microscope images were obtained by field emission scanning electron microscopy and then stitched together.

[0012] The stitched scanning electron microscope images were identified, and organic and inorganic pores were obtained and labeled. The pore area A of the shale sample was then calculated. i ;

[0013] Based on pore area A i The radius r of the equivalent circle of shale pores was obtained. i Establish a quasi-continuous shale pore size distribution curve;

[0014] Based on the continuous shale pore size distribution curve, the pore size distribution density function f(r) of the shale is obtained. i );

[0015] According to capillary theory, the pore size distribution density function f(r) of shale i A matrix permeability model was established to obtain the shale matrix permeability K, which is expressed as follows:

[0016]

[0017] in, τ represents the porosity of shale; τ represents the tortuosity of shale pores; r min The minimum pore radius of shale; r max λ represents the maximum pore radius of shale; c represents a constant with a value of 0.9; λ represents the mean free path of gas molecules.

[0018] Furthermore, the matrix porosity of the shale samples was measured using porosity and nitrogen adsorption tests. Langmuir pressure P L and Langmuir volume V L .

[0019] Furthermore, the nitrogen adsorption coefficient f of the shale a The expression is:

[0020]

[0021] Where, ρ r V represents the density of shale; std c represents the molar volume of a gas. g ρ represents the gas compressibility coefficient. g The gas density is represented by M; the relative molecular mass of the gas is represented by P; and the simulated test pressure is represented by P.

[0022] Furthermore, the aperture distribution density function f(r) i The expression for ) is:

[0023]

[0024] Where a, b, and c represent constants.

[0025] Furthermore, the derivation process of the constants a, b, and c is as follows:

[0026] For the pore size distribution density function f(r) i Taking the natural logarithm of both sides of ), we get:

[0027]

[0028] make:

[0029] F(r i )=ln(f(r i )),

[0030] but:

[0031]

[0032] Where A0, A1, and A2 represent intermediate parameters, and m represents the number of data sets;

[0033] Establish data group (r) i ,f(r i And obtain the data set (r) i ,F(r i ));

[0034] Calculate the coefficients and

[0035] Establish the parameter matrix to obtain the intermediate parameters A0, A1, and A2;

[0036]

[0037] Substituting the intermediate parameters A0, A1, and A2 into the expressions for constants a, b, and c, we obtain the fitted constants a, b, and c.

[0038]

[0039] Furthermore, the expression for the tortuosity τ of the shale pores is:

[0040]

[0041] in, This indicates the porosity of shale.

[0042] Furthermore, the expression for the mean free path λ of the gas molecules is:

[0043]

[0044] Where μ represents gas viscosity; Z represents gas compressibility factor; P represents simulated test pressure; R represents universal gas constant; and T represents temperature.

[0045] Furthermore, the expression for the gas viscosity μ is:

[0046] μ=6×10 -6 P 2 +0.0002P+0.0176(T=293.15K).

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] This invention obtains the porosity and adsorption coefficient of shale core samples by conducting porosity and nitrogen adsorption tests. Based on capillary theory, a shale matrix permeability calculation model is established based on different pore size distributions. The discrete pore size distribution is transformed into a quasi-continuous pore size distribution and directly applied to the calculation of shale permeability. The model also considers pore tortuosity, gas adsorption, and slippage effects, and can eliminate the influence of microcracks on sample permeability, thus obtaining a true and accurate sample matrix permeability. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope of protection. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0050] Figure 1 A flowchart for fitting shale pore size distribution curves provided by this invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0052] In this embodiment, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0053] The terms "first" and "second," etc., used in the specification and claims of this embodiment are used to distinguish different objects, not to describe a specific order of objects. For example, "first target object" and "second target object," etc., are used to distinguish different target objects, not to describe a specific order of target objects.

[0054] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0055] In the description of the embodiments in this application, unless otherwise stated, "multiple" means two or more. For example, multiple processing units means two or more processing units; multiple systems means two or more systems.

[0056] like Figure 1 As shown, this embodiment provides a method for determining the permeability of shale matrix based on pore size distribution. First, it should be noted that... Figure 1 Image A in the figure is a photograph of a core sample. Figure 1 Image B in the image is a scanning electron microscope image taken after polishing, which was then stitched together in a 10×10 format. Figure 1 Image C in the image is a stitched photograph showing the labeled organic and inorganic pores. Figure 1 The D-plot in the image shows the pore radius calculated from the pore area obtained through image analysis, and the discrete pore size distribution curve established with a step size of 10 nm. Figure 1 The E-plot in the figure shows a quasi-continuous aperture distribution curve established with a step size of 0.01 nm. Figure 1 The F-plot in the figure represents the pore size distribution density function f(r) obtained through fitting. i )curve.

[0057] The specific steps are as follows:

[0058] Step S10: Obtain highly evolved shale samples from the target area and dry them. Measure the matrix porosity of the shale samples using porosity and nitrogen adsorption tests. Langmuir pressure P L and Langmuir volume V L Calculate the nitrogen adsorption coefficient f in shale. a ;

[0059] Among them, the nitrogen adsorption coefficient f of shale a The expression is:

[0060]

[0061] Where, ρ r This indicates the density of shale, in g / cm³. 3 V std The molar volume of the gas is 22.4 L / mol at 0.1 MPa and 20 °C; c g Represents the gas compressibility coefficient, in MPa -1 ;ρ g This indicates the density of a gas, expressed in g / cm³. 3 M represents the relative molecular mass of the gas, in g / mol; P represents the simulated test pressure.

[0062] Step S20: Cut out shale samples, polish and gold-plat them, observe them under a field emission scanning electron microscope, take scanning electron microscope images and stitch them together.

[0063] Step S30: Manually identify the organic and inorganic pores in the above-mentioned stitched images, mark them with different colors, and then perform image analysis to obtain the pore area A of the shale. i With the continuous development of artificial intelligence, organic and inorganic pores can also be identified using current neural network models, through processes such as labeled training samples and training. Since AI recognition is a conventional and mature technology, it will not be elaborated upon further.

[0064] Step S40: Calculate the equivalent circle radius r of shale pores. i A quasi-continuous shale pore size distribution curve was established with a step size of 0.01 nm. Wherein, the equivalent circle radius r of the shale pores... i The expression is:

[0065]

[0066] Among them, A i The pore area of ​​shale is expressed in nm. 2 π is the mathematical constant of a circle, and is taken as 3.1415926.

[0067] Step S50: Fit the quasi-continuous shale pore size distribution data to obtain the shale pore size distribution density function f(r). i Its expression is:

[0068]

[0069] Where a, b, and c represent constants.

[0070] In this embodiment, the derivation process of constants a, b, and c is as follows:

[0071] (1) For the aperture distribution density function f(r) i Taking the natural logarithm of both sides of ), we get:

[0072]

[0073] make:

[0074]

[0075] but:

[0076]

[0077] Where A0, A1, and A2 represent intermediate parameters, and m represents the number of data sets;

[0078] (2) Create a data group (r) i ,f(r i And obtain the data set (r) i ,F(r i ));

[0079] (3) Obtain the coefficients and

[0080] (4) Establish the parameter matrix and obtain the intermediate parameters A0, A1 and A2;

[0081]

[0082] (5) Substitute the intermediate parameters A0, A1 and A2 into the expressions of constants a, b and c to obtain the fitted constants a, b and c;

[0083]

[0084] Step S60: Establish a matrix permeability model based on the pore size distribution obtained using scanning electron microscopy and image analysis, and calculate the shale matrix permeability, which is expressed as:

[0085]

[0086] in, τ represents the porosity of shale; τ represents the tortuosity of shale pores; r min The minimum pore radius of shale is expressed in nm; r max λ represents the maximum pore radius of shale, in nm; c represents a constant with a value of 0.9; λ represents the mean free path of gas molecules, in nm.

[0087] The expression for the tortuosity τ of shale pores is:

[0088]

[0089] in, This indicates the porosity of shale.

[0090] Furthermore, the expression for the mean free path λ of gas molecules is:

[0091]

[0092] Where μ represents gas viscosity in mPa·s; Z represents gas compressibility factor; P represents simulated test pressure in MPa; R represents universal gas constant, taken as 8.314 J / mol / K; and T represents temperature in K.

[0093] Furthermore, the expression for the gas viscosity μ is:

[0094] μ=6×10 -6 P 2 +0.0002P+0.0176(T=293.15K).

[0095] In this embodiment, the shale matrix permeability calculation model directly applies the pore size distribution of the sample to the shale permeability calculation process, while also considering the influence of shale pore tortuosity, gas adsorption, and slippage effect on shale matrix permeability.

[0096] The pore size distribution obtained in step S60 comes from a scanning electron microscope image taken after magnification of 30,000 times. The observed field of view is a very small part of the sample. The sample pore size distribution curve obtained by image analysis of this image is not affected by cracks in the sample and can eliminate the influence of cracks on the permeability of the sample matrix.

[0097] Therefore, when calculating the matrix permeability of shale, the test or calculation results of parameters such as porosity, tortuosity, gas adsorption coefficient, gas viscosity, and mean free path of gas molecules are substituted into the matrix permeability calculation model based on pore size distribution. By combining the fitting results of the pore size distribution density function, the matrix permeability of the shale sample can be calculated.

[0098] To illustrate the features and advantages of this invention, the invention will be further described below with reference to calculation examples and accompanying drawings.

[0099] The following is relevant data on shale gas reservoirs:

[0100] Table 1. Relevant Data on Shale Gas Reservoirs

[0101] parameter symbol numerical values unit Test gas <![CDATA[N2]]> / / Test stress P 6.4 MPa Test temperature T 293.15 K Rock density <![CDATA[ρ r ]]> 2.5 <![CDATA[g / cm 3 ]]> Langmuir volume of Longmaxi Formation shale <![CDATA[V L1 ]]> 4 <![CDATA[cm 3 / g]]> Langmuir pressure of Longmaxi Formation shale <![CDATA[P L1 ]]> 2 MPa Langmuir volume of Qiongzhusi Formation shale <![CDATA[V L2 ]]> 2 <![CDATA[cm 3 / g]]> Langmuir pressure in Qiongzhusi Formation shale <![CDATA[P L2 ]]> 1 MPa relative molecular mass of gas M 28 g / mol Gas compressibility <![CDATA[c g ]]> 0.125 <![CDATA[MPa -1 ]]> gas density <![CDATA[ρ g ]]> 0.071 <![CDATA[g / cm 3 ]]> Gas compressibility factor Z 1.035 /

[0102] Two samples from the Longmaxi Formation taken from field outcrops and three samples from the Qiongzhusi Formation taken from well cores were made into standard rock samples. Porosity and permeability were tested and observed by scanning electron microscopy. The scanning electron microscopy images were stitched together into a 10×10 image. Then, organic and inorganic pores were manually identified using image analysis to obtain pore parameters. After data processing, pore size distribution data was obtained. The pore size distribution density function expression was obtained by data fitting. Combined with the relevant parameters given in Table 1, the shale matrix permeability was finally calculated using the shale matrix permeability calculation model based on pore size distribution. The test and calculation results are shown in Table 2.

[0103] Table 2 Results of Shale Porosity Testing and Permeability Calculation

[0104]

[0105]

[0106] The calculation results from the two samples of the Longmaxi Formation show that the permeability of the shale matrix is ​​very close to that of the pressure pulse decay permeability, indicating that the method for determining the permeability of the shale matrix based on pore size distribution proposed in this invention has high accuracy.

[0107] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications made thereon, shall fall within the scope of protection of the present invention.

Claims

1. A method for determining the permeability of shale matrix based on pore size distribution, characterized in that, Includes the following steps: Highly evolved shale samples from the target area were obtained and dried; the nitrogen adsorption coefficient of the shale was determined using porosity and nitrogen adsorption tests. ; Shale samples were taken, and scanning electron microscope images were obtained by field emission scanning electron microscopy and then stitched together. The stitched scanning electron microscope images were identified, and organic and inorganic pores were obtained and labeled to calculate the pore area of ​​the shale sample. ; Based on pore area Find the radius of the equivalent circle of shale pores Establish a quasi-continuous shale pore size distribution curve; Based on the continuous shale pore size distribution curve, the pore size distribution density function of shale is obtained. ; Based on capillary theory and the pore size distribution density function of shale... A matrix permeability model was established to obtain the shale matrix permeability K, which is expressed as follows: ， in, Indicates the porosity of shale; Indicates the tortuosity of shale pores; Indicates the minimum pore radius of shale; Indicates the maximum pore radius of shale; This represents a constant with a value of 0.9; Indicates the mean free path of gas molecules; Among them, the matrix porosity of the shale sample was measured using porosity and nitrogen adsorption tests. Langmuir pressure and Langmuir volume ; The nitrogen adsorption coefficient of shale The expression is: ， in, Indicates shale density; Represents the molar volume of a gas; Indicates the gas compressibility coefficient; M represents the gas density; M represents the relative molecular mass of the gas. This indicates simulated test stress.

2. The method for determining shale matrix permeability based on pore size distribution according to claim 1, characterized in that, The aperture distribution density function The expression is: ， in, , , Represents a constant.

3. The method for determining shale matrix permeability based on pore size distribution according to claim 2, characterized in that, The constant ,constant and constant The derivation process is as follows: For pore size distribution density function Taking the natural logarithm of both sides, we get: ， make: ， but: ， in, , , This represents an intermediate parameter, and m represents the number of data sets. Create a data group and obtain the data set ; Calculate the coefficients j=0, 1, 2, 3, 4 and F(r i ), j=0, 1, 2; Establish a parameter matrix and obtain intermediate parameters. , and ; ， intermediate parameters , and Substitute constant ,constant and constant The expression is used to obtain the fitted constant. ,constant and constant ; 。 4. The method for determining shale matrix permeability based on pore size distribution according to claim 1, characterized in that, The tortuosity of the shale pores The expression is: ， in, This indicates the porosity of shale.

5. The method for determining shale matrix permeability based on pore size distribution according to claim 1, characterized in that, The mean free path of the gas molecules The expression is: ， in, Z represents gas viscosity; P represents gas compressibility factor; R represents simulated test pressure; T represents universal gas constant; and T represents temperature.

6. The method for determining shale matrix permeability based on pore size distribution according to claim 5, characterized in that, The gas viscosity The expression is: ,T=293.15 K。

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