A shale gas apparent permeability prediction method

Abstract

The application discloses a shale gas apparent permeability prediction method, comprising the following steps: step one, collecting an electron microscope image of shale in a target block and performing binaryzation processing; step two, preparing an organic matter size distribution curve; step three, generating a shale two-dimensional digital core; step four, calculating the gas apparent permeability of each grid in the shale two-dimensional digital core; step five, calculating the gas apparent permeability of the entire shale core; step six, judging whether the grid size reaches the characterization unit scale of the shale in the target block; if not, the length of the two-dimensional digital core is increased, and the step three is returned; if yes, the length of the two-dimensional digital core is determined as the characterization unit scale of the shale in the target block, and the gas apparent permeability calculated in the step five is determined as the gas apparent permeability value of the shale in the target block under a given temperature and pressure condition. The application can provide key input parameters for accurate numerical simulation of shale gas.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas extraction, and specifically relates to a method for calculating shale gas permeability. Background Technology

[0002] Shale reservoirs are rich in micro- and nano-sized pores. Due to the large specific surface area of ​​these pores, fluid transport within them is significantly affected by the interactions of molecules on the pore walls. Therefore, the transport of gas, oil, or water in shale cannot be predicted using traditional methods. In particular, for gases (methane) in shale reservoirs, collisions between gas molecules and the pore walls affect gas transport capacity. This effect is generally characterized by the Knudsen number: under typical shale reservoir conditions, depending on the Knudsen number, continuous flow, slip flow, and transitional flow can occur.

[0003] Shale gas reservoirs have small pore sizes and complex pore structures, making conventional displacement methods unsuitable for permeability testing. While unsteady-state methods such as pressure exhaustion are commonly used to evaluate shale flowability, these methods are often time-consuming and costly. Therefore, many researchers have attempted to determine the apparent gas permeability of shale using analytical / semi-analytical modeling. Due to the diverse mineral composition of shale reservoirs, the inconsistent pore wall properties of different minerals lead to variations in gas transport mechanisms, particularly between organic and inorganic pores. For organic pores, in addition to the Knudsen effect, the adsorption / desorption dynamics of adsorbed gas at different pressures and the surface diffusion effect of adsorbed gas must be considered. For inorganic pores, besides the Knudsen effect, the influence of adsorbed water films on the pore walls on gas transport cannot be ignored. Furthermore, the pore size variation patterns of organic and inorganic materials under the same overlying stress differ due to differences in rock mechanical properties. All of the above factors indicate that when modeling and characterizing the apparent permeability of shale, it is necessary to consider organic and inorganic porosity separately. Unfortunately, currently used methods for calculating apparent gas permeability are mainly based on capillary number models or digital cores. These methods either make overly idealistic assumptions about the porous medium of shale (failing to effectively consider the differences between organic and inorganic matter) or have a small scale of application, making them difficult to use in engineering. Therefore, there is an urgent need to establish a method for calculating apparent gas permeability that can consider the different transport mechanisms of organic and inorganic matter and can also characterize the unit scale.

[0004] To this end, this invention proposes a method for calculating apparent gas permeability based on Monte Carlo random sampling. Based on parameters such as organic matter cluster distribution curves, organic / inorganic pore size distribution curves, and temperature and pressure conditions, a two-dimensional core representing the unit scale is established, and the apparent gas permeability of shale is obtained using geostatistical methods. Summary of the Invention

[0005] To overcome the aforementioned shortcomings of existing technologies, this invention proposes a method for predicting the apparent permeability of shale gas that can take into account the differences in the transport mechanisms of organic and inorganic matter in shale and characterize the unit scale, thus laying the foundation for accurate numerical simulation of shale gas reservoirs.

[0006] The technical solution adopted by this invention to solve its technical problem is: a method for predicting the apparent permeability of shale gas, comprising the following steps:

[0007] Step 1: Acquire electron microscopy images of the shale in the target block and perform binarization processing;

[0008] Step 2: Construct an organic matter size distribution curve;

[0009] Step 3: Generate a two-dimensional digital core of the shale;

[0010] Step 4: Calculate the apparent gas permeability of each grid in the shale two-dimensional digital core.

[0011] Step 5: Calculate the apparent gas permeability of the entire shale core;

[0012] Step 6: Determine if the grid size meets the characterization unit scale of the target block shale. If not, increase the side length of the two-dimensional digital core and return to Step 3. If yes, determine the side length of the two-dimensional digital core as the characterization unit scale of the target block shale, and simultaneously determine the apparent gas permeability calculated in Step 5 as the apparent gas permeability value of the target block shale under given temperature and pressure conditions.

[0013] Compared with the prior art, the positive effects of the present invention are:

[0014] This invention innovatively considers the transport mechanisms of organic and inorganic matter when calculating the apparent permeability of shale gas. For organic matter, it considers the Knudsen effect, adsorption / desorption effect, surface diffusion effect, real gas effect, and stress sensitivity effect. For inorganic matter, it considers the Knudsen effect, real gas effect, and stress sensitivity effect. This invention can provide key input parameters for accurate numerical simulation of shale gas and has important theoretical and practical significance. Attached Figure Description

[0015] The present invention will be described by way of example and with reference to the accompanying drawings, wherein:

[0016] Figure 1 This is a flowchart of the method of the present invention;

[0017] Figure 2 This is the size distribution curve of organic matter;

[0018] Figure 3Input parameters for the pore size distribution of organic and inorganic matter;

[0019] Figure 4 Organic matter distribution map obtained by Monte Carlo random sampling method;

[0020] Figure 5 This is a diagram showing the apparent permeability distribution of gas with a two-dimensional size of 100*100μm.

[0021] Figure 6 The apparent permeability of gas in the target block is defined as the pressure range of 0.7–3.5 MPa. Detailed Implementation

[0022] A method for predicting apparent gas permeability in shale, such as Figure 1 As shown, it includes the following steps:

[0023] S1: Use micron-level CT or scanning electron microscope (SEM) to scan and observe the shale of the target block. Use image processing software to binarize the scanned images. During the binarization process, pay attention to removing noise interference.

[0024] S2: In the binarized image, the size of organic matter clusters is statistically analyzed to obtain the organic matter cluster size distribution curves of different scanned images. Then, these curves are normalized to obtain the "organic matter size distribution curve" that is representative of the current block.

[0025] S3: In two-dimensional space, generate square grids of a certain size, each grid representing a porous medium of uniform diameter. Based on the "organic matter size distribution curve" obtained from S2 using the Monte Carlo sampling method, select a value and assign it to a randomly selected grid of the corresponding size. These grids are considered to represent organic matter, while the unselected grids represent inorganic matter. Repeat the selection and assignment process multiple times until the organic matter volume ratio in the square two-dimensional space matches the organic matter volume ratio of the actual block.

[0026] S4: The pore size distribution at a slightly larger scale (above 100 nm) of the target core is obtained using mercury intrusion porosimetry, and the pore size distribution at a slightly smaller scale (below 100 nm) of the target core is obtained using low-temperature nitrogen adsorption method, thus obtaining the first full-scale pore size distribution of the core; cores obtained from adjacent locations are selected and the organic matter in the core is corroded with chemical agents such as NaOCl, and the second full-scale pore size distribution of the shale is obtained again using mercury intrusion porosimetry and nitrogen adsorption method. After correcting for the size of the organic matter clusters, this pore size distribution is the pore size distribution of the inorganic matter; the pore size distribution of the organic matter is obtained by subtracting the second inorganic matter pore size distribution from the first pore size distribution.

[0027] S5: Traverse the grid of the two-dimensional digital core in S3. If the traversed grid is an organic matter grid, randomly sample and assign the value to the organic matter pore size distribution curve obtained in S4. If the traversed grid is an inorganic matter grid, randomly sample and assign the value to the inorganic matter pore size distribution curve obtained in S4, until all grids are assigned the corresponding pore size.

[0028] S6: Based on the pore size of each grid, the apparent permeability of each grid in the two-dimensional digital core is calculated using the following formula;

[0029] ① The apparent gas permeability of the organic matter grid is calculated using the following formulas (1) to (3). This calculation method takes into account the Knudsen effect of gas in organic matter, the adsorption / desorption dynamic effect of adsorbed gas, the surface diffusion effect, the real gas effect, and the stress sensitivity effect:

[0030]

[0031] Where θ is the real gas coverage, a dimensionless quantity θ = p / Z / (p / Z+p L ); p and p L These are the current pore pressure and Langmuir pressure, respectively, in Pa; d m α is the molecular diameter of the gas, in meters; α0 is the coefficient of the rarefied gas under the condition Kn→∞; α1 and β are fitting constants; κ b and κ m These are the blocking rate and the migration rate, respectively, in m / s; when κ m >κ b At this time, gas molecules move forward, surface diffusion occurs, H(1-κ) m / κ b ) = 1; conversely, when κ = 1. m <κ b At this time, gas molecules are blocked, surface diffusion stops, H(1-κ) m / κ b ) = 1; It is the surface diffusion coefficient when the gas coverage is 0, m 2 / s, ΔH is the isothermal heat of adsorption when the gas coverage is 0, J / mol; τ is the tortuosity; T is the absolute temperature, K; R is the universal gas constant, Pa·mol. -1 ·K -1 M is molecular weight, g / mol; N A This is Avogadro's constant. Kn is the value considering real gas effects.

[0032]

[0033] Where A1, A2, and A3 are fitting constants; μgi The gas viscosity under standard conditions is expressed in mPa·s; p r =p / p c ,T r =T / T c ,p c and T c These are the critical pressure and critical temperature, respectively; Z is the compressibility coefficient.

[0034]

[0035] in and These are the initial porosity and the porosity under maximum stress, respectively. K(p) and K(p) are the current porosity and permeability of the matrix, respectively, with units of dimensionless and nD; η and ψ are the stress sensitivity coefficients of porosity and permeability, respectively, in Pa. -1 ;p i It is the original gas reservoir pressure, Pa; r i It is the actual radius of the organic pores, in meters. ② For the apparent gas permeability of the inorganic mesh, the following formulas (4) to (5) are used for calculation. This calculation method takes into account the Knudsen effect, real gas effect and stress sensitivity effect of the gas in the inorganic material:

[0036]

[0037]

[0038] Where w is the width of the inorganic pores; h i It is the actual radius of the inorganic pores, in meters (m).

[0039] S7: Based on the apparent permeability values ​​of each grid obtained in S6, the overall apparent permeability of the two-dimensional core is obtained using an averaging algorithm. The average permeability of the shale matrix can be expressed as:

[0040]

[0041] Where m and n are the number of grid cells in the vertical and horizontal directions, respectively; K x,y It is the grid permeability at coordinates x and y.

[0042] S8: Increase the side length of the two-dimensional square digital core in S3, and repeat the work of steps S3 to S7. Calculate the apparent permeability of the two-dimensional core more than 50 times at each scale. When the difference in the apparent permeability values ​​of 50 calculations at a certain size is less than 0.1%, the size is considered to be the characterization unit scale of the shale in the target block (generally between micrometer and millimeter scale). At the same time, the apparent permeability calculated at this size is the gas apparent permeability value of the shale in the target block under given temperature and pressure conditions.

[0043] The prediction results of the method of the present invention were verified by the following embodiments:

[0044] The shale in the target block was observed using a scanning electron microscope (SEM). The images acquired were binarized and normalized to obtain the "organic matter size distribution curve," as shown below. Figure 2 As shown. A combination of mercury intrusion porosimetry, low-temperature nitrogen adsorption, and NaOCl chemical treatment was used to obtain the pore size distribution of organic and inorganic matter in the target block shale, as shown. Figure 3 As shown in Table 1 below, the relevant reservoir parameters and other basic parameters of the target block were collected.

[0045] Table 1 shows the model input parameters for the example.

[0046]

[0047] A 100*100μm two-dimensional grid was generated. By randomly sampling data from the "organic matter size distribution curve" and assigning it to the two-dimensional grid, a two-dimensional digital core of shale with a certain organic matter size distribution was generated. Figure 4 As shown in the figure, the black part represents organic matter and the white part represents inorganic matter. Data from the "organic matter pore size distribution curve" is randomly sampled and assigned to the organic matter grid. Similarly, data from the "inorganic matter pore size distribution curve" is randomly sampled and assigned to the inorganic matter grid. The apparent gas permeability of the organic and inorganic matter grids is calculated according to formulas (1)-(5). The results are shown in the figure. Figure 5 As shown.

[0048] The apparent gas permeability of the entire shale core was estimated using formula (6). The results of 50 calculations at this scale ranged from 100 nD to 400 nD, failing to meet the condition that the difference in permeability values ​​between calculations was less than 0.1%, indicating that the generated two-dimensional grid scale was smaller than the characterization unit scale. Continuing the numerical calculations by increasing the grid scale by 5 μm each time, when the calculated two-dimensional grid scale was greater than 160*160 μm, the calculated apparent gas permeability was found to be approximately 212 nD, and the difference in permeability values ​​between calculations was less than 0.1%, indicating that the characterization unit scale of the target block shale had been reached. This permeability is the apparent gas permeability under the conditions of a temperature of 294.26 K and a pressure of 2 MPa in the target block. Further, by changing the pressure range, the apparent gas permeability of the target block was obtained within the pressure range of 0.7–3.5 MPa, as shown below. Figure 6 As shown.

Claims

1. A method for predicting apparent gas permeability in shale, characterized in that: Includes the following steps: Step 1: Acquire electron microscopy images of the shale in the target block and perform binarization processing; Step 2: Construct an organic matter size distribution curve; Step 3: Generate a two-dimensional digital core of the shale; Step 4: Calculate the apparent gas permeability of each grid in the shale two-dimensional digital core. Step 5: Calculate the apparent gas permeability of the entire shale core; Step 6: Determine if the grid size reaches the characterization unit scale of the target block shale: If not, increase the side length of the two-dimensional digital core and return to Step 3; if yes, determine the side length of the two-dimensional digital core as the characterization unit scale of the target block shale, and at the same time determine the apparent gas permeability calculated in Step 5 as the apparent gas permeability value of the target block shale under the given temperature and pressure conditions. The apparent gas permeability of the organic matter grid is calculated using the following formula: In the formula, θ It is the true gas coverage, a dimensionless quantity. θ=p / Z / ( p / Z+ p L ), p and p L These are the current pore pressure and Langmuir pressure, respectively. d m It is the diameter of the gas molecules; α 0 yes Kn Coefficient of rarefied gas under →∞ conditions; α 1 and β It is the fitting constant; κ b and κ m These are the blocking rate and the migration rate, respectively. when κ m > κ b At this time, gas molecules move forward, surface diffusion occurs, H(1- κ m / κ b )=1; Conversely, when κ m < κ b At this time, gas molecules are blocked, surface diffusion stops, and H(1- κ m / κ b )=1; ΔH It is the isothermal heat of adsorption when the gas coverage is 0; τ It is the degree of curvature; T It is absolute temperature; R It is a universal gas constant; M It refers to molecular weight; N A It is Avogadro's constant; A 1 , A 2, A 3 These are all fitting constants; μ gi It is the gas viscosity under standard conditions; p r = p / p c , T r = T / T c , p c and T c These are the critical pressure and the critical temperature, respectively. Z It is the compression factor; d m It is the diameter of the gas molecules; r i It is the actual radius of the organic matter pores; φ i and φ r These are the initial porosity and the porosity under maximum stress, respectively. φ ( p ) represents the current porosity of the matrix.

2. The method for predicting apparent permeability of shale gas according to claim 1, characterized in that: The method for generating the organic matter size distribution curve in step two is as follows: In the image after binarization, the size of the organic matter clusters is statistically analyzed to obtain the organic matter cluster size distribution curves of different scanned images. Then, these curves are normalized to obtain the organic matter size distribution curve of the target block shale image.

3. The method for predicting apparent permeability of shale gas according to claim 1, characterized in that: Step 3 describes the method for generating a two-dimensional digital core of shale, which includes the following steps: Step 1: Generate a square grid of a preset size in two-dimensional space; The second step is to select a value from the organic matter size distribution curve using the Monte Carlo sampling method and assign it to a randomly selected grid of the corresponding size, and use this grid to represent the organic matter. Step 3: Determine whether the volume ratio of organic matter in the two-dimensional space is equal to the actual value: If not, return to step 2; If so, proceed to step four; Step 4: Determine the organic and inorganic pore size distributions of the shale in the target block; Step 5: Assign pore size distributions to the organic and inorganic meshes respectively, and treat each mesh as an equivalent porous medium of equal diameter.

4. The method for predicting apparent permeability of shale gas according to claim 3, characterized in that: The method for determining the pore size distribution of organic and inorganic matter in the target block shale in step four is as follows: The pore size distribution above 100 nm in the target core is obtained using mercury intrusion porosimetry, and the pore size distribution below 100 nm in the target core is obtained using low-temperature nitrogen adsorption, thus obtaining the full-scale pore size distribution of the core, denoted as value one; Cores obtained from adjacent locations are selected, and the organic matter in the cores is corroded using a chemical agent. The full-scale pore size distribution of the shale is then obtained again using mercury intrusion porosimetry and nitrogen adsorption, denoted as value two. The pore size distribution of inorganic matter is obtained by correcting the size distribution of organic matter clusters in value two, denoted as value three; The pore size distribution of organic matter is obtained by subtracting value three from value one.

5. The method for predicting apparent permeability of shale gas according to claim 3, characterized in that: The method for assigning pore size distributions to organic and inorganic meshes in step 5 is as follows: traverse the mesh in two-dimensional space. If the traversed mesh is an organic mesh, randomly sample and assign values ​​to that mesh on the organic pore size distribution curve; if the traversed mesh is an inorganic mesh, randomly sample and assign values ​​to that mesh on the inorganic pore size distribution curve, until all meshes are assigned the corresponding pore size.

6. The method for predicting apparent permeability of shale gas according to claim 1, characterized in that: The apparent gas permeability of the inorganic grid is calculated using the following formula: In the formula, w It is the width of the pores in the inorganic material; h i It is the actual radius of the inorganic pores.

7. The method for predicting apparent permeability of shale gas according to claim 6, characterized in that: The apparent gas permeability of the entire shale core is calculated using the following formula: In the formula, m and n These are the number of grid cells in the vertical and horizontal directions, respectively. K x,y The coordinates are x and y Grid penetration rate at location.

8. The method for predicting apparent permeability of shale gas according to claim 1, characterized in that: The method for determining whether the grid size reaches the characterization unit scale of the target block shale in step six is ​​as follows: the apparent permeability of the two-dimensional digital core is calculated more than 50 times for each size. When the difference in the apparent permeability values ​​calculated 50 times for a certain size is less than 0.1%, it is determined that the size reaches the characterization unit scale of the target block shale.

9. The method for predicting apparent permeability of shale gas according to claim 1, characterized in that: The characterization unit scale of the target block shale is between micrometer and millimeter.

Images