Method for detecting gas starting pressure of water-containing coal seam microcosmic pore

Abstract

This invention discloses a method, system, and storage medium for detecting the gas initiation pressure in the micropores of water-bearing coal seams. The core of this method lies in: First, establishing a fractal model to quantify the water saturation of adsorption pores and seepage pores, a boundary layer model to quantify the water film thickness within the pores, and a calculation model to determine the critical diameters of both. Second, establishing apparent velocity models for gas movement in adsorption pores, seepage pores, and pore throats. Next, combining the above models, constructing a calculation model for the total fluid flow rate per unit cross-section of the coal body, considering pore structure, water saturation, and water film thickness. Finally, by setting the total flow rate to zero, the gas initiation pressure gradient is calculated. This invention, by coupling factors such as pore microstructure, dynamic water saturation, effective stress, boundary layer effect, and local resistance in the pore throat, more closely reflects the complex pore structure and dynamic water-bearing conditions in actual coalbed methane drainage processes, achieving accurate and dynamic prediction of the gas initiation pressure during drainage.

Description

Technical Field

[0001] This invention relates to the field of gas start-up pressure detection technology in coalbed methane development, and particularly to a method for detecting the gas start-up pressure in microscopic water-bearing pores during the coalbed methane drainage process. Background Technology

[0002] In water-bearing coal seams, the coal body has a complex pore structure, and gas often exists in an adsorbed state on the coal matrix, while being confined by fractures and water. In the initial stage of gas flow, the flow exhibits "non-Darcy" behavior; only when the pressure exceeds the initiation pressure can the gas desorb, diffuse, and enter the fracture system to achieve seepage. The initiation pressure is the minimum pressure or pressure gradient required for gas to overcome various flow resistances such as capillary forces, adsorption forces, and viscous resistance to achieve effective flow. Especially in deep coal seams (burial depth > 2000m), which generally exhibit high stress, high water content, and low porosity and permeability, the initiation pressure becomes a key threshold determining "whether gas can be produced" and "when gas will be produced." Predicting the initiation pressure gradient of water-bearing coal bodies is crucial for revealing the adsorption-desorption-seepage coupling mechanism and improving the nonlinear seepage theory of coalbed methane (initiation pressure gradient model). However, the influence of pore morphology and complexity on the initiation pressure gradient has not been fully explored. The starting pressure gradient of coalbed methane varies significantly under different microstructures and water-bearing conditions. The complex pore structure inside the coal body and the complex interaction law of the gas-water two-phase fluid make it difficult to accurately predict the starting pressure gradient, which has become a key factor restricting the efficient development of coalbed methane.

[0003] Currently, there are some achievements in the calculation of the gas initiation pressure gradient in water-bearing pores. The calculation methods proposed by scholars either only rely on permeability and fracture size to calculate the initiation pressure gradient (CN120465912A) or only consider the influence of effective stress and water saturation (CN120489862A). However, the water saturation and effective stress of coalbed methane change continuously during the drainage process. Static water saturation cannot be used as a parameter to describe the initiation pressure gradient. Moreover, the initiation pressure gradient is strongly correlated with water saturation, effective stress, coal body structure, etc. The influence of multiple factors on the initiation pressure gradient needs to be considered. Therefore, it is necessary to obtain the gas initiation pressure gradient in water-bearing coal seams more accurately. Summary of the Invention

[0004] In view of this, the present invention provides a method for detecting the gas initiation pressure in the micropores of water-bearing coal seams, so as to solve the technical problem of accurately obtaining the gas initiation pressure gradient in coal seams under the influence of various factors such as water saturation, effective stress, and coal structure.

[0005] The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams according to the present invention includes the following measures:

[0006] A fractal model for water saturation is established to quantify the water saturation of adsorption pores and seepage pores in water-bearing coal seams; a boundary layer model is established to quantify the water film thickness in adsorption pores and seepage pores; and a critical diameter calculation model is established to quantify the critical diameter of adsorption pores and seepage pores.

[0007] Establish an apparent velocity model for adsorption pore gas to quantify the apparent velocity of gas movement in adsorption pores, an apparent velocity model for seepage pore gas to quantify the apparent velocity of gas movement in seepage pores, and an apparent velocity model for pore throat gas to quantify the apparent velocity of gas movement at the pore throat.

[0008] A flow calculation model is established to quantify the total flow rate of fluid per unit cross-section in a coal body. The flow calculation model includes the relationship between the total flow rate and the pore water saturation, the thickness of the water film in the pores, and the apparent velocity of gas in the pores.

[0009] A pressure calculation model is established to quantify the gas initiation pressure gradient in microscopic water-bearing pores during coalbed methane drainage. The pressure calculation model includes parameters determined by the flow calculation model. The gas initiation pressure gradient is obtained by setting the total flow rate in the calculation model to zero.

[0010] Furthermore, the expression for the fractal model of water saturation in the seepage pores is as follows:

[0011] (1)

[0012] In the formula, Indicates the initial water content of the seepage pores. This represents the effective stress change. Indicates the pressure sensitivity coefficient;

[0013] The expression for the fractal model of water saturation of the adsorption pores is as follows:

[0014] (2)

[0015] In the formula, It represents the total water saturation in the pores.

[0016] Furthermore, the expression for the boundary layer model is as follows:

[0017] (3)

[0018] In the formula, The thickness of the boundary layer, Indicates the pore diameter.

[0019] Furthermore, the expression for the critical diameter calculation model is as follows:

[0020] (4)

[0021] In the formula, Indicates the maximum pore diameter. Indicates porosity. This represents the fractal dimension of the aperture area.

[0022] Furthermore, the expression for the apparent velocity model of the adsorbed pore gas is as follows:

[0023] (5)

[0024] In the formula: This represents the apparent velocity of adsorbed pore gas. Indicates pore pressure, Indicates the pore length. Indicates the viscosity coefficient of the gas. Indicates the viscosity coefficient of a liquid; Indicates the effective diameter of the water-bearing pores. .

[0025] Furthermore, the expression for the apparent velocity model of the seepage pore gas is as follows:

[0026] (6)

[0027] In the formula, This represents the apparent velocity of gas flowing through the pores. This indicates the porosity of the seepage pores.

[0028] Furthermore, the expression for the apparent velocity model of the pore throat gas is as follows:

[0029] (7)

[0030] In the formula, The calculation formula is:

[0031] (8)

[0032] In the formula, Indicates the diameter of the throat. Indicates particle diameter;

[0033] The orifice-throat ratio is expressed by the following formula:

[0034] (9)

[0035] This represents the average capillary diameter in an aqueous porous medium. The calculation formula is:

[0036] (10)

[0037] The number of throats in a single pore is represented by the following formula:

[0038] (11)

[0039] The fractal dimension, representing tortuosity, is calculated using the following formula:

[0040] (12)

[0041] This indicates the fluid density.

[0042] Furthermore, the expression for the flow calculation model is as follows:

[0043] (13)

[0044] In the formula, The fractal dimension of the pore area represents the adsorption pore size. The fractal dimension of the pore area represents the seepage pores. Indicates the effective diameter of the largest pore. , Indicates the effective diameter of the smallest pore. .

[0045] Furthermore, the expression for the pressure calculation model is as follows:

[0046] (14)

[0047] In the formula, For the gas initiation pressure gradient, b and c are parameters determined by the flow calculation model, and their expressions are as follows:

[0048] ,

[0049] ,

[0050] .

[0051] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-described method for detecting the gas start-up pressure in the micropores of water-bearing coal seams.

[0052] The present invention also provides a microporous gas start-up pressure detection system for water-bearing coal seams, which includes the aforementioned computer-readable storage medium, a processor executing the computer program, a data input module connected to the processor, and a data output module connected to the processor.

[0053] The beneficial effects of this invention are:

[0054] This invention reveals the mechanism by which pore size affects gas flow resistance under water-bearing conditions by constructing fractal models and critical diameter models of water saturation for adsorption pores and seepage pores. Furthermore, it establishes apparent gas velocity models for adsorption pores, seepage pores, and pore throats, and, combined with pore structure and water saturation characteristics, presents an improved flow rate calculation model. Finally, by coupling local resistance loss and boundary layer effects, a calculation model for the gas initiation pressure in micro-scale water-bearing pores is constructed, adaptable to dynamically changing conditions. This model not only considers the influence of water saturation and effective stress but also reveals the coupling effects of pore type, scale distribution, and water-gas interaction on the initiation pressure. Compared with existing technologies, the detection method proposed in this invention better reflects the complex pore structure and dynamic water-bearing conditions in actual coalbed methane drainage processes, enabling more accurate detection of the initiation pressure of water-bearing coalbed methane. It provides key parameter support for the efficient development and low-carbon drainage technology of deep coalbed methane and also provides important reference for the improvement of unconventional natural gas non-Darcy flow theory and the optimization of calculation methods. Attached Figure Description

[0055] Figure 1 This is a logic flowchart of the detection method of the present invention;

[0056] Figure 2 This is a flowchart of experimental data acquisition and parameter acquisition in an embodiment of the present invention;

[0057] Figure 3 This is a numerical comparison chart of the experimental and detection methods for the initiation pressure gradient of gas in microscopic water-bearing pores in this invention.

[0058] Figure 4 A system for detecting the starting pressure of gas in microscopic water-bearing pores. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0060] Example 1:

[0061] The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams in this embodiment includes the following measures:

[0062] A fractal model for water saturation is established to quantify the water saturation of adsorption pores and seepage pores in water-bearing coal seams; a boundary layer model is established to quantify the water film thickness within adsorption pores and seepage pores; and a critical diameter calculation model is established to quantify the critical diameter of adsorption pores and seepage pores. Pores with diameters smaller than the critical diameter are classified as adsorption pores, where the pore space is completely filled with water; pores with diameters larger than the critical diameter are classified as seepage pores, where some residual water exists on the pore surface and forms a water film on the pore wall surface.

[0063] An apparent velocity model for gas in adsorption pores is established to quantify the apparent velocity of gas in adsorption pores, an apparent velocity model for gas in seepage pores is established to quantify the apparent velocity of gas in seepage pores, and an apparent velocity model for gas in pore throats is established to quantify the apparent velocity of gas in pore throats.

[0064] A flow calculation model is established to quantify the total flow rate of fluid per unit cross-section within a coal body. The flow calculation model includes the relationship between the total flow rate and the pore water saturation, the thickness of the water film in the pores, and the apparent velocity of gas in the pores.

[0065] A pressure calculation model is established to quantify the gas initiation pressure gradient in microscopic water-bearing pores during coalbed methane drainage. The pressure calculation model includes parameters determined by the flow calculation model. The gas initiation pressure gradient is obtained by setting the total flow rate in the calculation model to zero.

[0066] In this embodiment, the expression for the fractal model of the water saturation of the seepage pores is as follows:

[0067] (1)

[0068] In the formula, Indicates the initial water content of the seepage pores. This represents the effective stress change (which can be calculated from downhole pressure gauge monitoring data). This represents the pressure sensitivity coefficient (which can be experimentally measured; for example, using a rock core, setting two confining pressures of 18-12 MPa, stabilizing each pressure for 10 minutes, and automatically saving the T2 spectrum). Follow The linear slope, One-time calibration, applicable to the same block.

[0069] The expression for the fractal model of water saturation of the adsorption pores is as follows:

[0070] (2)

[0071] In the formula, It represents the total water saturation in the pores.

[0072] The model directly links the start-up pressure to the dynamic drainage process, and the water saturation in the seepage pores is considered. Includes effective stress The changing terms mean that the prediction of the starting pressure is no longer a static value, but can respond to pressure changes caused by drainage.

[0073] The expression for the boundary layer model is as follows:

[0074] (3)

[0075] In the formula, The thickness of the boundary layer, This represents the pore diameter. The boundary layer model is directly related to water saturation.

[0076] The expression for the critical diameter calculation model is as follows:

[0077] (4)

[0078] In the formula, Indicates the maximum pore diameter. Indicates porosity. This represents the fractal dimension of the aperture area.

[0079] The process of establishing the apparent velocity model of the adsorbed pore gas includes:

[0080] Assume that the gas and liquid flow simultaneously along the boundary layer in the adsorption pore, the fluid flow is in a steady state, and the fluid has no acceleration;

[0081] According to Newton's second law, the driving force equals the viscous force, and the calculation formula is:

[0082]

[0083] In the formula, Indicates pore pressure, Indicates the pore length. Indicates the viscosity coefficient of the gas. Indicates the viscosity coefficient of a liquid. This represents the apparent velocity of the adsorbed pore gas, from which we can obtain:

[0084]

[0085]

[0086] In the formula, C is an additional term. Since the liquid velocity at the boundary layer is zero, the apparent velocity model of the adsorbed pore gas is obtained, and the calculation formula is as follows:

[0087] (5)

[0088] In the formula: This represents the apparent velocity of adsorbed pore gas. Indicates pore pressure, Indicates the pore length. Indicates the viscosity coefficient of the gas. Indicates the viscosity coefficient of a liquid; Indicates the effective diameter of the water-bearing pores. .

[0089] The process of establishing the apparent velocity model of the seepage pore gas includes:

[0090] The flow of gas in the seepage pores is affected by the original structure of the coal body and the boundary layer. Based on the HP equation and considering the boundary layer effect, the formula for calculating the gas velocity in a single pore is defined as follows:

[0091]

[0092] In the formula, This represents the gas velocity within a single pore. The average velocity of the fluid within a capillary is the ratio of the velocity to the capillary cross-sectional area, calculated using the following formula:

[0093]

[0094] In the formula, This represents the pressure gradient in the pores. , This represents the cross-sectional area of ​​the capillary.

[0095] Relationship between average velocity and apparent velocity of fluid in porous media Therefore, the apparent velocity model of the seepage pore gas is calculated.

[0096] (6)

[0097] In the formula, This represents the apparent velocity of gas flowing through the pores. This indicates the porosity of the seepage pores.

[0098] The process of establishing the apparent velocity model of the pore throat gas includes:

[0099] The formula for calculating the porosity of the pore throat is defined as follows:

[0100]

[0101] In the formula, Indicates the diameter of the throat. Indicates the pore diameter. Indicates the pore-throat ratio;

[0102] The porosity of the pore throat is equal to the porosity of the porous medium; therefore, the formulas for calculating the diameter of the pore and the diameter of the throat are:

[0103]

[0104]

[0105] The pore-throat ratio of the model is the ratio of the pore diameter to the throat diameter. The calculation formula is:

[0106]

[0107] Calculate local kinetic energy loss in porous media pipes The calculation formula is:

[0108]

[0109] In the formula, This represents the local kinetic energy loss coefficient. Represents gravitational acceleration;

[0110] The total kinetic energy loss of the fluid flowing through the orifice throat is calculated using the following formula:

[0111]

[0112] The pressure drop of the fluid passing through the orifice throat is calculated using the following formula:

[0113]

[0114] In the formula, Indicates fluid density;

[0115] The pressure drop at the orifice throat is calculated using the following formula:

[0116]

[0117] The pore length is defined as equal to the average pore diameter, and the number of pore throats in a single pore is... Therefore, the governing equation for the total pressure drop in porous media considering local resistance losses is obtained, and the calculation formula is as follows:

[0118]

[0119] In the formula, Given the average capillary diameter in a water-containing porous medium ;

[0120] Calculation of the apparent gas velocity model considering the pore throat structure ( The calculation formula is:

[0121] (7).

[0122] The process of establishing the flow calculation model includes:

[0123] The formula for calculating the flow rate of fluid in a single pore is as follows:

[0124]

[0125] The total flow rate of fluid per unit cross-section within the coal seam is the integral of the flow rate through a single pore, calculated using the following formula:

[0126] (8)

[0127] In the formula, The fractal dimension of the pore area represents the adsorption pore size. The fractal dimension of the pore area represents the seepage pores. Indicates the effective diameter of the largest pore. , Indicates the effective diameter of the smallest pore. .

[0128] The expression for the pressure calculation model is as follows:

[0129] (9)

[0130] In the formula, For the gas initiation pressure gradient, b and c are parameters determined by the flow calculation model, and their expressions are as follows:

[0131] ,

[0132] ,

[0133] .

[0134] Taking a coalbed methane field as an example, the initial water cut and microstructure parameters of the coal seam seepage pores were measured based on nuclear magnetic resonance experiments. Other required parameter values ​​are shown in Table 1.

[0135] Table 1 Parameter Values

[0136]

[0137] Substituting the above data and the microstructure data obtained from NMR into equation (9), the pore gas pressure gradient curves of water-bearing coal under different pressure conditions can be plotted. The pressure gradient value when the flow rate is 0 is the starting pressure gradient, and the corresponding pressure value is the starting pressure. Figure 3 As shown in the figure, the vertical axis represents the gas flow rate.

[0138] Example 2: A computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the gas initiation pressure detection method for micropores in water-bearing coal seams as described in Example 1.

[0139] Example 3: A micro-pore gas start-up pressure detection system for water-bearing coal seams, comprising the computer-readable storage medium described in Example 2, a processor executing the computer program, a data input module connected to the processor, and a data output module connected to the processor.

[0140] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for detecting the initiation pressure of gas in the fine pores of a water-bearing coal seam, characterized in that: Including the following measures: A fractal model for water saturation is established to quantify the water saturation of adsorption pores and seepage pores in water-bearing coal seams; a boundary layer model is established to quantify the water film thickness in adsorption pores and seepage pores; and a critical diameter calculation model is established to quantify the critical diameter of adsorption pores and seepage pores. Establish an apparent velocity model for adsorption pore gas to quantify the apparent velocity of gas movement in adsorption pores, an apparent velocity model for seepage pore gas to quantify the apparent velocity of gas movement in seepage pores, and an apparent velocity model for pore throat gas to quantify the apparent velocity of gas movement at the pore throat. A flow calculation model is established to quantify the total flow rate of fluid per unit cross-section in a coal body. The flow calculation model includes the relationship between the total flow rate and the pore water saturation, the thickness of the water film in the pores, and the apparent velocity of gas in the pores. A pressure calculation model is established to quantify the gas initiation pressure gradient in microscopic water-bearing pores during coalbed methane drainage. The pressure calculation model includes parameters determined by the flow calculation model. The gas initiation pressure gradient is obtained by setting the total flow rate in the calculation model to zero.

2. The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams according to claim 1, characterized in that: The expression for the fractal model of water saturation in the seepage pores is as follows: （1） In the formula, Indicates the initial water content of the seepage pores. This represents the effective stress change. Indicates the pressure sensitivity coefficient; The expression for the fractal model of water saturation of the adsorption pores is as follows: （2） In the formula, It represents the total water saturation in the pores.

3. The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams according to claim 2, characterized in that: The expression for the boundary layer model is as follows: （3） In the formula, The thickness of the boundary layer, Indicates the pore diameter.

4. The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams according to claim 2, characterized in that: The expression for the critical diameter calculation model is as follows: （4） In the formula, Indicates the maximum pore diameter. Indicates porosity. This represents the fractal dimension of the aperture area.

5. The method for detecting the gas start-up pressure in the micropores of water-bearing coal seams according to claim 1, characterized in that: The expression for the apparent velocity model of the adsorbed pore gas is as follows: （5） In the formula: This represents the apparent velocity of adsorbed pore gas. Indicates pore pressure, Indicates the pore length. Indicates the viscosity coefficient of the gas. Indicates the viscosity coefficient of a liquid; Indicates the effective diameter of the water-bearing pores. .

6. The method for detecting the gas start-up pressure in the micropores of water-bearing coal seams according to claim 5, characterized in that: The expression for the apparent velocity model of the seepage pore gas is as follows: （6） In the formula, This represents the apparent velocity of gas flowing through the pores. This indicates the porosity of the seepage pores.

7. The method for detecting the gas start-up pressure in the micropores of water-bearing coal seams according to claim 1, characterized in that: The expression for the apparent velocity model of the pore throat gas is as follows: （7） In the formula, The calculation formula is: （8） In the formula, Indicates the diameter of the throat. Indicates particle diameter; The orifice-throat ratio is expressed by the following formula: （9） This represents the average capillary diameter in an aqueous porous medium. The calculation formula is: （10） The number of throats in a single pore is represented by the following formula: （11） The fractal dimension, representing tortuosity, is calculated using the following formula: （12） This indicates the fluid density.

8. The method for detecting the gas start-up pressure in the micropores of water-bearing coal seams according to claim 1, characterized in that: The expression for the flow calculation model is as follows: (13) In the formula, The fractal dimension of the pore area represents the adsorption pore size. The fractal dimension of the pore area represents the seepage pores. Indicates the effective diameter of the largest pore. , Indicates the effective diameter of the smallest pore. .

9. The method for detecting the gas initiation pressure in the micropores of water-bearing coal seams according to claim 8, characterized in that: The expression for the pressure calculation model is as follows: （14） In the formula, For the gas initiation pressure gradient, b and c are parameters determined by the flow calculation model, and their expressions are as follows: ， ， 。 10. A system for detecting the starting pressure of gas in the fine pores of a water-bearing coal seam, characterized in that: The method includes a computer-readable storage medium, a processor for executing the computer program, a data input module connected to the processor, and a data output module connected to the processor. When the computer program is executed by the processor, it implements the method for detecting the gas initiation pressure in the micropores of a water-bearing coal seam as described in any one of claims 1 to 9.

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