Method for identifying master control mass transfer form of coal seam gas migration

Abstract

The invention discloses a method for identifying a coal seam gas migration master control mass transfer form. Comprising the following steps: constructing a unified desorption double-seepage control model by analyzing a mathematical relation between a seepage behavior and a diffusion behavior; the pressure gradient and the flow sectional area of the fracture and the matrix system are calculated by analyzing the mass transfer process under the endogenous gas desorption condition; calculating the flow mass of the gas in the matrix and the fracture through the Darcy law; defining a characteristic permeability ratio through the quantitative relationship of the flow masses; and identifying the master control mass transfer form of coal seam gas migration by analyzing the apparent permeability ratio of the matrix to the fracture. According to the method, the master control mass transfer form of gas migration under the coal seam endogenous gas desorption condition can be accurately, objectively and quickly identified.

Description

Technical Field

[0001] The present invention belongs to the field of mine gas prevention and control, and relates to a method for identifying the main mass transfer form of coal seam gas migration, and specifically, a method for identifying whether the main mass transfer form of gas migration under the condition of coal seam endogenous gas desorption is seepage or diffusion. Background Art

[0002] Coal is a dual-porous medium containing a pore system and a fracture system. The migration process of gas in coal seams can be simply divided into two processes: diffusion and seepage. Both diffusion and seepage have a controlling effect on the migration of gas in coal. For the engineering practice of gas extraction, the gas migration process is one of the key factors affecting gas extraction. Therefore, accurately identifying the main mass transfer form of coal seam gas migration is very important for efficient differentiated gas extraction.

[0003] There are two theories in the academic community: one is the pore diffusion control theory, and the other is the fracture seepage control theory. These two theories often only focus on the gas transport capacity of fractures, but ignore the gas flow rate entering the fractures by diffusion, so they cannot accurately identify the main mass transfer form of gas migration under the conditions of endogenous gas desorption in coal seams. Summary of the invention

[0004] The purpose of the present invention is to provide a method for accurately identifying the main mass transfer form of coal seam gas migration, so as to solve the current technical problem that the main mass transfer form of coal seam gas migration cannot be accurately identified.

[0005] The purpose of the present invention can be achieved by the following technical scheme: by analyzing the mathematical connection between the permeability behavior and the diffusion behavior, a unified desorption and dual permeability control model of the two is constructed; by analyzing the mass transfer process under the desorption condition of endogenous gas, the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system are calculated; by Darcy's law, the flow quality of the gas in the matrix and the fracture is calculated; the characteristic permeability ratio is defined by the quantitative relationship of the flow quality; by analyzing the apparent permeability ratio of the matrix and the fracture, the main mass transfer form of coal seam gas migration is identified, and the specific steps are as follows:

[0006] S1. Construct desorption and dual permeability control model;

[0007] S2. Calculate the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system under the condition of endogenous gas desorption;

[0008] S3. Calculate the flow quality of gas in the matrix and cracks by Darcy's law;

[0009] S4. define characteristic permeability ratio;

[0010] S5. Analyze the ratio of matrix and fracture apparent permeability to identify the main mass transfer mode controlling coal seam gas migration.

[0011] Furthermore, the step S1 derives the mathematical relationship between the apparent permeability and the apparent diffusion coefficient through two approaches: the ideal gas state equation or the formula describing the Klinkenberg effect, and establishes a unified desorption and dual permeability control model for the two.

[0012] Furthermore, the step S2 analyzes the mass transfer process of the series relationship under the endogenous gas desorption condition, and calculates the flow cross-sectional area and pressure gradient of the matrix system and the fracture system;

[0013] Furthermore, the step S3 uses the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system calculated in the step S2 to calculate the flow quality of the gas in the matrix and the fracture by Darcy's law;

[0014] Furthermore, in step S4, the ratio of the apparent permeabilities of the two systems when the gas flow quality in the matrix and the fracture system is equal is ε m / ε f It is defined as the characteristic permeability ratio η;

[0015] Furthermore, the step S5 follows the following principles when determining the main mass transfer form of gas migration: m / ε f >η, the matrix gas flow quality is greater than the fracture gas flow quality, and the main mass transfer form is seepage; when ε m / ε f <η, the matrix gas flow quality is less than the fracture gas flow quality, and the main mass transfer form is diffusion. m / ε f =η, the matrix gas flow quality is equal to the fracture gas flow quality, and diffusion and seepage equally control gas migration;

[0016] Beneficial effects of the present invention:

[0017] 1. The present invention can accurately identify the main controlling mass transfer form of coal seam gas migration.

[0018] 2. The present invention can further explain the influence of the main mass transfer form on the desorption curve. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will be further described below in conjunction with the accompanying drawings.

[0020] Figure 1 A flow chart of the steps of a method for identifying the main control mass transfer form of coal seam gas migration provided by the present invention;

[0021] Figure 2 A microscopic comparison diagram of the seepage main control and the diffusion main control in a method for identifying the main control mass transfer form of coal seam gas migration provided by the present invention;

[0022] Figure 3 A simplified model of the mass transfer process of gas in the matrix and cracks in a method for identifying the main mass transfer form of coal seam gas migration provided by the present invention;

[0023] Figure 4 A COMSOL numerical simulation PDE setting diagram in a method for identifying the main mass transfer form of coal seam gas migration provided by the present invention;

[0024] Figure 5 A COMSOL numerical simulation geometric model establishment diagram in a method for identifying the main mass transfer form of coal seam gas migration provided by the present invention;

[0025] Figure 6 The desorption curve simulation results under different matrix and fracture apparent permeability ratios in a method for identifying the main mass transfer form of coal seam gas migration provided by the present invention; DETAILED DESCRIPTION

[0026] The following will be combined with the accompanying drawings provided by the present invention to further describe the implementation methods in the embodiments of the present invention in detail and completely. It should be understood that the described embodiments are only for illustrating the present invention and are not intended to limit the scope of the present invention. Based on the embodiments mentioned in the present invention, those skilled in the art may make modifications or changes to the present invention, and the equivalent forms after these changes also belong to the protection scope of the present invention.

[0027] The present invention is a method for identifying the main mass transfer form of coal seam gas migration. By analyzing the mathematical connection between permeability behavior and diffusion behavior, a unified desorption dual-permeability control model of the two is constructed; by analyzing the mass transfer process under the desorption conditions of endogenous gas, the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system are calculated; by Darcy's law, the flow quality of gas in the matrix and fracture is calculated; the characteristic permeability ratio is defined by the quantitative relationship of the flow quality; and the main mass transfer form of coal seam gas migration is identified by analyzing the apparent permeability ratio of the matrix and the fracture. The specific steps are:

[0028] S1. Construct a desorption and dual-permeability control model. By analyzing the mathematical connection between permeation behavior and diffusion behavior, a unified desorption and dual-permeability control model is constructed.

[0029] Usually under experimental conditions, the values ​​derived from the diffusion coefficient derived from the measured gas desorption curve or the permeability measured by the transient method are both apparent values, that is, the apparent diffusion coefficient or the apparent permeability. When the pressure and concentration can be converted into each other, the apparent diffusion coefficient and the apparent permeability can be converted into each other.

[0030] For matrix flow, the relationship between pressure and diffusion rate per unit matrix volume is:

[0031] According to Fick's law of diffusion:

[0032] From the ideal gas state equation we can get:

[0033] Combining the above formulas, we can get the relationship between the apparent permeability and apparent diffusion coefficient of coal matrix:

[0034] Where, Q: diffusion rate per unit matrix volume, g / (s·ml); θ: matrix shape factor, cm -2 ; ε m : Coal matrix apparent permeability, m 2 ; ν: kinematic viscosity, m 2 / s;P m , P f : Matrix and fissure gas pressure, MPa; Apparent diffusion coefficient, m 2 / s;c m , c f : matrix and fissure gas concentration, g / ml; M: gas molar mass, g / mol; R: ideal gas constant, 8.314 J / (mol·K); T: gas temperature, K; μ: dynamic viscosity, Pa·s.

[0035] At the same time, the relationship between the apparent permeability and apparent permeability coefficient of coal matrix can also be obtained from the relevant formula of Klinkenberg effect:

[0036] Relationship between coal matrix apparent permeability and its overall permeability:

[0037] in The relationship between the apparent value of the effective diffusion coefficient (apparent diffusion coefficient) and the effective diffusion coefficient is:

[0038] Combining the above formulas, we can get the relationship between the apparent permeability and apparent diffusion coefficient of coal matrix:

[0039] Among them, ε m : Coal matrix apparent permeability, m 2 ; ε: overall permeability of coal matrix, m 2 ;P m : matrix gas pressure, MPa; b: Klinkenberg effective factor; μ: dynamic viscosity, Pa·s; D e : effective diffusion coefficient; Apparent diffusion coefficient.

[0040] S2. Calculate the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system under the condition of endogenous gas desorption. Figure 3 , it is assumed that the endogenous gas desorption process takes place in a parallel plate model and a single-layer crack is taken as an example.

[0041] The pressure gradient calculation formula in the matrix system is:

[0042] The cross-sectional area through which the matrix flows is: S m =la

[0043] The pressure gradient of the fracture system is

[0044] The cross-sectional area of ​​the flow in the crack is: S f =ca

[0045] Among them, P m : Gas pressure in the matrix, MPa; P fx : gas pressure when the pore channel is x meters away from the right end of the fracture channel, MPa; d: thickness of the parallel plate, m; l: length of the parallel plate, m; a: width of the parallel plate, m; c: interval between the two parallel plates, m; S m , S f : Flow cross-sectional area of ​​matrix system and fracture system, m 2 .

[0046] S3. Calculate the flow quality of gas in the matrix and cracks using Darcy's law.

[0047] Assuming that the matrix flow completely enters the fracture flow, since the matrix flow enters the fracture from both the upper and lower directions, the matrix flow should be doubled. Therefore, the flow mass calculation formula of a single matrix gas source is:

[0048] Integrate it to get the total matrix gas flow quality

[0049] The quality of fracture gas flow is

[0050] Among them, Q mi : The flow mass of the gas source in a single matrix, g / s; Q m : Matrix gas flow quality, g / s; Q f : fracture gas flow quality, g / s; ε m , ε f : matrix apparent permeability, fracture apparent permeability, m 2 ; μ: dynamic viscosity, Pa·s; ΔP: pressure drop along the flow direction, MPa;

[0051] S4. Define the characteristic permeability ratio.

[0052] Analyze the quantitative relationship between matrix and fracture gas flow quality. m >Q f At this time, seepage mainly controls gas migration, when Q m f , at this time, diffusion mainly controls gas migration; when Q m =Q f ,Right now At this time, seepage and diffusion have equal control over gas migration. m =Q f , defining the characteristic permeability ratio

[0053] S5. Analyze the ratio of matrix and fracture apparent permeability to identify the main mass transfer form of coal seam gas migration. Analyze the ratio of matrix and fracture apparent permeability in combination with S4 to identify the main mass transfer form of coal seam gas migration.

[0054] When ε m / ε f >η, the matrix flow mass is greater than the fracture flow mass, and the main mass transfer form is seepage; when ε m / ε f <η, the matrix flow mass is less than the fracture flow mass, and diffusion is the main mass transfer mode; when ε m / ε f =η, the matrix flow mass is equal to the fracture flow mass, and diffusion and seepage equally control gas migration.

[0055] Example 1

[0056] Since the pore pressure and fracture pressure are non-uniformly distributed in their respective regions and have geometric distribution characteristics, the exact value of the characteristic permeability ratio k of the matrix permeability and fracture permeability is difficult to determine, and only an approximate order of magnitude can be obtained (the range should be between 0.1 and 0.001). The desorption curve simulation results under different matrix fracture permeability ratios were plotted through COMSOL simulation, and these desorption curves were analyzed to verify the accuracy of the above-mentioned method for identifying the main mass transfer form of coal seam gas migration. The details are as follows:

[0057] The ratio of matrix permeability to fracture permeability is changed, and the PDE module of COMSOL multiphysics software is used for modeling and calculation. Figure 4 , Figure 5 shown.

[0058] ​For ease of understanding, this embodiment compares the desorption process to a model of a water tank and a pipeline in series. Matrix-controlled flow and crack-controlled flow can be respectively compared to the "insufficient water pressure" or "valve throttling" phenomenon in the water supply process. Obviously, when the water flow is not enough to fill the pipeline, the difficulty of the pipeline itself in conveying is unlikely to affect the water outlet speed. When the water pressure reaches a certain level, the water flow rate at the faucet outlet is only related to the size of the faucet valve opening. Similar "underpressure effect" and "throttling effect" also exist in the gas desorption process.

[0059] Figure 6 The results show that when ε m / ε f <η, it belongs to the diffusion-dominated area. In this area, the desorption curve shows the characteristics of achieving a high desorption quality in a short time and a high desorption rate due to the insufficient "throttling" effect of pores and cracks. The desorption curve is getting closer and closer to the y-axis. m / ε f When >η, it belongs to the main seepage control area. With the increase of the pore-fracture permeability ratio, the "throttling" effect of the desorption curve in this area gradually strengthens, showing the characteristics of low speed and long time, and the desorption curve shape is getting closer and closer to the x-axis.

Claims

1. A method for identifying the main mass transfer form of coal seam gas migration, characterized by: By analyzing the mathematical connection between permeability and diffusion behavior, a unified desorption and dual-permeability control model of the two is constructed; by analyzing the mass transfer process under the desorption condition of endogenous gas, the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system are calculated; the flow quality of gas in the matrix and fracture is calculated by Darcy's law; the characteristic permeability ratio is defined by the quantitative relationship of the flow quality; by analyzing the apparent permeability ratio of the matrix and the fracture, the main mass transfer form of coal seam gas migration is identified. The specific steps are as follows: S1. Construct desorption and dual permeability control model; S2. Calculate the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system under the condition of endogenous gas desorption; S3. Calculate the flow quality of gas in the matrix and cracks by Darcy's law; S4. define characteristic permeability ratio; S5. Analyze the ratio of matrix and fracture apparent permeability to identify the main mass transfer mode controlling coal seam gas migration.

2. A method for identifying the main mass transfer form of coal seam gas migration according to claim 1, characterized in that: The step S1 derives the mathematical relationship between the apparent permeability and the apparent diffusion coefficient through two approaches: the ideal gas state equation or the formula describing the Klinkenberg effect, and establishes a unified desorption and dual permeability control model for the two; The ideal gas state equation is a variation of the relationship between concentration and pressure: Where, c: gas concentration, g / mol; M: gas molar mass, g / mol; R: ideal gas constant, 8.314 J / (mol·K); T: gas temperature, K; P: gas pressure, MPa; The formula describing the Klinkenberg effect is: Among them, ε m : Coal matrix apparent permeability, m 2 ; ε: overall permeability of coal matrix, m 2 ;P m : Matrix gas pressure, MPa; b: Klinkenberg effective factor; The desorption and dual permeability control model is a formula for the conversion relationship between the derived apparent permeability and the apparent diffusion coefficient: Among them, ε m : Coal matrix apparent permeability, m 2 ; Apparent diffusion coefficient; μ: dynamic viscosity, Pa·s; P m : Matrix gas pressure, MPa.

3. A method for identifying the main mass transfer form of coal seam gas migration according to claim 1, characterized in that: The step S2 calculates the pressure gradient and flow cross-sectional area of ​​the matrix system and the fracture system by analyzing the mass transfer process of the series relationship under the desorption condition of the endogenous gas; The mass transfer process refers to a mass transfer process in which, under the condition of endogenous gas desorption, the gas desorption first passes through the matrix system and then passes through the fracture system in series; The pressure gradient and flow cross-sectional area are calculated by assuming a single-layer fractured plate model; The single-layer fractured plate model refers to the assumption that a certain fracture microelement is a combination of two parallel plates with a length of l, a width of a, a thickness of d and a spacing of c.

4. A method for identifying the main mass transfer form of coal seam gas migration according to claim 1, characterized in that: The step S3 uses the pressure gradient and flow cross-sectional area of ​​the fracture and matrix system calculated in the step S2 to calculate the flow quality of the gas in the matrix and the fracture by Darcy's law.

5. A method for identifying the main mass transfer form of coal seam gas migration according to claim 1, characterized in that: In step S4, the ratio of the apparent permeabilities of the two systems when the gas flow quality in the matrix and the fracture system is equal is calculated as ε m / ε f Defined as the characteristic permeability ratio η.

6. A method for identifying the main mass transfer form of coal seam gas migration according to claim 1, characterized in that: The method of determining the main mass transfer form of gas migration in step S5 is as follows: m / ε f >η, the matrix gas flow quality is greater than the fracture gas flow quality, and the main controlling factor of flow is fracture flow, that is, the main controlling mass transfer form is seepage; when ε m / ε f <η, the matrix gas flow quality is less than the fracture gas flow quality, and the main controlling factor of the flow is the matrix flow, that is, the main controlling mass transfer form is diffusion; when ε m / ε f =η, the matrix gas flow quality is equal to the fracture gas flow quality, and the equal effects of seepage and diffusion jointly control gas migration.

Images