Method for calculating migration of methane in shale gas reservoir matrix-fracture system under microwave radiation

Abstract

The invention discloses a method for calculating migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation. The method specifically comprises the following steps: collecting physical and mechanical parameters of a shale gas reservoir matrix and engineering parameters of the shale gas reservoir matrix and fracture system; according to the engineering parameters, establishing a geometric model for simulating the shale gas reservoir, and taking the whole geometric model as a computational domain; a mutual coupling relation is established for the computational domains, and then a coupling model covering crack deformation is formed; initial conditions and boundaries are distributed, the separation coupling model is solved, then a dynamic change curve of the content of the methane gas in the matrix and fracture system under microwave radiation is obtained, and the migration track of the methane is obtained. The model integrates the interaction among the electromagnetic effect, solid deformation, fluid and moisture transportation and heat transfer, can effectively evaluate the change of various reservoir parameters under microwave radiation, and can accurately track the dynamic change process of the methane exploitation content in the shale gas reservoir.

Description

Technical Field

[0001] The present invention belongs to the technical field of shale gas exploitation, and particularly relates to a calculation method for methane migration in the matrix-fracture system of shale gas reservoirs under microwave radiation. Background Art

[0002] Shale gas mainly exists in the reservoir in the form of free gas or adsorbed gas, and its main component is methane. Shale gas reservoirs usually have the characteristics of low porosity and permeability, which limits the gas mobility and brings considerable challenges to exploitation. To improve the exploitation rate of shale gas, the key technology of hydraulic fracturing has been widely applied in this field. This technology induces the formation of fractures by injecting high-pressure fluids into the reservoir, improves the shale gas mobility, and thus improves the exploitation efficiency. Although this technology is very effective in exploiting free gas, it has limited influence on the gas existing in the adsorbed state, and the gas in the adsorbed state accounts for 20% - 85% of shale gas, resulting in insufficient development of resources. In addition, the fracturing fluid remains in the rock interior, which may produce a water lock effect, reduce the reservoir permeability, and have an adverse impact on subsequent gas flow and exploitation efficiency. Therefore, the innovation and optimization of gas exploitation technology have become the focus of recent research.

[0003] The hydraulic fracturing assisted technology has emerged as the times require and has attracted wide attention in the field of shale gas exploitation in recent years. Combining microwave thermal stimulation with traditional hydraulic fracturing provides innovative methods and solutions for increasing shale gas production, such as Figure 2 shown, the heating method uses microwaves, that is, electromagnetic waves with frequencies between 300 MHz and 300 GHz, which are characterized by strong penetration ability. Polar molecules in the shale gas reservoir can effectively absorb microwave energy under microwave radiation and convert it into heat energy to achieve rapid heating. Compared with traditional heating methods, microwave heating has many advantages, such as high efficiency, energy saving, selective heating, easy control, etc. These characteristics make microwave thermal stimulation a promising technical tool for shale gas exploitation.

[0004] At present, researchers have made significant progress in the application of microwave-assisted shale gas extraction. For example, through experiments, it has been found that microwave heating can induce rock fractures, forming a dense fracture network, thereby significantly increasing the intrinsic permeability of shale. In addition, this technology enhances the connectivity of the pores initially sealed within the formation, which is crucial for shale gas flow. Through comparative analysis of shale before and after microwave treatment, it has been found that the maximum methane adsorption capacity has decreased by 16.38%, highlighting the impact of microwave heating on methane adsorption and desorption behavior. In addition, through numerical simulation, it has been proven that microwave radiation can effectively increase the pore volume and fracture width, which is crucial for enhancing shale gas production. By establishing a fully coupled electromagnetic-thermal-fluid model, it has been pointed out that microwave heating can significantly promote shale gas extraction. In addition to the above research on the thermal effect of microwave radiation, its significant impact on the moisture in the shale gas reservoir has also been explored. It has been found that microwave heating can effectively change the moisture state, thereby reducing the water lock effect and changing the characteristics of the water-gas two-phase flow. The evaporation of liquid water in the reservoir changes the water saturation, thereby affecting the production behavior of shale gas. The increase in moisture within the reservoir affects the microwave absorption capacity, and thus affects the heating effect. It is worth noting that although previous studies have provided a preliminary understanding of the thermal effect of microwave heating and the change in the moisture state within shale, the comprehensive impact of these factors on methane extraction efficiency has not been fully studied. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for calculating the migration of methane in the matrix-fracture system of a shale gas reservoir under microwave radiation, which can accurately track the dynamic change process of the methane extraction content in the shale gas reservoir.

[0006] The technical solution adopted by the present invention is a method for calculating the migration of methane in the matrix-fracture system of a shale gas reservoir under microwave radiation, which is specifically implemented according to the following steps:

[0007] Step 1: Collect the physical and mechanical parameters of the matrix of the shale gas reservoir and the engineering parameters of the matrix and fracture system of the shale gas reservoir;

[0008] Step 2: According to the engineering parameters, use COMSOL software to establish a geometric model of the simulated shale gas reservoir, and use the entire geometric model as the calculation domain;

[0009] Step 3: Establish a coupling relationship among the calculation domains, and then form a coupling model covering fracture deformation; the coupling model synthesizes the interactions among electromagnetic effects, solid deformation, fluid and moisture transport, and heat transfer; the coupling model includes electromagnetic field equations, solid deformation field equations, moisture transport field equations, methane transport field equations, and heat transfer field equations;

[0010] Step 4: Assign initial conditions and boundaries, and use COMSOL software to solve the decoupled model, so as to obtain the dynamic change curve of methane gas content in the matrix and fracture system under microwave radiation, and thus obtain the migration trajectory of methane.

[0011] The features of the present invention also lie in that

[0012] In Step 1, the physical and mechanical parameters of the shale gas reservoir matrix include: temperature, elastic modulus, Poisson's ratio, bulk modulus, isothermal expansion coefficient, diffusion coefficient, adsorption constant, Boltzmann constant, thermal conductivity and specific heat capacity; the engineering parameters of the shale gas reservoir matrix and fracture system include: permeability, pore pressure, porosity, relative humidity.

[0013] The electromagnetic field equation is shown as follows:

[0014]

[0015] In the formula, k0 = ω / c0 is the free space wave number, c0 is the speed of light in vacuum, ω = 2πf is the angular frequency, and f is the frequency of the electromagnetic wave; E is the electric field strength; μ r is the relative magnetic permeability; ε r is the relative dielectric constant; j is the imaginary number; σ E is the conductivity; ε0 is the vacuum permittivity.

[0016] The solid deformation field equation is shown as follows:

[0017]

[0018] In the formula, f i represents the stress component caused by the body force, T, i is the shale temperature in the direction of the Cauchy stress, K is the bulk modulus of the shale, P f,,i is the pore pressure of the shale fracture in the direction of the Cauchy stress, α f is the Biot coefficient of the shale fracture, P m ,i is the pore pressure of the shale matrix in the direction of the Cauchy stress, α m is the Biot coefficient of the shale matrix, α Ts is the thermal expansion coefficient of the shale; ν is the Poisson's ratio, and G is the shear modulus;

[0019] The equations for the seepage of methane in the matrix and fracture system, that is, the methane transport field equations, are respectively shown as follows:

[0020]

[0021] In the formula, β gm is the compressibility coefficient of methane gas in the matrix, α Tgm is the thermal expansion coefficient of methane gas in the matrix; is the relative permeability of methane gas in the matrix; β gf is the compressibility factor of methane gas in the fracture, α Tgf is the coefficient of thermal expansion of methane gas in the fracture; is the relative permeability of methane gas in the fracture; p a is the standard atmospheric pressure, T a is the standard temperature; represents the porosity of the matrix; S wm and S wf are the water saturation of the matrix and the fracture respectively; Z m is the deviation factor of the real gas in the matrix medium; K(T) is the adsorption equilibrium constant related to temperature; λ is the gas adsorption decay coefficient; p gm and p gf are the methane gas pressures in the matrix and the fracture respectively; k mapp is the effective permeability in the shale matrix; is the porosity of the shale fracture; R is the universal gas constant;

[0022] The moisture changes in the matrix and the fracture can be described by the following governing equations, as shown in the following equations respectively, which are the moisture transport field equations;

[0023]

[0024]

[0025] In the formula, w m (φ m ) is the total moisture content in the matrix; ω vm is the mass fraction of water vapor in the matrix, v wm is the convective rate of liquid water in the matrix, g wm is the binary diffusion coefficient of methane in the gas phase in the matrix, g wcm is the capillary diffusion coefficient of liquid water in the matrix; w f (φ f ) is the total moisture content in the fracture; ω vf is the mass fraction of water vapor in the fracture, v wf is the convective rate of liquid water in the fracture, g wf is the binary diffusion coefficient of methane in the gas phase in the fracture; g wcf is the capillary diffusion coefficient of liquid water in the fracture.

[0026] The heat transfer field equation is as shown in the following equation;

[0027]

[0028] In the formula, Q evap is the evaporation heat source, Q Eis a microwave heat source; C represents the specific heat capacity, (ρC eq ) eff is the effective specific heat capacity; κ eq is the thermal conductivity, and Q1 represents the heat source term.

[0029] The beneficial effects of the present invention are as follows:

[0030] Considering the characteristics of two-phase flow in shale gas reservoirs, the present invention proposes a multi-physical field model that is fully coupled with the dual-porosity medium theory to capture this complex evolution process. This model synthesizes the interactions between electromagnetic effects, solid deformation, fluid and moisture transport, and heat transfer, and can effectively evaluate the changes in various reservoir parameters under microwave radiation, and can accurately track the dynamic change process of the methane production content in shale gas reservoirs. The results show that the increase in relative humidity enhances the contribution of adsorbed methane to the cumulative methane production, microwave heating significantly increases the water-vapor exchange rate between the matrix and the fractures, and improves the desorption efficiency of shale gas in the later production stage, thereby improving the methane production efficiency. Description of the Drawings

[0031] Figure 1 is a schematic diagram of the multi-physical field cross-coupling relationship of the present invention;

[0032] Figure 2 is a schematic diagram of the principle of microwave heating promoting shale gas production of the present invention;

[0033] Figure 3 is a computational model of microwave-assisted shale gas production including boundary conditions of the present invention;

[0034] Figure 4a is a curve graph of the change in pore pressure of a shale gas reservoir;

[0035] Figure 4b is a curve graph of the change in relative humidity of a shale gas reservoir;

[0036] Figure 4c is a curve graph of the change in relative permeability of the gas phase in the matrix;

[0037] Figure 4d is a curve graph of the change in relative permeability of the gas phase in the fractures;

[0038] Figure 5a is a curve graph of the change in water-vapor content in the matrix;

[0039] Figure 5b is a curve graph of the change in water-vapor content in the fractures;

[0040] Figure 6a is a curve graph of the change in methane exchange rate;

[0041] Figure 6bIt is a curve graph showing the change in the amount of methane adsorbed in the matrix;

[0042] Figure 6c It is a curve graph showing the change in the water exchange rate;

[0043] Figure 6d It is a curve graph showing the change in the water vapor content adsorbed in the matrix;

[0044] Figure 7a It is a curve graph showing the change in the relative permeability in the fracture;

[0045] Figure 7b It is a curve graph showing the change in the relative permeability in the matrix;

[0046] Figure 7c It is a curve graph showing the change in the methane exchange rate under different humidities;

[0047] Figure 7d It is a curve graph showing the change in the water exchange rate under different humidities;

[0048] Figure 7e It is a curve graph showing the change in the methane production rate under different humidities;

[0049] Figure 7f It is a curve graph showing the change in the cumulative methane production;

[0050] Figure 8a It is a graph showing the influence of the initial permeability on the methane recovery rate in the matrix;

[0051] Figure 8b It is a graph showing the change in the cumulative production of methane in the matrix under different permeabilities;

[0052] Figure 8c It is a graph showing the influence of the initial permeability on the methane recovery rate in the fracture;

[0053] Figure 8d It is a graph showing the change in the cumulative production of methane in the fracture under different permeabilities. Detailed implementation manners

[0054] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0055] The calculation method for methane migration in the matrix - fracture system of shale gas reservoirs under microwave radiation of the present invention is specifically implemented according to the following steps:

[0056] Step 1, collect the physical and mechanical parameters of the shale gas reservoir matrix and the engineering parameters of the shale gas reservoir matrix and the fracture system;

[0057] The physical and mechanical parameters of the shale gas reservoir matrix include: temperature T, elastic modulus E s, Poisson's ratio ν, bulk modulus K, isothermal coefficient of expansion, diffusion coefficient, adsorption constant, Boltzmann constant, thermal conductivity, and specific heat capacity;

[0058] The engineering parameters of the shale gas reservoir matrix and fracture system include: permeability, pore pressure, porosity, and relative humidity.

[0059] Step 2: According to the engineering parameters, use COMSOL software to establish a geometric model of the simulated shale gas reservoir, and take the entire geometric model as the computational domain;

[0060] The specific steps to use COMSOL software to establish a geometric model of the shale gas reservoir matrix to be simulated are as follows: Based on the engineering geological characteristics of the shale gas reservoir matrix, establish a computational geometric model. Define the geometric shape and size of the reservoir on the canvas;

[0061] Step 3: Establish the coupling relationship between the computational domains, and then form a coupling model covering fracture deformation; the coupling model synthesizes the interactions between electromagnetic effects, solid deformation, fluid and moisture transport, and heat transfer, and integrates a coupled numerical model of multi-physical field interactions.

[0062] Specifically: The coupling model includes the coupling relationship between the electromagnetic field equation, solid deformation field equation, moisture transport field equation, methane transport field equation, and heat transfer field equation. The governing equations for each physical field are as follows:

[0063] The establishment of the theoretical model of the shale gas reservoir is based on the following assumptions: (a) The shale is regarded as a double-porosity elastic continuous medium with a spatially uniformly distributed fracture system; (b) The strain calculation in the shale follows the small deformation theory; (c) It is assumed that there is local thermal equilibrium in the shale gas reservoir; (d) The gas phase is simulated as a mixture of dry methane and steam; (e) The solid, liquid, and gas phases are regarded as overlapping but different continuous media.

[0064] 1. Electromagnetic wave transmission:

[0065] The propagation characteristics of electromagnetic waves in free space are determined by Maxwell's equations, which are represented by the following equations, as shown in Equation (1):

[0066]

[0067] In the formula, E is the electric field strength, B is the magnetic flux density, H is the magnetic field strength, J is the current density, D is the electric displacement or electric flux density, t is the time, and ρ E is the charge density.

[0068] The above equations are supplemented by the following constitutive relations, as shown in Equation (2):

[0069] D = ε0ε r E, B = μ0μ rH, J = σ E E (2);

[0070] where ε0 is the vacuum permittivity, ε r is the relative permittivity, which can be determined by the following formula, ε r = ε'+jε”; where ε' is the permittivity of the material, ε” is the loss factor of the material, j is the imaginary number, μ0 is the vacuum permeability, μ r is the relative permeability, σ E is the conductivity.

[0071] By substituting the constitutive relation of formula (1), the Helmholtz vector equation describing the electromagnetic wave problem in the time domain is derived. Substituting formula (2) into formula (1), formula (3) is obtained, which is the electromagnetic field equation of the coupling model;

[0072]

[0073] where k0 = ω / c0 is the free space wave number, c0 is the speed of light in vacuum, ω = 2πf is the angular frequency, and f is the frequency of the electromagnetic wave.

[0074] The dielectric properties of shale gas reservoirs depend on the moisture content and deformation under microwave radiation, as shown in formula (4):

[0075]

[0076] where and represents the porosity of the matrix, S wm represents the water saturation of the matrix.

[0077] The process of converting electric field energy into heat energy can be expressed as formula (5):

[0078] Q E = 2πfε0ε”|E| 2 (5);

[0079] 2. Rock deformation:

[0080] For shale gas reservoirs, the volume strain caused by gas adsorption - desorption can be ignored. Based on the elastic theory of double - porosity media, considering the changes of in - situ stress, temperature, pore pressure and moisture content in the reservoir, the constitutive equation describing the stress - strain relationship of shale is shown in formula (6):

[0081]

[0082] where the shear modulus G can be obtained from the elastic modulus E s and the Poisson's ratio ν, i.e., G = E s / 2(1 + ν); K is the shale bulk modulus, T is the shale temperature, i and j are the directions of the Cauchy stress, and δ ij is the Kronecker function; the stress trace σ kk = σ 11 + σ 22 + σ 33 , α Ts is the shale coefficient of thermal expansion; the Biot coefficient of the shale matrix α m = 1 - K / K m , where K m is the bulk modulus of the shale skeletal particles, and the Biot coefficient of the shale fractures α f = 1 - K / K f . In the formula, K f is the bulk modulus of the shale fractures, P m is the pore pressure of the shale matrix, and p f is the pore pressure of the shale fractures.

[0083] Neglecting the inertia effect, the stress equilibrium equation of the shale is shown in Equation (7):

[0084] σ ij,j + f i = 0 (7)

[0085] In the formula, σ ij is the component of the total stress, and f i represents the stress component caused by the body force.

[0086] Due to the small elastic deformation of the shale, the strain-displacement relationship can be defined as Equation (8):

[0087]

[0088] In the formula, u is the component of the displacement vector.

[0089] In the matrix and fracture systems, the pore pressure is determined by the fluid pressures of gas and water, as shown in Equation (9):

[0090]

[0091] In the formula, p gm and p gf are the methane gas pressures in the matrix and fractures respectively, p wm and p wf are the water pressures in the matrix and fractures respectively, S wm and S wf are the water saturations in the matrix and fractures respectively.

[0092] According to Equation (8), the volumetric strain of the shale can be obtained, as shown in Equation (10):

[0093]

[0094] In the formula, represents the average compressive stress.

[0095] Combined with formulas (6)-(8), the modified Navier-type control equation for shale deformation based on the dual porosity model is derived, which is the solid deformation field equation, as shown in formula (11):

[0096]

[0097] u i，kk is the component of displacement in the i direction; u k,ki represents the mixed partial derivative of u k with respect to the k direction and the i direction;

[0098] 3. Methane migration:

[0099] Describing the stress-dependent porosity of the matrix, as shown in formula (12):

[0100]

[0101] In the formula, B m is the pore compressibility of the shale matrix, defined as The subscript 0 represents the initial condition.

[0102] Substituting formula (10) into formula (12), formula (13) is obtained:

[0103]

[0104] The relationship between the permeability and porosity in the matrix can be described by the cubic law, as shown in formula (14):

[0105]

[0106] In the formula, k m is the intrinsic permeability of the shale matrix.

[0107] Combined with formulas (12)-(14), the intrinsic permeability of the shale matrix is obtained, as shown in formula (15):

[0108]

[0109] The porosity of the fracture can be defined by the Cui-Bustin model, as shown in formula (16):

[0110]

[0111] In the formula, φ f is the shale fracture porosity, pf is the pore pressure in the shale fracture, B f is the pore compressibility of the shale fracture, which can be obtained from B f = α f / (φ f0 K f ).

[0112] Substituting Equation (10) into Equation (16) gives the pore porosity equation of the shale fracture, as shown in Equation (17):

[0113]

[0114] According to the cubic law, the intrinsic permeability k of the shale fracture f , as shown in Equation (18):

[0115]

[0116] The mass conservation equation of methane, as shown in Equation (19):

[0117]

[0118] In the formula, m i is the methane gas content, t is the time, ρ ai is the methane gas density, v gi is the gas seepage velocity, Q gi is the gas mass source term; the subscript i = m or f, representing the matrix system and the fracture system respectively;

[0119] Methane in the shale gas reservoir mainly exists in two forms: free gas and adsorbed gas. Gas adsorption is considered to occur only in the matrix system. The methane gas contents in the matrix and the fracture are defined as shown in Equations (20) and (21):

[0120]

[0121] In the formula, ρ ga is the methane gas density in the matrix under standard conditions, ρ s is the density of the shale, V L is the Langmuir adsorption volume constant, λ is the gas adsorption attenuation coefficient; m m is the methane gas content in the matrix; ρ am is the methane gas density in the matrix; m f is the methane gas content in the fracture; ρ af is the methane gas density in the fracture;

[0122] K(T) is the adsorption equilibrium constant related to temperature, and the expression is as shown in Equation (22):

[0123]

[0124] In the formula, K0 is the pre-exponential constant, and E ads is the characteristic adsorption energy, and R is the universal gas constant.

[0125] The density of methane gas can be calculated using the real gas state equation, as shown in Equation (23):

[0126]

[0127] In the formula, M g is the molar mass of methane gas. Z i represents the deviation coefficient of the real gas in the medium and can be determined using an empirical formula, as shown in Equation (24):

[0128]

[0129] In the formula, p pr = p g / p cr represents the critical pressure of methane. T pr = T / T cr , and T cr is the critical temperature of methane.

[0130] In the shale matrix, the gas flow pattern is usually classified using the Knudsen number, which is expressed as Equation (25):

[0131]

[0132] In the formula, r is the characteristic length of the flow medium, and λ n is the mean free path of gas molecules, as shown in Equation (26):

[0133]

[0134] In the formula, K B is the Boltzmann constant, and σ is the molecular collision radius.

[0135] Considering the influence of the gas flow mechanism, the effective permeability in the shale matrix is as shown in Equation (27):

[0136] k mapp = k m ·f(K n ) (27);

[0137] In the formula, f(K n ) is the permeability enhancement function, as shown in Equation (28):

[0138]

[0139] Where ξ is the sparsity coefficient.

[0140] According to the mass transfer theory of the medium, the source term for the transfer of gas mass from the matrix system to the fracture system can be obtained, as shown in Equation (29):

[0141]

[0142] Where G m-f is the shape factor related to the average matrix block size. For matrix blocks equally spaced by fractures, G m-f = 8 / a 2 .

[0143] When there is two-phase seepage of gas and water in the shale gas reservoir, the seepage rates v gm and v gf of methane gas in the matrix and fractures are as shown in Equations (30) and (31):

[0144]

[0145] Where μ a is the dynamic viscosity of methane gas;

[0146] is the relative permeability of the gas phase, expressed as Equation (32):

[0147]

[0148] The calculation of the relative permeability of the liquid phase is as shown in Equation (33):

[0149]

[0150] Where S rw is the residual water saturation.

[0151] Substituting Equations (20)-(33) into Equation (19), the seepage equations of methane in the matrix and fracture systems can be obtained, as shown in Equations (34) and (35), which are the methane transport field equations;

[0152]

[0153] Where β gm is the compression coefficient of methane gas in the matrix, and α Tgm is the thermal expansion coefficient of methane gas in the matrix; is the relative permeability of methane gas in the matrix; β gf is the compression coefficient of methane gas in the fracture, and α Tgf is the thermal expansion coefficient of methane gas in the fracture; is the relative permeability of methane gas in the fracture; p ais the standard atmospheric pressure, and T a is the standard temperature.

[0154] 4. Water transportation:

[0155] The total water content in the shale gas reservoir consists of two forms: vapor and liquid water, as shown in Equation (36):

[0156]

[0157] In the formula, w(φ) is the total water content, ρ w is the density of liquid water, and ρ g is the density of the gas;

[0158] ω v is the mass fraction of water vapor, as shown in Equation (37):

[0159]

[0160] In the formula, M v is the molar mass of water vapor, φ is the relative humidity, and C sat is the saturation concentration of water vapor, as shown in Equation (38):

[0161]

[0162] The vapor saturation pressure p sat can be expressed as Equation (39):

[0163]

[0164] The binary diffusion expression of methane in the gas phase is Equation (40):

[0165]

[0166] The effective diffusion coefficient (D effi ) is usually related to the Millington Quirk model and is expressed as Equation (41):

[0167]

[0168] In the formula, D0 = 2.5×10 -5 [m 2 / s] is the diffusion coefficient of water vapor in the gas phase under standard temperature and pressure conditions, T b represents normal temperature and pressure, and τ represents the tortuosity factor, which can be expressed as Equation (42):

[0169]

[0170] The flow field ν wiIt can be determined by Darcy's law to describe the convective flow of liquid water driven by the total pressure gradient, as shown in Equations (43) and (44):

[0171]

[0172] where μ w is the dynamic viscosity of liquid water.

[0173] The water pressure is calculated based on the difference between the gas pressure and the capillary pressure, as shown in Equation (45):

[0174]

[0175] where p cm and p cf are the capillary pressures in the matrix and the fracture, respectively, which can be obtained from the following equation, as shown in Equation (46):

[0176]

[0177] The capillary diffusion of liquid water in the reservoir can be described by Kelvin's law as Equation (47):

[0178]

[0179] The water content in the porous medium changes with time, where the steam and liquid water in the shale satisfy the mass conservation equation. The water content changes in the matrix and the fracture can be described by the following governing equations, as shown in Equations (48) and (49), which are the water transport field equations;

[0180]

[0181] where w m (φ m ) is the total water content in the matrix; ω vm is the mass fraction of water vapor in the matrix, v wm is the convective rate of liquid water in the matrix, g wm is the binary diffusion coefficient of methane in the gas phase in the matrix, g wcm is the capillary diffusion coefficient of liquid water in the matrix; w f (φ f ) is the total water content in the fracture; ω vf is the mass fraction of water vapor in the fracture, v wf is the convective rate of liquid water in the fracture, g wf is the binary diffusion coefficient of methane in the gas phase in the fracture; g wcfis the capillary diffusion coefficient of liquid water in the crack; the first term on the left side of the equation represents the change rate of shale water content, the second term represents the convection of steam, the third term represents the binary diffusion of steam and methane gas, the fourth term describes the convection of liquid water, and the fifth term represents the capillary diffusion of liquid water in shale.

[0182] Moisture mass source term Q w Defined based on the mass transfer theory between media, as shown in Equation (50):

[0183]

[0184] 5. Heat transfer:

[0185] For heat transfer in a dual-porosity geological reservoir, ignoring the heat filtration effect, the total heat flux rate q T is given by the following formula (51):

[0186]

[0187] Thermal conductivity, as shown in Equation (52):

[0188]

[0189] In the formula, the subscripts s, w, and g represent the solid phase, liquid phase, and gas phase respectively. κ is the thermal conductivity coefficient, is the solid-phase volume fraction;

[0190] Considering the temperature change, thermal deformation, and convective heat transfer coupling between methane and moisture in the shale gas reservoir, referring to the heat transfer equation of water-containing porous media in COMSOL software, the energy conservation law equation of the shale gas reservoir is established, as shown in Equation (53), which is the heat transfer field equation;

[0191]

[0192] The initial term on the left represents the change rate of heat flux with temperature change, the second term represents the heat change due to thermal strain in the shale skeleton, the third term is the heat transfer term in the shale gas reservoir, and the fourth term is the thermal convection term of gas and moisture in shale. Q1 represents the heat source term, which explains the enthalpy diffusion flux caused by steam diffusion in the gas and the capillary flux related to the liquid water in the pores. Q evap is the evaporation heat source, Q E is the microwave heat source. C represents the specific heat capacity, (ρC eq ) eff is the effective specific heat capacity, expressed as Equation (54):

[0193]

[0194] The heat source term Q1 can be calculated according to the following formula (55);

[0195]

[0196] Wherein, C v is the specific heat capacity of steam.

[0197] The evaporation heat source in the heat transfer equation is shown in Equation (56):

[0198] Q evap = L v G evap (56)

[0199] Wherein, L v is the latent heat of vaporization, and G evap is the evaporation source, which can be expressed as Equation (57) and Equation (58):

[0200] G evap = G evapm + G evapf (57)

[0201]

[0202] From the above, a multi-physics fully coupled model considering the interactions of electromagnetic fields, solid deformations, fluid migrations, and heat transfers is established.

[0203] In summary, the governing equations of each physical field are respectively Equation (3), Equation (11), Equation (34), Equation (35), Equation (48), Equation (49), and Equation (53);

[0204] Step 4: Assign initial conditions and boundaries, and use COMSOL software to solve the separated coupling model, thereby obtaining the dynamic change curve of the methane gas content in the matrix and fracture system under microwave radiation, and thus obtaining the migration trajectory of methane.

[0205] For the electromagnetic field equation, input the relative permittivity, relative permeability, conductivity, and the frequency of the electromagnetic wave in the coupling model. Subsequently, use Equation (3) to solve the electric field strength E. And use Equation (5) to convert the electric field energy into heat energy;

[0206] In the solid deformation field equation, input the physical and mechanical parameters of the shale gas reservoir, including the elastic modulus, Poisson's ratio, bulk modulus, isothermal expansion coefficient, maximum horizontal in-situ stress, minimum horizontal in-situ stress, initial porosity and permeability of the matrix and fractures, and Biot coefficient. Use Equation (11) to find the displacement u of the shale gas reservoir. Obtain the volumetric strain ε of the reservoir according to the strain-displacement relationship in Equation (8) v .

[0207] Considering the volumetric strain of shale gas reservoirs, a porosity and permeability model related to the stress of the matrix and fracture system was established (as shown in Formulas (12) and (16)), and the changes in porosity and permeability would affect the transport of gas phase and liquid phase inside the reservoir.

[0208] In the methane transport field equation, the initial pore pressure of the matrix and fracture system, the density of methane gas under standard conditions, the density of shale, the Langmuir adsorption volume constant, the adsorption equilibrium constant related to temperature, the gas adsorption attenuation coefficient, and the Boltzmann constant were input. And the influence of the flow form of methane gas and the relative permeability of the gas phase was considered. The pressure change curve of methane gas in the matrix was obtained using Formula (34); the pressure change curve of methane gas in the fracture was obtained using Formula (35); the change in pore pressure reduced the pressure difference inside and outside the reservoir, reducing the seepage process of water and methane inside the reservoir, thereby causing the gas production rate of shale gas to gradually decrease. And according to the relationship between pore pressure and density in Formula (23), the changes in the methane gas content in the matrix and fracture system in Formulas (20) and (21) were obtained.

[0209] In the water transport field equation, the initial relative humidity, total water content, mass fraction of steam, and diffusion coefficient of water vapor in the gas phase under standard temperature and pressure conditions of the matrix and fracture system were input. The change curves of relative humidity (φ m and φ f ) in the matrix and fracture were solved using Formulas (48) and (49); the change in relative humidity affected the dielectric properties inside the reservoir and the efficiency of microwave heating. The decrease in relative humidity enhanced the relative permeability of the gas phase and promoted the flow of methane gas.

[0210] In the heat transfer field equation, the thermal conductivities and specific heat capacities of the solid phase, liquid phase, and gas phase in the shale gas reservoir and each heat source term were input. The evolution of the internal temperature T of the reservoir was solved using Formula (53). The change in temperature would, on the one hand, promote the desorption of shale gas. On the other hand, it would cause the evaporation of water inside the reservoir and thermal expansion of the reservoir, resulting in changes in porosity and permeability. Thus, it affected the two-phase water-gas flow inside the reservoir.

[0211] Example 1

[0212] In the method of the present invention, the shale gas reservoir absorbs electromagnetic wave energy and converts it into heat, thereby increasing the reservoir temperature and promoting methane desorption. The increase in temperature causes the evaporation of liquid water, thereby changing the relative permeability of the reservoir, which in turn affects the flow behavior of the water-gas two-phase system. In addition, the increase in temperature causes thermal expansion of the reservoir, thereby causing changes in porosity and permeability and affecting the transport characteristics. At the same time, the change in transport characteristics affects the dielectric properties and microwave absorption efficiency of the reservoir, which in turn affects the efficiency of microwave heating. In order to capture the complex interactions between the electromagnetic field, solid deformation, moisture transport, methane transport, and heat transfer during the microwave radiation process, Equations (3), (11), (34), (35), (48), (49), and (53) are fully coupled multi-physics models of the matrix-fracture system, as Figure 1 shown, and the coupled physical processes involve five groups of non-linear partial differential equations with complex boundary and initial conditions. The numerical simulation of the present invention uses COMSOL Multiphysics software.

[0213] In order to comprehensively study the water-gas exchange mechanism between the matrix and fractures of the shale gas reservoir under microwave radiation and evaluate its impact on the shale gas production efficiency, a coupled model integrating the interaction of multiple physical fields is established. As Figure 3 shown, to ensure the representativeness and applicability of the simulation results, the size of the calculation model is 50m × 50m. In order to simulate the water-gas exchange mechanism between the matrix and fractures of the shale gas reservoir under microwave radiation, the present invention establishes a coupled model integrating the interaction of multiple physical fields. For the electromagnetic wave transmission field, except for the four waveguide ports, scattering boundary conditions are applied to all boundaries, two of which are located at boundary AB and the other two are located at CD. This parametric design can more accurately characterize the propagation characteristics of electromagnetic waves in the reservoir and the energy transmission and absorption mechanism during the interaction between microwaves and shale media. The boundary conditions and simulation parameters of other physical fields are shown in Tables 1 and 2;

[0214] Table 1 Boundary Conditions of the Calculation Model

[0215]

[0216]

[0217] Table 2 Numerical Simulation Parameters

[0218]

[0219] Example 2

[0220] Figure 4aIt shows the change of pore pressure in the shale gas reservoir, which shows a downward trend as the mining process progresses. It is worth noting that the change of pore pressure in the matrix shows an obvious lag compared with that in the fracture area. In addition, as the measurement point gets closer and closer to the hydraulic fracture, the lag effect becomes more and more obvious. Figure 4b Indicates that the relative humidity at the measurement point decreases over time, which is mainly due to the gradual evaporation and outward transportation of water in the reservoir during the mining process. This reduction has a significant impact on the fluid flow characteristics in the matrix and fractures, such as Figure 4c and Figure 4d shown, the decrease in relative humidity leads to a significant increase in the relative permeability of the gas phase, while the relative permeability of the liquid phase gradually decreases.

[0221] Example 3

[0222] Figure 5a and Figure 5b respectively represent the changes in the steam content along the measurement line in the reservoir matrix and fractures. The results show that the steam content is higher in the area far from the hydraulic fracturing zone. In the first 6000 days, the steam content shows a downward trend, mainly due to the gradual loss of steam in the reservoir. After 8000 days, an upward trend appears, which is due to the promotion of the conversion of liquid water to steam by the increase in reservoir temperature.

[0223] Example 4

[0224] As Figure 6a shown, the methane exchange rate increases with the increase of microwave power. This phenomenon is attributed to the enhanced microwave energy at higher power levels, which increases the matrix temperature. The increase in temperature causes thermal expansion of the matrix, increases its porosity and permeability, promotes methane flow, and thus increases the exchange rate. In addition, the increased temperature reduces the water saturation in the matrix, enhances the relative permeability of the gas phase, and further promotes the gas exchange between the matrix and fractures. Figure 6b Indicates that the increase in microwave power reduces the amount of methane adsorbed in the matrix, revealing the relationship between microwave power and methane adsorption / desorption. Specifically, as the microwave power increases from 0W to 120W, the final adsorption amount of methane in the matrix decreases from 43891 kg / m 3 to 28618 kg / m 3 , which is equivalent to a 6.5% increase in the desorption amount. This is mainly due to the increase in matrix temperature under enhanced microwave power, which accelerates the thermal motion of methane molecules and makes it easier for them to overcome the binding force of the adsorption sites. The change of water exchange rate under different microwave power conditions is as Figure 6c shown. In the early stage of gas mining (0 - 500 days), the heating time is short and the increase in reservoir temperature is not significant, so the influence of microwave power on the water exchange rate is very small.

[0225] After 500 days, with the increase of microwave power, the moisture exchange rate gradually increases. When the microwave power P in ≤ 30 W, the relatively low microwave power only causes a slow rise in formation temperature, and the vapor diffusion hardly enhances, with the improvement of moisture exchange rate being limited. As the mining progresses, the vapor concentration gradient between the matrix and the fractures gradually decreases, resulting in a reduction in the exchange rate. The combined effect of these factors leads to an initial increase and then a decrease in the moisture exchange rate within this power range. When P in ≥ 60 W, the relatively high microwave energy causes a rapid increase in formation temperature and an increase in vapor diffusion rate, which is conducive to the moisture exchange between the matrix and the fractures. This results in a continuous increase in the moisture exchange rate over time. Microwave power also significantly affects the steam content in the matrix ( Figure 6d ). When P in ≤ 30 W, the reservoir temperature rises slowly, the evaporation rate of liquid water is slow, and almost no evaporation occurs, so the steam content in the matrix will not increase significantly during the mining process. On the contrary, when P in ≥ 60 W, the rapid increase in formation temperature accelerates the evaporation rate of liquid water. As the temperature continues to rise, the evaporation rate in the matrix eventually exceeds the moisture exchange rate, causing the steam content in the matrix to increase. The temperature of the microwave-heated reservoir is an important factor affecting the methane and water vapor content in the reservoir, playing an important regulatory role in the exchange rate of methane and water vapor in the reservoir, providing useful inspiration for optimizing the application of microwave-heated reservoirs in natural gas production.

[0226] Example 5

[0227] As Figure 7a and Figure 7b shown, the increase in the initial relative humidity RH0 significantly affects the relative permeabilities of the gas phase and the liquid phase. The higher the relative humidity, the higher the water content in the reservoir and the stronger the water lock effect. Microwave radiation can increase the reservoir temperature, promote the evaporation of liquid water, and reduce the water saturation. This process alleviates the adverse effect of water on the relative permeability of the gas phase, thereby enhancing the gas mobility. Therefore, the relative permeability of the gas phase gradually increases, while the relative permeability of the liquid phase decreases over time.

[0228] Figure 7c shows that the increase in the initial relative humidity significantly reduces the methane exchange rate. During the entire production process, the methane exchange rate experiences a trend of first increasing and then decreasing. The early increase is due to the rapid decline in pore pressure in the fractures at the initial stage of production, which amplifies the pore pressure difference between the matrix and the fractures, thereby enhancing methane exchange. However, over time, the pore pressure in the fractures gradually stabilizes, reducing the pore pressure difference and resulting in a decrease in the methane exchange rate. As Figure 7dAs shown, when RH0 ≥ 0.4, the moisture exchange rate shows a trend of increasing first, then decreasing, and then increasing again. At relatively high relative humidity, there is a large difference in the water content between the reservoir and the external environment. In the initial stage of production, moisture exchange mainly occurs between the liquid water in the matrix and the fractures. Due to the large pressure difference between the fractures and the external environment, it promotes the rapid inflow of liquid water in the fractures into the hydraulic fractures, increasing the pressure difference between the matrix and the fractures and rapidly rising the moisture exchange rate. As the liquid water in the matrix gradually flows into the fractures, the pressure difference decreases, resulting in a decrease in the moisture exchange rate. Thereafter, with the progress of production, moisture exchange mainly occurs between the steam in the matrix and the fractures. The increase in reservoir temperature and the decrease in pressure accelerate the diffusion of steam in the matrix, thus greatly enhancing the moisture exchange and leading to an upward trend in the second moisture exchange rate. On the contrary, when RH0 ≤ 0.3, the difference in water content between the reservoir and the external environment is small. This results in a slower increase in the moisture exchange rate, which is not sufficient to produce the above-mentioned fluctuations observed at high relative humidity. Therefore, the moisture exchange rate shows a steadily increasing trend. Figure 7e It shows that the methane production efficiency decreases with the increase in relative humidity. This decrease is due to the high water content and high relative humidity in the reservoir, which hinders the gas flow channels and reduces the methane production efficiency. In addition, Figure 7f shows the influence of relative humidity on the contribution of different methane storage forms to the cumulative methane production. The contribution of free gas in the fractures is relatively small, while most of the methane production comes from adsorbed methane in the matrix. With the increase in relative humidity, the proportion of adsorbed methane in the total methane production also increases. Specifically, when the relative humidity increases from 0.2 to 0.6, the proportion of adsorbed methane increases from 51.7% to 71.0%. This phenomenon is mainly due to the higher water content occupying the space originally available for free gas, resulting in a significant decrease in the content of free gas in the reservoir. Relative humidity has a significant impact on methane production. Effectively managing relative humidity during production is crucial for optimizing methane recovery efficiency.

[0229] Example 6

[0230] The influence of the initial permeability of the matrix and fractures on methane recovery is as Figure 8a and Figure 8cAs shown, the gas production first increases and then decreases. In the initial stage of production, the free gas in the fractures rapidly flows out under the action of the pressure difference, resulting in an increase in gas production. However, as production progresses, the pore pressure in the fractures gradually decreases, leading to a corresponding decrease in gas production. At this stage, there is a pressure difference between the matrix and the fractures, driving the gas to be transported from the matrix to the fractures, and then the gas is produced in the fractures. An increase in matrix permeability enhances the methane exchange rate but reduces the peak production rate. This is because the accelerated gas exchange reduces the pressure difference within the fractures, thereby reducing the extraction rate. In addition, increasing fracture permeability improves gas flow in the fractures, thus having a positive impact on increasing gas production. Understanding the influence of reservoir permeability on cumulative methane production is crucial. In the early stage of natural gas production, the increase in matrix permeability has a relatively small impact on cumulative methane production ( Figure 8b ), while the increase in fracture permeability significantly increases the cumulative production ( Figure 8d ).

Claims

1. A method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation, characterized in that: Follow the steps below to implement it: Step 1, collecting physical and mechanical parameters of shale gas reservoir matrix and engineering parameters of shale gas reservoir matrix and fracture system; Step 2: Based on the engineering parameters, a geometric model for simulating the shale gas reservoir is established using COMSOL software, and the entire geometric model is used as the calculation domain; Step 3, establish the coupling relationship between the computational domains, and then form a coupling model covering the crack deformation; the coupling model integrates the interaction between electromagnetic effect, solid deformation, fluid and moisture transport and heat transfer; the coupling model includes electromagnetic field equations, solid deformation field equations, moisture transport field equations, methane transport field equations and heat transfer field equations; Step 4: Assign initial conditions and boundaries, use COMSOL software to solve the separation coupling model, and then obtain the dynamic change curve of methane gas content in the matrix and fracture system under microwave radiation, so as to derive the migration trajectory of methane.

2. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 1, characterized in that: In step 1, the physical and mechanical parameters of the shale gas reservoir matrix include: temperature, elastic modulus, Poisson's ratio, bulk modulus, isothermal expansion coefficient, diffusion coefficient, adsorption constant, Boltzmann constant, thermal conductivity and specific heat capacity; the engineering parameters of the shale gas reservoir matrix and the fracture system include: permeability, pore pressure, porosity, and relative humidity.

3. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 1, characterized in that: The electromagnetic field equation is shown below: Where k0=ω / c0 is the free space wave number, c0 is the speed of light in a vacuum, ω=2πf is the angular frequency, f is the frequency of the electromagnetic wave; E is the electric field strength; μ r is the relative magnetic permeability; ε r is the relative dielectric constant; j is an imaginary number; σ E is the electrical conductivity; ε0 is the dielectric constant of vacuum.

4. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 3, characterized in that: The solid deformation field equation is shown below: In the formula, f i represents the stress component due to body force, T, i is the shale temperature in the direction of Cauchy stress, K is the shale bulk modulus, P f,i is the pore pressure of shale fractures in the direction of Cauchy stress, α f is the Biot coefficient of shale fracture, P m , i is the pore pressure of the shale matrix in the direction of the Cauchy stress, α m is the shale matrix Biot coefficient, α Ts is the thermal expansion coefficient of shale; ν is Poisson's ratio, and G is the shear modulus.

5. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 4, characterized in that: The equations for methane seepage in the matrix and fracture system, that is, the methane transport field equations, are shown as follows: In the formula, β gm is the compressibility factor of methane gas in the matrix, α Tgm is the thermal expansion coefficient of methane gas in the matrix; is the relative permeability of methane gas in the matrix; β gf is the compressibility coefficient of methane gas in the fracture, α Tgf is the thermal expansion coefficient of methane gas in the crack; is the relative permeability of methane gas in the fracture; p a is standard atmospheric pressure, T a is the standard temperature; Indicates the porosity of the matrix; S wm and S wf are the water saturation of matrix and fracture respectively; Z m is the deviation coefficient of the real gas in the matrix medium; K(T) is the temperature-related adsorption equilibrium constant; λ is the gas adsorption attenuation coefficient; p gm and p gf are the methane gas pressures in the matrix and fractures, respectively; k mapp is the effective permeability in the shale matrix; is the shale fracture porosity; R is the universal gas constant; V L is the Langmuir adsorption volume constant; G m-f is the shape factor related to the average matrix block size; μ a is the dynamic viscosity of methane gas; T a is the standard temperature.

6. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 5, characterized in that: The moisture changes in the matrix and cracks can be described by the following governing equations, which are shown as follows: i.e., the moisture transport field equations; In the formula, w m (φ m ) is the total water content in the matrix; ω vm is the mass fraction of water vapor in the matrix, v wm is the liquid water convection rate in the matrix, g wm is the binary diffusion coefficient of methane in the matrix in the gas phase, g wcm is the capillary diffusion coefficient of liquid water in the matrix; w f (φ f ) is the total water content in the crack; ω vf is the mass fraction of water vapor in the crack, v wf is the liquid water convection rate in the crack, g wf is the binary diffusion coefficient of methane in the crack in the gas phase; g wcf is the capillary diffusion coefficient of liquid water in the crack.

7. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 6, characterized in that: The heat transfer field equation is shown below; In the formula, Q evap is the evaporation heat source, Q E is the microwave heat source; C represents the specific heat capacity, (ρC eq ) eff is the effective specific heat capacity; κ eq is the thermal conductivity, and Q1 represents the heat source term.

8. The method for calculating the migration of methane in a shale gas reservoir matrix-fracture system under microwave radiation according to claim 7, characterized in that: In step 4, for the electromagnetic field equation, relative dielectric constant, relative magnetic permeability, conductivity, and the frequency of the electromagnetic wave are input into the coupling model to solve the electric field intensity, and the electric field energy is converted into heat energy; In the solid deformation field equation, the physical and mechanical parameters of the shale gas reservoir, including elastic modulus, Poisson's ratio, bulk modulus, isothermal expansion coefficient, maximum horizontal geostress, minimum horizontal geostress, initial porosity and permeability of the matrix and fractures, and Biot coefficient are input to calculate the volume strain of the shale gas reservoir; in the water transport field equation, the change curve of relative humidity in the matrix and fractures is solved; in the heat transfer field equation, the evolution of the temperature inside the reservoir is solved; in the methane transport field equation, the formula is used to obtain the pressure change curve of methane gas in the matrix and the pressure change curve of methane gas in the fracture; and based on the relationship between pore pressure and density, the change of methane gas content in the matrix and fracture system is calculated to obtain the migration trajectory of methane.

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