Shale gas multi-scale percolation mechanism coupling method

Abstract

The invention discloses a coupling method of a shale gas multi-scale percolation mechanism. The coupling method comprises the following steps: establishing a percolation equation based on a quadruple-pore shale matrix model of spherical matrix particles and columnar matrix bars; establishing a seepage equation considering a gas slippage effect, a diffusion effect and adsorption gas desorption; establishing a seepage equation considering the starting pressure gradient and the crack stress sensitive effect; establishing a seepage equation considering desorption of adsorbed gas on the surfaces of the organic matter particles and diffusion of dissolved gas in the organic matter particles; carrying out simultaneous solution on a total seepage equation obtained by coupling the boundary conditions and the pore model characteristics to obtain a bottom hole pressure solution of the fractured horizontal well; drawing a well testing curve chart according to the well bottom pressure solution of the fractured horizontal well; and fitting measured data by adjusting model parameters to obtain inversion results of reservoir parameters and fracture geometric parameters. According to the method, the seepage rule of the shale gas reservoir fractured horizontal well is more comprehensively simulated, and the interpretation precision and range of well testing parameters are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of unconventional natural gas exploration and development, and particularly to a coupling method for shale gas multi-scale seepage mechanisms. Background Art

[0002] At present, the development of shale gas in China is in a rapid development stage with great potential. The matrix pore scale of shale gas reservoirs is very small, the permeability is extremely low, there are a large number of microfractures, and the actual situation of the reservoir is extremely complex. Due to the special reservoir-forming, occurrence and development modes of shale gas reservoirs, there are multiple transport mechanisms for gas in the reservoir, with obvious multi-scale characteristics, and it is difficult to couple the gas flow laws in each scale space.

[0003] Shale gas reservoirs have diverse pore types and a large scale span, with nanoscale matrix pores and micron-scale natural fractures developed, and there are also secondary fractures with a scale of microns to millimeters formed by fracturing and hydraulic main fractures with a larger scale. Therefore, it is necessary to consider the characteristics of shale gas multi-scale seepage. Gas is mainly viscous flow in microfractures, but its migration in matrix pores is mainly controlled by microscopic seepage mechanisms such as slippage and diffusion. When flowing at a low speed in nanoscale matrix pores, a certain starting pressure gradient needs to be overcome. And relevant research shows that in some shale gas reservoir organic matters, the proportion of dissolved gas in the total reserves exceeds 22%, and the dissolution coefficient can reach 1.43×10 -6 m 3 / (Pa·m 3 ), so the dissolved gas in organic matters is also worthy of attention. At present, the existing models do not fully consider multi-scale media and seepage mechanisms, and the simulated seepage law of horizontal wells in shale gas reservoirs is relatively idealized. Summary of the Invention

[0004] In order to overcome the above-mentioned disadvantages of the prior art, the present invention proposes a coupling method for shale gas multi-scale seepage mechanisms, making the simulated seepage law of horizontal wells in shale gas reservoirs more in line with the actual situation.

[0005] The technical solution adopted by the present invention to solve its technical problems is: a coupling method for shale gas multi-scale seepage mechanisms, including the following steps:

[0006] Step 1: Obtain the basic parameters related to the formation and fluid required for model calculation;

[0007] Step 2: Establish a seepage equation based on a quadruple-porosity shale matrix model of spherical matrix particles and columnar matrix bars;

[0008] Step 3: Establish a seepage equation considering gas slippage effect, diffusion effect, and desorption of adsorbed gas;

[0009] Step 4: Establish a seepage equation considering starting pressure gradient and fracture stress sensitivity effect;

[0010] Step 5: Establish a percolation equation that takes into account the desorption of adsorbed gas on the surface of organic matter particles and the diffusion of dissolved gas inside them;

[0011] Step 6: Solve the total seepage equation obtained by coupling the boundary conditions and the pore model characteristics to obtain the bottom hole pressure solution of the fractured horizontal well;

[0012] Step 7: Draw a well test curve chart based on the bottom hole pressure solution of the fractured horizontal well;

[0013] Step 8: Obtain the inversion results of reservoir parameters and fracture geometry parameters by adjusting the model parameters to fit the measured data.

[0014] Compared with the prior art, the present invention has the following positive effects:

[0015] The present invention fully considers the seepage mechanisms such as gas slippage, Knudsen diffusion, adsorption-desorption of adsorbed gas, fracture stress sensitivity and starting pressure gradient effect, and constructs a quadruple porosity shale matrix model based on "cylindrical matrix sticks + spherical organic particles" taking into account the intrapores of organic particles, intergranular pores, inorganic pores and fractures for coupled solution; the present invention applies the Green function and other methods to solve the equations in cylindrical coordinates, reduces the nonlinearity of the seepage equation, effectively solves the problem of non-homogeneous terms appearing in the solution process, fully considers the complex seepage mechanism of shale gas, more comprehensively simulates the seepage law of horizontal wells in shale gas reservoirs, and improves the interpretation accuracy and range of well test parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The present invention will now be described by way of example with reference to the accompanying drawings, in which:

[0017] Figure 1 This is a table of relevant basic parameters involved in the embodiment model;

[0018] Figure 2 This is a schematic diagram of the cylindrical matrix stick quadruple pore model structure;

[0019] Figure 3 This is the effect of matrix permeability on typical well test curves;

[0020] Figure 4 This is the effect of the Langmuir volume constant on a typical well test curve;

[0021] Figure 5 This is the influence diagram of the startup pressure gradient effect on the typical well test curve;

[0022] Figure 6 This is the influence diagram of stress sensitivity effect on typical well test curve;

[0023] Figure 7Fitting curve chart for actual well test data 1

[0024] Figure 8 Fitting curve chart for actual well test data 2 Specific implementation manner

[0025] A coupling method for shale gas multi-scale seepage mechanism, comprising the following steps:

[0026] S1: Obtain formation physical property parameters, well data, and well test pressure and flow rate data:

[0027] Prepare basic parameters related to the formation and fluid required for model calculation. The said related basic parameters are shown in Figure 1 , including: proportion of clay content, proportion of organic matter content, original formation pressure, formation temperature, gas viscosity, gas compressibility factor, comprehensive compressibility coefficient, Langmuir adsorption volume, Langmuir pressure, permeability, porosity, etc.;

[0028] S2: Establish a quadruple-porosity shale matrix model of "cylindrical matrix stick + spherical organic matter particle", as shown in Figure 2 ;

[0029] The voids between the cylindrical matrix sticks are micro-fracture spaces. The inside of the cylindrical matrix sticks is composed of spherical particles of triple media (kerogen, inorganic matter, clay) and natural fractures between them. The radius of the cylindrical matrix stick is R m , m; the fluid flow direction of the natural fractures is radial flow, and the seepage equation can be expressed in cylindrical coordinates. Considering seepage mechanisms such as gas slippage, Knudsen diffusion, gas adsorption difference between organic matter and matrix-free, fracture stress sensitivity effect, and starting pressure gradient effect, the following assumptions are proposed:

[0030] (1) Only single-phase gas seepage exists, and the influence of temperature and gravity on seepage is not considered;

[0031] (2) The influence of Knudsen diffusion and starting pressure gradient is considered in the gas seepage in the matrix pores; the seepage in the fracture system conforms to Darcy's law; the adsorption and desorption of adsorbed gas satisfy Langmuir isothermal adsorption law; there are surface adsorbed gas desorption and internal dissolved gas diffusion mechanisms in the organic matter particles;

[0032] Using the spherical matrix particle model, the seepage control equation is:

[0033]

[0034] Using the cylindrical matrix stick model, the seepage control equation is:

[0035]

[0036] Where: r m is the internal distance of the matrix, m; m m is the pseudo-pressure of the matrix, Pa / s; K m is the permeability, m 2 ; φ m is the porosity, decimal; μ g is the gas viscosity, Pa·s; is the total compressibility of the matrix, Pa -1 .

[0037] The pseudo-pressure is defined as follows:

[0038]

[0039] Where: m is the gas pseudo-pressure, Pa / s; z is the gas deviation factor; m, f, F are the matrix, micro-fracture, and hydraulic fracture respectively.

[0040] The boundary conditions are as follows:

[0041]

[0042] Where: m i is the initial pseudo-pressure, Pa / s; R m is the radius of the cylindrical matrix, m; m f is the gas pseudo-pressure of the micro-fracture, Pa / s.

[0043] S3: Establish a seepage equation considering slip, Knudsen diffusion effect, and desorption of adsorbed gas, as follows:

[0044] S31: The motion equation considering the Knudsen diffusion effect during gas seepage:

[0045]

[0046] Where: v m is the seepage velocity of the matrix fluid, m / s; v Dm is the velocity component controlled by viscous flow, m / s; v Kn is the Knudsen velocity component, m / s; c g is the gas compressibility, Pa -1 ; K m is the matrix permeability, m 2 ; μ g is the gas viscosity, Pa·s; D g is the gas diffusion constant; p m is the internal pressure of the matrix pores, Pa; r m is the internal distance of the matrix, m.

[0047] Where D g is the diffusion coefficient constant:

[0048]

[0049] Where: M g is the molar mass of the gas, mol / kg.

[0050] S32: Considering the gas slippage effect, the concept of apparent permeability is applied to correct the conventional Darcy permeability:

[0051]

[0052] Where: K ma is the matrix apparent permeability, m 2 ; K m is the matrix permeability, m 2 ; b ma is the slippage factor, Pa; p r is the reference pressure (usually taken as the average pressure at the outlet end face), Pa.

[0053] S33: Further express the seepage equation as:

[0054]

[0055] S34: The desorption law of adsorbed gas is usually described by the Langmuir isothermal adsorption law, and the desorbed amount of adsorbed shale gas can be expressed as:

[0056]

[0057] Where: q m is the mass flow rate of desorbed gas, kg / m 3 ; f rm is the proportion of solid medium in the matrix per unit volume, decimal; V E is the desorption volume of adsorbed gas, m 3 ; ρ sc is the standard condition gas density, kg / m 3 .

[0058] The proportion of solid medium in the matrix of shale gas reservoir satisfies the following relationship:

[0059] f rm + φ m + f f = 1

[0060] Where: f f is the proportion of microfracture volume, decimal.

[0061] Combining the above formula, we get:

[0062]

[0063] Where: V L is the Langmuir adsorption volume, m 3 / m 3 ; p L is the Langmuir pressure, Pa.

[0064] S35: Substituting into the partial differential equation gives:

[0065]

[0066] Where: T is the system temperature, K.

[0067] S36: The pseudo-pressure form is expressed as:

[0068]

[0069] Where: c tm is the comprehensive compressibility of the matrix, Pa -1 .

[0070] S4: Establish the seepage equation considering the starting pressure gradient and fracture stress sensitivity effect, specifically as follows:

[0071] S41: The expression method of the starting pressure gradient is as follows:

[0072]

[0073] Where: v is the seepage velocity, m / s; K is the permeability, μm 2 ; μ is the viscosity, mPa·s; is the pressure gradient, MPa / m; λ T is the starting pressure gradient, MPa / m.

[0074] S42: For the stress sensitivity effect, use the pressure-controlled permeability exponential formula introducing the permeability modulus:

[0075]

[0076] Where: γ is the permeability modulus, Pa -1 ; p is the formation pressure, Pa; K i is the reservoir permeability corresponding to the initial formation pressure, m 2 .

[0077] S43: When considering both the starting pressure gradient effect and the stress sensitivity effect in the low-speed seepage stage, the fracture seepage equation is expressed in pseudo-pressure as:

[0078]

[0079] Where: m mfiis the initial pseudo-pressure, Pa / s; m mf is the fracture pseudo-pressure, Pa / s; β is the permeability modulus controlled by pseudo-pressure, s / Pa; λ m is the starting pressure gradient, Pa / m.

[0080] S5: Establish a seepage equation considering the desorption of adsorbed gas on the surface of organic matter particles and the diffusion of dissolved gas inside them, as follows:

[0081] S51: Establish the dissolved gas diffusion equation inside organic matter particles as follows:

[0082]

[0083] In the formula: D o is the diffusion coefficient, m 2 / s; C is the concentration of dissolved gas inside organic matter, sm 3 / m 3 ; r o is the radial distance, m; C i is the concentration of dissolved shale gas under the original pressure inside organic matter.

[0084] For the calculation of dissolved gas concentration, Henry's law can be applied:

[0085] C = H(p oi - p o )

[0086] In the formula: H is the Henry coefficient, Pa -1 ; p oi is the original pressure of the internal system of organic matter, Pa; p o is the pressure of the internal system of organic matter, Pa.

[0087] S52: The seepage equation considering the dissolved gas and adsorption-desorption laws in the intra-granular pores and inter-granular pores of organic matter is:

[0088]

[0089] In the formula: f k is the kerogen content, decimal; φ k is the percentage of inter-granular pores of organic matter in the volume of shale gas reservoir matrix rock, decimal; c kt is the compressibility coefficient of inter-granular pores of organic matter, Pa -1 ; r k is the distance from any point in the inter-granular pores of organic matter to the center of the sphere, m; R k is the radius of kerogen particles; p k is the pressure in the inter-granular pores of organic matter, Pa; the subscripts L, k represent the surface of organic matter.

[0090] Satisfy the boundary conditions:

[0091]

[0092]

[0093] S6: Based on the boundary conditions and the characteristics of the pore model, couple the above seepage equation, and comprehensively apply methods such as Laplace transform, Green's function, perturbation method, and line source function for simultaneous solution to obtain the bottom-hole pressure solution:

[0094] The total seepage equation obtained by coupling is:

[0095]

[0096] In the formula: the subscripts L and m represent the adsorbed gas from the clay mineral surface.

[0097] The model solution gives:

[0098]

[0099] The third term on the right side is the Green's function integral, and the expression is as follows:

[0100]

[0101] In the formula: u mc , u k are process variables, and the expressions are as follows:

[0102]

[0103] Apply the Stehfest numerical inversion to transform the solution in the Laplace space into the solution in the real space.

[0104] S7: Draw a well test curve chart based on the bottom-hole pressure solution of the horizontal fractured well:

[0105] Through all the data of the bottom-hole pressure solution, a dimensionless typical curve of the well test model pressure varying with time for the coupled multi-scale seepage mechanism of shale gas can be made. At the same time, it can also be divided into the following according to the flow stages: (1) pure wellbore storage stage; (2) wellbore storage effect and skin effect influence stage; (3) bilinear flow stage; (4) natural fracture-microfracture fluid replenishment stage; (5) linear flow stage; (6) shale matrix pore to natural fracture fluid replenishment stage; (7) transitional flow stage; (8) boundary control flow stage.

[0106] S71: Keeping other parameters unchanged, adjust the matrix permeability to 1×10 -5 mD, 5×10 -6 mD, 1×10 -6mD, analyze the influence of matrix permeability on the shape of well test curves, see Figure 3 ;

[0107] S72: Keep other parameters unchanged, adjust the Langmuir volume constant to 5, 10, 15, and analyze the influence of the Langmuir volume constant on the shape of well test curves, see Figure 4 ;

[0108] S73: Keep other parameters unchanged, adjust the starting pressure gradient to 0.01, 0.05, 0.1, and analyze the influence of the starting pressure gradient on the shape of well test curves, see Figure 5 ;

[0109] S74: Keep other parameters unchanged, adjust the dimensionless fracture permeability modulus to 0, 0.05, 0.1, and analyze the influence of stress sensitivity on the shape of well test curves, see Figure 6 ;

[0110] S8: Fit the measured data by adjusting the model parameters to obtain the inversion results of reservoir parameters and fracture geometric parameters:

[0111] S81: Adjust the skin factor S c = 0.0031, the half-length of the hydraulic fracture x F = 52 m, the permeability of the hydraulic fracture K HF = 4.5 mD, the matrix permeability K mc = 3×10 -6 mD, the permeability of the microfracture K f = 0.8 mD and other parameters, the spacing of the hydraulic fractures is 21 m, fit the test data of Example 1, and predict the shape of the well test curve, see Figure 7 ;

[0112] S82: Adjust the skin factor S c = 0.01, the half-length of the hydraulic fracture x F = 40 m, the permeability of the hydraulic fracture K HF = 5 mD, the matrix permeability K mc = 1.5×10 -4 mD, the permeability of the microfracture K f = 0.8 mD and other parameters, fit the test data of Example 2, and predict the shape of the well test curve, see Figure 8 .

Claims

1. A coupling method for multi-scale seepage mechanism of shale gas, Features: The steps include: Step 1: Obtain the basic parameters related to formation and fluid required for model calculation; Step 2: Establishing the seepage equation based on the quadruple-pore shale matrix model of spherical matrix particles and columnar matrix sticks; Step 3: Establish a percolation equation that takes into account gas slippage effect, diffusion effect, and adsorbed gas desorption; Step 4: Establish a seepage equation that takes into account the start-up pressure gradient and fracture stress sensitivity effect; Step 5: Establish a percolation equation that takes into account the desorption of adsorbed gas on the surface of organic matter particles and the diffusion of dissolved gas inside them; Step 6: Solve the total seepage equation obtained by coupling the boundary conditions and the pore model characteristics to obtain the bottom hole pressure solution of the fractured horizontal well; Step 7: Draw a well test curve chart based on the bottom hole pressure solution of the fractured horizontal well; Step 8: Obtain the inversion results of reservoir parameters and fracture geometry parameters by adjusting the model parameters to fit the measured data.

2. A coupling method for multi-scale seepage mechanism of shale gas according to claim 1, Features: The basic parameters related to the formation and fluid described in step 1 include: clay content ratio, organic matter content ratio, original formation pressure, formation temperature, gas viscosity, gas compression factor, comprehensive compression coefficient, Langmuir adsorption volume, Langmuir pressure, permeability, and porosity.

3. The coupling method of multi-scale seepage mechanism of shale gas according to claim 1, Features: In the quadruple-porosity shale matrix model based on spherical matrix particles and columnar matrix sticks described in step 2, the gaps between the columnar matrix sticks are micro-fracture spaces, the interior of the columnar matrix sticks is composed of triple-medium spherical matrix particles and the natural fractures between them, the flow direction of the natural fracture fluid is radial flow, and the seepage equation is expressed by cylindrical coordinates.

4. A coupling method for multi-scale seepage mechanism of shale gas according to claim 3, Features: The ternary medium includes kerogen, inorganic matter and clay.

5. The coupling method of shale gas multi-scale seepage mechanism according to claim 1, Features: The method for establishing the seepage equation based on the quadruple-pore shale matrix model of spherical matrix particles and columnar matrix sticks in step 2 is: (1) The seepage equation is established using the spherical matrix particle model: (2) The seepage equation is established using the columnar matrix stick model: where: r m is the internal distance of the matrix, m; m m is the pseudo-pressure of the matrix, Pa / s; K m is the permeability, m 2 ; φ m is the porosity, decimal; μ g is the gas viscosity, Pa·s; is the total compressibility of the matrix, Pa -1 ; The boundary conditions are as follows: where: m i is the original pseudo-pressure, Pa / s.

6. The coupling method of shale gas multi-scale seepage mechanism according to claim 1, Features: The method for establishing the percolation equation considering the gas slippage effect, diffusion effect and adsorbed gas desorption described in step 3 is: The first step is to establish the motion equation considering the Knudsen diffusion effect when gas seepage: Where: v m is the seepage velocity of the matrix fluid, m / s; v Dm is the velocity component controlled by viscous flow, m / s; v Km is the Knudsen velocity component, m / s; c g is the gas compressibility, Pa -1 ; K m is the matrix permeability, m 2 ; μ g is the gas viscosity, Pa·s; D g is the gas diffusion constant; p m is the internal pressure of the matrix pores, Pa; r m is the internal distance of the matrix, m; The second step is to consider the gas slippage effect and use the apparent permeability to correct the conventional Darcy permeability to establish the following seepage equation: In the formula: K ma is the matrix apparent permeability, m 2 ; K m is the matrix permeability, m 2 ; b ma is the slippage factor, Pa; p r is the reference pressure, Pa; The third step is to consider the desorption of adsorbed gas and establish the following permeation equation: where: z is the gas deviation factor; T is the system temperature, K; f f is the proportion of microfracture volume, in decimals; V L is the Langmuir adsorption volume, m 3 / m 3 ; p L is the Langmuir pressure, Pa; c tm is the comprehensive compressibility coefficient of the matrix, Pa -1 .

7. The coupling method of shale gas multi-scale seepage mechanism according to claim 1, Features: The method for establishing the seepage equation considering the start-up pressure gradient and the fracture stress sensitivity effect described in step 4 is: (1) Calculate the seepage velocity according to the following formula: Where: v is the seepage velocity, m / s; K is the permeability, μm 2 ; μ is the viscosity, mPa·s; is the pressure gradient, MPa / m; λ T is the starting pressure gradient, MPa / m; γ is the permeability modulus, Pa-1; p is the formation pressure, Pa; K i is the reservoir permeability corresponding to the initial formation pressure, m 2 ; (2) Establish the fracture seepage equation considering the start-up pressure gradient effect and stress sensitivity effect in the low-speed seepage stage: Where: m mfi is the initial pseudo-pressure, Pa / s; m mf is the fracture pseudo-pressure, Pa / s; β is the permeability modulus controlled by pseudo-pressure, s / Pa; λ m is the starting pressure gradient, Pa / m.

8. The coupling method of multi-scale seepage mechanism of shale gas according to claim 1, Features: The method for establishing the percolation equation taking into account the desorption of adsorbed gas on the surface of organic matter particles and the diffusion of dissolved gas inside the organic matter particles as described in step 5 is: (1) Establish the dissolved gas diffusion equation inside organic matter particles: Where: D o is the diffusion coefficient, m 2 / s; r o is the radial distance, m; C i is the dissolved shale gas concentration under the original pressure inside the organic matter; C is the dissolved gas concentration inside the organic matter, sm 3 / m 3 , and is calculated according to the following formula: C = H(p oi -p o ) Where: H is the Henry coefficient, Pa -1 ; p oi is the original pressure of the internal system of the organic matter, Pa; p o is the pressure of the internal system of the organic matter, Pa; (2) Establish a seepage equation that takes into account the dissolved gas and adsorption-desorption laws of the organic particles' intra-particle pores and inter-particle pores: where: r k is the distance from any point in the pore between organic matter particles to the center of the sphere, m; p k is the pressure in the pore between organic matter particles, Pa; is the mass flow rate intensity of gas diffusing from inside the organic matter particles to the pores between organic matter particles, kg / (m 3 ·s); is the mass flow rate intensity of the adsorbed gas desorbing and flowing into the pores between organic matter particles after desorption, kg / (m 3 ·s); φ kp is the porosity of the pore system between organic matter particles, in decimals.

9. The coupling method of shale gas multi-scale seepage mechanism according to claim 1, Features: The method for solving the total seepage equation obtained by coupling the boundary conditions and the pore model characteristics described in step 6 is: (1) Using boundary conditions and pore model characteristics, the total seepage equation is established: Where: subscript L, m represents the adsorbed gas from the surface of clay minerals; (2) The model is solved to obtain: Among them, the third term on the right is the Green function integral, and the expression is as follows: where: u mc , u k are process variables, and the expressions are as follows: Stehfest numerical inversion is used to transform the Laplace space solution into the real space solution.

10. The coupling method of multi-scale seepage mechanism of shale gas according to claim 1, Features: In step seven, the well test model is divided into the following flow stages using the drawn well test curve: 1) pure wellbore storage stage; 2) wellbore reservoir effect and skin effect influence stage; 3) dual linear flow stage; 4) natural fracture-micro fracture fluid replenishment stage; 5) linear flow stage; 6) fluid replenishment stage from shale matrix pores to natural fractures; 7) transition flow stage; 8) boundary controlled flow stage.

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