Shale matrix two-phase flow simulation and relative permeability curve determination method and device

Abstract

The invention relates to a shale matrix two-phase flow simulation and relative permeability curve determination method and device, and belongs to the technical field of shale gas multiphase flow simulation. The invention discloses a shale matrix two-phase flow simulation and relative permeability curve determination method and device. The method comprises the following steps: measuring single-phase permeability of a target reservoir core under different effective stresses; extracting a PNM model based on the connected pores; simulating and calculating the radius of the deformed pores and throats in the PNM model under different effective stresses and the permeability after deformation, and fitting the single-phase permeability after deformation; updating the PNM model under different effective stresses; calculating capillary inlet pressure; and calculating the relative permeability in the PNM model under different effective stresses. The method can be used for gas-water two-phase flow simulation of the shale gas reservoir under variable stress, can also be used for stress sensitive simulation and analysis of various lithologic reservoirs such as compact sandstone and carbonate rock, and has wide application value in the aspects of shale gas development practice and recovery efficiency improvement.

Description

Technical Field

[0001] The invention relates to a method and a device for shale matrix two-phase flow simulation and phase permeability curve determination, belonging to the technical field of shale gas multiphase flow simulation. Background Art

[0002] Shale gas production often faces severe stress sensitivity. As fluid is gradually extracted from the pores, the effective stress inside and outside the pores increases, causing the pores to shrink, thereby affecting the gas-water two-phase flow capacity. Current experimental methods are unable to achieve gas-water two-phase displacement in shale matrices under overburden pressure, resulting in a poor understanding of the dynamics of relative permeability curves under stress, which seriously hinders the development of reasonable on-site production systems.

[0003] Therefore, it is necessary to propose a method and device for simulating two-phase flow in shale matrix and determining phase permeability curves, which can be used to study the evolution law of phase permeability curves under variable stress in shale matrix and provide technical support for the input of key parameters in macroscopic numerical simulation and efficient development of blocks. Summary of the Invention

[0004] The purpose of the present invention is to address the problems existing in the prior art and to provide a method and device for simulating two-phase flow in a shale matrix and determining a phase permeability curve.

[0005] The present invention provides a technical solution to solve the above technical problems: a method for simulating two-phase flow in a shale matrix and determining a phase permeability curve, comprising the following steps: S1. Determine the single-phase permeability of the target reservoir core under different effective stresses by using the pressure pulse method; S2, constructing a digital core model of the target reservoir core and extracting a PNM model based on connected pores; S3. Based on the single-phase permeability under different effective stresses, simulate and calculate the radius of the pores and throats in the PNM model after deformation and the permeability after deformation under different effective stresses, and fit the deformed single-phase permeability; S4. Update the pore radius, throat radius, pore volume, throat volume, and clay volume in the PNM model under different effective stresses according to the radius of the pores and throat deformation after permeability fitting in step S3; S5, calculating the capillary inlet pressure in the PNM model under different effective stresses according to the radius of the pores and throat deformation after the permeability fitting in step S3; S6. Calculate the relative permeability in the PNM model under different effective stresses.

[0006] A further technical solution is to adjust the initial permeability of the PNM model during the simulation calculation in step S3, so as to make the initial permeability of the PNM higher than the permeability at the first effective pressure point measured by the pressure pulse method.

[0007] A further technical solution is that the radius calculation formula of the pore and throat after deformation in step S3 is:

[0008] Where: r and r 0 is the equivalent radius of the pore or throat before and after deformation, is the porosity of PNM, K rock is the bulk modulus of rock, α B is the Biot coefficient, Δ p is the change in pore pressure, λ The degree of laryngeal closure.

[0009] A further technical solution is that in the simulation calculation of step S3, the length, shape factor and coordination number of the pores and throats do not change, only the pore radius and throat radius change, and the throat will close.

[0010] A further technical solution is that in step S4, the pore radius and throat radius after permeability fitting in step S3 are selected to replace the pore radius and throat radius in the PNM model; and the volume of each pore and throat and the clay volume in the PNM are calculated one by one to replace the pore volume, throat volume, and clay volume in the PNM model.

[0011] A further technical solution is that the volume calculation formula of the pores and throats in step S4 is:

[0012] Where: V P 、 V uncT and V cT are the volume of pores after deformation, the volume of unclosed throats after deformation, and the volume of closed throats after deformation; V P0 、 V uncT0 and V cT0 are the volume of pores at 0 MPa, the volume of unclosed throats at 0 MPa, and the volume of closed throats at 0 MPa; δ c is the rate of change of the equivalent radius of the closed throat; δ unc is the rate of change of the equivalent radius of the pore or unclosed throat.

[0013] A further technical solution is that the calculation formula for the clay volume in step S4 is:

[0014] Where: V Pclay 、 V uncTclay and V cTclay They are the volume of clay attached to pores after deformation, the volume of clay attached to unclosed throats after deformation, and the volume of clay attached to closed throats after deformation; V Pclay0 、 V uncTclay0 and V cTclay0 They are the clay volume attached to pores at 0 MPa, the clay volume attached to unclosed throats at 0 MPa, and the clay volume attached to closed throats at 0 MPa.

[0015] A further technical solution is that the capillary inlet pressure in step S5 is the set of capillary inlet pressures of each pore and throat.

[0016] The present invention provides an electronic device comprising: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus, and the machine-readable instructions are executed by the processor to implement the above-mentioned method for shale matrix two-phase flow simulation and phase permeability curve determination.

[0017] Beneficial effects of the present invention: In addition to being used for simulating gas-water two-phase flow in shale gas reservoirs under variable stress, the present invention can also be used for stress sensitivity simulation and analysis of various lithologic reservoirs such as tight sandstone and carbonate rock, and has broad application value in shale gas development practice and improving recovery rates. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is the constructed pore network model at 0 MPa; Figure 2 Comparison of pore and throat radius before and after deformation; Figure 3 is the fitting plate of absolute permeability; Figure 4 Relative permeability curves under different effective stresses. DETAILED DESCRIPTION

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of the invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of the present invention.

[0020] The present invention provides a method for simulating two-phase flow in a shale matrix and determining a phase permeability curve, comprising the following steps: S1. Determine the single-phase permeability of the target reservoir core under different effective stresses by using the pressure pulse method; S2, constructing a digital core model of the target reservoir core and extracting a PNM model based on connected pores; The PNM model refers to the pore network model, and subsequent simulation calculations are all based on this PNM model; S3. Based on the single-phase permeability under different effective stresses, the radius of the pores and throats in the PNM model after deformation and the permeability after deformation were simulated and calculated under different effective stresses. The deformed single-phase permeability was fitted, and the relative error range of the fitting was within 10%. When calculating the model, In the first part, the initial permeability of the PNM model is adjusted to make the initial permeability of the PNM (i.e., the permeability when the effective stress is 0) higher than the permeability at the first effective pressure point measured by the pressure pulse method. The permeability in the PNM model is calculated using Darcy's law, and the adjustment method is to change the pore size distribution in the PNM model. The second part is the deformation simulation and permeability fitting of the PNM model under variable stress. This part first calculates the radius of the pores and throats in the PNM model after deformation, and then calculates the permeability of the deformed PNM model. The formula for calculating pore and throat deformation is as follows: (1) Where: r and r 0 is the equivalent radius of the pore or throat before and after deformation, is the porosity of PNM, K rock is the bulk modulus of rock, α B is the Biot coefficient, Δ p is the change in pore pressure, λ The degree of laryngeal closure.

[0021] At the same time, parameters such as the length, shape factor, and coordination number of the pores and throats do not change during the deformation simulation. Only the pore radius and throat radius change, and the throat closes. The purpose is to ensure that the three-dimensional physical scale of the entire PNM skeleton remains consistent before and after deformation.

[0022] The permeability fitting method is as follows: based on the single-phase permeability obtained in step S1, the throat closure ratio in the pore deformation method is adjusted so that the simulated permeability and the experimental permeability fit, and the relative error range of the fitting is within 10%.

[0023] S4. Update the pore radius, throat radius, pore volume, throat volume, and clay volume in the PNM model under different effective stresses according to the radius of the pores and throat deformation after permeability fitting in step S3; The method for updating the pore radius and throat radius is as follows: the pore radius and throat radius after permeability fitting in step S3 are selected and replaced with the pore radius and throat radius in the PNM model. The method for updating the pore volume and throat volume is as follows: after the pore radius and throat radius are updated, the volume of each pore and throat and the clay volume in the PNM model are calculated one by one, and the pore volume, throat volume, and clay volume in the PNM model are replaced with the pore volume, throat volume, and clay volume in the PNM model.

[0024] The pores only experience volumetric strain, while the throats are divided into closed throats and unclosed throats under the premise of volumetric strain. Therefore, the equivalent radius change rate of the pores or unclosed throats is as follows: (2) Where: δ unc is the rate of change of the equivalent radius of the pore or unclosed throat; The rate of change of the equivalent radius of the closed throat is: (3) Where: δ c is the rate of change of the equivalent radius of the closed throat; (4) Where: V P 、 V uncT and V cT are the volume of pores after deformation, the volume of unclosed throats after deformation, and the volume of closed throats after deformation; V P0 、 V uncT0 and V cT0They are the volume of pores at 0 MPa, the volume of unclosed throats at 0 MPa, and the volume of closed throats at 0 MPa.

[0025] Update the clay volume by the following formula; (5) Where: V Pclay 、 V uncTclay and V cTclay They are the volume of clay attached to pores after deformation, the volume of clay attached to unclosed throats after deformation, and the volume of clay attached to closed throats after deformation; V Pclay0 、 V uncTclay0 and V cTclay0 They are the clay volume attached to pores at 0 MPa, the clay volume attached to unclosed throats at 0 MPa, and the clay volume attached to closed throats at 0 MPa; S5, calculating the capillary inlet pressure in the PNM model under different effective stresses according to the radius of the pores and throat deformation after the permeability fitting in step S3; The two-phase contact angle of each pore and throat does not change with the change of effective stress. The capillary inlet pressure in PNM under different effective stresses is a series of different capillary inlet pressure sets. When the effective stress changes, the radius of each pore and throat will change, which in turn causes the capillary inlet pressure to change. (6) Where: P c is the capillary inlet pressure; ψ is the surface tension of the air-water phase; θ is the contact angle; r ins ' is the radius of the pore or throat under different effective stresses; n The number of filled throats representing pore connections; C i is an arbitrary parameter, X i Is a random number between 0 and 1; S6. Calculate the relative permeability in the PNM model under different effective stresses; The calculation method of gas-water two-phase permeability is as follows: (7) (8) Where:K rw and K rg are the relative permeabilities of water and gas, respectively; Q w and Q g are the flow rates of water and gas respectively; μ w and μ g are the viscosities of water and air, respectively; L is the length of PNM along the flow direction; K is the absolute permeability of PNM; A is the cross-sectional area of ​​PNM perpendicular to the flow direction; Δ P is the pressure difference between the inlet and outlet.

[0026] Each effective stress corresponds to a relative permeability curve. When the effective stress changes, the pore and throat radius in the PNM also change, which in turn affects the flow rates of the water and gas phases, ultimately leading to changes in the permeability of the two phases. The flow change caused by throat closure will be significantly higher than the flow change when closure does not occur.

[0027] The present invention provides an electronic device comprising: a processor, a memory, and a bus. The memory stores machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus, and the machine-readable instructions are executed by the processor to implement the above-mentioned method for shale matrix two-phase flow simulation and phase permeability curve determination.

[0028] Example The digital core used in this example comes from a shale block in China. The digital core is constructed using a numerical reconstruction method. The core is cylindrical with a diameter of 0.0012 m and a length of 0.0012 m. The porosity of the pore network model is 6%. The bulk modulus used in the pore and throat deformation process is 25 GPa, the Biot coefficient is 0.6, and the effective stress ranges from 5 MPa to 50 MPa. The density ratio of the wetting phase and the non-wetting phase used in the two-phase flow simulation is 1.27, the viscosity ratio is 0.039, the contact angle distribution range is 40-70°, and the interfacial tension of the two phases is 0.03 N / m.

[0029] The following demonstrates how a shale matrix two-phase flow simulation and phase permeability curve determination method proposed in the present invention performs pore and throat deformation and permeability fitting based on the above data, thereby calculating the phase permeability curve under different effective stresses.

[0030] like Figure 1The figure shows the PNM model based on connected pore space extraction, where the balls represent pores and the sticks represent throats. All subsequent simulations are based on this PNM model.

[0031] like Figure 2 The figure shows the pore and throat deformations at different effective stresses calculated using Equation (1). When the effective stress is 0 MPa, the pore throat does not deform, but its absolute permeability must be higher than the permeability of the first point measured by the pressure pulse method (at 5 MPa). As the effective stress increases, the parameters during the throat closure process are gradually changed to achieve permeability fitting.

[0032] Figure 2 The pore and throat radii are shown when the effective stress is 0 MPa and 50 MPa, respectively. The left and right images are collected in the same area. It can be seen from the figure that after simulating the deformation of the pore and throat, the pore will undergo slight deformation, while the throat radius will change significantly due to closure.

[0033] Figure 3 The results of permeability fitting are shown. The method of fitting permeability in this embodiment is as follows: the deformation of the pores follows the part of formula (1) that does not close, and the closure of the throat adopts random closure, following the part of formula (1) that closes.

[0034] Figure 4 Based on Figure 3 The two-phase relative permeability curves calculated by the PNM model obtained by fitting show that the relative permeability curves change significantly due to the gradual increase in the throat closure range, among which the water phase permeability gradually increases. When the number of closed throats increases significantly, the relative permeability curve also changes significantly and becomes extremely narrow.

[0035] The present invention provides a method and device for simulating two-phase flow in a shale matrix and determining a phase permeability curve. This method and device use digital cores and a PNM model as geometric foundations, single-phase permeability measured by a pressure pulse method as a fitting criterion, PNM deformation under different effective stresses as the fundamental concept, and a computer device as the implementation medium. The method and device theoretically explain the method and device for simulating two-phase flow in a shale matrix and determining a phase permeability curve under variable stress.

[0036] The above description does not limit the present invention in any form. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any technician familiar with the profession can use the technical content disclosed above to make some changes or modifications to equivalent embodiments without departing from the scope of the technical solution of the present invention. However, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention are within the scope of the technical solution of the present invention.

Claims

1. A method for simulating two-phase flow in shale matrix and determining phase permeability curve, characterized in that: The following steps are involved: S1. Determine the single-phase permeability of the target reservoir core under different effective stresses by using the pressure pulse method; S2, constructing a digital core model of the target reservoir core and extracting a PNM model based on connected pores; S3. Based on the single-phase permeability under different effective stresses, simulate and calculate the radius of the pores and throats in the PNM model after deformation and the permeability after deformation under different effective stresses, and fit the deformed single-phase permeability; S4. Update the pore radius, throat radius, pore volume, throat volume, and clay volume in the PNM model under different effective stresses according to the radius of the pores and throat deformation after permeability fitting in step S3; S5, calculating the capillary inlet pressure in the PNM model under different effective stresses according to the radius of the pores and throat deformation after the permeability fitting in step S3; S6. Calculate the relative permeability in the PNM model under different effective stresses.

2. A shale matrix two-phase flow simulation and phase permeability curve determination method according to claim 1, characterized in that: During the simulation calculation in step S3, the initial permeability of the PNM model is first adjusted, with the goal of making the initial permeability of the PNM higher than the permeability at the first effective pressure point measured by the pressure pulse method.

3. The method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 1, characterized in that: The calculation formula for the radius of the pore and throat after deformation in step S3 is: Where: r and r 0 is the equivalent radius of the pore or throat before and after deformation, is the porosity of PNM, K rock is the bulk modulus of rock, α B is the Biot coefficient, Δ p is the change in pore pressure, λ The degree of laryngeal closure.

4. The method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 1, characterized in that: In the simulation calculation of step S3, the length, shape factor and coordination number of the pores and throats do not change, and only the pore radius and throat radius change.

5. The method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 1, characterized in that: In step S4, the pore radius and throat radius after permeability fitting in step S3 are selected to replace the pore radius and throat radius in the PNM model; then, the volume of each pore and throat and the clay volume in the PNM are calculated one by one, and the pore volume, throat volume, and clay volume in the PNM model are replaced.

6. A method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 5, characterized in that: The calculation formulas for the pore volume and throat volume in step S4 are: Where: V P 、 V uncT and V cT are the volume of pores after deformation, the volume of unclosed throats after deformation, and the volume of closed throats after deformation; V P0 、 V uncT0 and V cT0 are the volume of pores at 0 MPa, the volume of unclosed throats at 0 MPa, and the volume of closed throats at 0 MPa; δ c is the rate of change of the equivalent radius of the closed throat; δ unc is the rate of change of the equivalent radius of the pore or unclosed throat.

7. The method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 5, characterized in that: The calculation formula of the clay volume in step S4 is: Where: V Pclay 、 V uncTclay and V cTclay They are the volume of clay attached to pores after deformation, the volume of clay attached to unclosed throats after deformation, and the volume of clay attached to closed throats after deformation; V Pclay0 、 V uncTclay0 and V cTclay0 They are the volume of clay attached to pores at 0 MPa, the volume of clay attached to unclosed throats at 0 MPa, and the volume of clay attached to closed throats at 0 MPa.

8. The method for simulating two-phase flow in shale matrix and determining phase permeability curve according to claim 1, characterized in that: The capillary inlet pressure in step S5 is the set of capillary inlet pressures of each pore and throat.

9. The present invention provides an electronic device, characterized in that: The electronic device includes: a processor, a memory, and a bus, the memory storing machine-readable instructions executable by the processor. When the electronic device is running, the processor and the memory communicate via the bus, and the machine-readable instructions are executed by the processor to implement the method for simulating two-phase flow in a shale matrix and determining a phase permeability curve according to any one of claims 1 to 8.

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