A method and device for shale matrix two-phase flow simulation and relative permeability curve determination

Abstract

The present application relates to a kind of shale matrix two-phase flow simulation and phase permeability curve determination method and device, belong to shale gas multiphase flow simulation technical field.The present application discloses a kind of shale matrix two-phase flow simulation and phase permeability curve determination method and device, comprising: the single-phase permeability of the target reservoir core under different effective stress is determined;PNM model is extracted based on connected pore;The radius of pore and throat after deformation in PNM model under different effective stress and the permeability after deformation are simulated and calculated, and the single-phase permeability after deformation is fitted;PNM model under different effective stress is updated;Capillary inlet pressure is calculated;Relative permeability in PNM model under different effective stress is calculated.The present application is used for the gas-water two-phase flow simulation of shale gas reservoir under variable stress, and also can be used for stress-sensitive simulation and analysis of dense sandstone and carbonate rock and other various lithology reservoirs, has wide application value in the aspect of shale gas development practice and enhanced recovery.

Description

TECHNICAL FIELD

[0001] The present application relates to a shale matrix two-phase flow simulation and relative permeability curve determination method and device, belonging to the technical field of shale gas multiphase flow simulation. BACKGROUND

[0002] During shale gas exploitation, there is often a serious stress sensitivity effect. As the fluid in the pore is gradually produced, the effective stress outside and inside the pore gradually increases, which will cause the pore to gradually become smaller, thereby affecting the gas-water two-phase flow capacity. The current experimental method cannot realize gas-water two-phase displacement in shale matrix under overburden pressure, which leads to unclear understanding of the change rule of relative permeability curve under stress action, and seriously hinders the development of reasonable production system in the field.

[0003] Therefore, it is necessary to provide a shale matrix two-phase flow simulation and relative permeability curve determination method and device for studying the evolution rule of relative permeability curve under variable stress in shale matrix, and providing technical support for input of key parameters in macro numerical simulation and efficient development of blocks. SUMMARY

[0004] The present application aims at the problems existing in the prior art, and provides a shale matrix two-phase flow simulation and relative permeability curve determination method and device.

[0005] The technical scheme provided by the present application to solve the above technical problems is: a shale matrix two-phase flow simulation and relative permeability curve determination method, comprising the following steps:

[0006] S1, determining the single-phase permeability of the target reservoir core under different effective stresses by pressure pulse method;

[0007] S2, constructing a digital core model of the target reservoir core, and extracting a PNM model based on connected pores;

[0008] S3, taking the single-phase permeability under different effective stresses as a benchmark, simulating and calculating the radius of the pores and throat deformation and the permeability after deformation in the PNM model under different effective stresses, and fitting the single-phase permeability after deformation;

[0009] S4, updating 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;

[0010] 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 permeability fitting in step S3;

[0011] S6, calculating the relative permeability in the PNM model under different effective stresses.

[0012] Further, in the step S3, the initial permeability of the PNM model is adjusted before the simulation calculation, so that the initial permeability of the PNM is higher than the permeability at the first effective pressure point determined by the pressure pulse method.

[0013] Further, in the step S3, the radius calculation formula of the deformed pore and throat is:

[0014]

[0015] In the formula: r And r 0 is the equivalent radius of the deformed and undeformed pore or throat, is the porosity of the PNM, K rock is the bulk modulus of the rock, α B is the Biot coefficient, Δ p is the change of the pore pressure, λ is the degree of throat closure.

[0016] Further, in the step S3, the length, shape factor, and coordination number of the pore and throat do not change, only the pore radius and throat radius change, and the throat may be closed.

[0017] Further, in the step S4, the pore radius and throat radius fitted in the step S3 are selected to replace the pore radius and throat radius in the PNM model; and the volume of each pore and throat in the PNM and the clay volume are calculated one by one to replace the pore volume, throat volume, and clay volume in the PNM model.

[0018] Further, in the step S4, the volume calculation formula of the pore and throat is:

[0019]

[0020] In the formula: V P , V uncT And V cT are the volume of the deformed pore, the volume of the deformed non-closed throat, and the volume of the deformed closed throat, respectively; V P0 , V uncT0 And V cT0 are the volume of the pore at 0 MPa, the volume of the non-closed throat at 0 MPa, and the volume of the closed throat at 0 MPa, respectively; δc 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 the un-closed throat.

[0021] Further technical solutions are that the formula for calculating the clay volume in step S4 is:

[0022]

[0023] In the formula: V Pclay , V uncTclay and V cTclay are the clay volumes attached to the pore, the un-closed throat and the closed throat after deformation, respectively; V Pclay0 , V uncTclay0 and V cTclay0 are the clay volumes attached to the pore, the un-closed throat and the closed throat at 0 MPa, respectively.

[0024] Further technical solutions are that the capillary inlet pressure in step S5 is a set of capillary inlet pressures of each pore and throat.

[0025] The present application provides an electronic device, which comprises 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 through the bus, and the machine readable instructions are executed by the processor to implement the shale matrix two-phase flow simulation and relative permeability curve determination method.

[0026] The present application has the beneficial effects that: in addition to being used for gas-water two-phase flow simulation of shale gas reservoirs under variable stress, the present application can also be used for stress-sensitive simulation and analysis of various lithological reservoirs such as tight sandstone and carbonate rock, and has wide application value in shale gas development practice and enhanced oil recovery. BRIEF DESCRIPTION OF DRAWINGS

[0027] Figure 1 is the pore network model at 0 MPa;

[0028] Figure 2 is the comparison of the pore and throat radii before and after deformation;

[0029] Figure 3 is the fitting chart of the absolute permeability;

[0030] Figure 4 for different effective stresses. DETAILED DESCRIPTION

[0031] The technical solutions of the present application will be described clearly and completely below in conjunction with the drawings. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0032] The present application provides a shale matrix two-phase flow simulation and relative permeability curve determination method, comprising the following steps:

[0033] S1, determining the single-phase permeability of the target reservoir core under different effective stresses by the pressure pulse method;

[0034] S2, constructing a digital core model of the target reservoir core, and extracting a PNM model based on connected pores;

[0035] The PNM model refers to a pore network model, and subsequent simulation calculations are all based on this PNM model;

[0036] S3, taking the single-phase permeability under different effective stresses as a benchmark, simulating and calculating the radii of the pores and the throat after deformation under different effective stresses in the PNM model and the permeability after deformation, and fitting the single-phase permeability after deformation, wherein the relative error of the fitting is within 10%;

[0037] Wherein in the model calculation,

[0038] The first part is to adjust the initial permeability of the PNM model, the purpose of which is 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 stress point determined by the pressure pulse method. The calculation method of the permeability in the PNM model is to use Darcy's law, and the adjustment method is to change the pore size distribution in the PNM model;

[0039] The second part is the deformation simulation of the PNM model under variable stress and the fitting of the permeability. This part first calculates the radii of the pores and the throat after deformation in the PNM model, and then calculates the permeability of the PNM model after deformation.

[0040] The formula for calculating the deformation of the pores and the throat is as follows:

[0041] (1)

[0042] In the formula, r and r 0 are the equivalent radii of the pores or the throat after deformation and before deformation, respectively, porosity of the PNM, K rock bulk modulus of the rock, α B Biot coefficient, p change of pore pressure, λ throat closure degree.

[0043] In the simultaneous deformation simulation, the length, shape factor, coordination number and other parameters of the pore and throat do not change, only the pore radius and throat radius change, and the throat will close, the purpose is to ensure that the three-dimensional physical scale of the entire PNM skeleton remains consistent before and after deformation.

[0044] The fitting method of permeability is as follows: taking the single-phase permeability obtained in the step S1 as the benchmark, adjusting the closure ratio of the throat in the above pore deformation method to make the simulated permeability and the experimental permeability fit, and the relative error of the fitting is within 10%.

[0045] S4, according to the pore and throat radius after the permeability fitting in step S3, updating the pore radius, throat radius, pore volume, throat volume, clay volume in the PNM model under different effective stresses;

[0046] The method for updating the pore radius and throat radius is as follows: selecting the pore radius and throat radius after the permeability fitting in step S3, replacing the pore radius and throat radius in the PNM model; the method for updating the pore volume and throat volume is as follows: after updating the pore radius and throat radius, the volume of each pore and throat in the PNM model and the clay volume are calculated one by one, and the pore volume, throat volume and clay volume in the PNM model are replaced.

[0047] Wherein the pore only has volume strain, and the throat is divided into closed throat and unclosed throat under the premise of volume strain, thus the equivalent radius change rate of the pore or unclosed throat is as follows:

[0048] (2)

[0049] In the formula: δ unc is the equivalent radius change rate of the pore or unclosed throat;

[0050] The equivalent radius change rate of the closed throat is:

[0051] (3)

[0052] In the formula: δ c is the equivalent radius change rate of the closed throat;

[0053] (4)

[0054] wherein: V P , V uncT and V cT are the volume of the pore after deformation, the volume of the non-closed throat after deformation, the volume of the closed throat after deformation, respectively; V P0 , V uncT0 and V cT0 are the volume of the pore at 0 MPa, the volume of the non-closed throat at 0 MPa, the volume of the closed throat at 0 MPa, respectively.

[0055] The clay volume is updated by the following equation:

[0056] (5)

[0057] wherein: V Pclay , V uncTclay and V cTclay are the clay volume attached to the pore after deformation, the clay volume attached to the non-closed throat after deformation, the clay volume attached to the closed throat after deformation, respectively; V Pclay0 , V uncTclay0 and V cTclay0 are the clay volume attached to the pore at 0 MPa, the clay volume attached to the non-closed throat at 0 MPa, the clay volume attached to the closed throat at 0 MPa, respectively.

[0058] S5, calculating the capillary inlet pressure in the PNM model under different effective stresses according to the radii of the pores and the throats after deformation in the permeability fitting in step S3;

[0059] wherein the two-phase contact angle of each pore and throat does not change with the change of the effective stress, the capillary inlet pressure in the 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 changes, and then the capillary inlet pressure changes;

[0060] (6)

[0061] wherein: P c is the capillary inlet pressure;ψ is the gas-water interfacial tension; θ is the contact angle; r ins is the radius of the pore or throat under different effective stresses; n represents the number of filled throats connected to the pore; C i is an arbitrary parameter, X i is a random number between 0 and 1;

[0062] S6, calculating the relative permeability in the PNM model under different effective stresses;

[0063] wherein the gas-water two-phase permeability is calculated as follows:

[0064] (7)

[0065] (8)

[0066] In the formula: 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 gas, respectively; L is the length of the PNM along the flow direction; K is the absolute permeability of the PNM; A is the cross-sectional area of the PNM perpendicular to the flow direction; Δ P is the pressure difference between the inlet and the outlet.

[0067] Each effective stress corresponds to a relative permeability curve. When the effective stress changes, the pore and throat radii in the PNM also change, thereby affecting the flow rates of the water phase and the gas phase, and ultimately leading to changes in the two-phase permeability. The flow rate change caused by throat closure will be significantly higher than that when no closure occurs.

[0068] The present application 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 through the bus, the machine readable instructions are executed by the processor to realize the above-mentioned shale matrix two-phase flow simulation and relative permeability curve determination method.

[0069] Embodiment

[0070] The digital core used in this embodiment is from a shale in a certain block in China, and the construction method of the digital core is numerical reconstruction method. The core is a cylindrical shape 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 deformation process of the pores and the throats is 25 GPa, and the value of the Biot coefficient is 0.6. The effective stress varies from 5 MPa to 50 MPa. The density ratio of the wet phase and the non-wetting phase used in the two-phase flow simulation is 1.27, the viscosity ratio is 0.039, the distribution range of the contact angle is 40-70°, and the interfacial tension of the two phases is 0.03 N / m.

[0071] The following shows how the shale matrix two-phase flow simulation and relative permeability curve determination method proposed by the present application carries out pore and throat deformation and permeability fitting based on the above data to calculate the relative permeability curve under different effective stresses.

[0072] As shown in Figure 1 , the PNM model extracted based on the connected pore space is shown, in which the ball represents the pore and the stick represents the throat. All subsequent simulations are based on this PNM model.

[0073] As shown in Figure 2 , the pore and throat deformation under different effective stresses calculated by formula (1) is shown. When the effective stress is 0 MPa, the pore and throat do not deform, but it is necessary to ensure that the absolute permeability is higher than the permeability of the first point measured by the pressure pulse method (5 MPa). With the increase of the effective stress, the parameters in the process of throat closure are changed one by one to realize the fitting of the permeability.

[0074] Figure 2 The pore and throat radii under effective stresses of 0 MPa and 50 MPa are shown. The left and right images are collected in the same area. It can be found from the figure that after the simulation of the deformation of the pores and the throats, the pores will deform slightly, and the radii of the throats will change greatly due to the closure.

[0075] Figure 3 The fitting result of the permeability is shown. The method for fitting the permeability in this embodiment is as follows: the deformation of the pores follows the part in formula (1) that does not close, and the closure of the throats uses random closure, which follows the part in formula (1) that closes.

[0076] Figure 4 The two-phase relative permeability curves calculated based on a series of PNM models fitted in Figure 3 . Due to the gradual increase of the range of throat closure, the relative permeability curve changes greatly, in which the water phase permeability gradually increases, and when the number of closed throats increases greatly, the relative permeability curve also changes greatly and becomes extremely narrow.

[0077] The shale matrix two-phase flow simulation and phase permeability curve determination method and device provided by the present application take digital cores and PNM models as the geometric basis, take single-phase permeability measured by the pressure pulse method as the fitting standard, take PNM deformation under different effective stresses as the basic idea, and take computer devices as the implementation medium, and theoretically expound the shale matrix two-phase flow simulation and phase permeability curve determination method and device under variable stresses.

[0078] The above description does not limit the present application in any form, although the present application has been disclosed by the above examples, however, is not used to limit the present application, any person skilled in the art, without departing from the technical scheme of the present application, can make some changes or modifications for equivalent examples with the above disclosed technical content, but any simple modification, equivalent change and modification made on the above examples according to the technical essence of the present application, as long as it does not deviate from the technical scheme of the present application, belongs to the scope of the technical scheme of the present application.

Claims

1. A method for simulating two-phase flow in shale matrix and determining relative permeability curves, characterized in that, Includes the following steps: S1. Determine the single-phase permeability of the target reservoir core under different effective stresses using the pressure pulse method; S2. Construct a digital core model of the target reservoir core and extract the PNM model based on the interconnected pores; S3. Using the single-phase permeability under different effective stresses as a benchmark, simulate and calculate the radius of pores and throats after deformation and the permeability after deformation in the PNM model under different effective stresses, and fit the single-phase permeability after deformation. S4. Update the pore radius, throat radius, pore volume, throat volume, and clay volume in the PNM model under different effective stresses based on the radii of the pores and throats after deformation following the permeability fitting in step S3. S5. Calculate the capillary inlet pressure in the PNM model under different effective stresses based on the radius of the pores and throats after permeability fitting in step S3. S6. Calculate the relative permeability in the PNM model under different effective stresses.

2. The method for simulating two-phase flow in shale matrix and determining relative permeability curves according to claim 1, characterized in that, In step S3, the initial permeability of the PNM model is first adjusted during the simulation calculation. The purpose is to make the initial permeability of the PNM higher than the permeability at the first effective pressure point determined by the pressure pulse method.

3. The method for simulating two-phase flow in shale matrix and determining relative permeability curves according to claim 1, characterized in that, The formula for calculating the radius of the pores and throats after deformation in step S3 is as follows: In the formula: r and r 0 represents the equivalent radius of the pore or throat before and after deformation, respectively. Porosity of PNM K rock The bulk modulus of the rock. α B For Biot coefficients, Δ p This is the change in pore pressure. λ This refers to the degree of larynx closure.

4. The method for simulating two-phase flow in shale matrix and determining relative permeability curves 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; only the pore radius and throat radius change.

5. The method for simulating two-phase flow in shale matrix and determining relative permeability curves according to claim 1, characterized in that, In step S4, the pore radius and throat radius fitted by the permeability in step S3 are selected and replaced with 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 model are calculated one by one and replaced with the pore volume, throat volume and clay volume in the PNM model.

6. The method for simulating two-phase flow in shale matrix and determining relative permeability curves according to claim 5, characterized in that, The formulas for calculating pore volume and throat volume in step S4 are as follows: In the formula: V P , V uncT and V cT These are the volumes of the pores after deformation, the unclosed throats after deformation, and the closed throats after deformation, respectively. V P0 , V uncT0 and V cT0 These are the volumes of the pores at 0 MPa, the unclosed throats at 0 MPa, and the closed throats at 0 MPa, respectively. δ c It is the rate of change of the equivalent radius of the closed larynx; δ unc It is the rate of change of the equivalent radius of a pore or an unclosed throat.

7. The method for simulating two-phase flow in shale matrix and determining relative permeability curves according to claim 5, characterized in that, The formula for calculating the clay volume in step S4 is as follows: In the formula: V Pclay , V uncTclay and V cTclay These are, respectively, the volume of clay attached to the pores after deformation, the volume of clay attached to the unclosed throat after deformation, and the volume of clay attached to the closed throat after deformation; V Pclay0 , V uncTclay0 and V cTclay0 These represent the clay volume attached to the pores at 0 MPa, the clay volume attached to the unclosed throat at 0 MPa, and the clay volume attached to the closed throat at 0 MPa.

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

9. An electronic device, characterized in that, The electronic device includes 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 communicates with the memory via the bus, and the machine-readable instructions are executed by the processor to implement the method for simulating two-phase flow in shale matrix and determining relative permeability curves as described in any one of claims 1-8.

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