Method for determining change rule of permeability of artificial fractures in different directions along with pore pressure

Abstract

The invention discloses a method for determining a change rule of permeability of artificial fractures in different directions along with pore pressure, which comprises the following steps of: aiming at a target oil-gas well or oil-gas reservoir, establishing a relational expression of permeability of fractures in a single direction and effective stress; establishing a relational expression of effective stress and pore pressure of the single-direction crack; determining the relationship between the single-direction fracture permeability and the pore pressure; establishing a relational expression of effective stress and pore pressure of the multidirectional crack; and determining the relationship between the multidirectional fracture permeability and the pore pressure. According to the method for determining the change rule of the permeability of the artificial fractures in different directions along with the pore pressure, the change rule of the permeability of the fractures in the vertical direction, the fractures in the vertical minimum horizontal principal stress direction and the fractures in the vertical maximum horizontal principal stress direction along with the pore pressure in the flowback-production process can be quantitatively evaluated; and different characterization of permeability changes of different cracks under the condition of multidirectional cracks can be realized, and more convenient and more accurate application of indoor stress sensitive data on site is realized.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas field development engineering, and in particular to a method for determining the variation law of permeability of artificial fractures in different directions along with pore pressure. Background Art

[0002] For unconventional reservoirs such as tight oil and gas and shale oil and gas, due to the extremely low permeability of the reservoir, large-scale volume fracturing and the formation of complex artificial fractures are usually required to achieve efficient development. During the production process, due to the continuous decrease in fluid pressure in the fracture, the effective stress on the fracture wall gradually increases, resulting in a gradual decrease in the fracture width or even closure, and a significant decrease in the fracture conductivity, that is, a stress sensitivity effect. At present, domestic and foreign scholars have generally recognized the existence of fracture stress sensitivity and have carried out a large number of studies. Jones and other scholars pointed out that the permeability of carbonate rock fractures is logarithmically decreasing with effective stress, Walsh and other scholars derived the relationship between the stress sensitivity of plate fracture permeability and effective stress, and Gangi and other scholars derived the polynomial permeability decrease curve of fracture core under confining pressure conditions. Wu Jianfa and other scholars conducted a shale artificial fracture permeability sensitivity experiment using a constant confining pressure variable flow pressure test method, and clarified the proppant backflow and fracture stress sensitivity under different effective stresses.

[0003] It can be seen that the existing fracture stress sensitivity evaluation, whether based on theoretical model derivation or indoor experimental analysis, is to explore the relationship between fracture permeability and effective stress. However, effective stress is a parameter that is difficult to obtain on-site in oil and gas fields, so the fracture stress sensitivity curve established above often needs to be converted before it can be applied on-site. The general practice is to replace the confining pressure with the overlying formation pressure of the reservoir, and then calculate the effective stress based on the reservoir fluid pressure value. For shallow reservoirs, the vertical stress is small, and the cracks formed after fracturing are mainly in the horizontal direction. The above treatment method is not a big problem, but for deep reservoirs, due to the large vertical stress, the cracks formed after fracturing are mostly in the vertical direction. At this time, the effective stress on the fracture wall should be the difference between the horizontal stress and the pore pressure in the fracture. The above treatment method often has a large deviation. In addition, the current fracture stress sensitivity research is mainly based on single fractures, and there is little research on the stress sensitivity of multi-directional fractures that may be formed during the fracturing of low stress difference reservoirs. Summary of the invention

[0004] In view of the problem that the existing fracture stress sensitivity is related to the effective stress and cannot be directly applied on site, the present invention proposes a method for determining the law of change of the permeability of artificial fractures in different directions with pore pressure. According to different fracture characteristics, single-direction fractures and multi-directional fractures are respectively targeted. On the basis of establishing a method for obtaining the effective stress of fractures under different scenarios, the relationship between the fracture permeability and the pore pressure is clarified, and a method for determining the law of change of the permeability of artificial fractures in different directions with pore pressure is formed.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for determining the variation law of permeability of artificial fractures in different directions with pore pressure comprises the following steps:

[0007] Step 1: For the target oil and gas well or oil and gas reservoir, establish the relationship between the permeability of the single-direction fracture and the effective stress;

[0008] Step 2: Establish the relationship between effective stress and pore pressure of single-direction cracks;

[0009] Step 3: Determine the relationship between the permeability of a single-direction fracture and the pore pressure;

[0010] Step 4: Establish the relationship between effective stress and pore pressure of multi-directional fractures;

[0011] Step 5: Determine the relationship between multi-directional fracture permeability and pore pressure.

[0012] Furthermore, the step 1 of establishing a relationship between a single fracture permeability and effective stress includes the following sub-steps:

[0013] For the target oil and gas well or oil and gas reservoir, based on the permeability data of a single fracture at different effective stresses, the relationship between the permeability of a single direction fracture and the effective stress is fitted and established:

[0014]

[0015] Where: K0 is the initial permeability, in mD; γ is the permeability modulus, in 1 / MPa; σ eff is the effective stress in MPa.

[0016] Furthermore, based on the experimental test data of fracture permeability under different effective stresses, the coefficient γ is obtained by exponential fitting, thereby establishing the relationship between the fracture permeability in a single direction and the effective stress, namely, formula (1).

[0017] Furthermore, the establishment of the relationship between the effective stress of a single-direction crack and the pore pressure in step 2 includes establishing the relationship between the effective stress of a horizontal-direction crack and the pore pressure:

[0018] For horizontal cracks, the effective stress on the crack wall is the difference between the vertical stress and the equivalent pore pressure, that is:

[0019] σ eff =σ v -αP p (2)

[0020] Where: v is the vertical stress, in MPa; α is the Biot coefficient, dimensionless; P p is the pore pressure, in MPa.

[0021] Furthermore, the vertical stress is the gravity of the formation above the fracture surface, which can be obtained by integrating the rock density obtained from well logging:

[0022]

[0023] Where: H is the vertical depth of the fracture wall, in m; ρ is the rock density, in kg / m 3 ; g is the gravity coefficient, the unit is N / kg.

[0024] Furthermore, the establishment of the relationship between the effective stress of a single-direction crack and the pore pressure in step 2 also includes establishing the relationship between the effective stress of a vertical-direction crack and the pore pressure:

[0025] Usually, the cracks formed by fracturing are perpendicular to the direction of the minimum horizontal principal stress, and the effective stress on the crack wall is the difference between the minimum horizontal stress and the equivalent pore pressure, that is:

[0026] σ eff =σ h -αP p (3)

[0027] Where: h is the minimum horizontal principal stress, in MPa.

[0028] Furthermore, according to the geostress calculation model of inclined strata, the minimum horizontal principal stress calculation formula is:

[0029]

[0030] Where: ω1 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless; is the formation dip angle, in degrees; μ is Poisson’s ratio, dimensionless; β is the formation updip azimuth, in degrees; β0 is the maximum horizontal principal stress azimuth, in degrees;

[0031] After a simple transformation of formula (4), we can get:

[0032]

[0033] For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let:

[0034]

[0035] Then formula (5) is simplified to:

[0036] σ h =C1σ V -(C1-1)αp P (7)

[0037] Substituting formula (7) into formula (3), the relationship between the effective stress and pore pressure of a single fracture in the vertical direction is obtained as follows:

[0038] σ eff =C1(σ V -αp P ) (8)

[0039] Among them, C1 and α are approximately constants in the same oil and gas structural unit. Therefore, if the three-dimensional principal stress and pore pressure values ​​of two groups of target strata are known, the equations can be solved simultaneously to obtain the C1 and α values, which can then be used for the subsequent calculation of effective stress under different pore pressures.

[0040] Furthermore, determining the relationship between the permeability of a single-direction fracture and the pore pressure in step 3 includes the following sub-steps:

[0041] Substituting the relationship between the effective stress and pore pressure of horizontal cracks and vertical cracks obtained in step 2 into equation (1), the permeability variation of a single horizontal crack and a single vertical crack with pore pressure is obtained as follows:

[0042]

[0043]

[0044] Among them, formula (9) is applicable to a single crack in the horizontal direction, and formula (10) is applicable to a single crack in the vertical direction.

[0045] Furthermore, the step 4 of establishing the relationship between the effective stress of multi-directional fractures and the pore pressure includes the following sub-steps:

[0046] When the net pressure in the fracture exceeds the horizontal stress difference during hydraulic fracturing, there is a probability that multi-directional fractures will be formed, with some fractures extending along the direction of the maximum horizontal principal stress and some fractures extending along the direction of the minimum horizontal principal stress. For fractures extending along the direction of the maximum horizontal principal stress, the calculation method of the effective stress is the same as that in step 2, while for fractures extending along the direction of the minimum horizontal principal stress, the effective stress is the difference between the maximum horizontal stress and the equivalent pore pressure, that is:

[0047] σ eff =σ H -αP p (11)

[0048] Where: H is the maximum horizontal principal stress, in MPa;

[0049] According to the geostress calculation model of inclined strata, the maximum horizontal principal stress calculation formula is:

[0050]

[0051] Where: ω2 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless;

[0052] After a simple transformation of formula (12), we can get:

[0053]

[0054] For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let:

[0055]

[0056] Then formula (13) is simplified to:

[0057] σ H =C1σ V -(C1-1)αp P (15)

[0058] Substituting formula (15) into formula (11), the relationship between the vertical crack effective stress and the pore pressure in the direction perpendicular to the maximum horizontal principal stress is obtained as follows:

[0059] σ eff =C2(σ V -αp P ) (16)

[0060] If the vertical stress and pore pressure values ​​of the two target layers are known, the equations can be solved simultaneously to obtain the C2 and α values, which can then be used for subsequent calculations of effective stresses under different pore pressures;

[0061] In summary, the relationship between the effective stress and pore pressure of multi-directional fractures is as follows:

[0062]

[0063] Furthermore, determining the relationship between the multi-directional fracture permeability and the pore pressure in step 5 includes the following sub-steps:

[0064] According to the relationship between fracture permeability and effective stress established in step 1, the relationship between effective stress and pore pressure of multi-directional fractures is determined as follows:

[0065]

[0066] The beneficial effects of the present invention are:

[0067] The method for determining the variation law of the permeability of artificial fractures in different directions with pore pressure of the present invention can quantitatively evaluate the variation law of the permeability of vertical fractures, fractures in the direction of vertical minimum horizontal principal stress, and fractures in the direction of vertical maximum horizontal principal stress with pore pressure during the backflow-production process, and can realize the differential characterization of the permeability variation of different fractures in the case of multi-directional fractures, and realize the more convenient and accurate application of indoor stress sensitive data on site. The present invention can be widely applied to the prediction of the permeability variation law and production dynamic simulation of artificially transformed oil and gas wells and oil and gas reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of a method for determining the variation law of the permeability of artificial fractures in different directions with pore pressure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0069] In order to have a clearer understanding of the technical features, purposes and effects of the present invention, the specific implementation methods of the present invention are now described. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the embodiments described are only part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present invention.

[0070] like Figure 1 As shown, this embodiment provides a method for determining the variation law of the permeability of artificial fractures in different directions with pore pressure, comprising the following steps:

[0071] Step 1: For the target oil and gas well or oil and gas reservoir, establish the relationship between the permeability of the single-direction fracture and the effective stress;

[0072] Step 2: Establish the relationship between effective stress and pore pressure of single-direction cracks;

[0073] Step 3: Determine the relationship between the permeability of a single-direction fracture and the pore pressure;

[0074] Step 4: Establish the relationship between effective stress and pore pressure of multi-directional fractures;

[0075] Step 5: Determine the relationship between multi-directional fracture permeability and pore pressure.

[0076] Preferably, establishing a relationship between a single fracture permeability and effective stress in step 1 includes the following sub-steps:

[0077] For the target oil and gas well or oil and gas reservoir, based on the permeability data of a single fracture at different effective stresses, the relationship between the permeability of a single direction fracture and the effective stress is fitted and established:

[0078]

[0079] Where: K0 is the initial permeability, in mD; γ is the permeability modulus, in 1 / MPa; σ eff is the effective stress in MPa.

[0080] Based on the experimental test data of fracture permeability under different effective stresses, the coefficient γ is obtained by exponential fitting, thus establishing the relationship between fracture permeability in a single direction and effective stress, namely, formula (1).

[0081] Preferably, in step 2, establishing a relationship between effective stress and pore pressure of a single-direction crack includes establishing a relationship between effective stress and pore pressure of a horizontal-direction crack:

[0082] For horizontal cracks, the effective stress on the crack wall is the difference between the vertical stress and the equivalent pore pressure, that is:

[0083] σ eff =σ v -αP p (2)

[0084] Where: v is the vertical stress, in MPa; α is the Biot coefficient, dimensionless; P p is the pore pressure, in MPa.

[0085] The vertical stress is the gravity of the formation above the fracture surface, which can be obtained by integrating the rock density obtained from well logging:

[0086]

[0087] Where: H is the vertical depth of the fracture wall, in m; ρ is the rock density, in kg / m 3 ; g is the gravity coefficient, the unit is N / kg.

[0088] Preferably, in step 2, establishing a relationship between effective stress and pore pressure of a single-direction crack further includes establishing a relationship between effective stress and pore pressure of a vertical-direction crack:

[0089] Usually, the cracks formed by fracturing are perpendicular to the direction of the minimum horizontal principal stress, and the effective stress on the crack wall is the difference between the minimum horizontal stress and the equivalent pore pressure, that is:

[0090] σ eff =σ h -αP p (3)

[0091] Where: h is the minimum horizontal principal stress, in MPa.

[0092] According to the geostress calculation model of inclined strata, the minimum horizontal principal stress calculation formula is:

[0093]

[0094] Where: ω1 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless; is the formation dip angle, in degrees; μ is Poisson’s ratio, dimensionless; β is the formation updip azimuth, in degrees; β0 is the maximum horizontal principal stress azimuth, in degrees;

[0095] After a simple transformation of formula (4), we can get:

[0096]

[0097] For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let:

[0098]

[0099] Then formula (5) is simplified to:

[0100] σ h =C1σ V -(C1-1)αp P (7)

[0101] Substituting formula (7) into formula (3), the relationship between the effective stress and pore pressure of a single fracture in the vertical direction is obtained as follows:

[0102] σ eff =C1(σ V -αp P) (8)

[0103] Among them, C1 and α are approximately constants in the same oil and gas structural unit. Therefore, if the three-dimensional principal stress and pore pressure values ​​of two groups of target strata are known, the equations can be solved simultaneously to obtain the C1 and α values, which can then be used for the subsequent calculation of effective stress under different pore pressures.

[0104] Preferably, determining the relationship between the permeability of a single-direction fracture and the pore pressure in step 3 includes the following sub-steps:

[0105] Substituting the relationship between the effective stress and pore pressure of horizontal cracks and vertical cracks obtained in step 2 into equation (1), the permeability variation of a single horizontal crack and a single vertical crack with pore pressure is obtained as follows:

[0106]

[0107]

[0108] Among them, formula (9) is applicable to a single crack in the horizontal direction, and formula (10) is applicable to a single crack in the vertical direction.

[0109] Preferably, establishing the relationship between the effective stress and pore pressure of multi-directional fractures in step 4 includes the following sub-steps:

[0110] When the net pressure in the fracture exceeds the horizontal stress difference during hydraulic fracturing, there is a probability that multi-directional fractures will be formed, with some fractures extending along the direction of the maximum horizontal principal stress and some fractures extending along the direction of the minimum horizontal principal stress. For fractures extending along the direction of the maximum horizontal principal stress, the calculation method of the effective stress is the same as that in step 2, while for fractures extending along the direction of the minimum horizontal principal stress, the effective stress is the difference between the maximum horizontal stress and the equivalent pore pressure, that is:

[0111] σ eff =σ H -αP p (11)

[0112] Where: H is the maximum horizontal principal stress, in MPa;

[0113] According to the geostress calculation model of inclined strata, the maximum horizontal principal stress calculation formula is:

[0114]

[0115] Where: ω2 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless;

[0116] After a simple transformation of formula (12), we can get:

[0117]

[0118] For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let:

[0119]

[0120] Then formula (13) is simplified to:

[0121] σ H =C1σ V -(C1-1)αp P (15)

[0122] Substituting formula (15) into formula (11), the relationship between the vertical crack effective stress and the pore pressure in the direction perpendicular to the maximum horizontal principal stress is obtained as follows:

[0123] σ eff =C2(σ V -αp P ) (16)

[0124] If the vertical stress and pore pressure values ​​of the two target layers are known, the equations can be solved simultaneously to obtain the C2 and α values, which can then be used for subsequent calculations of effective stresses under different pore pressures;

[0125] In summary, the relationship between the effective stress and pore pressure of multi-directional fractures is as follows:

[0126]

[0127] Preferably, determining the relationship between multi-directional fracture permeability and pore pressure in step 5 includes the following sub-steps:

[0128] According to the relationship between fracture permeability and effective stress established in step 1, the relationship between effective stress and pore pressure of multi-directional fractures is determined as follows:

[0129]

[0130] It should be noted that, for the aforementioned method embodiments, for the sake of simplicity of description, they are expressed as a series of action combinations, but those skilled in the art should be aware that the present application is not limited by the order of the actions described, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required by the present application.

Claims

1. A method for determining the variation law of permeability of artificial fractures in different directions with pore pressure, characterized in that: The following steps are involved: Step 1: For the target oil and gas well or oil and gas reservoir, establish the relationship between the permeability of the single-direction fracture and the effective stress; Step 2: Establish the relationship between effective stress and pore pressure of single-direction cracks; Step 3: Determine the relationship between the permeability of a single-direction fracture and the pore pressure; Step 4: Establish the relationship between effective stress and pore pressure of multi-directional fractures; Step 5: Determine the relationship between multi-directional fracture permeability and pore pressure.

2. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 1, characterized in that: The step 1 of establishing a relationship between the permeability of a single fracture and the effective stress includes the following sub-steps: For the target oil and gas well or oil and gas reservoir, based on the permeability data of a single fracture at different effective stresses, the relationship between the permeability of a single direction fracture and the effective stress is fitted and established: Where: K0 is the initial permeability, in mD; γ is the permeability modulus, in 1 / MPa; σ eff is the effective stress in MPa.

3. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 2, characterized in that: Based on the experimental test data of fracture permeability under different effective stresses, the coefficient γ is obtained by exponential fitting, thus establishing the relationship between fracture permeability in a single direction and effective stress, namely, formula (1).

4. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 2, characterized in that: The step 2 of establishing the relationship between the effective stress of a single-direction crack and the pore pressure includes establishing the relationship between the effective stress of a horizontal-direction crack and the pore pressure: For horizontal cracks, the effective stress on the crack wall is the difference between the vertical stress and the equivalent pore pressure, that is: s eff =s v -αP p (2) Where: v is the vertical stress, in MPa; α is the Biot coefficient, dimensionless; P p is the pore pressure, in MPa.

5. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 4, characterized in that: The vertical stress is the gravity of the formation above the fracture surface, which can be obtained by integrating the rock density obtained from well logging: Where: H is the vertical depth of the fracture wall, in m; ρ is the rock density, in kg / m 3 ; g is the gravity coefficient, the unit is N / kg.

6. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 5, characterized in that: The step 2 of establishing the relationship between the effective stress of a single-direction crack and the pore pressure also includes establishing the relationship between the effective stress of a vertical-direction crack and the pore pressure: Usually, the cracks formed by fracturing are perpendicular to the direction of the minimum horizontal principal stress, and the effective stress on the crack wall is the difference between the minimum horizontal stress and the equivalent pore pressure, that is: s eff =s h -αP p (3) Where: h is the minimum horizontal principal stress, in MPa.

7. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 6, characterized in that: According to the geostress calculation model of inclined strata, the minimum horizontal principal stress calculation formula is: Where: ω1 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless; is the formation dip, in degrees; μ is Poisson’s ratio, dimensionless; β is the up-dip azimuth of the formation, in degrees; β0 is the maximum horizontal principal stress orientation, in degrees; After a simple transformation of formula (4), we can get: For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let: Then formula (5) is simplified to: s h =C1σ V -(C1-1)αp P (7) Substituting formula (7) into formula (3), the relationship between the effective stress and pore pressure of a single vertical fracture is obtained as follows: s eff =C1(σ V -αp P ) (8) Among them, C1 and α are approximately constants in the same oil and gas structural unit. Therefore, if the three-dimensional principal stress and pore pressure values ​​of two groups of target strata are known, the equations can be solved simultaneously to obtain the C1 and α values, which can then be used for the subsequent calculation of effective stress under different pore pressures.

8. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 7, characterized in that: Determining the relationship between the permeability of a single-direction fracture and the pore pressure in step 3 includes the following sub-steps: Substituting the relationship between the effective stress and pore pressure of horizontal cracks and vertical cracks obtained in step 2 into equation (1), the permeability variation of a single horizontal crack and a single vertical crack with pore pressure is obtained as follows: Among them, formula (9) is applicable to a single crack in the horizontal direction, and formula (10) is applicable to a single crack in the vertical direction.

9. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 8, characterized in that: The step 4 of establishing the relationship between the effective stress and pore pressure of multi-directional fractures includes the following sub-steps: When the net pressure in the fracture exceeds the horizontal stress difference during hydraulic fracturing, there is a probability that multi-directional fractures will be formed, with some fractures extending along the direction of the maximum horizontal principal stress and some fractures extending along the direction of the minimum horizontal principal stress. For fractures extending along the direction of the maximum horizontal principal stress, the calculation method of the effective stress is the same as that in step 2, while for fractures extending along the direction of the minimum horizontal principal stress, the effective stress is the difference between the maximum horizontal stress and the equivalent pore pressure, that is: s eff =s H -αP p (11) Where: H is the maximum horizontal principal stress, in MPa; According to the geostress calculation model of inclined strata, the maximum horizontal principal stress calculation formula is: Where: ω2 is the tectonic stress coefficient that characterizes the intensity of tectonic movement, dimensionless; After a simple transformation of formula (12), we can get: For the same oil and gas structural unit, the parameters including the structural stress coefficient and the formation dip angle are approximately constant, let: Then formula (13) is simplified to: s H =C1σ V -(C1-1)αp P (15) Substituting formula (15) into formula (11), the relationship between the vertical crack effective stress and the pore pressure in the direction perpendicular to the maximum horizontal principal stress is obtained as follows: s eff =C2(σ V -αp P ) (16) If the vertical stress and pore pressure values ​​of the two target layers are known, the equations can be solved simultaneously to obtain the C2 and α values, which can then be used for subsequent calculations of effective stresses under different pore pressures; In summary, the relationship between the effective stress and pore pressure of multi-directional fractures is as follows:

10. The method for determining the variation law of artificial fracture permeability in different directions with pore pressure according to claim 9, characterized in that: Determining the relationship between the multi-directional fracture permeability and the pore pressure in step 5 includes the following sub-steps: According to the relationship between fracture permeability and effective stress established in step 1, the relationship between effective stress and pore pressure of multi-directional fractures is determined as follows:

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