Numerical simulation method for extra-low permeability reservoir

Abstract

The present application relates to the technical field of oil production engineering, and particularly relates to a numerical simulation method for extra-low permeability reservoirs, comprising: sequentially determining the relationship between apparent permeability and throat size, the relationship between apparent permeability and air permeability, and the relationship between the radius of the bulk phase fluid and the pressure gradient, to obtain the relationship between permeability and apparent permeability under the condition of a definite solution; correction of oil-water relative permeability; water injection development is carried out by using a reverse nine-spot well pattern, and simulation is carried out by using Darcy seepage and low-speed non-Darcy equivalent seepage respectively with a month as a time step; fixed liquid production is carried out, and the indicators of the whole region are fitted. The present application analyzes and compares Darcy seepage and non-Darcy seepage by using the numerical simulation method for extra-low permeability reservoirs, obtains the seepage characteristics of the extra-low permeability reservoirs, and provides a guiding role for exploitation and other work.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil production engineering, and particularly relates to a numerical simulation method for extra-low permeability reservoirs. BACKGROUND

[0002] Generally, the throat diameter of the pore channel of the porous medium in the extra-low permeability reservoir is small, and the microstructure is very complex. Many scholars at home and abroad have confirmed through indoor experiments and field tests that the fluid seepage of the low permeability reservoir needs to break through the starting pressure gradient. The seepage characteristics of the fluid existing in the middle of the pore channel (referred to as the bulk fluid) and the fluid directly contacting the inner surface of the pore medium (referred to as the boundary fluid) are different. The properties of these boundary fluids are affected by the interface phenomenon, and a boundary layer is formed close to the pore wall. The fluid in the boundary layer is not easy to flow. The thickness of the boundary layer is affected by the starting pressure gradient, the greater the starting pressure gradient, the smaller the thickness of the boundary layer, and the greater the radius of the bulk fluid. On the contrary, the smaller the starting pressure gradient, the greater the thickness of the boundary layer, and the smaller the radius of the bulk fluid. The influence of this boundary fluid is one of the main influencing factors leading to the nonlinear seepage of the low permeability reservoir. The existing literature establishes the relationship between the seepage velocity and the pressure gradient to characterize the seepage mechanism of the extra-low permeability reservoir through experimental means, and ignores the change of the boundary layer thickness caused by the change of the starting pressure gradient. The change of the boundary layer thickness leads to the change of the effective pore throat radius, and the oil-water seepage channel is not constant, but changes with the change of the boundary layer thickness, and ultimately leads to the change of the permeability. The oil-water relative permeability curve obtained under the laboratory conditions is calculated according to the linear seepage mode, which is not consistent with the nonlinear seepage characteristics of the extra-low permeability reservoir, and therefore needs to be corrected. SUMMARY

[0003] The technical problem to be solved by the present application is to analyze and compare the Darcy seepage and the non-Darcy seepage through the numerical simulation method for the extra-low permeability reservoir, to obtain the seepage characteristics of the extra-low permeability reservoir, and to provide guidance for exploitation and other work.

[0004] The technical scheme adopted by the present application is that a numerical simulation method for an extra-low permeability reservoir comprises the following steps:

[0005] Step one, the relationship between the apparent permeability and the throat size, the relationship between the apparent permeability and the air permeability, and the relationship between the bulk fluid radius and the pressure gradient are determined in sequence, and the relationship between the permeability and the apparent permeability under the definite solution condition is obtained;

[0006] Further, the relationship formula between the permeability and the apparent permeability is:

[0007]

[0008] wherein k is air permeability, k' is apparent permeability, P represents pressure gradient, and b represents a coefficient related to pressure gradient;

[0009] Step two, correction of oil-water relative permeability;

[0010] Further, the detailed process includes:

[0011] S21, monitoring oil-water instantaneous flow rate v i and differential pressure ΔP between both ends of the core, to calculate oil-water relative permeability through formula (11):

[0012]

[0013] wherein v i is oil-water instantaneous flow rate, μ i represents viscosity, A represents area, ΔP represents differential pressure between both ends of the core, and ΔL represents core length.

[0014] S22, substituting formula (8) into formula (11) to obtain:

[0015]

[0016] wherein k -3 ' represents apparent relative permeability, and b represents a coefficient related to pressure gradient;

[0017] S23, according to the relative permeability determination method of two-phase fluid, under the condition of determining relative permeability at constant differential pressure, the relative permeability calculation formula is as follows:

[0018]

[0019] wherein k 2 represents relative permeability, 10 o μm wi ; k -3 (S 2 ) represents oil phase permeability at irreducible water saturation, 10 3 μm wi ;

[0020] After correction by formula (12), the oil phase permeability at irreducible water saturation is:

[0021]

[0022] wherein, is oil phase flow rate at irreducible water saturation, cm i,j,k / min; ΔP(S i,j,k ) is differential pressure between both ends at irreducible water saturation, MPa;

[0023] Substitute formula (12) and formula (14) into formula (13), and the corrected oil-water relative permeability is obtained:

[0024]

[0025] Step three: adopt the reverse nine-point well pattern to carry out water injection development, and adopt Darcy seepage mode and low-speed non-Darcy equivalent seepage mode to carry out simulation respectively with month as a time step;

[0026] Further, the low-speed non-Darcy equivalent seepage mode formula is as follows:

[0027] For i direction,

[0028]

[0029] For j direction,

[0030]

[0031] For k direction,

[0032]

[0033] Wherein, PERMX i,j,k represents the X direction permeability of the i, j, k grid in the three-dimensional grid system; PERMX' i,j,k represents the X direction apparent permeability of the i, j, k grid; PERMY i,j,k represents the Y direction permeability of the i, j, k grid; PERMY' i,j,k represents the Y direction apparent permeability of the i, j, k grid; PERMZ i,j,k represents the Z direction permeability of the i, j, k grid; PERMZ' i,j,k represents the Z direction apparent permeability of the i, j, k grid; P i,j,k represents the grid pressure of the i, j, k grid in the three-dimensional grid system; DX i,j,k represents the grid step length of the i direction of the i, j, k grid in the three-dimensional grid system; DY i,j,k represents the grid step length of the j direction of the i, j, k grid in the three-dimensional grid system; DZ i,j,k represents the grid step length of the k direction of the i, j, k grid in the three-dimensional grid system.

[0034] Step four: produce with a fixed liquid production, and fit the whole area index.

[0035] The beneficial effects of the present application are:

[0036] 1, First, the apparent permeability when the fluid does not flow, that is, gradP=0, at this time the body fluid radius r=0; when gradP tends to infinity, r=R is obtained, then the relative permeability curve calculated by Darcy seepage method is corrected according to the established oil-water two-phase relative permeability curve correction method, which is used in numerical simulation; the concept model of inverted nine-spot well pattern is established for verification, the calculation result is consistent with the actual situation, finally the full-area index fitting is carried out, and the full-area index fitting curve is compared with the actual development curve, which provides guidance for the research and exploitation of ultra-low permeability reservoir. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 It is the flow chart of the numerical simulation method of the ultra-low permeability reservoir of the application;

[0038] Figure 2 It is the relationship between the boundary layer thickness and the starting pressure gradient;

[0039] Figure 3 It is the comparison chart of oil-water permeability K curve before and after correction;

[0040] Figure 4 It is the comparison chart of oil-water relative permeability Kr curve before and after correction;

[0041] Figure 5 It is the porosity model and permeability model chart;

[0042] Figure 6 It is the Darcy seepage pressure distribution chart and the non-Darcy seepage pressure distribution chart in January;

[0043] Figure 7 It is the Darcy seepage pressure distribution chart and the non-Darcy seepage pressure distribution chart in March;

[0044] Figure 8 It is the Darcy seepage pressure distribution chart and the non-Darcy seepage pressure distribution chart in June;

[0045] Figure 9 It is the Darcy seepage mode remaining oil saturation and the non-Darcy seepage mode remaining oil saturation chart in January;

[0046] Figure 10 It is the Darcy seepage mode remaining oil saturation and the non-Darcy seepage mode remaining oil saturation chart in March;

[0047] Figure 11 It is the Darcy seepage mode remaining oil saturation and the non-Darcy seepage mode remaining oil saturation chart in June;

[0048] Figure 12 It is the pressure change schematic diagram between injection and production wells;

[0049] Figure 13 is the distribution map of permeability under the non-Darcy seepage mode in January and March of the present application;

[0050] Figure 14 is the fitting map of comprehensive water content in the whole area of the present application;

[0051] Figure 15 is the fitting map of daily oil production in the whole area of the present application;

[0052] Figure 16 is the fitting map of cumulative oil production in the whole area of the present application;

[0053] Figure 17 is the fitting map of cumulative liquid production in the whole area of the present application;

[0054] Figure 18 is the pressure distribution map of Darcy and non-Darcy of the present application. DETAILED DESCRIPTION

[0055] The present application will be further described below in conjunction with the accompanying drawings and examples, which are simplified schematic diagrams and only schematically show the basic structure of the present application, and thus only show the components related to the present application.

[0056] As shown in Figure 1 , a numerical simulation method for a very low permeability reservoir comprises:

[0057] Step one, sequentially determine the relationship between apparent permeability and throat size, the relationship between apparent permeability and air permeability, and the relationship between the radius of the bulk phase fluid and the pressure gradient, to obtain the relationship between permeability and apparent permeability under the condition of determining the solution;

[0058] Further, the detailed content comprises:

[0059] S11, determine the relationship between permeability and throat size;

[0060] According to the Kozeny formula, the air permeability k and the throat size have the following relationship:

[0061]

[0062] In the formula, r represents the throat radius, μm; n represents the number of capillaries per unit area, pieces;

[0063] S12, determine the relationship between apparent permeability and air permeability;

[0064] For the same reservoir, the number of capillaries per unit area is fixed, so the apparent permeability k' and the air permeability k have the following relationship:

[0065]

[0066] In the formula, R represents the pore throat radius, μm; r represents the bulk fluid radius, μm;

[0067] That is:

[0068] Since the bulk fluid radius r is always less than the pore throat radius R, the apparent permeability is less than the air permeability.

[0069] S13, determining the relationship between the bulk fluid radius and the pressure gradient;

[0070] Under laboratory conditions, the relationship between the pressure gradient and the boundary layer thickness is measured by using the equal-diameter micro-tube, and it is found that the boundary layer thickness and the pressure gradient are in an exponential relationship:

[0071] δ=a·exp(b·gradP)+c (4)

[0072] In the formula, δ represents the boundary layer thickness, μm; a, b, c represent coefficients related to the pressure gradient, decimal; P represents the pressure gradient, MPa / cm;

[0073] Then the bulk fluid radius r=R-δ, that is, the bulk fluid radius and the pressure gradient are also in an exponential relationship, which is expressed as:

[0074] r=R-(a·exp(b·gradP)+c) (5)

[0075] S14, determining the apparent permeability under the definite solution condition;

[0076] Suppose two definite solution conditions, when the fluid does not flow, that is, gradP=0, at this time the bulk fluid radius r=0; when gradP tends to infinity, r=R, thus:

[0077]

[0078] It is found that c=0, a=R, then formula (5) is as follows:

[0079] r=R·(1-exp(b·gradP)) (7)

[0080] Then

[0081]

[0082] The relationship between the boundary layer thickness and the starting pressure gradient is obtained through experiments, as shown in the following figure: Figure 2 From the figure, it can be seen that a=0.2426 μm, b=-2.749;

[0083] According to formula (8), the relationship between the permeability and the apparent permeability is obtained:

[0084] k' = k · (1 - exp(-2.749 gradP)) 4 (9)

[0085] Step two, oil-water relative permeability correction;

[0086] Darcy's law is:

[0087]

[0088] Wherein: μ i represents the viscosity, mPa·s, wherein i represents oil, gas, water, etc.; k i represents the relative permeability 10 -3 μm 2 , i represents oil, gas, water, etc.; ΔP represents the differential pressure of the core, Mpa; ΔL represents the length of the core, cm; A represents the area, cm 2 ;

[0089] Through the experiment, the instantaneous flow rate of oil and water v i and the differential pressure of the core ΔP can be monitored, and then the oil-water relative permeability can be calculated by the following formula:

[0090]

[0091] But considering the change of boundary layer thickness caused by the change of differential pressure, formula (8) is substituted into formula (11) to get:

[0092]

[0093] Wherein, k i ' represents the apparent relative permeability, 10 -3 μm 2 ;

[0094] According to the method for determining the relative permeability of two-phase fluid in rock in the national standard GB / T 28912-2012 of the People's Republic of China, under the condition of determining the relative permeability at a constant differential pressure, the relative permeability calculation formula is as follows:

[0095]

[0096] Wherein, k i represents the relative permeability, 10 -3 μm 2 ; k o (S wi ) represents the oil phase permeability at irreducible water saturation, 10 -3 μm 2 .

[0097] After correction by formula (12), the oil phase permeability at irreducible water saturation can be obtained:

[0098]

[0099] in, The oil phase flow rate at the bound water saturation level is expressed in cm. 3 / min;ΔP(S wi Pressure difference at both ends when bound water is saturated, MPa;

[0100] Substituting equations (12) and (14) into equation (13) yields the corrected relative permeability of oil and water:

[0101]

[0102] The correction results for the lithological sample data are as follows:

[0103] Table 1 Core Sampling Data

[0104] Oilfield BN Rock sample number 6 Horizon ES3 Well section 3374.00-3380.30 Rock sample length 5 cm Porosity 16.59％ Bound water establishment method Oil displaces water Rock sample diameter 3 cm Air permeability 0.036um 2 ]]> Test method Unsteady state Test temperature 50.0℃ Water viscosity 0.582 mPa-s Injection water name 3% KCL Oil viscosity 7.250 mPa-s Injection water PH value 6.7 Injection water salinity 26306 mg / L Interfacial tension 26.01 mN / m Average pore throat radius 0.2426 μm

[0105] Table 2 Comparison of oil-water relative permeability curves before and after correction

[0106]

[0107] From Table 2, Figure 3-4 It can be seen that, due to the influence of the boundary layer, the permeability of both the oil phase and the water phase after correction is lower than the result calculated by Darcy's formula. The water phase permeability and the relative permeability of the water phase show an exponential upward trend after the water saturation is higher than 0.6, which reflects that the thickness of the boundary layer (residual oil) attached to the inner wall of the pores has a weaker influence on the water phase in the near residual oil saturation stage. This is also consistent with the characteristic of rapid water cut increase in the later stage of development of low-permeability and ultra-low-permeability reservoirs.

[0108] Step 3: Implementation of numerical simulation of non-Darcy equivalent seepage mode;

[0109] A 20×20×5 conceptual model was established for verification. Water injection development was carried out using a reverse nine-point well pattern, with a monthly time step and the same operating regime. Simulations were conducted for eight months using both Darcy flow and low-velocity non-Darcy equivalent flow methods (see...). Figure 5 The low-velocity non-Darcy equivalent seepage method is implemented as follows:

[0110] For the i direction,

[0111]

[0112] For the j-direction,

[0113]

[0114] For the k direction,

[0115]

[0116] where, PERMX i,j,k represents the X-direction permeability of the i,j,k grid in the three-dimensional grid system; PERMX' i,j,k represents the X-direction apparent permeability of the i,j,k grid; PERMY i,j,k represents the Y-direction permeability of the i,j,k grid; PERMY' i,j,k represents the Y-direction apparent permeability of the i,j,k grid; PERMZ i,j,k represents the Z-direction permeability of the i,j,k grid; PERMZ' i,j,k represents the Z-direction apparent permeability of the i,j,k grid; P i,j,k represents the grid pressure of the i,j,k grid in the three-dimensional grid system; DX i,j,k represents the grid step length of the i-direction of the i,j,k grid in the three-dimensional grid system; DY i,j,k represents the grid step length of the j-direction of the i,j,k grid in the three-dimensional grid system; DZ i,j,k represents the grid step length of the k-direction of the i,j,k grid in the three-dimensional grid system.

[0117] By Figure 6-11 From the comparison results, in the Darcy seepage result, the remaining oil is only concentrated near the four corners in the large area washed by water, and the overall pressure level is low from the pressure distribution condition. In the non-Darcy seepage result, the area washed by water is smaller than that in the Darcy seepage, the injected water shows a fingering phenomenon, and the bottom hole pressure of the injection well is much higher than that in the Darcy seepage mode. This is because, in the water injection process, the pressure gradient is large along the straight line with the shortest distance, the boundary layer thickness is small, and the radius of the bulk fluid is large, so the contribution value of the absolute permeability in the straight line direction is relatively large compared with the angle well direction, and the injected water breaks through quickly. It can also be seen from the figure that the water cut in the P2 well in the straight line direction under the non-Darcy seepage mode is lower than that in the Darcy seepage mode in the early stage, and the water cut starts to be higher than that in the Darcy seepage mode from the 8th month. This is because the permeability contribution value is low under the non-Darcy seepage at the initial state, so the water flow rate is slow, and in the later period, the injected water breaks through due to the fingering effect, causing the water cut to gradually be higher than that in the Darcy seepage mode.

[0118] It can be seen from the permeability change graph over time (see Figure 13), the permeability changes rapidly at the bottom of the production well and the injection well, while the permeability changes slowly between the wells. This is mainly because the energy supplied by the injected water is mainly consumed around the bottom of the injection well, resulting in a faster lifting speed of the bottom flow pressure of the injection well; the bottom of the production well is affected by the starting pressure gradient, and the sweep is weak, resulting in a faster pressure drop. Therefore, the pressure difference is large near the injection well and the production well, and the permeability change amplitude is large. The grid pressure difference between the wells is small, resulting in a small permeability change amplitude. As can be seen from the figure, although the displacement pressure difference between the injection well and the production well is large, the production pressure difference is small, which is mainly due to the pressure consumption between the wells, as shown in Figure 12 .

[0119] The four corner wells have a large well spacing from the injection well, slow pressure propagation, and a fast bottom pressure drop, resulting in a large grid pressure difference and a large permeability change amplitude. The four edge wells have a slightly smaller well spacing from the injection well, slightly faster pressure propagation, and a slower bottom pressure drop, resulting in a smaller grid pressure difference than the corner well position, and thus a smaller permeability change amplitude than the corner well position.

[0120] Step four: production with a fixed liquid production, fitting of the whole area index;

[0121] As Figure 14-17 , the whole area index mainly includes four indexes: comprehensive water cut, daily oil production, cumulative oil production, and cumulative liquid production; since the number of pressure measurement wells and the time points in the study area are small, it is difficult to reflect the overall pressure level of the study area, therefore, in the fitting process, pressure is not used as a fitting index to avoid errors caused by partiality.

[0122] In the fitting process, it is not necessary to adjust the calculation formula of the apparent permeability, but only to adjust the original permeability of the grid as needed, which can meet the needs of history matching.

[0123] As Figure 18 and the table below, the Darcy seepage and non-Darcy seepage calculation results are compared. Under the Darcy seepage mode, the difference between the formation pressures of the oil and water wells is small, basically less than 3 MPa, while under the non-Darcy seepage mode, the pressure difference between the oil and water wells is large, the pressure around the water well is high, and the pressure around the oil well is low, indicating that the injection pressure propagation is slow. Compared with the actual monitoring results, the model calculation results of the non-Darcy seepage are more accurate.

[0124]

[0125] Based on the above ideal embodiments according to the present application, through the above description, relevant personnel can make various changes and modifications without deviating from the technical idea of the present application. The technical scope of the present application is not limited to the contents of the specification, and must be determined by the scope of the claims.

Claims

1. A method for numerical simulation of ultra-low permeability reservoirs, characterized in that, Comprise the following steps: Step one, in turn determine the relationship between air permeability and throat size, the relationship between apparent permeability and air permeability, the relationship between the radius of the bulk phase fluid and pressure gradient, get the relationship between air permeability and apparent permeability under the condition of definite solution; Step 11, determine the relationship between air permeability and throat size, the formula is: （1） wherein R represents the throat radius; represents the number of capillaries per unit area; Step 12, determine the relationship between apparent permeability and air permeability, the formula is: （2） wherein R represents the throat radius; r represents the bulk fluid radius; That is, (3) Step 13, determine the relationship between the radius of the bulk phase fluid and pressure gradient; The thickness of the boundary layer is calculated to be exponentially related to the pressure gradient, and the formula is: （4） In the formulae: δ denotes the boundary layer thickness; a, b, c denotes a coefficient related to the pressure gradient; P denotes the pressure gradient; The bulk fluid radius The bulk fluid radius is also exponentially related to the pressure gradient, expressed as: （5） Step 14, determine the apparent permeability under the condition of definite solution; Assume two definite conditions, when the fluid does not flow, that is , the body fluid radius ; when tends to infinity, , get: （6） is obtained c =0, a =0, R then equation (5) is as follows: （7） Then, the formula for the relationship between air permeability and apparent permeability is: （8） wherein is the air permeability, is the apparent permeability, P denotes the pressure gradient, b denotes a coefficient related to the pressure gradient; R denotes the throat radius, r denotes the bulk fluid radius; Step two, correct the oil-water relative permeability; Step three, adopt the inverted nine-spot well pattern for water injection development, take months as the time step, and simulate by Darcy seepage and low-speed non-Darcy equivalent seepage respectively; Step four, produce with a certain liquid rate, and fit the whole area index.

2. The method of numerical simulation of ultra-low permeability reservoirs according to claim 1, characterized in that, Step two in detail includes: Step 21, monitoring oil-water instantaneous flow rate and the differential pressure between the two ends of the core P, the oil-water relative permeability is calculated by formula (11): （11） wherein, instantaneous flow rate of oil and water, viscosity, A represents area, P pressure difference across the core, Δ L core length; Step 22, substitute formula (8) into formula (11) to get: （12） wherein, represents the apparent permeability, b represents a coefficient related to the pressure gradient; Step 23, according to the relative permeability determination method of two-phase fluid, under the condition of determining relative permeability at a constant pressure difference, the relative permeability calculation formula is as follows: （13） wherein, represents the relative permeability of the phase; represents the relative permeability of the oil phase at the irreducible water saturation; After correction by formula (12), the oil phase permeability at irreducible water saturation is: （14） wherein, oil phase flow rate at irreducible water saturation; pressure differential across the core at irreducible water saturation Substitute formula (12) and formula (14) into formula (13) to get the corrected oil-water relative permeability: （15）。 3. The method of numerical simulation of ultra-low permeability reservoirs according to claim 1, characterized in that, The formula of low-speed non-Darcy equivalent seepage method is: For X direction, （16） For Y direction, （17） For Z direction, （18） in, PERMX i,j,k In a three-dimensional mesh system, the first... i, j, k X-direction permeability of each grid; PERMX ´ i,j,k Indicates the first i, j, k Apparent permeability in the X direction of each grid; PERMY i,j,k Indicates the first i, j, k Y-direction permeability of each grid; PERMY ´ i,j,k Indicates the first i, j, k Apparent permeability in the Y direction of each grid; PERMZ i,j,k Indicates the first i, j, k Z-direction permeability of each grid; PERMZ ´ i,j,k Indicates the first i, j, k Apparent permeability in the Z direction of each grid; P i,j,k In a three-dimensional mesh system, the first... i, j, k The grid pressure of each grid; DX i,j,k In a three-dimensional mesh system, the first... i, j, k grid i Grid step size in the direction; DY i,j,k In a three-dimensional mesh system, the first... i, j, k grid j Grid step size in the direction; DZ i,j,k In a three-dimensional mesh system, the first... i, j, k grid k Grid step size in the direction.

4. The method of numerical simulation of ultra-low permeability reservoirs according to claim 1, characterized in that, The whole area index includes: comprehensive water cut, daily oil production, cumulative oil production.

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