CN111079260A - Nonlinear seepage numerical simulation method - Google Patents

Nonlinear seepage numerical simulation method Download PDF

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CN111079260A
CN111079260A CN201911153628.4A CN201911153628A CN111079260A CN 111079260 A CN111079260 A CN 111079260A CN 201911153628 A CN201911153628 A CN 201911153628A CN 111079260 A CN111079260 A CN 111079260A
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CN111079260B (en
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石立华
党海龙
喻高明
薛颖
贾自力
王雨
石彬
曾俊
王继超
张亮
朱争
谢旭强
白璞
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Shaanxi Yanchang Petroleum Group Co Ltd
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    • E—FIXED CONSTRUCTIONS
    • E21—EARTH OR ROCK DRILLING; MINING
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Abstract

The invention relates to a nonlinear seepage numerical simulation method. A nonlinear seepage numerical simulation method comprises establishing a model; setting a hypothesis condition, establishing an equation of motion of oil, gas and water phases on the premise of meeting the hypothesis condition, and obtaining a rock compression coefficient, compression coefficients of oil, gas and water phases and a continuity equation of oil, gas and water components; substituting the motion equation of the oil phase, the gas phase and the water phase into the corresponding continuity equation, and converting the motion equation into a volume conservation form under the ground standard condition; converting the non-Newtonian fluid motion equation into an expression consisting of apparent viscosity, apparent gradient and flow correction coefficient; solving the established model to obtain so、sg、sw. The method provided by the invention is more suitable for the actual situation of the heavy oil reservoir, has higher prediction index precision, and is more suitable for the actual situation of the reservoirThe method is described.

Description

Nonlinear seepage numerical simulation method
Technical Field
The invention relates to a nonlinear seepage numerical simulation method.
Background
The particularity of the fluid and the nonlinear seepage characteristics are two major factors restricting the high-efficiency development of the heavy oil reservoir, and the establishment of the numerical reservoir simulation model considering the nonlinear seepage characteristics has important practical significance for the development of the heavy oil reservoir. The existing common numerical reservoir simulation means are all based on Darcy seepage mathematical models, and the influence of nonlinear seepage characteristics on the production dynamics of heavy oil reservoirs cannot be accurately and effectively predicted. Scholars at home and abroad improve the numerical model to better describe the seepage law of non-Newtonian fluid, and mainly comprise a numerical simulation method based on a pressure gradient model to be started and a variable permeability numerical simulation method based on the nonlinear seepage law. The non-Darcy characteristics of the reservoir are described based on the numerical model of the pressure gradient to be started, and the defects of a numerical simulation method based on Darcy seepage are overcome to a certain extent; the time-of-flight and clear et al establishes an oil-water two-phase non-Darcy seepage mathematical model based on a simulated starting pressure gradient motion equation; zhao national loyalty et al establishes a non-Darcy equation by assuming that the oil-water simulated starting pressure gradient is a function of the permeability of a medium and the shunt coefficient of water, realizes a numerical simulation method of variable starting pressure gradient, better describes a nonlinear seepage process, but cannot solve the problems of finite difference discretization of a permeability state equation and the like, and is difficult to realize a full-implicit numerical solution method. Aiming at the problems of the existing numerical model, a nonlinear seepage mathematical model which is relatively stable and has no accuracy is needed to be researched to represent the nonlinear seepage characteristics of the heavy oil reservoir.
Disclosure of Invention
The invention aims to solve the problems, provides a method for converting apparent viscosity into a potential gradient function by considering the change rule of fluid to apparent viscosity in the movement of a porous medium, converts an constitutive equation into an expression consisting of the apparent viscosity, the apparent gradient and a flow correction coefficient on the basis, and establishes a novel viscous oil reservoir nonlinear seepage numerical simulation model.
The technical scheme of the invention is as follows:
a nonlinear seepage numerical simulation method is characterized in that: the method comprises the following steps:
establishing a model;
setting a hypothesis condition, establishing an equation of motion of oil, gas and water phases on the premise of meeting the hypothesis condition, and obtaining a rock compression coefficient, compression coefficients of oil, gas and water phases and a continuity equation of oil, gas and water components; substituting the motion equation of the oil phase, the gas phase and the water phase into the corresponding continuity equation, and converting the motion equation into a volume conservation form under the ground standard condition; converting the non-Newtonian fluid motion equation into an expression consisting of apparent viscosity, apparent gradient and flow correction coefficient;
solving the established model to obtain so、sg、sw。
The concrete process of establishing the model comprises the following steps:
experimental oil: e28 well stratum crude oil and kerosene are mixed to form simulated oil, and the viscosity of the simulated oil is 64.92 mPa.s;
experimental cores: the diameter is 2.480-2.530cm, the length is 5.658-5.680cm, the porosity is 34.565-36.721%, the saturation of the irreducible water is 19.08-22.130%, and the permeability is 100.32-500.15 mD;
a model establishing part:
experimental oil: e28 well stratum crude oil and kerosene are mixed to form simulated oil, and the viscosity of the simulated oil is 64.92 mPa.s;
experimental cores: the diameter is 2.480-2.530cm, the length is 5.658-5.680cm, the porosity is 34.565-36.721%, the saturation of the irreducible water is 19.08-22.130%, and the permeability is 100.32-500.15 mD;
a model establishing part:
(1) setting a hypothetical condition
① the oil reservoir is isothermal seepage, ② the oil reservoir is three-phase of oil, gas and water, the oil phase flow conforms to the pressure gradient model to be started, the gas and water phase flow conforms to Darcy seepage, ③ the oil reservoir rock is slightly compressible and anisotropic, the reservoir fluid is compressible, capillary force and gravity are considered, ④ the oil component and the gas component exist in a gas phase and oil phase mode, ⑤ the water component only exists in the water phase;
(2) establishing an equation of motion of oil, gas and water phases, which is respectively as follows:
Figure BDA0002284232030000021
Figure BDA0002284232030000022
Figure BDA0002284232030000023
▽Φl＝▽(Pl-ρlgD)(l＝o，g，w) (5-10)
in the formula:
Figure BDA0002284232030000024
respectively the seepage velocity of oil, gas and water phases, KoIs the phase permeability of the oil phase, K is the permeability tensor
Figure BDA0002284232030000025
G is the oil phase starting pressure gradient, phioThe flow potential of the oil phase is obtained, a and b are experimental fitting coefficients, and the fitting coefficients are obtained by fitting a curve of the fluidity of the indoor rock core and the starting pressure gradient; mu.so、μg、μwThe viscosity of oil, gas and water phases; kroIs the relative permeability, K, of the oilrgIs the relative permeability, K, of gasrwIs the relative permeability of water; phioIs the flow potential of oil, phigIs the flow potential of gas, phiwIs the flow potential of water; d is depth or height in m; g is gravity acceleration, and the specific numerical value is 9.8N/kg;
(3) on the premise that the above-mentioned assumption conditions are satisfied,
the compression coefficients of the rock and the compression coefficients of the oil phase, the gas phase and the water phase are respectively as follows:
Figure BDA0002284232030000031
Figure BDA0002284232030000032
Figure BDA0002284232030000033
Figure BDA0002284232030000034
in the formula: cPIs the compression coefficient of rock, Co、Cg、CwThe fluid compression coefficients of oil, gas and water phases are respectively;
Figure BDA0002284232030000035
is the rock porosity; p is the formation pressure; b iso、Bg、BwThe volume coefficients of oil, gas and water phases are respectively; rhoo、ρg、ρwOf three phases, oil, gas and water respectivelyDensity; rVIs the ratio of volatile oil to gas; rSThe dissolved gas-oil ratio is adopted; po、Pg、PwThe pressure of oil, gas and water phases;
(4) on the premise of meeting the above assumed conditions, the continuity equations of the oil, gas and water components are respectively:
oil component:
Figure BDA0002284232030000036
gas component:
Figure BDA0002284232030000037
water component:
Figure BDA0002284232030000038
in the formula: rhoosc、ρgsc、ρwscThe densities of oil, gas and water phases under the standard condition are respectively; q. q.sO、qG、qWThe mass of oil component, gas component and water component injected or extracted in unit time in unit volume of rock; so、sg、swThe saturation of oil, gas and water phases;
(4) respectively substituting motion equations of oil, gas and water phases into corresponding continuity equations, converting the motion equations into a volume conservation form under a ground standard condition, and establishing a model as follows:
oil component:
Figure BDA0002284232030000039
gas component:
Figure BDA0002284232030000041
water component:
Figure BDA0002284232030000042
in the formula: q. q.sOV、qGV、qWVRespectively the volumes of oil component, gas component and water component injected or extracted in unit time in unit volume of rock under the standard condition;
wherein, the flow correction coefficient expression
Figure BDA0002284232030000043
Its additional equation:
so+sg+sw＝1 (8)
Pcow＝Po-Pw(9)
Pcgo＝Pg-Po(10)
in the formula: pcowIs capillary force between oil and water phases, PcgoThe capillary force between the gas phase and the oil phase;
the initial conditions are as follows:
P(x,y,z)|t＝0＝Pi(x,y,z) (11)
Sw(x,y,z)|t＝0＝Swi(x,y,z) (12)
So(x,y,z)|t＝0＝Soi(x,y,z) (13)
outer boundary condition (closed):
Figure BDA0002284232030000044
inner boundary conditions: and (3) giving bottom hole flow pressure or given oil production, liquid production and water production to the production well, and giving injection pressure or injection quantity to the water injection well.
The solving process of the model comprises the following steps:
(1) carrying formulas (5-18) to (5-20) of formulas (5-22) and (5-23) to eliminate Pg、PwComprises the following steps:
Figure BDA0002284232030000045
Figure BDA0002284232030000051
Figure BDA0002284232030000052
wherein
Figure BDA0002284232030000053
(2) Combining the equation of state and let Ct＝CP+CoSo+CgSg+CwSwElimination of s for (5-28) - (5-30)o、sg、swEstablishing a signal containing only the unknown PoThe equation of (c):
Figure BDA0002284232030000054
wherein M iso、Mg、MwIs (5-28) to (5-30) left-end terms, and has the following expression
Figure BDA0002284232030000059
Figure BDA00022842320300000510
Figure BDA00022842320300000511
(3) Volume V of unit bodies with same multiplication at two sides of pair formula (5-31)b＝ΔxiΔyjΔzkAnd also records QOV＝qOVVb、QGV＝qGVVb、QWV＝qWVVbThen the equation is differenced on both sides to get PoBy implicit handling, other time-dependent non-linesIf the property items are all processed explicitly, the node (i, j, k) corresponds to PoThe algebraic equation for the unknowns is as follows:
Figure BDA0002284232030000055
the coefficients of the above equation are simplified as follows:
Figure BDA0002284232030000056
Figure BDA0002284232030000057
Figure BDA0002284232030000058
Figure BDA0002284232030000061
Figure BDA0002284232030000062
Figure BDA0002284232030000063
Figure BDA0002284232030000064
due to Hi,j,kThe expressions are complicated, so notation is introduced
Figure BDA0002284232030000065
Order:
OREST＝Δ(RVTg)nΔ(Pcgo-ρggD)n-Δ(fTo)nΔ(ρogD)n
GREST＝Δ(Tg)nΔ(Pcgo-ρggD)n-Δ(fRSTo)nΔ(ρogD)n
WREST＝-Δ(Tw)nΔ(Pcow+ρwgD)n
then there are
Figure BDA0002284232030000066
For the conductivities in the formulae (5-33) to (5-40)
Figure BDA0002284232030000069
The expression is specifically as follows:
Figure BDA0002284232030000067
Figure BDA0002284232030000068
Figure BDA0002284232030000071
(4) for each node (1 ≦ i ≦ Nx，1≤j≤Ny，1≤k≤Nz) The unknown number P can be obtained by listing the algebraic equations corresponding to the nodes (i, j, k) in the node (3) one by oneoi,j,kIs (N)x·Ny·Nz) The linear algebraic equation system AX of order B is solved by a preprocessing conjugate gradient algorithm to obtain Poi,j,kThen carrying in the formulas (5-22) and (5-23) to obtain Pgi,j,k、Pwi,j,k；
(5) Respectively matching the unit volume V of the same multiplication on two sides of the formulas (5-28) - (5-30)b＝ΔxiΔyjΔzkThe difference is as follows:
Figure BDA0002284232030000072
Figure BDA0002284232030000073
Figure BDA0002284232030000074
simultaneous (5-44) - (5-46), explicit calculation of so、sg、sw。
The invention has the technical effects that:
on the basis of a rheological equation, a difference equation set is established by adopting an IMPES method, the apparent viscosity is converted into a potential gradient function by considering the change rule of fluid to the apparent viscosity in the movement of a porous medium, and on the basis, an constitutive equation is converted into an expression consisting of the apparent viscosity, the apparent gradient and a flow correction coefficient, so that a novel nonlinear seepage numerical simulation model of the heavy oil reservoir is established, the model is more in line with the actual condition of the heavy oil reservoir, the accuracy of a prediction index is higher, and the model is more in line with the actual condition of the reservoir.
Drawings
FIG. 1 is a graph of QHD32-6 startup pressure gradient versus fluidity.
FIG. 2 is a graph of the QHD32-6 oilfield E28 well crude oil rheology.
FIG. 3 is a seepage curve for the same viscosity at different permeabilities.
FIG. 4 is a graph of the seepage at the same permeability and different viscosity.
FIG. 5 is a schematic view of a variable start pressure gradient seepage curve.
FIG. 6 is a pressure field saturation field comparison graph.
Fig. 7 is a graph comparing development index curves.
FIG. 8 is a graph comparing residual oil saturation field.
FIG. 9 is a comparison chart of development indicators for the presence of an activation pressure gradient in the actual well group in QHD 32-6B.
FIG. 10 is a plot of actual well group residual oil saturation versus time.
Detailed Description
The method is characterized in that natural rock cores of different permeability levels of a QHD32-6 oil field and artificial cemented rock cores with similar permeability levels to a block are adopted to conduct seepage rule research, crude oil of an E28 well and kerosene are mixed and prepared to serve as experimental oil, and the viscosity of the experimental oil accords with the viscosity of formation oil of the actual block. The experiment researches the single-phase seepage law under the conditions of different crude oil viscosities and different permeabilities respectively, in order to measure the real starting pressure gradient more accurately and effectively, the experiment adopts a micro-flow displacement pressure difference experiment method, the formation crude oil and kerosene are mixed and prepared into simulated oil with the viscosity of 64.92mPa.s at the room temperature of 24 ℃, and the experiment core parameters are as follows: diameter 2.480cm, length 5.658cm, porosity 34.565, irreducible water saturation 19.08%, permeability 100.32mD, and experimental results as shown in Table 1 below.
TABLE 1 Experimental data on seepage laws
Figure BDA0002284232030000081
Experimental research shows that the thick oil starting pressure gradient and the fluidity of an actual oil field conform to a power relation, and the starting pressure gradient is reduced along with the increase of the fluidity. When the fluidity is smaller, the pressure gradient is started to decrease faster along with the increase of the fluidity; when the fluidity exceeds a certain range, the starting pressure gradient decreases with increasing fluidity, as shown in fig. 1.
According to the crude oil flow curve, the following steps are carried out: the slope of the curve decreases with increasing temperature, indicating that the viscosity of the thick oil decreases with increasing temperature. In a lower temperature range, the viscosity of the thickened oil has a strong dependence on the temperature, and the viscosity is greatly increased and the fluidity is poor along with the reduction of the temperature; as shown in fig. 2.
According to the experimental results of seepage with the same viscosity and different permeabilities, as shown in fig. 3, compared with a low-permeability reservoir, the seepage curve of a heavy oil reservoir is of a seepage type with an unobvious bent section and an initial pressure gradient, crude oil has a starting pressure gradient when seeping in a stratum, and the crude oil flows approximately according to a quasi-linear seepage section after a displacement pressure gradient is larger than the starting pressure gradient, the lower the permeability of a core is, the closer the curve is to a transverse axis, and the larger the nonlinear section is.
According to the seepage experiment results with the same permeability and different viscosities, as shown in FIG. 4, the higher the viscosity of ① crude oil, the more the seepage curve is shifted to the lower right, and the larger the nonlinear section, therefore, the smaller the flow rate under the same pressure difference, the larger the starting pressure gradient required by the flow is, and the larger the viscosity of ② crude oil, the larger the starting pressure gradient is.
Because the bending section of the thick oil seepage curve is not obvious, the crude oil flows according to the quasi-linear section of the seepage curve after being started, and therefore, it is reasonable to describe the non-Darcy flow of the thick oil by applying a quasi-starting pressure gradient model; since the onset pressure gradient varies with mobility, it is not reasonable for the mathematical model to treat the onset pressure gradient as a constant value due to the non-uniform nature of the reservoir. The seepage curve of the actual reservoir is shown in fig. 5, wherein curve 1 is linear seepage, and curves 2 and 3 are seepage curves under two kinds of fluidity, and the starting pressure gradient is G respectively1And G2(and have
Figure BDA0002284232030000091
G1＜G2)。
For the above reasons, in order to better describe the change law of apparent viscosity of the movement of the non-Newtonian fluid in the porous medium, the method innovatively adopts the treatment of the non-Newtonian fluid as a function of the potential gradient.
The simulation application of the model proposed by the present invention is as follows.
1. Symmetry testing, as shown in fig. 6.
The grid division of the built oil reservoir model is 27 multiplied by 4, X, Y and Z-direction grid step length division27m, 27m and 6m respectively, a net-to-wool ratio of 0.7, a porosity of 0.32, a permeability in both X and Y directions of 3497mD, a permeability in Z direction of 349.7mD, and a rock compressibility of 5.9X 10-3MPa-1Compression factor of water is 4.38X 10-4MPa-1The formation water viscosity was 0.49 mpa.s. The bubble point pressure of oil layer fluid is 11.0MPa, the inverse nine-point well pattern has the well spacing of 350m and the injection speed of water well of 329m3D, oil well constant liquid is 38.25m3And d, simulating and developing for 20 years, extracting the liquid once every 2 years, and increasing the daily liquid production of a single well by 1.5 times each time for 6 times.
2. An index curve comparison was developed as shown in fig. 7.
It is seen from the comparison graph of the saturation field in fig. 6 and the comparison graph of the development index in fig. 7 that the model has good calculation symmetry, obtains a good prediction result, and is consistent with the ECLIPSE prediction result, which proves that the established model has good applicability and extrapolation property, and can be used for dynamic prediction of water flooding development.
3. The technical effect is achieved.
3.1 comparison of the saturation field of the mechanistic model
As shown in fig. 8, the left graph in fig. 8 is considered to be the non-linear actuation pressure gradient, and the right graph is considered to be not considered to be the non-linear actuation pressure gradient; the comparison and simulation results can obtain that: the starting pressure gradient has a large influence on the distribution of the residual oil, the residual oil is obviously more than the residual oil considered in the starting pressure gradient, the residual oil is mostly enriched near the corner well, and the periphery of the side well is less; considering the starting pressure gradient, the residual oil is not considered to be more enriched at 1/4 which is close to the side well corner well distance, and as the development proceeds, the residual oil becomes dead oil, but the residual quantity is sufficient, so that the development value is higher.
3.2 actual well group production indicator prediction comparison a typical well group simulation time period in the northern area of QHD32-6 was selected to be 2001.10.1 to 2017.12.31, and a saturation field versus production indicator curve with and without consideration of the startup pressure gradient is shown in FIG. 9. When the pressure gradient is started, additional resistance is increased in the whole area, the crude oil displacement effect is influenced, the production degree is low, the water content is high, and the development effect is poor. The model prediction value can well reflect the production dynamics, so that the model is verified to have better practicability and can be used for simulating the dynamic prediction of later-stage water drive development. The whole hypotonic layer is influenced by interlayer contradiction, injected water is not easy to flow into the hypotonic layer, the influence of starting pressure gradient is not obvious, the difference of saturation field is not large, but the influence of starting pressure gradient (nonlinear seepage) in the injected water wave range is obvious, and the residual oil is relatively more.
FIG. 10 is a plot of actual well group remaining oil saturation. Wherein, the left graph is without starting pressure gradient, and the right graph is with starting pressure gradient.
TABLE 2 actual well group development index comparison
Figure BDA0002284232030000101

Claims (3)

1. A nonlinear seepage numerical simulation method is characterized in that: the method comprises the following steps:
establishing a model;
setting a hypothesis condition, establishing an equation of motion of oil, gas and water phases on the premise of meeting the hypothesis condition, and obtaining a rock compression coefficient, compression coefficients of oil, gas and water phases and a continuity equation of oil, gas and water components; substituting the motion equation of the oil phase, the gas phase and the water phase into the corresponding continuity equation, and converting the motion equation into a volume conservation form under the ground standard condition; converting the non-Newtonian fluid motion equation into an expression consisting of apparent viscosity, apparent gradient and flow correction coefficient;
solving the established model to obtain so、sg、sw。
2. The nonlinear seepage numerical simulation method of claim 1, wherein: the specific process of establishing the model comprises the following steps:
experimental oil: e28 well stratum crude oil and kerosene are mixed to form simulated oil, and the viscosity of the simulated oil is 64.92 mPa.s;
experimental cores: the diameter is 2.480-2.530cm, the length is 5.658-5.680cm, the porosity is 34.565-36.721%, the saturation of the irreducible water is 19.08-22.130%, and the permeability is 100.32-500.15 mD;
a model establishing part:
(1) setting a hypothetical condition
① the oil reservoir is isothermal seepage, ② the oil reservoir is three-phase of oil, gas and water, the oil phase flow conforms to the pressure gradient model to be started, the gas and water phase flow conforms to Darcy seepage, ③ the oil reservoir rock is slightly compressible and anisotropic, the reservoir fluid is compressible, capillary force and gravity are considered, ④ the oil component and the gas component exist in a gas phase and oil phase mode, ⑤ the water component only exists in the water phase;
(2) establishing an equation of motion of oil, gas and water phases, which is respectively as follows:
Figure FDA0002284232020000011
Figure FDA0002284232020000012
Figure FDA0002284232020000013
▽Φl＝▽(Pl-ρlgD)(l＝o，g，w) (5-10)
in the formula:
Figure FDA0002284232020000014
respectively the seepage velocity of oil, gas and water phases, KoIs the phase permeability of the oil phase, K is the permeability tensor
Figure FDA0002284232020000015
G is the oil phase starting pressure gradient, phioThe flow potential of the oil phase is obtained, a and b are experimental fitting coefficients, and the fitting coefficients are obtained by fitting a curve of the fluidity of the indoor rock core and the starting pressure gradient; mu.so、μg、μwThe viscosity of oil, gas and water phases; kroIs the relative permeability, K, of the oilrgIs the relative permeability, K, of gasrwIs the relative permeability of water; phioIs the flow potential of oil, phigIs the flow potential of gas, phiwIs the flow potential of water; d is depth or height in m; g is gravity acceleration, and the specific numerical value is 9.8N/kg;
(3) on the premise that the above-mentioned assumption conditions are satisfied,
the compression coefficients of the rock and the compression coefficients of the oil phase, the gas phase and the water phase are respectively as follows:
Figure FDA0002284232020000021
Figure FDA0002284232020000022
Figure FDA0002284232020000023
Figure FDA0002284232020000024
in the formula: cPIs the compression coefficient of rock, Co、Cg、CwThe fluid compression coefficients of oil, gas and water phases are respectively;
Figure FDA0002284232020000025
is the rock porosity; p is the formation pressure; b iso、Bg、BwThe volume coefficients of oil, gas and water phases are respectively; rhoo、ρg、ρwThe densities of oil, gas and water phases are respectively; rVIs the ratio of volatile oil to gas; rSThe dissolved gas-oil ratio is adopted; po、Pg、PwThe pressure of oil, gas and water phases;
(4) on the premise of meeting the above assumed conditions, the continuity equations of the oil, gas and water components are respectively:
oil component:
Figure FDA0002284232020000026
gas component:
Figure FDA0002284232020000027
water component:
Figure FDA0002284232020000028
in the formula: rhoosc、ρgsc、ρwscThe densities of oil, gas and water phases under the standard condition are respectively; q. q.sO、qG、qWThe mass of oil component, gas component and water component injected or extracted in unit time in unit volume of rock; so、sg、swThe saturation of oil, gas and water phases;
(4) respectively substituting motion equations of oil, gas and water phases into corresponding continuity equations, converting the motion equations into a volume conservation form under a ground standard condition, and establishing a model as follows:
oil component:
Figure FDA0002284232020000031
gas component:
Figure FDA0002284232020000032
water component:
Figure FDA0002284232020000033
in the formula: q. q.sOV、qGV、qWVRespectively the volumes of oil component, gas component and water component injected or extracted in unit time in unit volume of rock under the standard condition;
wherein, the flow correction coefficient expression
Figure FDA0002284232020000034
Its additional equation:
so+sg+sw＝1 (8)
Pcow＝Po-Pw(9)
Pcgo＝Pg-Po(10)
in the formula: pcowIs capillary force between oil and water phases, PcgoThe capillary force between the gas phase and the oil phase;
the initial conditions are as follows:
P(x,y,z)|t＝0＝Pi(x,y,z) (11)
Sw(x,y,z)|t＝0＝Swi(x,y,z) (12)
So(x,y,z)|t＝0＝Soi(x,y,z) (13)
outer boundary condition (closed):
Figure FDA0002284232020000035
inner boundary conditions: and (3) giving bottom hole flow pressure or given oil production, liquid production and water production to the production well, and giving injection pressure or injection quantity to the water injection well.
3. The nonlinear seepage numerical simulation method of claim 2, wherein: the concrete process of solving the model is as follows:
(1) the general formulae (5-22) and (5-23)) Elimination of P by bringing into formula (5-18) to (5-20)g、PwComprises the following steps:
Figure FDA0002284232020000041
Figure FDA0002284232020000042
Figure FDA0002284232020000043
wherein
Figure FDA0002284232020000044
(2) Combining the equation of state and let Ct＝CP+CoSo+CgSg+CwSwElimination of s for (5-28) - (5-30)o、sg、swEstablishing a signal containing only the unknown PoThe equation of (c):
Figure FDA0002284232020000045
wherein M iso、Mg、MwIs (5-28) to (5-30) left-end terms, and has the following expression
Figure FDA0002284232020000048
Figure FDA0002284232020000049
Mw＝▽·[λw▽Po]-▽·[λw▽(Pcow+ρwgD)]+qWV
(3) Volume V of unit bodies with same multiplication at two sides of pair formula (5-31)b＝ΔxiΔyjΔzkAnd is combined withNote QOV＝qOVVb、QGV＝qGVVb、QWV＝qWVVbThen the equation is differenced on both sides to get PoIf implicit processing is carried out and other time-dependent nonlinear items are explicitly processed, P is used for corresponding nodes (i, j, k)oThe algebraic equation for the unknowns is as follows:
Figure FDA0002284232020000046
the coefficients of the above equation are simplified as follows:
Figure FDA0002284232020000047
Figure FDA0002284232020000051
Figure FDA0002284232020000052
Figure FDA0002284232020000053
Figure FDA0002284232020000054
Figure FDA0002284232020000055
Figure FDA0002284232020000056
due to Hi,j,kThe expressions are complicated, so notation is introduced
Figure FDA0002284232020000057
Order:
OREST＝Δ(RVTg)nΔ(Pcgo-ρggD)n-Δ(fTo)nΔ(ρogD)n
GREST＝Δ(Tg)nΔ(Pcgo-ρggD)n-Δ(fRSTo)nΔ(ρogD)n
WREST＝-Δ(Tw)nΔ(Pcow+ρwgD)n
then there are
Figure FDA0002284232020000061
For the conductivities in the formulae (5-33) to (5-40)
Figure FDA0002284232020000062
The expression is specifically as follows:
Figure FDA0002284232020000063
Figure FDA0002284232020000064
Figure FDA0002284232020000065
(4) for each node (1 ≦ i ≦ Nx，1≤j≤Ny，1≤k≤Nz) The unknown number P can be obtained by listing the algebraic equations corresponding to the nodes (i, j, k) in the node (3) one by oneoi,j,kIs (N)x·Ny·Nz) The linear algebraic equation system AX of order B is solved by a preprocessing conjugate gradient algorithm to obtain Poi,j,kThen carrying in the formulas (5-22) and (5-23) to obtainGo out of Pgi,j,k、Pwi,j,k；
(5) Respectively matching the unit volume V of the same multiplication on two sides of the formulas (5-28) - (5-30)b＝ΔxiΔyjΔzkThe difference is as follows:
Figure FDA0002284232020000066
Figure FDA0002284232020000067
Figure FDA0002284232020000068
simultaneous (5-44) - (5-46), explicit calculation of so、sg、sw。
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