CN110259441A - A kind of low-permeability oil deposit two dimension CO2Non-phase-mixing driving Mathematical Modelling Method - Google Patents
A kind of low-permeability oil deposit two dimension CO2Non-phase-mixing driving Mathematical Modelling Method Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/16—Enhanced recovery methods for obtaining hydrocarbons
- E21B43/164—Injecting CO2 or carbonated water
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B47/00—Survey of boreholes or wells
- E21B47/06—Measuring temperature or pressure
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
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- E—FIXED CONSTRUCTIONS
- E21—EARTH DRILLING; MINING
- E21B—EARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
- E21B49/00—Testing the nature of borehole walls; Formation testing; Methods or apparatus for obtaining samples of soil or well fluids, specially adapted to earth drilling or wells
- E21B49/08—Obtaining fluid samples or testing fluids, in boreholes or wells
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02A—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
- Y02A10/00—TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
- Y02A10/40—Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping
Abstract
The present invention provides a kind of low-permeability oil deposit two dimension CO2Non-phase-mixing driving Mathematical Modelling Method.This method comprises: establishing low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model；The low-permeability oil deposit two dimension CO2The processing of parameter and boundary condition that non-phase-mixing driving solution procedure needs；The low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model solves, and the mathematical model is solved using numerical method, i.e., shows degree of saturation method using hidden pressure and solved；It chooses low-permeability oil deposit and obtains its geologic parameter, using the low-permeability oil deposit two dimension CO2Non-phase-mixing driving Mathematical Modelling Method is calculated, and carries out interpretation of result.This method considers CO2Viscosity of crude variation and the variation of fluid starting pressure gradient, establish low-permeability oil deposit CO during immiscible displacement2Non-phase-mixing driving mathematical model, model and oil reservoir actual attribute are more close, and give method for solving and interpretation of result method, and calculated result is more reliable, for instructing low-permeability oil deposit CO2Non-phase-mixing driving exploitation.
Description
Technical field
The present invention relates to oil-gas mining technical fields, more specifically, are related to a kind of low-permeability oil deposit two dimension CO2Non- mixed phase
Drive Mathematical Modelling Method.
Background technique
CO2Technology of reservoir sweep is exactly CO2The technology of oil extraction in oil field rate is improved in injection oil reservoir.CO2Mechanism of oil displacement mainly wraps
It includes: (1) CO2There is good intersolubility with crude oil, can significantly reduce viscosity of crude；(2)CO2It is dissolved in crude oil and water, makes its carbonic acid
Change, improves the mobility ratio of crude oil and water；(3)CO2After injecting oil reservoir, crude oil volume is largely expanded, stratum can be increased
Elastic energy；(4)CO2Lighter hydrocarbons in extraction and vaporization crude oil；(5)CO2After mixing with crude oil, original can not only be extracted and vaporized
Light hydrocarbon in oil, and CO can also be formed2With the oily band of light hydrocarbon mixing；(6)CO2During mixed phase drives, CO2It extracts light in crude oil
Matter component makes its vaporization, to reduce interfacial tension；(7) a large amount of CO2Being dissolved in crude oil has the function of dissolved gas drive；
(8)CO2It is dissolved in crude oil and water, makes its carbonating.The carbonate reaction of carbonated water and oil reservoir generates bicarbonate.Bicarbonate
It is soluble easily in water, lead to a large amount of water and CO around carbonate especially pit shaft2By carbonatite permeability improve, seep stratum
Saturating rate is improved, and above-mentioned effect can make Permeability of Sandstone improve 5%-15%, while CO2Also help inhibition clay swell.
In practical CO2During drive, according to the variation relation of minimum miscibility pressure (MMP) and strata pressure, the seepage flow of fluid in stratum
Three types can be divided into: non-phase-mixing driving, mixed phase drive, mixed phase drives jointly with non-mixed phase.When strata pressure is greater than minimum mixed phase pressure
When power (MMP), displacement process is mixed phase drive；When strata pressure is less than MMP, displacement process is non-phase-mixing driving；When MMP is between note
When adopting between pressure at two ends, mixed phase drives and non-phase-mixing driving collective effect, referred to as CO2Mixed phase drives jointly with non-mixed phase, seepage flow mould
Type is increasingly complex.
In recent years, many scholars are in CO2It improves recovery ratio field and has carried out desk research, be CO2Improve the examination of recovery ratio mining site
It tests and provides theoretical basis.Shen Ping equality application tubule and multiple-contact experiment are to CO2Multi-phase multi-component seepage flow mechanism carries out
Research, Liu Yuzhang is to CO2It is analyzed with the influence factor of crude oil miscible conditions, Ju Binshan establishes CO2Most with crude oil system
Small miscible pressure prediction model, Su Yuliang is to CO2Miscible displacement of reservoir mechanism, CO2Well-test curve feature is driven to be analyzed, Cheng Jiecheng,
Zhu Weiyao is to CO2Displacement of reservoir oil multiphase porous flow model is stated, and the Chinese selects to CO2Mixed phase drives raising recovery ratio method and is changed
Into.In low-permeability oil deposit well spacing calculating field, in recent years to Start-up Pressure Gradients in Low Permeability Reservoir, non-linear flow mathematical model of reservoir
It is more with the research of water drive critical spacing, but about low-permeability oil deposit two dimension CO2The research of non-phase-mixing driving is very rare.
The prior art is about low-permeability oil deposit CO2The research of non-phase-mixing driving is broadly divided into the research of experiment indoor simulation, mining site
The research in upper pilot experiments area and one-dimensional low-permeability oil deposit CO2Non-phase-mixing driving Mathematical Modelling Method research, and really about
CO2The mechanism study of non-phase-mixing driving is very rare, especially two dimension CO2Research in terms of non-phase-mixing driving mathematical model is more few
See.CO2Non-phase-mixing driving is different from water drive, CO2Dissolution, mass transfer, extracting the effects of change the physical property of crude oil, seepage flow mechanism ratio
Water drive oil is complicated.For low-permeability oil deposit, often there is higher starting pressure gradients, this is also actual development oil reservoir process
An important factor for middle influence yield.In addition to this, along with CO2Injection, viscosity of crude can also change, starting pressure ladder
The variation of degree and the variation of oil phase viscosity all make CO2The foundation of non-phase-mixing driving mathematical model becomes increasingly complex.About hypotonic
Saturating oil reservoir two dimension CO2The research of non-phase-mixing driving Mathematical Modelling Method is a completely new direction in development of low-permeability oil reservoir field.
Therefore, be badly in need of propose it is a kind of consider starting pressure gradient variation and oil phase viscosity variation low-permeability oil deposit two dimension CO2
Non-phase-mixing driving Mathematical Modelling Method is to instruct the exploitation of practical oil reservoir.
Summary of the invention
It is an object of the invention to solve the prior art at present it is insurmountable consider starting pressure gradient variation and
The low-permeability oil deposit CO of the variation of oil phase viscosity2Immiscible flood mechanism study provides a kind of low-permeability oil deposit two dimension CO2It is non-
Mixed phase drives Mathematical Modelling Method.
The present invention is to be achieved through the following technical solutions: a kind of low-permeability oil deposit CO2 non-phase-mixing driving critical spacing calculating side
Method, comprising the following steps:
Step S1: two-dimentional low-permeability oil deposit CO is established2Non-phase-mixing driving mathematical model；
The foundation of the mathematical model includes: the foundation of low-permeability oil deposit assumed condition；Percolation equationk and subsidiary equation
It establishes；The foundation of definite condition；It is former that the assumed condition, percolation equationk, subsidiary equation and definite condition together constitute consideration
Oil viscosity variation, the CO for considering the variation of fluid starting pressure gradient2Non-phase-mixing driving seepage experiment；
Step S2: the low-permeability oil deposit two dimension CO2The place of parameter and boundary condition that non-phase-mixing driving solution procedure needs
Reason；
The parameter processing includes: the processing of absolute permeability, the processing of flow coefficient, the processing of gas mixture viscosity
And the processing of starting pressure gradient；The processing of boundary condition includes: the processing of Outer Boundary Conditions and internal boundary condition；
Step S3: the low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model solves；
The mathematical model is solved using numerical method, i.e., shows degree of saturation method using hidden pressure and solved；
Step S4: it chooses low-permeability oil deposit and obtains its geologic parameter, using the low-permeability oil deposit two dimension CO2Non- mixed phase
It drives Mathematical Modelling Method to be calculated, and carries out interpretation of result；
Analysis only considers pressure field, saturation field, viscosity field distribution when viscosity of crude variation；Analysis considers that viscosity of crude becomes
Pressure field, saturation field, viscosity field distribution and analysis starting pressure gradient are to low-permeability oil when change, starting pressure gradient variation
Hide two dimension CO2The influence of non-phase-mixing driving yield.
In a preferred embodiment of the present invention, in the step S1, the low-permeability oil deposit assumed condition includes:
Fluid is isothermal seepage flow in oil reservoir；Rock is heterogeneous micro- compressible pore media；Fluid is compressible fluid；Consider that crude oil is viscous
Degree variation；Consider the variation of fluid starting pressure gradient；Do not consider gravity and capillary force.
In a preferred embodiment of the present invention, in the step S1, the percolation equationk includes oily phase seepage flow side
Journey and gas phase percolation equationk；The oil phase percolation equationk are as follows:
The gas phase percolation equationk are as follows:
In formula, k-absolute permeability, 10- 3μm2；kro- oil relative permeability, dimensionless, value 0-1；krg- gas phase
Relative permeability, dimensionless, value 0-1；μoThe viscosity of-crude oil, mPas；μg—CO2Viscosity, mPas；T-time,
d；po- oil phase pressure, MPa；pg- gaseous pressure, MPa；Go- oil phase starting pressure gradient, MPa/m；qo- oil phase shunt volume,
m3/d；qg- gas phase shunt volume, m3/d；So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless take
Value 0-1；φ-porosity, dimensionless, value 0-1；Rso—CO2Solubility in crude oil, dimensionless, value 0-1；ρo- ground
Layer oil density, kg/m3；ρg- stratum CO2Gas density, kg/m3。
In a preferred embodiment of the present invention, in the step S1, the subsidiary equation include saturation equation,
Capillary force equation, oil relative permeability equation, gas phase relative permeability equation, CO2Solubility equation, calculating in crude oil
CO2Volume fraction coefficient of colligation simultaneously corrects viscosity of crude equation, amendment fluid starting pressure gradient equation.
In a preferred embodiment of the present invention, in the step S1, the definite condition include primary condition and
Boundary condition, the boundary condition include Outer Boundary Conditions and internal boundary condition, and the Outer Boundary Conditions show oil reservoir side
Pressure locating for boundary and whether closed state, the internal boundary condition then show injection well and produce well state.
In a preferred embodiment of the present invention, the saturation equation are as follows:
so+sg=1；
The capillary force equation are as follows:
po=pg-pcgo；
The oil relative permeability equation are as follows:
kro=kro(sg)；
The gas phase relative permeability equation are as follows:
krg=krg(sg)；
The CO2Solubility equation in crude oil are as follows:
The calculating CO2Volume fraction coefficient of colligation and amendment viscosity of crude equation are as follows:
lnμom=Xo lnμo+Xs lnμg；
The amendment fluid starting pressure gradient equation are as follows:
In formula, So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless, value 0-1；po—
Oily phase pressure, MPa；pg- gaseous pressure, MPa；pcgo- capillary force, MPa；kro- oil relative permeability, dimensionless, value
0-1；krg- gas phase relative permeability, dimensionless, value 0-1；Rso—CO2Solubility in crude oil, dimensionless, value 0-1；
ρo- oil density, kg/m3；a1, a2, a3, a4, a5, a6, a7- computational constant, dimensionless；T-formation temperature, K；P-oil
The pressure of each point, MPa in hiding；Xs—CO2Volume fraction coefficient of colligation, dimensionless；Xo- crude oil volume fraction coefficient of colligation, nothing
Dimension；Fco2For CO2The ratio between the volume under volume and reservoir temperature, pressure at standard conditions, dimensionless；FoIt is crude oil in oil
Hide the ratio between the volume under temperature and 0.1MPa and volume under reservoir temperature and reservoir pressure, dimensionless；Fs- expansion factor, nothing
Dimension；α-empirical coefficient, dimensionless；μom- revised gas mixture viscosity, mPas；μoThe viscosity of-crude oil,
mPa·s；μg—CO2Viscosity, mPas；Gom- revised gas mixture starting pressure gradient, MPa/m；ko- oil phase
Phase permeability, 10- 3μm2；A, b-regression constant, dimensionless.
In a preferred embodiment of the present invention, the primary condition are as follows:
The Outer Boundary Conditions include closed outer boundary condition and constant pressure outer boundary condition, the closed outer boundary are as follows:
The constant pressure outer boundary condition
The internal boundary condition includes determining yield equation and stable bottom hole pressure equation, described to determine yield equation are as follows:
Qvl=constant, l=o, g；
The stable bottom hole pressure equation are as follows:
For producing well, pgfIt is known；For gas injection well, pigfIt is known；
The production well yield can indicate are as follows: Qvli,j=PIl(pli,j-pgf)
The gas injection rate of the gas injection well can indicate are as follows: Qvgi,j=GIg(pigf-pgi,j)
Wherein, PIlFor the liquid phase production index, GIgFor gas phase injectivity index；
In formula, po- oil phase pressure, MPa；Abscissa at x-initial point, m；Ordinate at y-initial point, m；t—
Time, d；poiOily phase pressure at-initial point, MPa；Lx- model horizontal axis total length, m；Ly- model longitudinal axis total length, m；
sg- gas saturation, dimensionless；sgiGas saturation at-initial point, dimensionless；The pressure of each point in p-oil reservoir,
MPa；peReservoir pressure at-model outer boundary, MPa；Qvl- inner boundary fixed output quota amount, m3/d；pgf- producing well flowing bottomhole pressure (FBHP),
MPa；pigf- gas injection well bottom pressure, MPa；Qvli,jWell production, m are produced at-grid cell (i, j)3/d；PIl- l phase produces
Index, dimensionless；pli,jL phase pressure, MPa at-grid cell (i, j)；Qvgi,jGas injection well gas injection at-grid cell (i, j)
Amount, m3/d；GIg- gas phase injectivity index, dimensionless；pgi,jGaseous pressure at-grid cell (i, j), MPa.
In a preferred embodiment of the present invention, in the step S2, the processing method of the absolute permeability are as follows:
The absolute permeability is the function of space coordinate, is calculated according to harmonic-mean:
The processing method of the flow coefficient are as follows:
The flow coefficientIn, the absolute permeability k takes the harmonic average of two neighboring grid
Value；Part is then handled using single-point upstream weighted:
The gas mixture viscosity processing method are as follows: gas mixture viscosity then uses described in gas phase percolation equationk
CO2Solubility equation in crude oil, the calculating CO2Volume fraction coefficient of colligation and amendment viscosity of crude equation are modified,
And it is handled using single-point upstream weighted value；
The starting pressure gradient processing method are as follows:
Consider oily phased soln CO2The viscosity change of gas mixture later starts pressure ladder according to the amendment fluid
The variation of gas mixture starting pressure gradient caused by spending equation calculation thus, and handled using single-point upstream weighted value；
In formula,The right boundary of-grid cell (i, j)Locate permeability value when the n-th moment, 10- 3μ
m2；Δxi±1The step-length in the direction x, m at the adjacent block in the left and right of-grid cell (i, j)；ΔxiThe direction x at-grid cell (i, j)
Step-length, m；Permeability value at the adjacent block (i ± 1, j) in the left and right of-grid cell (i, j) when the n-th moment, 10- 3μm2；
Permeability value at-grid cell (i, j) when the n-th moment, 10- 3μm2；The up-and-down boundary of-grid cell (i, j)Locate permeability value when the n-th moment, 10- 3μm2；Δyj±1The direction y at the block adjacent up and down of-grid cell (i, j)
Step-length, m；ΔyjThe step-length in the direction y, m at-grid cell (i, j)；- grid cell (i, j) block adjacent up and down (i, j ±
1) permeability value when the n-th moment of place, 10- 3μm2；Permeability value at-grid cell (i, j) when the n-th moment, 10- 3μ
m2；λl- flow coefficient, dimensionless；K-absolute permeability, 10- 3μm2；krl- l phase relative permeability, dimensionless, value 0-1；
ρl- l phase density, kg/m3；μl- l phase viscosity, mPas；pl- l phase pressure, MPa；Explanation about footmark: subscript represents
Space coordinate, superscript represent time coordinate；The center of (i, j)-grid cell (i, j)；(i ± 1, j)-grid cell (i,
J) center of the adjacent block (i ± 1, j) in left and right；The center of the block (i, j ± 1) adjacent up and down of (i, j ± 1)-grid cell (i, j)；The right boundary of-grid cell (i, j) The up-and-down boundary of-grid cell (i, j)
In a preferred embodiment of the present invention, in the step S2, the processing method of the Outer Boundary Conditions are as follows:
To closed outer boundary condition, virtual hoop net lattice outside closed boundary enable the pressure of boundary mesh be equal to virtual grid
Pressure, it may be assumed that
The processing method of the internal boundary condition are as follows:
Injection-production well in oil reservoir is special grid cell, includes source sink term in such grid cell, and oil-producing well produces
Amount is negative value, and gas injection well injection rate is positive value；If grid (i, j) has a well, volume flow Qv, determine producing well flowing bottomhole pressure (FBHP)
It produces, then volume flow QvIt needs with grid pressure pijWith flowing bottomhole pressure (FBHP) pgfTo express；
The radial fluid flow quasi-stable state formula of producing well oil production are as follows:
Qvo=-PID λo[poi,j-pgf-Go(re-rw)]；
The radial fluid flow quasi-stable state formula of gas injection well gas injection rate are as follows:
Qvg=-WID λg[pgi,j-pgf+Gg(re-rw)]；
In formula,Reservoir pressure value at-grid cell (i, j) when the (n+1)th moment, MPa；nxThe total grid in the direction-x
Number, dimensionless；nyThe total grid number in the direction-y, dimensionless；Qv- volume flow, m3/d；pi,jOil reservoir at-grid cell (i, j)
Pressure, MPa；pgf- producing well flowing bottomhole pressure (FBHP), MPa；Qvo- producing well oil production, m3/d；PID-the production index, dimensionless；
λoThe opposite mobility of-oil, μm2/(Pa·s)；poi,jOil phase pressure, MPa at-grid cell (i, j)；pgf- producing well shaft bottom
Stream pressure, MPa；Go- oil phase starting pressure gradient, MPa/m；reThe equivalent drainage radius of-well, cm；rwThe radius of-well, cm；
Qvg- gas injection well gas injection rate, m3/d；WID-injection well injectivity index, dimensionless；λg- gas phase with respect to mobility, μm2/(Pa·
s)；pgi,jGaseous pressure at-grid cell (i, j), MPa；Gg- gas phase starting pressure gradient, MPa/m.
In a preferred embodiment of the present invention, in the step S3, it is a kind of that the hidden pressure, which shows degree of saturation method,
The sequence method for solving of multiphase porous flow is solved, first using finite difference method to continuous partial differential equation discretization, then
Equation group after discrete is linearized, is solved by the method for solving system of linear equations；Specific steps are as follows: (1) will be described
Oily phase percolation equationk carries out discretization with the gas phase percolation equationk and is added to obtain about unknown quantity poTotal pressure equation；
(2) pressure equation is linearized, equation group is solved using Newton iteration method, finds out n+1 moment pressure iterative value
By the capillary pressure subsidiary equation po=pg-pcgo, can find outBy what is found outGas phase seepage flow difference equation is substituted into, it can
Explicitly find out(3) it finds outIt later, can be by saturation degree subsidiary equation so=1-sgIt finds outIn formula,- the (n+1)th
Oily phase pressure value when the moment, MPa；po- oil phase pressure, MPa；pg- gaseous pressure, MPa；pcgo- capillary force, MPa；
Gaseous pressure value when the-the (n+1)th moment, MPa；Gas saturation when the-the (n+1)th moment, dimensionless, value 0-1；
So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless, value 0-1；When the-the (n+1)th moment
Oil saturation, dimensionless, value 0-1.
The present invention includes at least compared with prior art: 1. the present invention considers CO2Immiscible displacement process Crude Oil is viscous
Degree variation and the variation of fluid starting pressure gradient, establish low-permeability oil deposit CO2Non-phase-mixing driving mathematical model, model and oil reservoir
Actual attribute is more close；2. showing degree of saturation method using hidden pressure solves low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model
Calculated result is more accurate reliable；3. in the case where given low-permeability oil deposit parameter, using low-permeability oil deposit two of the invention
Victoria C O2Non-phase-mixing driving Mathematical Modelling Method can quickly calculate pressure field under different situations, saturation field, viscosity field distribution with
And analysis starting pressure gradient is to low-permeability oil deposit two dimension CO2The influence of non-phase-mixing driving yield.
Detailed description of the invention
Fig. 1 is a kind of low-permeability oil deposit two dimension CO provided by the invention2The flow chart of non-phase-mixing driving Mathematical Modelling Method；
Fig. 2 is the pressure field point when the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=300d
Butut；
Fig. 3 is pressure field when not considering that oil phase viscosity changes t=300d using the F142 oil reservoir that the method for the present invention obtains
Distribution map；
Fig. 4 is the pressure field point when the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=900d
Butut；
Fig. 5 is the oil-containing saturation when F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=300d
Spend field pattern；
Fig. 6 is that oil-containing when not considering that oil phase viscosity changes t=300d using the F142 oil reservoir that the method for the present invention obtains is full
With degree field pattern；
Fig. 7 is the oil-containing saturation when F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=900d
Spend field pattern；
Fig. 8 is the oil phase viscosity when F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=300d
Field pattern；
Fig. 9 is the oil phase viscosity when F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity variation t=900d
Field pattern；
When Figure 10 is that the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity, starting pressure gradient t=300d
Pressure field distribution figure；
Figure 11 is that the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity, starting pressure gradient variation t=
Oil saturation field pattern when 300d；
Figure 12 is that the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity, starting pressure gradient variation t=
Oil phase viscosity field pattern when 300d；
Figure 13 is that the F142 oil reservoir obtained using the method for the present invention considers oil phase viscosity, starting pressure gradient variation t=
Starting pressure gradient field pattern when 300d；
Figure 14 is the influence diagram of the F142 oil reservoir starting pressure gradient that obtains using the method for the present invention to yield.
Specific embodiment
Detailed be explicitly described is carried out to technical solution of the present invention in the application of practical oil reservoir below in conjunction with the present invention.?
In actual application, the present invention presses a kind of low-permeability oil deposit two dimension CO that Fig. 1 is provided2The stream of non-phase-mixing driving Mathematical Modelling Method
Journey figure carries out.Shown in concrete operations following examples.
Step S1: low-permeability oil deposit CO is established2Non-phase-mixing driving mathematical model；
The foundation of mathematical model includes: the foundation of low-permeability oil deposit assumed condition；The foundation of percolation equationk and subsidiary equation；
The foundation of definite condition；Assumed condition, percolation equationk, subsidiary equation and definite condition, which together constitute, considers that viscosity of crude becomes
Change, consider the CO of fluid starting pressure gradient variation2Non-phase-mixing driving seepage experiment；
Low-permeability oil deposit assumed condition include: in (1) oil reservoir fluid be isothermal seepage flow；(2) rock is heterogeneous micro- presses
Contracting pore media；(3) fluid is compressible fluid；(4) consider viscosity of crude variation；(5) consider that fluid starting pressure gradient becomes
Change；(6) do not consider gravity and capillary force；
The foundation of percolation equationk and subsidiary equation: it is convenient to write, it enablesTwo-dimentional CO2Non-phase-mixing driving seepage flow number
It is as follows to learn model:
Oily phase percolation equationk:
Gas phase percolation equationk:
Subsidiary equation includes saturation equation, capillary force equation, oil relative permeability equation, gas phase relative permeability side
Journey, CO2Solubility equation, calculating CO in crude oil2Volume fraction coefficient of colligation simultaneously corrects viscosity of crude equation, amendment fluid
Starting pressure gradient equation:
Saturation equation: so+sg=1 (3)
Capillary force equation: po=pg-pcgo (4)
Oil relative permeability equation: kro=kro(sg) (5)
Gas phase relative permeability equation: krg=krg(sg) (6)
CO2Solubility equation in crude oil:
Calculate CO2Volume fraction coefficient of colligation simultaneously corrects viscosity of crude:
lnμom=Xo lnμo+Xs lnμg (9)
Correct fluid starting pressure gradient:
Definite condition: definite condition includes primary condition and boundary condition, and boundary condition includes Outer Boundary Conditions and inner edge
Boundary's condition, Outer Boundary Conditions show pressure locating for oil reservoir boundary and whether closed state, internal boundary condition then shows
The state of injection well and extraction well.
Primary condition are as follows:
Outer Boundary Conditions are divided into two kinds:
(1) closed outer boundary:
(2) constant pressure outer boundary:
Internal boundary condition is also classified into two kinds:
(1) fixed output quota amount:
Qvl=constant, l=o, g (14)
(2) stable bottom hole pressure
For producing well, pgfIt is known；For gas injection well, pigfIt is known.
Production well yield can indicate are as follows: Qvli,j=PIl(pli,j-pgf) (15)
The gas injection rate of gas injection well can indicate are as follows: Qvgi,j=GIg(pigf-pgi,j) (16)
Step S2: low-permeability oil deposit CO2The processing of parameter and boundary condition that non-phase-mixing driving solution procedure needs；
Parameter processing include: the processing of absolute permeability, the processing of flow coefficient, the processing of gas mixture viscosity and
The processing of starting pressure gradient；
(1) absolute permeability: absolute permeability is the function of space coordinate, is calculated according to harmonic-mean:
(2) flow coefficient: flow coefficientIn, absolute permeability k takes the tune of two neighboring grid
And average value；Part is then handled using single-point upstream weighted:
(3) gas mixture viscosity is handled: the oil phase viscosity μ in oily phase percolation equationkoIt is constant, and in gas phase percolation equationk
Gas mixture viscosity, mumixIt is then modified using equation (7), (8) and (9), is equally handled using single-point upstream weighted value.
(4) starting pressure gradient is handled: considering oily phased soln CO2The viscosity change of gas mixture later, therefore root
The variation of gas mixture starting pressure gradient caused by being calculated thus according to equation (10), also using at single-point upstream weighted value
Reason.
The processing of boundary condition includes: the processing of Outer Boundary Conditions and internal boundary condition；
(1) Outer Boundary Conditions: to closed outer boundary condition, virtual hoop net lattice, enable the pressure of boundary mesh outside closed boundary
Power is equal to virtual grid pressure, it may be assumed that
(2) internal boundary condition: the injection-production well in oil reservoir is special grid cell, includes source in such grid cell
Converge item, oil-producing well production is negative value, and gas injection well injection rate is positive value.If grid (i, j) has a well, volume flow Qv, fixed
Producing well flowing bottomhole pressure (FBHP) produces, then volume flow QvIt needs with grid pressure pijWith flowing bottomhole pressure (FBHP) pgfTo express.
The radial fluid flow quasi-stable state formula of producing well oil production are as follows:
Qvo=-PID λo[poi,j-pgf-Go(re-rw)] (22)
The radial fluid flow quasi-stable state formula of gas injection well gas injection rate are as follows:
Qvg=-WID λg[pgi,j-pgf+Gg(re-rw)] (23)
Step S3: low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model solves；
The mathematical model established is solved using numerical method.It is solved using implicit pressure explicit saturation method, hidden pressure is aobvious full
Method is a kind of sequence method for solving for solving multiphase porous flow.It is discrete to continuous partial differential equation using finite difference method first
Change, then the equation group after discrete is linearized, is solved by the method for solving system of linear equations.
Capillary force equation (4) are substituted into gas phase percolation equationk (2), are mutually re-written as oily with gas phase percolation equationk:
Define flow coefficient:
Then, oil mutually can simplify with gas phase percolation equationk are as follows:
Finite difference non-uniformity interval is used below, and time and spatial discretization first are carried out to oily phase percolation equationk:
By equation both sides with multiplied by mesh volume Δ xiΔyiH, and enable:
The volume of grid (i, j): Vij=Δ xiΔyih
Equation (28) can be written as:
Definition oil is mutually in the coefficient of conductivity in the direction x and y respectively:
Then oily phase percolation equationk becomes:
Wherein, the produced quantity of grid (i, j)Above formula is unfolded, starting pressure gradient item is merged to obtain:
For simplicity, introduce following difference operator, enable:
Δxη=ηi+1,j-ηi,j (34)
Δyη=ηi,j+1-ηi,j (35)
Therefore, linear difference operator can be introduced:
Oily phase difference equation can be write a Chinese character in simplified form are as follows:
On two-dimensional surface, linear difference operator can be unfolded are as follows:
Therefore it enables: Δ T Δ p=ΔxTxΔxp+ΔyTyΔyp (42)
Equation (40) continues to be reduced to (43):
Wherein, the starting pressure gradient of oily phase percolation equationk is constant, merges are as follows:
Identical as the derivation method of oily phase percolation equationk, the form of gas phase seepage flow difference equation is as follows:
Wherein, ToFor the oily phase coefficient of conductivity, TgFor vapor coefficient.
The gas injection rate of grid (i, j)
Wherein, the starting pressure gradient of gas mixture is variation in gas phase percolation equationk, is merged are as follows:
Oily phase seepage flow difference equation (43) is added to obtain about unknown quantity p with gas phase seepage flow difference equation (45)oIt is total
Pressure equation (48) it is as follows:
Equation deformation, starting pressure gradient and flow item are moved on on the right of equation:
Pressure equation is linearized, equation group is solved using Newton iteration method, finds out n+1 moment pressure iterative value
By capillary pressure subsidiary equation po=pg-pcgo, can find outBy what is found outGas phase seepage flow difference equation is substituted into, can be shown
Formula is found out
Gas saturation difference equation are as follows:
It finds outIt later, can be by saturation degree subsidiary equation so=1-sgIt finds out
It is conditional stability that hidden pressure, which shows degree of saturation method for solving, and stable condition is:
The explanation of variable symbol used in the present invention:
In formula, k --- absolute permeability, 10- 3μm2；kro--- oil relative permeability, dimensionless, value 0-1；
krg--- gas phase relative permeability, dimensionless, value 0-1；μo--- the viscosity of crude oil, mPas；μg——CO2Viscosity,
mPa·s；T --- time, d；po--- oily phase pressure, MPa；pg--- gaseous pressure, MPa；Go--- mutually starting pressure is terraced for oil
Degree, MPa/m；qo--- oily phase shunt volume, m3/d；qg--- gas phase shunt volume, m3/d；So--- oil saturation, dimensionless take
Value 0-1；Sg--- gas saturation, dimensionless, value 0-1；φ --- porosity, dimensionless, value 0-1；Rso——CO2?
Solubility in crude oil, dimensionless, value 0-1；ρo--- oil density, kg/m3；ρg--- stratum CO2Gas density,
kg/m3；pcgo--- capillary force, MPa；a1, a2, a3, a4, a5, a6, a7--- computational constant, dimensionless；T --- formation temperature, K；
P --- the pressure of each point, MPa in oil reservoir；Xs——CO2Volume fraction coefficient of colligation, dimensionless；Xo--- crude oil volume fraction
Coefficient of colligation, dimensionless；For CO2The ratio between the volume under volume and reservoir temperature, pressure at standard conditions, dimensionless；
FoIt is crude oil in the ratio between the volume under reservoir temperature and 0.1 MPa and the volume under reservoir temperature and reservoir pressure, dimensionless；
Fs--- expansion factor, dimensionless；α --- empirical coefficient, dimensionless；μom--- revised gas mixture viscosity, mPa
s；Gom--- revised gas mixture starting pressure gradient, MPa/m；ko--- oily phase phase permeability, 10- 3μm2；a,
B --- regression constant, dimensionless；X --- the abscissa at initial point, m；Y --- the ordinate at initial point, m；poi--- just
Oily phase pressure at initial point, MPa；Lx--- model horizontal axis total length, m；Ly--- model longitudinal axis total length, m；sg--- gassiness
Saturation degree, dimensionless；sgi--- the gas saturation at initial point, dimensionless；pe--- the reservoir pressure at model outer boundary,
MPa；Qvl--- inner boundary fixed output quota amount, m3/d；pgf--- producing well flowing bottomhole pressure (FBHP), MPa；pigf--- gas injection well bottom pressure,
MPa；Qvli,j--- well production, m are produced at grid cell (i, j)3/d；PIl--- the l phase production index, dimensionless；pli,j——
L phase pressure, MPa at grid cell (i, j)；Qvgi,j--- gas injection well gas injection rate, m at grid cell (i, j)3/d；GIg--- gas
Phase injectivity index, dimensionless；pgi,j--- gaseous pressure at grid cell (i, j), MPa；--- grid cell (i, j)
Right boundaryLocate permeability value when the n-th moment, 10- 3μm2；Δxi±1--- the left and right of grid cell (i, j) is adjacent
The step-length in the direction x, m at block；Δxi--- the step-length in the direction x, m at grid cell (i, j)；--- grid cell (i, j)
Permeability value at the adjacent block (i ± 1, j) in left and right when the n-th moment, 10- 3μm2；--- at grid cell (i, j) when the n-th moment
Permeability value, 10- 3μm2；--- the up-and-down boundary of grid cell (i, j)Locate permeability when the n-th moment
Value, 10- 3μm2；Δyj±1--- the step-length in the direction y, m at the block adjacent up and down of grid cell (i, j)；Δyj--- grid cell (i,
J) step-length in the direction place y, m；--- the permeability at the block (i, j ± 1) adjacent up and down of grid cell (i, j) when the n-th moment
Value, 10- 3μm2；--- the permeability value at grid cell (i, j) when the n-th moment, 10- 3μm2；λl--- flow coefficient, nothing
Dimension；krl--- l phase relative permeability, dimensionless, value 0-1；ρl--- l phase density, kg/m3；μl--- l phase viscosity,
mPa·s；pl--- l phase pressure, MPa；--- the reservoir pressure value at grid cell (i, j) when the (n+1)th moment, MPa；
nx--- the total grid number in the direction x, dimensionless；ny--- the total grid number in the direction y, dimensionless；Qv--- volume flow, m3/d；
pi,j--- reservoir pressure at grid cell (i, j), MPa；pgf--- producing well flowing bottomhole pressure (FBHP), MPa；Qvo--- producing well oil-producing
Amount, m3/d；PID --- the production index, dimensionless；λo--- the opposite mobility of oil, μm2/(Pa·s)；poi,j--- grid cell
Oil phase pressure at (i, j), MPa；pgf--- producing well flowing bottomhole pressure (FBHP), MPa；Go--- oily phase starting pressure gradient, MPa/m；
re--- the equivalent drainage radius of well, cm；rw--- the radius of well, cm；Qvg--- gas injection well gas injection rate, m3/d；WID --- note
Enter the injectivity index of well, dimensionless；λg--- gas phase with respect to mobility, μm2/(Pa·s)；pgi,j--- gas at grid cell (i, j)
Phase pressure, MPa；Gg--- gas phase starting pressure gradient, MPa/m；--- oily phase pressure value when the (n+1)th moment, MPa；
po--- oily phase pressure, MPa；pg--- gaseous pressure, MPa；pcgo--- capillary force, MPa；--- when the (n+1)th moment
Gaseous pressure value, MPa；--- gas saturation when the (n+1)th moment, dimensionless, value 0-1；So--- oil-containing saturation
Degree, dimensionless, value 0-1；Sg--- gas saturation, dimensionless, value 0-1；--- oil-containing when the (n+1)th moment is full
And degree, dimensionless, value 0-1；λg--- gas phase with respect to mobility, μm2/(Pa·s)；--- the oily phase point when the (n+1)th moment
Flow, m3/d；Δ t --- time step, d；H --- the thickness of two-dimentional oil reservoir, m；Vij--- the volume of grid cell (i, j),
m3；--- at the right boundary of grid cell (i, j) when the n-th moment the direction x the coefficient of conductivity, dimensionless；——
At the up-and-down boundary of grid cell (i, j) when the n-th moment the direction y the coefficient of conductivity, dimensionless；--- grid cell (i,
J) produced quantity, m3/d；--- the produced quantity of grid cell (i, j) unit volume, m3/d；Δxη --- the difference in the direction x
Operator, dimensionless；Δyη --- the difference operator in the direction y, dimensionless；Δ(ξxΔxη) --- the difference operator in the direction x is immeasurable
Guiding principle；Δ(ξyΔyη) --- the difference operator in the direction y, dimensionless；Δ(ToxΔxP) --- the direction x is about the coefficient of conductivity and pressure
Linear difference operator, dimensionless；Δ(ToyΔyP) --- linear difference operator of the direction y about the coefficient of conductivity and pressure, nothing
Dimension；To--- the oily phase coefficient of conductivity, dimensionless；Tg--- vapor coefficient, dimensionless；--- grid cell (i, j)
Gas injection rate, m3/d；--- the gas injection rate of grid cell (i, j) unit volume, m3/d；--- simplify mark, it is immeasurable
Guiding principle；--- simplify mark, dimensionless；ε --- control errors value, dimensionless.
Explanation about footmark: subscript represents space coordinate, and superscript represents time coordinate；(i, j) --- grid list
The center of first (i, j)；The center of the adjacent block (i ± 1, j) in the left and right of (i ± 1, j) --- grid cell (i, j)；(i,j±1)——
The center of the block (i, j ± 1) adjacent up and down of grid cell (i, j)；--- the right boundary of grid cell (i, j) --- the up-and-down boundary of grid cell (i, j)
Step S4: it chooses low-permeability oil deposit and obtains its geologic parameter, using the low-permeability oil deposit two dimension CO2Non- mixed phase
It drives Mathematical Modelling Method to be calculated, and carries out interpretation of result；
Analysis only considers pressure field, saturation field, viscosity field distribution when viscosity of crude variation；Analysis considers that viscosity of crude becomes
Pressure field, saturation field, viscosity field distribution and analysis starting pressure gradient are to low-permeability oil when change, starting pressure gradient variation
Hide two dimension CO2The influence of non-phase-mixing driving yield.
Example calculation is carried out using Shengli Oil Field F142 low-permeability oil deposit parameter, but individual parameters are finely tuned, oil reservoir
Parameter is as shown in table 1.The reason of selecting Shengli Oil Field low-permeability oil deposit parameter to be calculated is: in order to accord with calculated result more
Mining site actual conditions are closed, can preferably verify under conditions of considering viscosity of crude and oily phase starting pressure gradient variation, be built
The correctness of vertical seepage experiment and numerical solution, strong reference is provided for calculated result, also to continue to develop from now on
CO2Non-phase-mixing driving seepage experiment and its numerical solution provide solid foundation and reliable data are supported.
1 Shengli Oil Field F142 block low-permeability oil deposit parameter list of table
Working system is that inner edge defines volume flow injection, stable bottom hole pressure production, outer sealed boundary.It is taken in calculating process
Time step is 1d, and space uses 10 × 10 grids, and spatial mesh size X, Y-direction is respectively 50m, calculates time t=1000d in total.
Only consider pressure field, saturation field, viscosity field distribution when viscosity of crude variation；
Fig. 2, Fig. 3 and Fig. 4 show the distribution of pressure field.Comparison it is found that along with gas injection process, entire strata pressure by
Gradually rise, by gas injection well to producing well, strata pressure is gradually decreased, and the gradient of line side's upward pressure of injection-production well decline is most
Greatly, therefore on pressure field distribution figure show that injection-production well line direction isopleth is most close.When considering oil phase viscosity variation, in pressure field
The pressure of each point is less than pressure when not considering oil phase viscosity variation, due to CO2Being dissolved in crude oil declines viscosity of crude continuously,
The filtrational resistance of formation fluid reduces, it is easier to establish effective displacement barometric gradient, the fluid in stratum is easier to flow.By t
=900d pressure field distribution figure it is found that pressure is gradually propagated from gas injection well to producing well, pressure distribution in entire pressure field by
Edge up height.
The distribution of oil saturation field is shown by Fig. 5, Fig. 6 and Fig. 7.It can be seen that when considering viscosity of crude variation
Crude oil saturation degree in crude oil saturation field at each point is less than crude oil saturation degree when not considering viscosity of crude variation, this explanation
CO2Being dissolved in crude oil declines viscosity of crude, and the crude oil in blowhole is easy to be scanned out to come by drive.Crude oil is viscous near gas injection well
The amplitude for spending decline is big, and oil displacement efficiency improves, so nearby oil saturation is lower for gas injection well, and closer to producing well, crude oil
Saturation degree declines slower, and as time goes by, gas displacement front is promoted to producing well, and the crude oil close to producing well is gradually passive
With.It can see by t=900d crude oil saturation distribution figure, nearby crude oil saturation degree is minimum for gas injection well, crude oil near producing well
Saturation degree is maximum, and the region that gas feeds through to is increasing, and gas displacement front is gradually promoted to producing well from gas injection well.
Fig. 8 and Fig. 9 shows the distribution of oil phase viscosity field.By the distribution map of viscosity field can be seen that by gas injection well to
Producing well, oil viscosity gradually rise, but compare more initial oil viscosity, and formation crude oil viscosity significantly drops
Low, the viscosity of crude near gas injection well drops to the 32% of initial oil viscosity, the viscosity of crude decline near producing well
To the 25% of initial oil viscosity.In t=300d and t=900d, viscosity field distribution is had changed a lot, t=
Viscosity of crude downward gradient is larger near gas injection well when 300d；And viscosity of crude downward gradient is attached in producing well when t=900d
Close larger, the viscosity of crude of the most areas between gas injection well and producing well has fallen to 0.36mPas at this time, it is seen that CO2
It is very big to the viscosity reduction amplitude of in-place oil.
Consider pressure field, saturation field, viscosity field distribution when viscosity of crude variation, starting pressure gradient variation；
As seen from Figure 10, whole strata pressure when consideration oil phase viscosity, starting pressure gradient, pressure propagation speed
It is below when not considering starting pressure gradient, the reason is that, displacement pressure needs overcome starting to press when considering starting pressure gradient
Force gradient can establish effective displacement pressure system in the earth formation, and overcome starting pressure gradient then need to consume it is sizable
Pressure, therefore the strata pressure for considering that strata pressure when starting pressure gradient is compared when not considering starting pressure gradient is low.
It can be seen that, consider that the oil saturation on stratum when starting pressure gradient is higher than by Figure 11 and do not consider to start
Oil saturation when barometric gradient, because considering to establish effective displacement pressure difference when starting pressure gradient more difficult, required drive
Bigger for pressure, effective displacement pressure is then smaller, therefore it is fewer to drive the crude oil scanned out in blowhole, residual crude oil ratio
More, the oil saturation after sweeping is also relatively high.
Figure 12 display considers the distribution of oil phase viscosity field when oil phase viscosity, starting pressure gradient change.As can be seen that original
Oil viscosity is gradually risen by gas injection well to producing well, because of CO near gas injection well2Concentration is high, the CO being dissolved in crude oil2Quantity
Greatly, good for the viscosity reducing effect of crude oil, so nearby viscosity of crude is low for gas injection well, and close to CO near producing well2Concentration is low, molten
CO of the solution in crude oil2Also few, it is poor to the viscosity reducing effect of crude oil, therefore nearby viscosity of crude is high for producing well.It is compared by figure, it is bright
Aobvious can be seen that considers that the overall viscosity of starting pressure gradient formation crude oil is higher than original when not considering starting pressure gradient
Oily overall viscosity, because it is contemplated that strata pressure is relatively low when starting pressure gradient, and CO2The viscosity reduction effect of crude oil is laminated with ground
Power, formation temperature, oil density are related, and are influenced maximum by strata pressure, so lower ground stressor layer leads to CO2
To the viscosity reduction declines of crude oil, oil viscosity is made to want high compared with when not considering starting pressure gradient.
By the experiment of oil gas water starting pressure gradient it is found that starting pressure gradient is the function of fluid mobility, and fluid viscosity
Cause starting pressure gradient bigger more greatly, as shown in Figure 13, viscosity of crude is gradually risen by gas injection well to producing well, so starting
Barometric gradient is gradually increased by gas injection well to producing well.Closer to gas injection well, CO2It is better to the viscosity reducing effect of crude oil, starting pressure
Force gradient is smaller, and fluid neuron network resistance is smaller, more easily establishes effective displacement pressure system.
As shown in figure 14, production well production gradually rises increase with time, before initial stage t=300d, considers starting pressure
The yield that yield is higher than when not considering starting pressure gradient when force gradient is close, but in middle and later periods t > 300d, considers starting pressure
Yield when force gradient is then significantly lower than yield when not considering starting pressure gradient, and as the time increases, yield gap
It is increasing.
The foregoing is merely the schematical specific embodiment of the present invention, the range being not intended to limit the invention.It is any
Those skilled in the art, made equivalent changes and modifications under the premise of not departing from design and the principle of the present invention,
It should belong to the scope of protection of the invention.
Claims (10)
1. a kind of low-permeability oil deposit two dimension CO2Non-phase-mixing driving Mathematical Modelling Method, which comprises the following steps:
Step S1: low-permeability oil deposit CO is established2Non-phase-mixing driving mathematical model；The foundation of the mathematical model includes: low-permeability oil deposit
The foundation of assumed condition；The foundation of percolation equationk and subsidiary equation；The foundation of definite condition；The assumed condition, percolation equationk,
Subsidiary equation and definite condition together constitute the CO for considering viscosity of crude variation, considering the variation of fluid starting pressure gradient2It is non-
Mixed phase drives seepage experiment；
Step S2: the low-permeability oil deposit CO2The processing of parameter and boundary condition that non-phase-mixing driving solution procedure needs；The ginseng
Number processing includes: the processing of absolute permeability, the processing of flow coefficient, the processing of gas mixture viscosity and starting pressure ladder
The processing of degree；The processing of boundary condition includes: the processing of Outer Boundary Conditions and internal boundary condition；
Step S3: the low-permeability oil deposit two dimension CO2Non-phase-mixing driving mathematical model solves；The mathematical model uses numerical method
It is solved, i.e., degree of saturation method is shown using hidden pressure and solved；
Step S4: it chooses low-permeability oil deposit and obtains its geologic parameter, using the low-permeability oil deposit two dimension CO2Non-phase-mixing driving number
It learns analogy method to be calculated, and carries out interpretation of result；
Analysis only considers pressure field, saturation field, viscosity field distribution when viscosity of crude variation；The variation of analysis consideration viscosity of crude,
Pressure field, saturation field, viscosity field distribution and analysis starting pressure gradient are to low-permeability oil deposit when starting pressure gradient changes
Two-dimentional CO2The influence of non-phase-mixing driving yield.
2. low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that in institute
State in step S1, the low-permeability oil deposit assumed condition include: in oil reservoir fluid be isothermal seepage flow；The rock is heterogeneous micro-
Compressible pore media；Fluid is compressible fluid；Consider viscosity of crude variation；Consider the variation of fluid starting pressure gradient；No
Consider gravity and capillary force.
3. low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that in institute
It states in step S1, the percolation equationk includes oily phase percolation equationk and gas phase percolation equationk；The oil phase percolation equationk are as follows:
The gas phase percolation equationk are as follows:
In formula, k-absolute permeability, 10- 3μm2；kro- oil relative permeability, dimensionless, value 0-1；krg- gas phase is opposite
Permeability, dimensionless, value 0-1；μoThe viscosity of-crude oil, mPas；μg—CO2Viscosity, mPas；T-time, d；
po- oil phase pressure, MPa；pg- gaseous pressure, MPa；Go- oil phase starting pressure gradient, MPa/m；qo- oil phase shunt volume, m3/
d；qg- gas phase shunt volume, m3/d；So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless, value
0-1；φ-porosity, dimensionless, value 0-1；Rso—CO2Solubility in crude oil, dimensionless, value 0-1；ρo- stratum
Oil density, kg/m3；ρg- stratum CO2Gas density, kg/m3。
4. low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that in institute
It states in step S1, the subsidiary equation includes that saturation equation, capillary force equation, oil relative permeability equation, gas phase are opposite
Permeability equation, CO2Solubility equation, calculating CO in crude oil2Volume fraction coefficient of colligation and correct viscosity of crude equation and
Correct fluid starting pressure gradient equation.
5. low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that in institute
It states in step S1, the definite condition includes primary condition and boundary condition, and the boundary condition includes Outer Boundary Conditions and interior
Boundary condition, the Outer Boundary Conditions show pressure locating for oil reservoir boundary and whether closed state, the inner boundary
Condition then shows injection well and produces the state of well.
6. low-permeability oil deposit two dimension CO according to claim 42Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that described
Saturation equation are as follows: so+sg=1；
The capillary force equation are as follows: po=pg-pcgo；
The oil relative permeability equation are as follows: kro=kro(sg)；
The gas phase relative permeability equation are as follows: krg=krg(sg)；
The CO2Solubility equation in crude oil are as follows:
The calculating CO2Volume fraction coefficient of colligation and amendment viscosity of crude equation are as follows:
lnμom=Xolnμo+Xslnμg；
The amendment fluid starting pressure gradient equation are as follows:
In formula, So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless, value 0-1；po- oil phase
Pressure, MPa；pg- gaseous pressure, MPa；pcgo- capillary force, MPa；kro- oil relative permeability, dimensionless, value 0-1；
krg- gas phase relative permeability, dimensionless, value 0-1；Rso—CO2Solubility in crude oil, dimensionless, value 0-1；ρo—
Oil density, kg/m3；a1, a2, a3, a4, a5, a6, a7- computational constant, dimensionless；T-formation temperature, K；In p-oil reservoir
The pressure of each point, MPa；Xs—CO2Volume fraction coefficient of colligation, dimensionless；Xo- crude oil volume fraction coefficient of colligation, dimensionless；For CO2The ratio between the volume under volume and reservoir temperature, pressure at standard conditions, dimensionless；FoIt is crude oil in oil reservoir temperature
Degree and the ratio between the volume under 0.1MPa and the volume under reservoir temperature and reservoir pressure, dimensionless；Fs- expansion factor, it is immeasurable
Guiding principle；α-empirical coefficient, dimensionless；μom- revised gas mixture viscosity, mPas；μoThe viscosity of-crude oil, mPa
s；μg—CO2Viscosity, mPas；Gom- revised gas mixture starting pressure gradient, MPa/m；ko- oil mutually mutually permeates
Rate, 10- 3μm2；A, b-regression constant, dimensionless.
7. low-permeability oil deposit two dimension CO according to claim 52Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that described
Primary condition are as follows:
The Outer Boundary Conditions include closed outer boundary condition and constant pressure outer boundary condition, the closed outer boundary are as follows:
The constant pressure outer boundary condition
The internal boundary condition includes determining yield equation and stable bottom hole pressure equation, described to determine yield equation are as follows:
Qvl=constant, l=o, g；
The stable bottom hole pressure equation are as follows:
For producing well, pgfIt is known；For gas injection well, pigfIt is known；
The production well yield can indicate are as follows: Qvli,j=PIl(pli,j-pgf)
The gas injection rate of the gas injection well can indicate are as follows: Qvgi,j=GIg(pigf-pgi,j)
Wherein, PIlFor the l phase production index, GIgFor gas phase injectivity index；
In formula, po- oil phase pressure, MPa；Abscissa at x-initial point, m；Ordinate at y-initial point, m；T-time,
d；poiOily phase pressure at-initial point, MPa；Lx- model horizontal axis total length, m；Ly- model longitudinal axis total length, m；sg- contain
Gas saturation, dimensionless；sgiGas saturation at-initial point, dimensionless；The pressure of each point, MPa in p-oil reservoir；pe—
Reservoir pressure at model outer boundary, MPa；Qvl- inner boundary fixed output quota amount, m3/d；pgf- producing well flowing bottomhole pressure (FBHP), MPa；pigf—
Gas injection well bottom pressure, MPa；Qvli,jWell production, m are produced at-grid cell (i, j)3/d；PIl- l phase the production index is immeasurable
Guiding principle；pli,jL phase pressure, MPa at-grid cell (i, j)；Qvgi,jGas injection well gas injection rate, m at-grid cell (i, j)3/d；
GIg- gas phase injectivity index, dimensionless；pgi,jGaseous pressure at-grid cell (i, j), MPa.
8. low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, which is characterized in that in institute
It states in step S2, the processing method of the absolute permeability are as follows:
The absolute permeability is the function of space coordinate, is calculated according to harmonic-mean:
The processing method of the flow coefficient are as follows:
The flow coefficientIn, the absolute permeability k takes the harmonic-mean of two neighboring grid；Part is then handled using single-point upstream weighted:
The gas mixture viscosity processing method are as follows: gas mixture viscosity then uses the CO in gas phase percolation equationk2In original
Solubility equation in oil, the calculating CO2Volume fraction coefficient of colligation and amendment viscosity of crude equation are modified, and are used
The processing of single-point upstream weighted value；
The starting pressure gradient processing method are as follows:
Consider oily phased soln CO2The viscosity change of gas mixture later, according to the amendment fluid starting pressure gradient equation
The variation of gas mixture starting pressure gradient caused by calculating thus, and handled using single-point upstream weighted value；
In formula,The right boundary of-grid cell (i, j)Locate permeability value when the n-th moment, 10- 3μm2；△
xi±1The step-length in the direction x, m at the adjacent block in the left and right of-grid cell (i, j)；△xiThe step-length in the direction x at-grid cell (i, j),
m；Permeability value at the adjacent block (i ± 1, j) in the left and right of-grid cell (i, j) when the n-th moment, 10- 3μm2；- grid
Permeability value at unit (i, j) when the n-th moment, 10- 3μm2；The up-and-down boundary of-grid cell (i, j)Place
Permeability value when the n-th moment, 10- 3μm2；△yj±1The step-length in the direction y, m at the block adjacent up and down of-grid cell (i, j)；△
yjThe step-length in the direction y, m at-grid cell (i, j)；When n-th at the block (i, j ± 1) adjacent up and down of-grid cell (i, j)
Permeability value when quarter, 10- 3μm2；Permeability value at-grid cell (i, j) when the n-th moment, 10- 3μm2；λl- flowing
Coefficient, dimensionless；K-absolute permeability, 10- 3μm2；krl- l phase relative permeability, dimensionless, value 0-1；ρl- l phase is close
Degree, kg/m3；μl- l phase viscosity, mPas；pl- l phase pressure, MPa；
Explanation about footmark: subscript represents space coordinate, and superscript represents time coordinate；(i, j)-grid cell (i, j)
Center；The center of the adjacent block (i ± 1, j) in the left and right of (i ± 1, j)-grid cell (i, j)；(i, j ± 1)-grid cell (i,
J) center of block (i, j ± 1) adjacent up and down；The right boundary of-grid cell (i, j)
The up-and-down boundary of-grid cell (i, j)
9. low-permeability oil deposit two dimension CO according to claim 1-82Non-phase-mixing driving Mathematical Modelling Method, feature
It is, in the step S2, the processing method of the Outer Boundary Conditions are as follows:
To closed outer boundary condition, virtual hoop net lattice outside closed boundary enable the pressure of boundary mesh be equal to virtual grid pressure,
I.e.
The processing method of the internal boundary condition are as follows:
Injection-production well in oil reservoir is special grid cell, includes source sink term in such grid cell, and oil-producing well production is
Negative value, gas injection well injection rate are positive value；If grid (i, j) has a well, volume flow Qv, it is raw to determine producing well flowing bottomhole pressure (FBHP)
It produces, then volume flow QvIt needs with grid pressure pijWith flowing bottomhole pressure (FBHP) pgfTo express；
The radial fluid flow quasi-stable state formula of producing well oil production are as follows:
Qvo=-PID λo[poi,j-pgf-Go(re-rw)]；
The radial fluid flow quasi-stable state formula of gas injection well gas injection rate are as follows:
Qvg=-WID λg[pgi,j-pgf+Gg(re-rw)]；
In formula,Reservoir pressure value at-grid cell (i, j) when the (n+1)th moment, MPa；nxThe total grid number in the direction-x, nothing
Dimension；nyThe total grid number in the direction-y, dimensionless；Qv- volume flow, m3/d；pi,jReservoir pressure at-grid cell (i, j),
MPa；pgf- producing well flowing bottomhole pressure (FBHP), MPa；Qvo- producing well oil production, m3/d；PID-the production index, dimensionless；λo- oil
Opposite mobility, μm2/(Pa·s)；poi,jOil phase pressure, MPa at-grid cell (i, j)；pgf- producing well flowing bottomhole pressure (FBHP),
MPa；Go- oil phase starting pressure gradient, MPa/m；reThe equivalent drainage radius of-well, cm；rwThe radius of-well, cm；Qvg- note
Gas well gas injection rate, m3/d；WID-injection well injectivity index, dimensionless；λg- gas phase with respect to mobility, μm2/(Pa·s)；
pgi,jGaseous pressure at-grid cell (i, j), MPa；Gg- gas phase starting pressure gradient, MPa/m.
10. -9 described in any item low-permeability oil deposit two dimension CO according to claim 12Non-phase-mixing driving Mathematical Modelling Method, feature
It is, in the step S3, it is a kind of sequence method for solving for solving multiphase porous flow that the hidden pressure, which shows degree of saturation method, first
Using finite difference method to continuous partial differential equation discretization, then the equation group after discrete is linearized, passes through solution
The method of system of linear equations is solved；Specific steps are as follows: (1) by the oily phase percolation equationk and the gas phase percolation equationk into
Row discretization and be added obtain about unknown quantity poTotal pressure equation；(2) pressure equation is linearized, using newton
Solution by iterative method equation group finds out n+1 moment pressure iterative valueBy the capillary pressure subsidiary equation po=pg-pcgo,
It can find outBy what is found outGas phase seepage flow difference equation is substituted into, can explicitly be found out(3) it finds outIt later, can be by
Saturation degree subsidiary equation so=1-sgIt finds out
In formula,Oily phase pressure value when the-the (n+1)th moment, MPa；po- oil phase pressure, MPa；pg- gaseous pressure, MPa；
pcgo- capillary force, MPa；Gaseous pressure value when the-the (n+1)th moment, MPa；Gassiness saturation when the-the (n+1)th moment
Degree, dimensionless, value 0-1；So- oil saturation, dimensionless, value 0-1；Sg- gas saturation, dimensionless, value 0-1；Oil saturation when the-the (n+1)th moment, dimensionless, value 0-1.
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| CN116663370A (en) * | 2023-07-05 | 2023-08-29 | 成都理工大学 | Fluid-solid coupling numerical simulation method for deep fracture-cavity type carbonate reservoir |
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