CN107526891A - A kind of polymer flooding macropore oil reservoir well test analysis method - Google Patents
A kind of polymer flooding macropore oil reservoir well test analysis method Download PDFInfo
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- CN107526891A CN107526891A CN201710735830.2A CN201710735830A CN107526891A CN 107526891 A CN107526891 A CN 107526891A CN 201710735830 A CN201710735830 A CN 201710735830A CN 107526891 A CN107526891 A CN 107526891A
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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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- 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
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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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- 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 invention discloses a kind of polymer flooding macropore oil reservoir well test analysis method, it is characterised in that:It comprises the following steps:1) according to polymer flooding macropore characteristics of reservoirs, polymer flooding macropore physical models of reservoir is established;2) according to the polymer flooding macropore physical models of reservoir obtained in step 1), polymer flooding macropore reservoir mathematical model is determined;3) use finite difference method solution procedure 2) in obtain polymer flooding macropore reservoir mathematical model, obtain the numerical solution of bottom pressure;4) relation that changed with time to pressure carries out nondimensionalization, draws polymer flooding macropore oil reservoir typical curve theory plate;5) the polymer flooding macropore oil reservoir typical curve theory plate obtained in step 4) is fitted with oil field measured data curve, obtains equivalent width, the Permeability Parameters of macropore.
Description
Technical field
The present invention relates to a kind of polymer flooding macropore oil reservoir well test analysis method, belong to Well Test Technology field.
Background technology
In long-term injecting water development process, oil reservoir pore structure is varied widely marine sandstone oil reservoir, due to
Reservoir permeability increases, and pore throat radius increase, high infiltration strip and special high permeable strip, i.e. macropore is formed easily in reservoir.Greatly
The presence in duct causes interlayer contradiction to aggravate, and the later stage takes the polymer for improving the injection of recovery ratio means, poorly efficient along macropore
Or inefficient cycle makes other positions in reservoir be difficult to be imitated, and has a strong impact on oil displacement efficiency, causes remaining oil saturation in plane
Difference is obvious, and polymer flooding development effectiveness is substantially deteriorated.Therefore, the identification of polymer flooding macropore oil reservoir and determine it in oil
Distribution situation in Tibetan, harvested for taking corresponding measure to block macropore, improving polymer flooding effect and improve
Rate is significant.
At present, the Main Means for identifying macropore are well test data identification, production performance observation, tracer monitoring, well logging
Data identifies.And development parameters most sensitive in macropore identification process are exactly yield and pressure, led to using pressure fall-off test data
Cross well testing means and judge the existing correlative study of the presence of macropore.Shi Yougang, Shang Zhiying use wellhead of water injection well pressure drop double-log
Curve establishes to diagnose the presence of macropore and macropore water-drive pool Well Testing Theory model be present.Yang Shirong is tried using pressure drop
Well test method, the situation of change of reservoir permeability is reflected by the feature of pressure drop double logarithmic curve after water filling.Gu Jianwei is proposed
A kind of injection well radial direction model for considering macropore and being intercoupled with non-macropore region, is changed by injection well bottom pressure
Feature judges the development area and development multiple of macropore.Liu Hong is established excellent by analyzing dominant flowing path grown form
Gesture seepage channel well test model.Li Chengyong establishes asymmetric dominant flowing path well test analysis mathematics on the basis of Shi Yougang
Model.But the method that they establish only is adapted to the identification of Water injected reservoir macropore, do not study noting poly- oil reservoir.
The content of the invention
In view of the above-mentioned problems, it is an object of the invention to provide a kind of polymer flooding macropore oil reservoir well test analysis method, should
Method can explain to oil field measured data exactly, obtain the relevant parameter of macropore, be provided for the closure of macropore
Data support that there is stronger filed application to be worth.
To achieve the above object, the present invention takes following technical scheme:A kind of polymer flooding macropore oil reservoir well test analysis
Method, it is characterised in that it comprises the following steps:
1) according to polymer flooding macropore characteristics of reservoirs, polymer flooding macropore physical models of reservoir is established;
2) according to the polymer flooding macropore physical models of reservoir obtained in step 1), polymer flooding macropore oil reservoir is determined
Mathematical modeling;
3) use finite difference method solution procedure 2) in obtain polymer flooding macropore reservoir mathematical model, obtain well
The numerical solution of bottom pressure;
4) relation that changed with time to pressure carries out nondimensionalization, draws polymer flooding macropore oil reservoir typical curve reason
By plate;
5) it is the polymer flooding macropore oil reservoir typical curve theory plate obtained in step 4) and oil field measured data is bent
Line is fitted, and obtains the equivalent width and Permeability Parameters of macropore.
For the physical model established in the step 1) using pit shaft as symmetrical centre, two macropores are symmetrically distributed in well
Cylinder both sides;The polymer flooding macropore characteristics of reservoirs in the step 1) includes:Reservoir-level, uniform thickness, homogeneous and respectively to
The same sex;The equivalent development length of macropore is xf;Macropore permeability is Kf, reservoir permeability K, macropore permeability with oil
The ratio between layer permeability is β, KfMuch larger than K;The thickness of macropore is core intersection H, equivalent width Wf;There is stream along macropore
Body exchanges, and pressure drop be present.
The step 2) determines that the detailed process of polymer flooding macropore reservoir mathematical model is as follows:
1. determine the transient seepage flow differential equation of single-phase micro- compressible liquid:
In formula, P is strata pressure;K is reservoir permeability;μaFor the initial viscosity of polymer;CmCompression system is integrated for oil reservoir
Number;φmFor oil reservoir porosity;T is fluid flow time;X is abscissa direction away from well centre distance;Y be ordinate direction away from
Well centre distance;
2. determine primary condition equation, internal boundary condition equation and the external boundary of polymer flooding macropore reservoir mathematical model
Conditional equation:
Wherein, the primary condition equation of polymer flooding macropore reservoir mathematical model is:
P(x,y,t)|T=0=P0 (2)
In formula, P0For original formation pressure;
The internal boundary condition equation of polymer flooding macropore reservoir mathematical model is:
In formula, H is core intersection;Q is well yield;C is bottom-hole storage coefficient;B is volume factor;S is reservoir epidermis system
Number;PwfFor flowing bottomhole pressure (FBHP);PwFor the pressure at the borehole wall;rwFor wellbore radius;reFor external boundary radius;x0、y0Respectively oil well well
The transverse and longitudinal coordinate at bottom center;Δ x, Δ y difference infinitesimals;E is constant, e=2.7182818;
The Outer Boundary Conditions equation of polymer flooding macropore reservoir mathematical model is:
In the step 3), using finite difference method solution procedure 2) in obtain polymer flooding macropore oil reservoir mathematics
The detailed process of model is as follows:
1. mesh generation is carried out in room and time to the polymer flooding macropore physical models of reservoir in step 1);
2. the transient seepage flow differential equation, primary condition equation, internal boundary condition equation and Outer Boundary Conditions equation are entered
Row difference discretization, i.e., difference discretization is carried out to (1)~(5) formula;
Wherein, the seepage flow diffusion equation after discrete is:
In formula, i, j are to the discrete of space;N is discrete to the time;Δ t is time step, and φ is porosity, works as φ
Under when being designated as f, i.e. φfFor the porosity of macropore, when being designated as m under φ, i.e. φmFor the porosity of oil reservoir;
Wherein in formula (6)Value come by harmonic average it is true
It is fixed, i.e.,:
Gauss-seidel solutions by iterative method equation (6), iterative equation formula are as follows:
In formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jIt is intermediate variable:
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j;
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jBe mesh coordinate be (i, j) place well yield, well point grid qi,j=q, non-well point grid qi,j=0;Pi,jIt is
The strata pressure at mesh coordinate (i, j) place;
For internal boundary condition, Huiyuan's item processing by well as place grid, because barometric gradient is larger near shaft bottom,
Linearization process is made to internal boundary condition difference gridding, obtained:
In formula:μ is viscosity of the polymer in any time;
Outer Boundary Conditions discretization is obtained:
P1,j=Pm,j=Pe(j=1,2 ... k) (13)
Pi,1=Pi,k=Pe(i=1,2 ... m) (14)
In formula, P1,jIt is the strata pressure that mesh coordinate is (1, j) place;Pm,jIt is that the ground that mesh coordinate is (m, j) place is laminated
Power;Pi,1It is the strata pressure that mesh coordinate is (i, 1) place;Pi,kIt is the strata pressure that mesh coordinate is (i, k) place;PeFor outside
Boundary's pressure;M represents the grid number in i directions, and k represents the grid number in j directions;
Solved for ease of Difference Calculation, the processing equation to barometric gradient is as follows:
3. iterative numerical solution is carried out to above-mentioned DIFFERENCE EQUATIONS, wherein, DIFFERENCE EQUATIONS is transient seepage flow differential side
Journey, primary condition, the equation group of boundary condition composition, try to achieve the numerical solution of polymer flooding macropore oil reservoir bottom pressure.
The grid is rectangle or square, when for Rectangular grid when,When for just
During square net, re=0.208 Δ x.
The step 4) the relation that changed with time to pressure carries out nondimensionalization, and its Non-di-mensional equation is as follows:
PwDFor polymer flooding macropore oil reservoir bottom pressure nondimensionalization value;CDFor bottom-hole storage coefficient nondimensionalization value;
xDFor abscissa nondimensionalization numerical value;yDFor total coordinate nondimensionalization numerical value;tDFor time nondimensionalization numerical value;CfFor macropore
System compressibility;CmFor oil reservoir system compressibility;φfFor macropore internal porosity;β is permeability ratio.
The plan of polymer flooding macropore oil reservoir typical curve theory plate and oil field measured data curve in the step 5)
Conjunction process is as follows:Basic data is inputted in the polymer flooding macropore oil reservoir theory plate program of establishment first, basic data
The porosity of thickness, oil reservoir, the permeability of oil reservoir, system compressibility, skin factor, bottom-hole storage coefficient including oil reservoir,
Injection well injection rate, volume factor, aqueous viscosity, polymer initial concentration, original formation pressure, hole diameter, the width of macropore
With the permeability of macropore;Then by adjust the permeability of oil reservoir, skin factor, bottom-hole storage coefficient, macropore width
And the permeability of macropore, theoretical pressure and theoretical pressure derivative curve is calculated;Then theoretical pressure curve, reason are utilized
By the measured data of differential of pressure curve and field pressure, fitting theory pressure curve and real well pressure curve, and theoretical pressure
Power derivative curve and real well pressure derivative curve;Width, the Permeability Parameters of macropore are finally obtained according to fitting result.
For the present invention due to taking above technical scheme, it has advantages below:The present invention is by establishing polymer flooding macropore
The physical model and mathematical modeling of road oil reservoir, the bottom pressure number of polymer flooding macropore oil reservoir is obtained using Finite Element Difference Method
Value solution, draws polymer flooding macropore oil reservoir typical curve theory plate, and polymer flooding macropore oil reservoir typical curve is theoretical
Plate is fitted with oil field measured data curve, obtains the parameters such as macropore width, permeability, to be carried out from suitable blocking agent
The closure of macropore, improve the raising recovery ratio offer data support of polymer flooding effect.
Brief description of the drawings
Fig. 1 is the overall flow schematic diagram of the present invention;
Fig. 2 is the structural representation that oil reservoir of the present invention simplifies physical model;
The schematic diagram of macropore oil reservoir typical curve plots contrast when Fig. 3 is water drive of the present invention and poly- drive;
Fig. 4 is the schematic diagram of oil reservoir well test analysis typical curve plots under the influence of the different initial polymer concentrations of the present invention;
Fig. 5 is the schematic diagram of oil reservoir well test analysis typical curve plots under the influence of the different permeability ratios of the present invention;
Fig. 6 is the schematic diagram of oil reservoir well test analysis typical curve plots under the different macropore widths affects of the present invention;
Fig. 7 is the schematic diagram of oil reservoir well test analysis theory plate of the present invention and real well test data matched curve.
Embodiment
The present invention is described in detail with reference to the accompanying drawings and examples.
As shown in figure 1, the present invention proposes a kind of polymer flooding macropore oil reservoir well test analysis method, it includes following step
Suddenly:
1) according to polymer flooding macropore characteristics of reservoirs, establish polymer flooding macropore physical models of reservoir, the model with
Pit shaft is symmetrical centre, and two macropores are symmetrically distributed in pit shaft both sides (as shown in Figure 2);
Wherein, polymer flooding macropore characteristics of reservoirs includes:Reservoir-level, uniform thickness, homogeneous and isotropism;2 macropores
Road is symmetrical with pit shaft, and the equivalent development length of macropore is xf;Macropore permeability is Kf, reservoir permeability K, macropore oozes
Saturating the ratio between rate and reservoir permeability are β, KfMuch larger than K;The thickness of macropore is core intersection H, equivalent width Wf;Along big
There is fluid communication in duct, pressure drop be present.
2) according to the polymer flooding macropore physical models of reservoir obtained in step 1), polymer flooding macropore oil reservoir is determined
Mathematical modeling, detailed process are as follows:
1. determine the transient seepage flow differential equation of single-phase micro- compressible liquid:
In formula, P is strata pressure;K is reservoir permeability;μaFor the initial viscosity of polymer;CmCompression system is integrated for oil reservoir
Number;φmFor oil reservoir porosity;T is fluid flow time;X is abscissa direction away from well centre distance;Y be ordinate direction away from
Well centre distance.
2. determine primary condition equation, internal boundary condition equation and the external boundary of polymer flooding macropore reservoir mathematical model
Conditional equation:
Wherein, the primary condition equation of polymer flooding macropore reservoir mathematical model is:
P(x,y,t)|T=0=P0 (2)
In formula, P0For original formation pressure;
The internal boundary condition equation of polymer flooding macropore reservoir mathematical model is:
In formula, H is core intersection;Q is well yield;C is bottom-hole storage coefficient;B is volume factor;S is reservoir epidermis system
Number;PwfFor flowing bottomhole pressure (FBHP);PwFor the pressure at the borehole wall;rwFor wellbore radius;reFor external boundary radius;x0、y0Respectively oil well well
The transverse and longitudinal coordinate at bottom center;Δ x, Δ y are difference infinitesimal;E is constant, e=2.7182818;
The Outer Boundary Conditions equation of polymer flooding macropore reservoir mathematical model is:
3) use finite difference method solution procedure 2) in obtain polymer flooding macropore reservoir mathematical model, obtain well
The numerical solution of bottom pressure, finite difference method detailed process are as follows:
1. mesh generation is carried out in room and time to the polymer flooding macropore physical models of reservoir in step 1);
2. the transient seepage flow differential equation, primary condition equation, internal boundary condition equation and Outer Boundary Conditions equation are entered
Row difference discretization, i.e., difference discretization is carried out to (1)~(5) formula:
Wherein, the seepage flow diffusion equation after discrete is:
In formula, i, j are to the discrete of space;N is discrete to the time;Δ t is time step;φ is porosity, works as φ
Under when being designated as f, i.e. φfFor the porosity of macropore, when being designated as m under φ, i.e. φmFor the porosity of oil reservoir;
WhereinValue determined by harmonic average, i.e.,:
Gauss-seidel solutions by iterative method equation (6), iterative equation formula are as follows:
In formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jIt is intermediate variable:
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j;
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jBe mesh coordinate be (i, j) place well yield, well point grid qi,j=q, non-well point grid qi,j=0;Pi,jIt is
The strata pressure at mesh coordinate (i, j) place.
For internal boundary condition, Huiyuan's item processing by well as place grid, because barometric gradient is larger near shaft bottom,
Linearization process is made to internal boundary condition difference gridding, obtained:
In formula:μ is viscosity of the polymer in any time;For Rectangular gridIt is right
In square net re=0.208 Δ x.
Outer Boundary Conditions discretization is obtained:
P1,j=Pm,j=Pe(j=1,2 ... k) (13)
Pi,1=Pi,k=Pe(i=1,2 ... m) (14)
In formula, P1,jIt is the strata pressure that mesh coordinate is (1, j) place;Pm,jIt is that the ground that mesh coordinate is (m, j) place is laminated
Power;Pi,1It is the strata pressure that mesh coordinate is (i, 1) place;Pi,kIt is the strata pressure that mesh coordinate is (i, k) place;PeFor outside
Boundary's pressure;M represents the grid number in i directions;K represents the grid number in j directions;
Solved for ease of Difference Calculation, the processing equation to barometric gradient is as follows:
3. iterative numerical solution is carried out to above-mentioned DIFFERENCE EQUATIONS, wherein, DIFFERENCE EQUATIONS is transient seepage flow differential side
Journey, primary condition, the equation group of boundary condition composition, try to achieve the numerical solution of polymer flooding macropore oil reservoir bottom pressure.
4) relation that changed with time to pressure carries out nondimensionalization, draws polymer flooding macropore oil reservoir typical curve reason
It is as follows by plate, dimensionless equation:
PwDFor polymer flooding macropore oil reservoir bottom pressure nondimensionalization value;CDFor bottom-hole storage coefficient nondimensionalization value;
xDFor abscissa nondimensionalization numerical value;yDFor total coordinate nondimensionalization numerical value;tDFor time nondimensionalization numerical value;CfFor macropore
System compressibility;CmFor oil reservoir system compressibility;φfFor macropore internal porosity;β is permeability ratio;
As shown in figure 3, it is water drive and the schematic diagram of macropore oil reservoir typical curve plots contrast during poly- drive;As shown in figure 4,
For the schematic diagram of oil reservoir well test analysis typical curve plots under the influence of different initial polymer concentrations;As shown in figure 5, oozed for difference
The schematic diagram of oil reservoir well test analysis typical curve plots under saturating rate ratios affect;As shown in fig. 6, it is different macropore widths affects
The schematic diagram of lower oil reservoir well test analysis typical curve plots.
5) it is the polymer flooding macropore oil reservoir typical curve theory plate obtained in step 4) and oil field measured data is bent
Line is fitted, you can obtains equivalent width, the Permeability Parameters (being macropore permeability) of macropore, stratum is filled
Divide profile control, select the blocking agent of suitable particles size to block macropore, so as to improve polymer flooding effect;
In step 5), basic data is inputted in the polymer flooding macropore oil reservoir theory plate program of establishment first,
Basic data includes the thickness of oil reservoir, the porosity of oil reservoir, the permeability of oil reservoir, system compressibility, skin factor, pit shaft storage
Collect coefficient, injection well injection rate, volume factor, aqueous viscosity, polymer initial concentration, original formation pressure, hole diameter, macropore
Width and macropore permeability, then by adjusting the permeability of oil reservoir, skin factor, bottom-hole storage coefficient, macropore
Width and macropore permeability, theoretical pressure and theoretical pressure derivative curve is calculated;Then theoretical pressure is utilized
The measured data of curve, theoretical pressure derivative curve and field pressure, fitting theory pressure curve and real well pressure curve, and
Theoretical pressure derivative curve and real well pressure derivative curve;The width of macropore is finally obtained according to fitting result, permeability is joined
Number, and explanation results are utilized, abundant profile control is carried out to stratum, selects the blocking agent of suitable particles size to block macropore,
Recovery ratio is improved so as to improve polymer flooding effect.
Specific embodiment is set forth below:
Embodiment
Instance data is derived from the drop of pressure data of Bohai Sea B oil fields injection well, and the oil reservoir is heterogeneous strong, porosity
For 0.31, mean permeability 2000mD, pilot wellgroup is implemented metaideophone from August, 2013 and gathered, and injection of polymer concentration is
1500mg/L, since note is poly-, producing well is shown in that poly- speed is fast, produces poly- concentration height, aqueous to rise soon, notes poly- effect and declines, tentatively
Conclude that the well group has macropore.The injection well carried out a pressure fall-off test on March 2nd, 2016.
Well testing solution is carried out to Bohai Sea B oil fields injection well using the polymer flooding macropore oil reservoir well test analysis method
Release, oil field measured data and theoretical plate matched curve (as shown in Figure 7) in the present embodiment, model explanation obtains large pore path parameter
For:β=4.4, Kf=8850mD, Wf=3.5m.According to explanation results, abundant profile control is carried out to stratum, selects suitable particles size
Blocking agent macropore is blocked, the well group is aqueous at present is effectively controlled, and produces poly- concentration and declines.
The various embodiments described above are merely to illustrate the present invention, wherein the structure of each part, connected mode etc. are all can be
Change, every equivalents carried out on the basis of technical solution of the present invention and improvement, it should not exclude the present invention's
Outside protection domain.
Claims (7)
1. a kind of polymer flooding macropore oil reservoir well test analysis method, it is characterised in that it comprises the following steps:
1) according to polymer flooding macropore characteristics of reservoirs, polymer flooding macropore physical models of reservoir is established;
2) according to the polymer flooding macropore physical models of reservoir obtained in step 1), polymer flooding macropore oil reservoir mathematics is determined
Model;
3) use finite difference method solution procedure 2) in obtain polymer flooding macropore reservoir mathematical model, obtain shaft bottom pressure
The numerical solution of power;
4) relation that changed with time to pressure carries out nondimensionalization, draws polymer flooding macropore oil reservoir typical curve theoretical diagram
Version;
5) the polymer flooding macropore oil reservoir typical curve theory plate obtained in step 4) is entered with oil field measured data curve
Row fitting, obtains the equivalent width and Permeability Parameters of macropore.
A kind of 2. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 1, it is characterised in that the step
1) for the physical model established in using pit shaft as symmetrical centre, two macropores are symmetrically distributed in pit shaft both sides;The step
1) the polymer flooding macropore characteristics of reservoirs in includes:Reservoir-level, uniform thickness, homogeneous and isotropism;Macropore etc.
Effect development length is xf;Macropore permeability is Kf, reservoir permeability K, the ratio between macropore permeability and reservoir permeability are β,
KfMuch larger than K;The thickness of macropore is core intersection H, equivalent width Wf;There is fluid communication along macropore, pressure drop be present.
A kind of 3. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 2, it is characterised in that the step
2) determine that the detailed process of polymer flooding macropore reservoir mathematical model is as follows:
1. determine the transient seepage flow differential equation of single-phase micro- compressible liquid:
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In formula, P is strata pressure;K is reservoir permeability;μaFor the initial viscosity of polymer;CmFor oil reservoir system compressibility;
φmFor oil reservoir porosity;T is fluid flow time;X is abscissa direction away from well centre distance;Y is ordinate direction away from well
Heart distance;
2. determine primary condition equation, internal boundary condition equation and the Outer Boundary Conditions of polymer flooding macropore reservoir mathematical model
Equation:
Wherein, the primary condition equation of polymer flooding macropore reservoir mathematical model is:
P(x,y,t)|T=0=P0 (2)
In formula, P0For original formation pressure;
The internal boundary condition equation of polymer flooding macropore reservoir mathematical model is:
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<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mi>w</mi>
</msub>
<msub>
<mo>|</mo>
<mrow>
<mi>x</mi>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<mi>y</mi>
<mo>=</mo>
<msub>
<mi>y</mi>
<mn>0</mn>
</msub>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mrow>
<mo>(</mo>
<mo>-</mo>
<mi>S</mi>
<mo>&times;</mo>
<mo>(</mo>
<mrow>
<mi>&Delta;</mi>
<mi>x</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>w</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>y</mi>
<mfrac>
<mrow>
<mo>&part;</mo>
<msub>
<mi>P</mi>
<mi>w</mi>
</msub>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mrow>
<mi>x</mi>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<mi>y</mi>
<mo>=</mo>
<msub>
<mi>y</mi>
<mn>0</mn>
</msub>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, H is core intersection;Q is well yield;C is bottom-hole storage coefficient;B is volume factor;S is reservoir skin factor;Pwf
For flowing bottomhole pressure (FBHP);PwFor the pressure at the borehole wall;rwFor wellbore radius;reFor external boundary radius;x0、y0Respectively oil well shaft bottom center
Transverse and longitudinal coordinate;Δ x, Δ y difference infinitesimals;E is constant, e=2.7182818;
The Outer Boundary Conditions equation of polymer flooding macropore reservoir mathematical model is:
<mrow>
<munder>
<munder>
<mi>lim</mi>
<mrow>
<mi>x</mi>
<mo>&RightArrow;</mo>
<mi>&infin;</mi>
</mrow>
</munder>
<mrow>
<mi>y</mi>
<mo>&RightArrow;</mo>
<mi>&infin;</mi>
</mrow>
</munder>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>,</mo>
<mi>y</mi>
<mo>,</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>P</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
A kind of 4. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 3, it is characterised in that:The step
3) in, using finite difference method solution procedure 2) in obtain polymer flooding macropore reservoir mathematical model detailed process such as
Under:
1. mesh generation is carried out in room and time to the polymer flooding macropore physical models of reservoir in step 1);
2. it is poor that the transient seepage flow differential equation, primary condition equation, internal boundary condition equation and Outer Boundary Conditions equation are carried out
Dispersion is separated, i.e., difference discretization is carried out to (1)~(5) formula;
Wherein, the seepage flow diffusion equation after discrete is:
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mfrac>
<msubsup>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mfrac>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>K</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mfrac>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>+</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&lsqb;</mo>
<mfrac>
<msubsup>
<mi>K</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mfrac>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>y</mi>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<msubsup>
<mi>K</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<msubsup>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>/</mo>
<mn>2</mn>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mfrac>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<msub>
<mi>y</mi>
<mi>j</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>&rsqb;</mo>
<mo>=</mo>
<msub>
<mi>&phi;C</mi>
<mi>t</mi>
</msub>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, i, j are to the discrete of space;N is discrete to the time;Δ t is time step, and φ is porosity, when under φ
When being designated as f, i.e. φfFor the porosity of macropore, when being designated as m under φ, i.e. φmFor the porosity of oil reservoir;
Wherein in formula (6)Value determined by harmonic average, i.e.,:
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
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<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
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<mn>1</mn>
<msub>
<mi>&mu;</mi>
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</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
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</msub>
<mo>)</mo>
</mrow>
<mi>i</mi>
</msub>
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<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
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<msub>
<mrow>
<mo>(</mo>
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<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
<mrow>
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<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
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<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mrow>
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<mrow>
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<msub>
<mi>&mu;</mi>
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</msub>
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</mrow>
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</msub>
<mo>+</mo>
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<msub>
<mi>&mu;</mi>
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</msub>
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</mrow>
<mrow>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&CenterDot;</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mn>1</mn>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
</mfrac>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mn>2</mn>
<mrow>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mi>j</mi>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>&mu;</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Gauss-seidel solutions by iterative method equation (6), iterative equation formula are as follows:
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>+</mo>
<msub>
<mi>b</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>+</mo>
<msub>
<mi>c</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>+</mo>
<msub>
<mi>d</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>+</mo>
<msub>
<mi>e</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>g</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mi>n</mi>
</msubsup>
<mo>-</mo>
<mn>11.57</mn>
<msub>
<mi>&mu;Bq</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jIt is intermediate variable:
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<msub>
<mi>H</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>K</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>b</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<msub>
<mi>H</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>K</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
<mo>-</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j;
<mrow>
<msub>
<mi>d</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<msub>
<mi>H</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>K</mi>
<mrow>
<mi>x</mi>
<mi>i</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>;</mo>
</mrow>
<mrow>
<msub>
<mi>a</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
<mo>(</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mrow>
<mo>(</mo>
<msub>
<mi>u</mi>
<mi>a</mi>
</msub>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mfrac>
<msub>
<mi>H</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<msub>
<mi>K</mi>
<mrow>
<mi>y</mi>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</mrow>
</msub>
<mo>;</mo>
</mrow>
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jBe mesh coordinate be (i, j) place well yield, well point grid qi,j=q, non-well point grid qi,j=0;Pi,jIt is grid
The strata pressure at coordinate (i, j) place;
For internal boundary condition, Huiyuan's item processing by well as place grid, because barometric gradient is larger near shaft bottom, internally
Boundary condition difference gridding makees linearization process, obtains:
<mrow>
<msub>
<mi>Bq</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mn>0.54</mn>
<msub>
<mrow>
<mo>(</mo>
<mfrac>
<mrow>
<mi>K</mi>
<mi>H</mi>
</mrow>
<mi>&mu;</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<mi>ln</mi>
<mfrac>
<msub>
<mi>r</mi>
<mi>e</mi>
</msub>
<msub>
<mi>r</mi>
<mi>w</mi>
</msub>
</mfrac>
<mo>+</mo>
<mi>S</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mn>24</mn>
<mi>C</mi>
<mfrac>
<mrow>
<msubsup>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
<mrow>
<mi>n</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>P</mi>
<mrow>
<mi>w</mi>
<mi>f</mi>
</mrow>
<mi>n</mi>
</msubsup>
</mrow>
<mrow>
<mi>&Delta;</mi>
<mi>t</mi>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula:μ is viscosity of the polymer in any time;
Outer Boundary Conditions discretization is obtained:
P1,j=Pm,j=Pe(j=1,2 ... k) (13)
Pi,1=Pi,k=Pe(i=1,2 ... m) (14)
In formula, P1,jIt is the strata pressure that mesh coordinate is (1, j) place;Pm,jIt is the strata pressure that mesh coordinate is (m, j) place;
Pi,1It is the strata pressure that mesh coordinate is (i, 1) place;Pi,kIt is the strata pressure that mesh coordinate is (i, k) place;PeFor external boundary
Pressure;M represents the grid number in i directions, and k represents the grid number in j directions;
Solved for ease of Difference Calculation, the processing equation to barometric gradient is as follows:
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>P</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>x</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>0.5</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>+</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>0.5</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;x</mi>
<mrow>
<mi>i</mi>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>15</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mfrac>
<mrow>
<mo>&part;</mo>
<mi>P</mi>
</mrow>
<mrow>
<mo>&part;</mo>
<mi>y</mi>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mrow>
<mo>(</mo>
<mo>|</mo>
<mfrac>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
</mrow>
<mrow>
<mn>0.5</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
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<mo>+</mo>
<mo>|</mo>
<mfrac>
<mrow>
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<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
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<msub>
<mi>P</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<mn>0.5</mn>
<mrow>
<mo>(</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>&Delta;y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
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</mrow>
</mrow>
</mfrac>
<mo>|</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>16</mn>
<mo>)</mo>
</mrow>
</mrow>
3. iterative numerical solution is carried out to above-mentioned DIFFERENCE EQUATIONS, wherein, DIFFERENCE EQUATIONS is the transient seepage flow differential equation, just
The equation group of beginning condition, boundary condition composition, try to achieve the numerical solution of polymer flooding macropore oil reservoir bottom pressure.
A kind of 5. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 4, it is characterised in that:The grid
For rectangle or square, when for Rectangular grid when,When for square net when, re=
0.208Δx。
A kind of 6. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 1, it is characterised in that the step
4) relation that changed with time to pressure carries out nondimensionalization, and its Non-di-mensional equation is as follows:
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<mi>&pi;</mi>
<mi>K</mi>
<mi>H</mi>
</mrow>
<mrow>
<mn>1.842</mn>
<mo>&times;</mo>
<msup>
<mn>10</mn>
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<mo>-</mo>
<mn>3</mn>
</mrow>
</msup>
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<mo>)</mo>
</mrow>
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<mn>19</mn>
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<mn>3.6</mn>
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PwDFor polymer flooding macropore oil reservoir bottom pressure nondimensionalization value;CDFor bottom-hole storage coefficient nondimensionalization value;xDFor horizontal stroke
Coordinate nondimensionalization numerical value;yDFor total coordinate nondimensionalization numerical value;tDFor time nondimensionalization numerical value;CfFor macropore trace integration pressure
Contracting coefficient;CmFor oil reservoir system compressibility;φfFor macropore internal porosity;β is permeability ratio.
A kind of 7. polymer flooding macropore oil reservoir well test analysis method as claimed in claim 1, it is characterised in that the step
5) fit procedure of polymer flooding macropore oil reservoir typical curve theory plate and oil field measured data curve is as follows in:First will
In the polymer flooding macropore oil reservoir theory plate program of basic data input establishment, basic data includes thickness, the oil of oil reservoir
The porosity of layer, permeability, system compressibility, skin factor, bottom-hole storage coefficient, injection well injection rate, the volume of oil reservoir
Coefficient, aqueous viscosity, polymer initial concentration, original formation pressure, hole diameter, the permeability of the width of macropore and macropore;
Then by adjusting the permeability of oil reservoir, skin factor, bottom-hole storage coefficient, the width of macropore and the infiltration of macropore
Rate, theoretical pressure and theoretical pressure derivative curve is calculated;Then using theoretical pressure curve, theoretical pressure derivative curve and
The measured data of field pressure, fitting theory pressure curve and real well pressure curve, and theoretical pressure derivative curve and real well
Differential of pressure curve;Width, the Permeability Parameters of macropore are finally obtained according to fitting result.
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CN109441415A (en) * | 2018-12-19 | 2019-03-08 | 克拉玛依新科澳石油天然气技术股份有限公司 | The Well Test Data Analysis Method of Polymer Flooding Reservoirs testing well based on disturbance from offset wells |
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