CN107526891B - Polymer flooding large-pore oil reservoir well testing analysis method - Google Patents

Polymer flooding large-pore oil reservoir well testing analysis method Download PDF

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CN107526891B
CN107526891B CN201710735830.2A CN201710735830A CN107526891B CN 107526891 B CN107526891 B CN 107526891B CN 201710735830 A CN201710735830 A CN 201710735830A CN 107526891 B CN107526891 B CN 107526891B
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pore
polymer flooding
pressure
oil reservoir
reservoir
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CN107526891A (en
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康晓东
张健
曾杨
唐恩高
谢晓庆
石爻
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China National Offshore Oil Corp CNOOC
Beijing Research Center of CNOOC China Co Ltd
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China National Offshore Oil Corp CNOOC
Beijing Research Center of CNOOC China Co Ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING; COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00Computer-aided design [CAD]
    • G06F30/20Design optimisation, verification or simulation
    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21BEARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B43/00Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
    • E21B43/16Enhanced recovery methods for obtaining hydrocarbons
    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21BEARTH DRILLING, e.g. DEEP DRILLING; OBTAINING OIL, GAS, WATER, SOLUBLE OR MELTABLE MATERIALS OR A SLURRY OF MINERALS FROM WELLS
    • E21B49/00Testing 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
    • YGENERAL 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
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02ATECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE
    • Y02A10/00TECHNOLOGIES FOR ADAPTATION TO CLIMATE CHANGE at coastal zones; at river basins
    • Y02A10/40Controlling or monitoring, e.g. of flood or hurricane; Forecasting, e.g. risk assessment or mapping

Abstract

The invention discloses a polymer flooding large-pore oil reservoir well testing analysis method, which is characterized by comprising the following steps of: it comprises the following steps: 1) establishing a polymer flooding large-pore oil reservoir physical model according to the characteristics of the polymer flooding large-pore oil reservoir; 2) determining a mathematical model of the polymer flooding large-pore oil reservoir according to the physical model of the polymer flooding large-pore oil reservoir obtained in the step 1); 3) solving the mathematical model of the polymer flooding large-pore oil reservoir obtained in the step 2) by adopting a finite difference method to obtain a numerical solution of bottom hole pressure; 4) carrying out dimensionless on the change relation of the pressure along with the time, and drawing a typical curve theoretical plate of the polymer flooding large-pore oil reservoir; 5) fitting the typical curve theoretical plate of the polymer flooding large pore oil reservoir obtained in the step 4) with an oil field measured data curve to obtain the equivalent width and permeability parameters of the large pore.

Description

Polymer flooding large-pore oil reservoir well testing analysis method
Technical Field
The invention relates to a polymer flooding large-pore oil reservoir well testing analysis method, and belongs to the technical field of well testing.
Background
In the process of long-term water injection development, the offshore sandstone oil reservoir has large change in pore structure, and because the permeability of the reservoir is increased and the pore throat radius is increased, a high permeability strip and an extra-high permeability strip, namely a large pore channel, are easily formed in the reservoir. The existence of the large pore channel aggravates the interlayer contradiction, and the polymer injected by means of improving the recovery ratio is adopted in the later period, so that other parts in the reservoir layer are difficult to be affected along the low-efficiency or ineffective circulation in the large pore channel, the oil displacement efficiency is seriously influenced, the saturation difference of residual oil on the plane is obvious, and the polymer flooding effect is obviously poor. Therefore, the identification of the polymer flooding large-pore oil reservoir and the determination of the distribution condition of the polymer flooding large-pore oil reservoir have important significance for plugging the large pore, improving the polymer flooding effect and increasing the recovery ratio by adopting corresponding measures.
At present, the main means for identifying the large pore path are well testing data identification, production dynamic monitoring, tracer monitoring and well logging data identification. The most sensitive development parameters in the process of identifying the large pore passage are yield and pressure, and related researches are carried out on judging the existence of the large pore passage by using pressure drop test data through a well testing means. Steady history and Shi Ying adopt a double logarithmic curve of wellhead pressure drop of a water injection well to diagnose the existence of a large pore passage, and establish a theoretical model of water drive reservoir well testing with the large pore passage. Yangsheron utilizes a pressure drop well testing method to reflect the change condition of the permeability of the reservoir through the characteristics of a pressure drop log-log curve after water injection. The Kjeldahl provides an injection well radial model considering mutual coupling of a large pore passage and a non-large pore passage region, and the development area and the development multiple of the large pore passage are judged according to the bottom hole pressure change characteristic of the injection well. And the Liuhua flood establishes a dominant seepage channel well testing model by analyzing the basic form of the dominant seepage channel. The Li Chengyonguan establishes an asymmetric dominant seepage channel well testing interpretation mathematical model on the basis of history and rigor. However, the method established by the method is only suitable for identifying the large pore path of the water-flooding reservoir, and the water-flooding reservoir is not researched.
Disclosure of Invention
Aiming at the problems, the invention aims to provide a polymer flooding large-pore oil reservoir well testing analysis method, which can accurately explain measured data of an oil field to obtain related parameters of a large pore, provides data support for plugging the large pore and has high application value in a mine field.
In order to achieve the purpose, the invention adopts the following technical scheme: a polymer flooding large-pore oil reservoir well testing analysis method is characterized by comprising the following steps:
1) establishing a polymer flooding large-pore oil reservoir physical model according to the characteristics of the polymer flooding large-pore oil reservoir;
2) determining a mathematical model of the polymer flooding large-pore oil reservoir according to the physical model of the polymer flooding large-pore oil reservoir obtained in the step 1);
3) solving the mathematical model of the polymer flooding large-pore oil reservoir obtained in the step 2) by adopting a finite difference method to obtain a numerical solution of bottom hole pressure;
4) carrying out dimensionless on the change relation of the pressure along with the time, and drawing a typical curve theoretical plate of the polymer flooding large-pore oil reservoir;
5) fitting the typical curve theoretical plate of the polymer flooding large pore oil reservoir obtained in the step 4) with an oil field measured data curve to obtain the equivalent width and permeability parameters of the large pore.
The physical model established in the step 1) takes a shaft as a symmetric center, and two large channels are symmetrically distributed on two sides of the shaft; the polymer flooding large pore reservoir characteristics in the step 1) comprise: the reservoir is horizontal, equal thickness, homogeneous and isotropic; the equivalent extended length of the large pore channel is xf(ii) a Large pore permeability of KfThe oil layer permeability is K, the ratio of the large pore permeability to the oil layer permeability is beta, KfIs far greater than K; the thickness of the large pore passage is the oil layer thickness H, and the equivalent width is Wf(ii) a There is fluid exchange along the large channels and there is a pressure drop.
The specific process of determining the mathematical model of the polymer flooding large-pore oil reservoir in the step 2) is as follows:
determining an unstable seepage differential equation of the single-phase slightly compressible liquid:
wherein P is the formation pressure; k is the oil layer permeability; mu.saIs the initial viscosity of the polymer; cmIs an oil layerSynthesizing the compression coefficient; phi is amIs the oil layer porosity; t is the fluid flow time; x is the distance from the horizontal coordinate direction to the center of the well; y is the distance from the longitudinal coordinate direction to the center of the well;
determining an initial condition equation, an inner boundary condition equation and an outer boundary condition equation of the mathematical model of the polymer flooding large-channel oil reservoir:
the initial condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
P(x,y,t)|t=0=P0 (2)
in the formula, P0Is the original formation pressure;
the inner boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
wherein H is the thickness of the oil layer; q is the well flow rate; c is a wellbore storage coefficient; b is a volume coefficient; s is the epidermal coefficient of the reservoir; pwfIs bottom hole flowing pressure; pwIs the pressure at the borehole wall; r iswIs the wellbore radius; r iseIs the outer boundary radius; x is the number of0、y0Respectively are the horizontal and vertical coordinates of the center of the bottom of the oil well; delta x, delta y differential infinitesimal; e is a constant, e ═ 2.7182818;
the outer boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
in the step 3), the specific process of solving the mathematical model of the polymer flooding large oil reservoir obtained in the step 2) by adopting a finite difference method is as follows:
carrying out grid division on the polymer flooding large-pore oil reservoir physical model in the step 1) in space and time;
performing differential discretization on an unstable seepage differential equation, an initial condition equation, an inner boundary condition equation and an outer boundary condition equation, namely performing differential discretization on the formulas (1) to (5);
wherein, the dispersed seepage diffusion equation is as follows:
in the formula, i and j are the dispersion of space; n is the dispersion over time; Δ t is the time step, φ is the porosity, when φ is subscript f, i.e., φfIs the porosity of the macropores, when phi is subscript m, i.e. + -. phimPorosity of the oil layer;
wherein in formula (6)Is determined according to harmonic mean, namely:
solving equation (6) by using Gauss-seidel iterative method, wherein the iterative equation is as follows:
in the formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jAre all intermediate variables:
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jis the well flow rate at grid coordinates (i, j), well point grid qi,jQ, non-well point grid qi,j=0;Pi,jIs the formation pressure at grid coordinate (i, j);
for the inner boundary condition, the well is taken as the convergent source item of the grid where the well is located for processing, and the differential grid of the inner boundary condition is subjected to linearization processing due to the fact that the pressure gradient near the bottom of the well is large, so that the following steps are obtained:
in the formula: μ is the viscosity of the polymer at any one time;
discretizing the external boundary condition to obtain:
P1,j=Pm,j=Pe(j=1,2…k) (13)
Pi,1=Pi,k=Pe(i=1,2…m) (14)
in the formula, P1,jIs the formation pressure at grid coordinates (1, j); pm,jIs the formation pressure at grid coordinates (m, j); pi,1Is the formation pressure at grid coordinates (i, 1); pi,kIs the formation pressure at grid coordinates (i, k); peIs the outer boundary pressure; m represents the number of meshes in the i direction, and k represents the number of meshes in the j direction;
to facilitate the differential calculation solution, the processing equation for the pressure gradient is as follows:
and thirdly, carrying out numerical iteration solution on the differential equation set, wherein the differential equation set is an equation set consisting of an unstable seepage differential equation, initial conditions and boundary conditions, and solving the numerical solution of the bottom hole pressure of the polymer flooding large-pore oil reservoir.
The grid is rectangular or square, when the grid is rectangular,when a square grid, re=0.208Δx。
Step 4) is to perform non-dimensionalization on the change relation of the pressure along with the time, and the non-dimensional equation is as follows:
PwDthe polymer flooding large-channel reservoir bottom hole pressure dimensionless value is obtained; cDDimensionless values for wellbore reservoir coefficients; x is the number ofDIs a non-dimensionalized numerical value of the abscissa; y isDDimensionless numerical values for the total coordinates; t is tDIs a time dimensionless numerical value; cfThe large pore comprehensive compression coefficient; cmThe comprehensive compression coefficient of the oil layer; phi is afPorosity in macropores; beta is the permeability ratio.
The fitting process of the polymer flooding large-pore oil reservoir typical curve theoretical plate and the oil field measured data curve in the step 5) is as follows: firstly, inputting basic data into a theoretical plate program of a polymer flooding large-pore oil reservoir, wherein the basic data comprises the thickness of an oil layer, the porosity of the oil layer, the permeability of the oil layer, a comprehensive compression coefficient, a skin coefficient, a shaft reservoir coefficient, the injection amount of a polymer injection well, a volume coefficient, water phase viscosity, initial concentration of a polymer, original formation pressure, well diameter, the width of a large pore and the permeability of the large pore; then, calculating to obtain theoretical pressure and a theoretical pressure derivative curve by adjusting the permeability of an oil layer, a skin coefficient, a shaft reservoir coefficient, the width of a large pore passage and the permeability of the large pore passage; then, fitting the theoretical pressure curve and the real well pressure curve, and the theoretical pressure derivative curve and the real well pressure derivative curve by using the theoretical pressure curve, the theoretical pressure derivative curve and the measured data of the oil field pressure; and finally obtaining the width and permeability parameters of the large pore channel according to the fitting result.
Due to the adoption of the technical scheme, the invention has the following advantages: the method comprises the steps of establishing a physical model and a mathematical model of the polymer flooding large-pore oil reservoir, obtaining a numerical value solution of bottom hole pressure of the polymer flooding large-pore oil reservoir by using a finite element difference method, drawing a typical curve theoretical plate of the polymer flooding large-pore oil reservoir, fitting the typical curve theoretical plate of the polymer flooding large-pore oil reservoir with an oil field actual measurement data curve to obtain parameters such as large pore width, permeability and the like, and providing data support for plugging large pores by selecting a proper plugging agent, improving the polymer flooding effect and improving the recovery ratio.
Drawings
FIG. 1 is a schematic overall flow diagram of the present invention;
FIG. 2 is a schematic diagram of a simplified physical model of a reservoir in accordance with the present invention;
FIG. 3 is a schematic diagram of a typical curve chart comparison of a large-pore reservoir in water flooding and polymer flooding according to the present invention;
FIG. 4 is a schematic illustration of a graphical representation of an exemplary well test interpretation of a reservoir under the influence of different initial polymer concentrations in accordance with the present invention;
FIG. 5 is a schematic diagram of a typical plot plate for reservoir well testing interpretation under the influence of different permeability ratios in accordance with the present invention;
FIG. 6 is a schematic diagram of a typical plot plate for reservoir well testing interpretation under the influence of different large pore widths according to the present invention;
FIG. 7 is a schematic diagram of a theoretical plate for reservoir well testing interpretation and a fitted curve of real well test data in the invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
As shown in FIG. 1, the invention provides a polymer flooding large-pore oil reservoir well testing analysis method, which comprises the following steps:
1) establishing a physical model of the polymer flooding large-pore oil reservoir according to the characteristics of the polymer flooding large-pore oil reservoir, wherein the model takes a shaft as a symmetric center, and two large pores are symmetrically distributed on two sides of the shaft (as shown in figure 2);
wherein, the polymer flooding large pore oil reservoir characteristics comprise: the reservoir is horizontal, equal thickness, homogeneous and isotropic; the 2 large channels are symmetrical to the shaft, and the equivalent extension length of the large channels is xf(ii) a Large pore permeability of KfThe oil layer permeability is K, the ratio of the large pore permeability to the oil layer permeability is beta, KfIs far greater than K; the thickness of the large pore passage is the oil layer thickness H, and the equivalent width is Wf(ii) a There is fluid exchange along the large channels and there is a pressure drop.
2) Determining a mathematical model of the polymer flooding large-pore oil reservoir according to the physical model of the polymer flooding large-pore oil reservoir obtained in the step 1), wherein the specific process is as follows:
determining an unstable seepage differential equation of the single-phase slightly compressible liquid:
wherein P is the formation pressure; k is the oil layer permeability; mu.saIs the initial viscosity of the polymer; cmThe comprehensive compression coefficient of the oil layer; phi is amIs the oil layer porosity; t is the fluid flow time; x is the distance from the horizontal coordinate direction to the center of the well; y is the distance from the center of the well in the ordinate direction.
Determining an initial condition equation, an inner boundary condition equation and an outer boundary condition equation of the mathematical model of the polymer flooding large-channel oil reservoir:
the initial condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
P(x,y,t)|t=0=P0 (2)
in the formula, P0Is the original formation pressure;
the inner boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
wherein H is the thickness of the oil layer; q is the well flow rate; c is a wellbore storage coefficient; b is a volume coefficient; s is the epidermal coefficient of the reservoir; pwfIs bottom hole flowing pressure; pwIs the pressure at the borehole wall; r iswIs the wellbore radius; r iseIs the outer boundary radius; x is the number of0、y0Respectively are the horizontal and vertical coordinates of the center of the bottom of the oil well; Δ x and Δ y are differential infinitesimals; e is a constant, e ═ 2.7182818;
the outer boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
3) solving the mathematical model of the polymer flooding large-pore oil reservoir obtained in the step 2) by adopting a finite difference method to obtain a numerical solution of bottom hole pressure, wherein the finite difference method comprises the following specific processes:
carrying out grid division on the polymer flooding large-pore oil reservoir physical model in the step 1) in space and time;
secondly, carrying out differential discretization on an unstable seepage differential equation, an initial condition equation, an inner boundary condition equation and an outer boundary condition equation, namely carrying out differential discretization on equations (1) to (5):
wherein, the dispersed seepage diffusion equation is as follows:
in the formula, i and j are the dispersion of space; n is the dispersion over time; Δ t is the time step; phi is the porosity, when phi has the subscript f, i.e. + -fIs the porosity of the macropores, when phi is subscript m, i.e. + -. phimPorosity of the oil layer;
whereinIs determined according to harmonic mean, namely:
solving equation (6) by using Gauss-seidel iterative method, wherein the iterative equation is as follows:
in the formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jAre all intermediate variables:
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jis the well flow rate at grid coordinates (i, j), well point grid qi,jQ, non-well point grid qi,j=0;Pi,jIs the formation pressure at grid coordinate (i, j).
For the inner boundary condition, the well is taken as the convergent source item of the grid where the well is located for processing, and the differential grid of the inner boundary condition is subjected to linearization processing due to the fact that the pressure gradient near the bottom of the well is large, so that the following steps are obtained:
in the formula: μ is the viscosity of the polymer at any one time; for rectangular gridsFor a square grid re=0.208Δx。
Discretizing the external boundary condition to obtain:
P1,j=Pm,j=Pe(j=1,2…k) (13)
Pi,1=Pi,k=Pe(i=1,2…m) (14)
in the formula, P1,jIs the formation pressure at grid coordinates (1, j); pm,jIs the formation pressure at grid coordinates (m, j); pi,1Is the formation pressure at grid coordinates (i, 1); pi,kIs the formation pressure at grid coordinates (i, k); peIs the outer boundary pressure; m represents the number of meshes in the i direction; k represents the number of meshes in the j direction;
to facilitate the differential calculation solution, the processing equation for the pressure gradient is as follows:
and thirdly, carrying out numerical iteration solution on the differential equation set, wherein the differential equation set is an equation set consisting of an unstable seepage differential equation, initial conditions and boundary conditions, and solving the numerical solution of the bottom hole pressure of the polymer flooding large-pore oil reservoir.
4) Carrying out non-dimensionalization on the change relation of the pressure along with the time, and drawing a typical curve theoretical plate of the polymer flooding large-pore oil reservoir, wherein the non-dimensionalization equation is as follows:
PwDthe polymer flooding large-channel reservoir bottom hole pressure dimensionless value is obtained; cDDimensionless values for wellbore reservoir coefficients; x is the number ofDIs a non-dimensionalized numerical value of the abscissa; y isDDimensionless numerical values for the total coordinates; t is tDIs a time dimensionless numerical value; cfThe large pore comprehensive compression coefficient; cmThe comprehensive compression coefficient of the oil layer; phi is afPorosity in macropores; beta is the permeability ratio;
FIG. 3 is a schematic diagram showing a typical curve chart comparison of a large-pore reservoir in water flooding and polymer flooding; FIG. 4 is a schematic diagram illustrating a typical plot plate for reservoir well testing under the influence of different initial polymer concentrations; as shown in fig. 5, a schematic diagram of a typical curve chart is explained for reservoir well testing under the influence of different permeability ratios; as shown in fig. 6, a schematic diagram of a typical plot plate is explained for reservoir well testing under the influence of different large pore widths.
5) Fitting the typical curve theoretical plate of the polymer flooding large-pore oil reservoir obtained in the step 4) with an oil field actual measurement data curve to obtain the equivalent width and permeability parameters (namely the permeability of the large pore) of the large pore, fully profile-controlling the stratum, and selecting a plugging agent with a proper particle size to plug the large pore, thereby improving the polymer flooding effect;
in step 5), basic data are input into a theoretical plate program of the polymer flooding large pore channel oil reservoir, wherein the basic data comprise the thickness of an oil layer, the porosity of the oil layer, the permeability of the oil layer, a comprehensive compression coefficient, a skin coefficient, a wellbore storage coefficient, the injection amount of a polymer injection well, a volume coefficient, water phase viscosity, initial concentration of a polymer, original formation pressure, a well diameter, the width of a large pore channel and the permeability of the large pore channel, and then theoretical pressure and a theoretical pressure derivative curve are calculated by adjusting the permeability of the oil layer, the skin coefficient, the wellbore storage coefficient, the width of the large pore channel and the permeability of the large pore channel; then, fitting the theoretical pressure curve and the real well pressure curve, and the theoretical pressure derivative curve and the real well pressure derivative curve by using the theoretical pressure curve, the theoretical pressure derivative curve and the measured data of the oil field pressure; and finally, obtaining the width and permeability parameters of the large pore passage according to the fitting result, fully adjusting and profiling the stratum by utilizing the explanation result, and selecting a plugging agent with a proper particle size to plug the large pore passage, thereby improving the polymer flooding effect and improving the recovery ratio.
Specific examples are listed below:
examples
Example data is obtained from pressure drop data of a certain polymer injection well in a Bohai sea B oil field, the oil reservoir stratum is strong in heterogeneity, the porosity is 0.31, the average permeability is 2000mD, a test well group carries out transfer polymer injection from 2013 to 8 months, the concentration of injected polymers is 1500mg/L, since polymer injection, a production well has high polymer injection speed, the polymer production concentration is high, the water content rises quickly, the polymer injection effect is reduced, and the fact that a large pore channel exists in the well group is preliminarily judged. The injection well was tested for pressure drop in 2016, 3, and 2 days.
The polymer flooding large pore channel oil reservoir well testing analysis method is adopted to perform well testing explanation on a certain polymer injection well in the Bohai sea B oil field, the curve (shown in figure 7) is fitted by the actually measured data of the oil field and a theoretical plate in the embodiment, and the model explanation obtains the large pore channel parameters as follows: beta 4.4, Kf=8850mD,Wf3.5 m. According to the result of the interpretation,fully profile-controlling the stratum, selecting a plugging agent with proper particle size to plug a large pore, effectively controlling the water content of the well group at present, and reducing the aggregation concentration.
The above embodiments are only used for illustrating the present invention, and the structure, connection mode and the like of each component can be changed, and all equivalent changes and improvements made on the basis of the technical scheme of the present invention should not be excluded from the protection scope of the present invention.

Claims (5)

1. A polymer flooding large-pore oil reservoir well testing analysis method is characterized by comprising the following steps:
1) establishing a polymer flooding large-pore oil reservoir physical model according to the characteristics of the polymer flooding large-pore oil reservoir;
2) determining a mathematical model of the polymer flooding large-pore oil reservoir according to the physical model of the polymer flooding large-pore oil reservoir obtained in the step 1);
the specific process of determining the mathematical model of the polymer flooding large-pore oil reservoir in the step 2) is as follows:
determining an unstable seepage differential equation of the single-phase slightly compressible liquid:
wherein P is the formation pressure; k is the oil layer permeability; mu.saIs the initial viscosity of the polymer; cmThe comprehensive compression coefficient of the oil layer; phi is amIs the oil layer porosity; t is the fluid flow time; x is the distance from the horizontal coordinate direction to the center of the well; y is the distance from the longitudinal coordinate direction to the center of the well;
determining an initial condition equation, an inner boundary condition equation and an outer boundary condition equation of the mathematical model of the polymer flooding large-channel oil reservoir:
the initial condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
P(x,y,t)|t=0=P0 (2)
in the formula, P0Is the original formation pressure;
the inner boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
wherein H is the thickness of the oil layer; q is the well flow rate; c is a wellbore storage coefficient; b is a volume coefficient; s is the epidermal coefficient of the reservoir; pwfIs bottom hole flowing pressure; pwIs the pressure at the borehole wall; r iswIs the wellbore radius; r iseIs the outer boundary radius; x is the number of0、y0Respectively are the horizontal and vertical coordinates of the center of the bottom of the oil well; delta x, delta y differential infinitesimal; e is a constant, e ═ 2.7182818;
the outer boundary condition equation of the mathematical model of the polymer flooding large-pore oil reservoir is as follows:
3) solving the mathematical model of the polymer flooding large-pore oil reservoir obtained in the step 2) by adopting a finite difference method to obtain a numerical solution of bottom hole pressure;
4) carrying out dimensionless on the change relation of the pressure along with the time, and drawing a typical curve theoretical plate of the polymer flooding large-pore oil reservoir;
5) fitting the typical curve theoretical plate of the polymer flooding large pore oil reservoir obtained in the step 4) with an oil field measured data curve to obtain the equivalent width and permeability parameters of the large pore;
the physical model established in the step 1) takes a shaft as a symmetric center, and two large channels are symmetrically distributed on two sides of the shaft; the polymer flooding large pore reservoir characteristics in the step 1) comprise: the reservoir is horizontal, equal thickness, homogeneous and isotropic; of the large pore channelEffective extension length of xf(ii) a Large pore permeability of KfThe oil layer permeability is K, the ratio of the large pore permeability to the oil layer permeability is beta, KfGreater than K; the thickness of the large pore passage is the oil layer thickness H, and the equivalent width is Wf(ii) a There is fluid exchange along the large channels and there is a pressure drop.
2. The polymer flooding large pore reservoir well testing analysis method of claim 1, characterized by: in the step 3), the specific process of solving the mathematical model of the polymer flooding large oil reservoir obtained in the step 2) by adopting a finite difference method is as follows:
carrying out grid division on the polymer flooding large-pore oil reservoir physical model in the step 1) in space and time;
performing differential discretization on an unstable seepage differential equation, an initial condition equation, an inner boundary condition equation and an outer boundary condition equation, namely performing differential discretization on the formulas (1) to (5);
wherein, the dispersed seepage diffusion equation is as follows:
in the formula, i and j are the dispersion of space; n is the dispersion over time; Δ t is the time step, φ is the porosity, when φ is subscript f, i.e., φfIs the porosity of the macropores, when phi is subscript m, i.e. + -. phimPorosity of the oil layer;
wherein in formula (6)Is determined according to harmonic mean, namely:
solving equation (6) by using Gauss-seidel iterative method, wherein the iterative equation is as follows:
in the formula, ai,j、bi,j、ci,j、di,j、ei,jAnd gi,jAre all intermediate variables:
ci,j=-di,j-bi,j-ei,j-ai,j-gi,j
gi,j=277.78Hi,jΔxi,jΔyi,jφCt/Δt;
qi,jis the well flow rate at grid coordinates (i, j), well point grid qi,jQ, non-well point grid qi,j=0;Pi,jIs the formation pressure at grid coordinate (i, j);
for the inner boundary condition, the well is taken as the convergent source item of the grid where the well is located for processing, and because the pressure gradient near the bottom of the well is large, the difference grid of the inner boundary condition is subjected to linearization processing, so that the following steps are obtained:
in the formula: μ is the viscosity of the polymer at any one time;
discretizing the external boundary condition to obtain:
P1,j=Pm,j=Pe(j=1,2…k) (13)
Pi,1=Pi,k=Pe(i=1,2…m) (14)
in the formula, P1,jIs the formation pressure at grid coordinates (1, j); pm,jIs the formation pressure at grid coordinates (m, j); pi,1Is the formation pressure at grid coordinates (i, 1); pi,kIs the formation pressure at grid coordinates (i, k); peIs the outer boundary pressure; m represents the number of meshes in the i direction, and k represents the number of meshes in the j direction;
to facilitate the differential calculation solution, the processing equation for the pressure gradient is as follows:
and thirdly, carrying out numerical iteration solution on the differential equation set, wherein the differential equation set is an equation set consisting of an unstable seepage differential equation, initial conditions and boundary conditions, and solving the numerical solution of the bottom hole pressure of the polymer flooding large-pore oil reservoir.
3. The polymer flooding large pore reservoir well testing analysis method of claim 2, characterized in that: the grid is rectangular or square, when the grid is rectangular,when a square grid, re=0.208Δx。
4. The method for analyzing the well test of the polymer flooding large-pore oil reservoir according to claim 1, wherein the step 4) is a dimensionless method for the pressure change with time, and the dimensionless equation is as follows:
PwDthe polymer flooding large-channel reservoir bottom hole pressure dimensionless value is obtained; cDDimensionless values for wellbore reservoir coefficients; x is the number ofDIs a non-dimensionalized numerical value of the abscissa; y isDDimensionless numerical values for the total coordinates; t is tDIs a time dimensionless numerical value; cfThe large pore comprehensive compression coefficient; cmIs an oil layerSynthesizing the compression coefficient; phi is afPorosity of macropores; beta is the permeability ratio.
5. The method for analyzing the well testing of the polymer flooding large pore reservoir as claimed in claim 1, wherein the fitting process of the typical curve theoretical plate of the polymer flooding large pore reservoir and the measured data curve of the oil field in the step 5) is as follows: firstly, inputting basic data into a theoretical plate program of a polymer flooding large-pore oil reservoir, wherein the basic data comprises the thickness of an oil layer, the porosity of the oil layer, the permeability of the oil layer, a comprehensive compression coefficient, a skin coefficient, a shaft reservoir coefficient, the injection amount of a polymer injection well, a volume coefficient, water phase viscosity, initial concentration of a polymer, original formation pressure, well diameter, the width of a large pore and the permeability of the large pore; then, calculating to obtain theoretical pressure and a theoretical pressure derivative curve by adjusting the permeability of an oil layer, a skin coefficient, a shaft reservoir coefficient, the width of a large pore passage and the permeability of the large pore passage; then, fitting the theoretical pressure curve and the real well pressure curve, and the theoretical pressure derivative curve and the real well pressure derivative curve by using the theoretical pressure curve, the theoretical pressure derivative curve and the measured data of the oil field pressure; and finally obtaining the width and permeability parameters of the large pore channel according to the fitting result.
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