A method for analyzing interference well testing in polymer flooding reservoirs

Abstract

The present invention relates to a polymer drive reservoir interference well test analysis method, comprising: step S11, establishing a polymer drive reservoir interference well test physical model; step S12, establishing a polymer drive reservoir interference well test mathematical model according to the polymer drive reservoir interference well physical model; step S13, according to the polymer drive reservoir interference well test mathematical model, by fully implicitly solving the pressure, saturation and polymer concentration equation group, to obtain the bottom hole flow pressure numerical solution; step S14, according to the bottom hole flow pressure of different time steps, obtain the polymer drive interference well test curve; by adjusting the formation and fluid parameters, obtain the polymer drive interference well test theoretical curve plate under different parameter conditions; step S15, the polymer drive interference well test theoretical curve plate is fitted with the field measured curve to obtain the near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity parameters. The present invention improves the stability of the numerical solution by fully implicitly solving the pressure, saturation and polymer concentration.

Description

Technical Field

[0001] The invention relates to the technical field of petroleum development, and in particular to a polymer flooding reservoir interference well test analysis method. Background Art

[0002] Interference well testing uses one well as an exciting well and another or several wells as observation wells, keeping the observation well's own factors from causing pressure fluctuations. By changing the working system of the exciting well, a high-precision pressure gauge is lowered into the observation well to measure the change in bottom hole pressure, and finally the flow coefficient, energy storage coefficient and other parameters are determined based on the pressure change data. Interference well testing can determine the connectivity of the formation, the closure of the fault, and obtain the formation parameters such as the flow coefficient, pressure conductivity and energy storage coefficient of the formation between wells, and is widely used in actual oilfield development.

[0003] During the polymer flooding process, as the amount of polymer injected increases, the reservoir physical properties near some injection wells and between the injection and production wells change, resulting in increased injection pressure in the polymer injection wells and failure to achieve injection, which affects the polymer flooding effect. The use of interference well testing technology can determine the connectivity between wells, understand the degree of connectivity between wells, and judge the changes in physical properties between wells, so as to track the dynamics of polymer flooding reservoirs in a timely manner and take corresponding measures to further improve the polymer flooding development effect. However, the current research on interference well testing technology is based on water-driven reservoirs, and the interference well testing analysis method for polymer-driven reservoirs has not been reported. Therefore, research in this area has important practical significance. At the same time, it can provide strong technical support for the improvement of polymer-driven reservoir well testing methods. Summary of the invention

[0004] In view of the above-mentioned deficiencies of the prior art, the purpose of the present invention is to provide a polymer flooding reservoir interference well test analysis method to solve the problem that the existing water flooding interference well test interpretation model is difficult to interpret the measured data of the oil field, and provide a basis for adjusting the polymer flooding reservoir plan.

[0005] The present invention provides a polymer flooding reservoir interference well test analysis method, the method comprising the following steps:

[0006] Step S11, establishing a physical model of polymer flooding reservoir interference well testing;

[0007] Step S12, establishing a polymer flooding reservoir interference well test mathematical model according to the polymer flooding reservoir interference well physical model;

[0008] Step S13, according to the polymer flooding reservoir interference well test mathematical model, by fully implicitly solving the pressure, saturation and polymer concentration equations, a numerical solution for the bottom hole flowing pressure is obtained;

[0009] Step S14, obtaining a polymer flooding interference well test curve according to the bottom hole flowing pressure at different time steps; and obtaining a polymer flooding interference well test theoretical curve chart under different parameter conditions by adjusting formation and fluid parameters;

[0010] Step S15, fitting the polymer flooding interference well test theoretical curve chart with the field measured curve to obtain near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity parameters.

[0011] According to an embodiment of the present invention, establishing the polymer flooding reservoir interference well testing mathematical model in step S12 includes the following steps:

[0012] ① Establish fluid seepage control equations, including oil-water two-phase continuity equation, polymer continuity equation, oil-water two-phase seepage velocity equation, and polymer diffusion velocity equation;

[0013] ② giving the initial condition equations of the mathematical model of the polymer flooding reservoir interference well test, including the pressure initial condition equation, the saturation initial condition equation, and the concentration initial condition equation;

[0014] ③ The boundary condition equations of the polymer flooding reservoir interference well test mathematical model are given, including the inner boundary condition equations and the outer boundary condition equations.

[0015] According to an embodiment of the present invention, in step S12,

[0016] The oil phase continuity equation is:

[0017] Where φ is the reservoir porosity, a decimal; b o is the reciprocal of the oil phase volume coefficient; S o is the oil phase saturation, decimal; v o is the oil phase formation flow rate, in m 3 / s;q o is the oil phase wellbore production, in m 3 / s;

[0018] The continuity equation for the water phase is:

[0019] Where φ is the reservoir porosity, a decimal; b w is the inverse of the volume coefficient of the water phase; S w is the water phase saturation, decimal; v w is the water phase formation flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s;

[0020] The continuity equation for polymers is:

[0021] Where φ is the reservoir porosity, a decimal; f p is the accessible pore volume coefficient of the polymer, a decimal; bw is the inverse of the volume coefficient of the water phase; S w is the water phase saturation, decimal; C p is the polymer concentration, in g / L; ρ r is the rock density of the formation, in kg / m 3 ; is the adsorption concentration of the polymer in the rock pores, in g / L; v w is the water phase formation flow rate, in m 3 / s;v d is the polymer diffusion flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s;

[0022] The oil phase seepage velocity equation is:

[0023] Among them, v o is the oil phase formation flow rate, in m 3 / s; K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase, a decimal; S w is the water phase saturation, decimal; μ o is the oil phase viscosity, in mPa·s; p o is the oil phase formation pressure, in MPa; ρ o is the oil phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; z is the z-direction coordinate;

[0024] The water phase seepage velocity equation is:

[0025] Where K is the reservoir permeability, in μm 2 ;k rw is the relative permeability of water phase, decimal; S w is the water phase saturation, decimal; μ w is the viscosity of the water phase, in mPa·s; C p is the polymer concentration in g / L; v w is the water phase formation flow rate, in m 3 / s; R k is the permeability reduction coefficient, dimensionless; C p is the polymer concentration, in g / L; p w is the water phase formation pressure; ρ w is the water phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s2 ; z is the z-direction coordinate;

[0026] The polymer diffusion rate equation is:

[0027] Among them, D p is the diffusion coefficient, in m 2 / s; φ is the reservoir porosity, a decimal; f p is the accessible pore volume coefficient of the polymer, a decimal; S w is the water phase saturation, decimal; C p is the polymer concentration, in g / L;

[0028] According to one embodiment of the present invention,

[0029] The pressure initial condition equation is:

[0030] p o (x,y,z,0)=p i , where p o is the oil phase formation pressure, p i is the initial formation pressure, in MPa;

[0031] The initial condition equation for water saturation is:

[0032] S w (x,y,z,0)=S wi (x,y,z), where S w is the water phase saturation, decimal; S wi is the initial saturation of water phase, decimal;

[0033] The initial condition equation for polymer concentration is:

[0034] C p (x,y,z,0)=C pi (x,y,z), where C p is the polymer concentration, g / L; C pi is the initial polymer concentration, g / L;

[0035] The initial condition equation for oil saturation is:

[0036] S o (x,y,z,0)=S oi (x,y,z), where S o S is the oil phase saturation, decimal; oi is the initial saturation of the oil phase, a decimal.

[0037] According to one embodiment of the present invention,

[0038] The inner boundary condition equation is:

[0039] Among them, Q α is the oil phase or water phase wellbore production or injection volume, in m 3 / s;λ α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); h is the formation thickness, in m; b α is the reciprocal of the volume coefficient of the oil phase or water phase, a decimal; r e is the equivalent radius of the wellbore grid, in m; r w is the wellbore radius, in meters; S is the skin factor, in decimals; p wf is the bottom hole flowing pressure, in MPa; p α is the oil phase or water phase formation pressure, in MPa; α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); C is the wellbore storage coefficient, in m 3 / MPa; t is time, unit is s;

[0040] Among them, λ o is the fluidity of the single-layer oil phase, in μm 2 / (mPa·s);λ w is the single-layer water phase fluidity, in μm 2 / (mPa·s); K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase, a decimal; k rw is the relative permeability of water phase, decimal; μ o is the oil phase viscosity, in mPa·s; μ w is the viscosity of the water phase, in mPa·s; R k is the permeability reduction coefficient, dimensionless;

[0041] The outer boundary condition equation is:

[0042] Among them, p w is the water phase formation pressure; x, y, z are coordinates in different directions.

[0043] According to one embodiment of the present invention, in step S13, solving the mathematical model of polymer flooding reservoir interference well testing includes: dividing the space and time grids, establishing finite difference flow equations, processing boundaries and initial conditions, and on this basis solving the pressure, saturation and polymer concentration difference equations by fully implicit Newton iteration.

[0044] According to an embodiment of the present invention, in step S11, the physical model established includes the following factors:

[0045] ① Shear thinning, diffusion, convection and adsorption of polymers;

[0046] ② Differences in flow capacity between the near-wellbore and far-wellbore zones;

[0047] ③Influence of reservoir boundary.

[0048] According to an embodiment of the present invention, in step S14, the formation and fluid parameters include near-well permeability, far-well permeability, composite radius, and polymer concentration.

[0049] According to an embodiment of the present invention, in step S15, the well-to-well connectivity is calculated by the following formula:

[0050]

[0051] Wherein, μ is the average viscosity of each phase fluid, in mPa·s; C t is the comprehensive compression coefficient, in MPa -1 ; K is the reservoir permeability, in μm 2 ; φ is the reservoir porosity, a decimal.

[0052] According to one embodiment of the present invention, in step S11, the physical model established can be used for single-phase or two-phase model interpretation, and the physical model is three-dimensional and applicable to single-layer, two-layer or three-layer oil layers.

[0053] The present invention adopts the above technical solution, which has the following advantages:

[0054] 1. The present invention improves the stability of the numerical solution by performing fully implicit solutions for pressure, saturation and polymer concentration;

[0055] 2. The polymer flooding reservoir interference well test mathematical model established by the present invention can be used for single-phase or two-phase model interpretation, is applicable to single-layer or multi-layer reservoirs, and can also be used for water-flooding reservoirs, and has a wide range of applications;

[0056] 3. The polymer flooding reservoir interference well test analysis method proposed in the present invention makes up for the deficiency that the current interference well test technology research is based on water-driven reservoirs, and provides strong technical support for the improvement of polymer flooding reservoir well test methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a simplified physical model of interference well testing of three-layer polymer flooding reservoir in the present invention;

[0058] Figure 2A flow chart for solving the interference well test model of a three-layer polymer flooding reservoir in the present invention;

[0059] Figure 3 Comparison of interference well test curves between the three-layer polymer flooding reservoir and the water flooding reservoir in the present invention;

[0060] Figure 4 Interference well test curves of different composite radii for interference well test of three-layer polymer flooding oil reservoir in the present invention;

[0061] Figure 5 The interference well test curves of different far-well permeabilities in the interference well test of the three-layer polymer flooding oil reservoir in the present invention;

[0062] Figure 6 It is the fitting curve between the test data of the interference well test example well and the theoretical plate in the present invention. DETAILED DESCRIPTION

[0063] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings so that the purpose, features and advantages of the present invention can be more clearly understood. It should be understood that the embodiments shown in the accompanying drawings are not intended to limit the scope of the present invention, but are only intended to illustrate the essential spirit of the technical solution of the present invention.

[0064] In order to solve the problem that the existing water flooding interference well test interpretation model is difficult to interpret the measured data of the oil field and provide a basis for adjusting the polymer flooding reservoir plan, the present invention adopts the following technical scheme: The present invention provides a polymer flooding reservoir interference well test analysis method, which mainly includes the following contents:

[0065] 1) Considering polymer shear thinning, diffusion, convection, adsorption and retention, and the difference in flow capacity between near-wellbore and far-wellbore zones, a physical model for interference well testing in polymer flooding reservoirs is established;

[0066] 2) establishing a mathematical model of polymer flooding reservoir interference well testing based on the physical model of polymer flooding reservoir interference well testing;

[0067] 3) According to the mathematical model of polymer flooding reservoir interference well testing, a numerical solution of bottom hole flowing pressure is obtained by fully implicitly solving the pressure, saturation and polymer concentration equations;

[0068] 4) According to the bottom hole flow pressure at different time steps, the polymer flooding interference well test curve is obtained. By adjusting the formation and fluid parameters, the polymer flooding interference well test theoretical curve chart under different parameter conditions can be obtained.

[0069] 5) Fitting the theoretical curve of the polymer flooding interference well test with the field measured curve to obtain parameters such as near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity.

[0070] In the step 1), the physical model established takes the following factors into consideration and can be used for single-phase or two-phase model interpretation. The model is three-dimensional and is applicable to single-layer, two-layer and three-layer oil layers.

[0071] ① Shear thinning, diffusion, convection and adsorption of polymers;

[0072] ② Differences in flow capacity between the near-wellbore and far-wellbore zones;

[0073] ③Influence of reservoir boundary.

[0074] In the step 2), establishing a mathematical model for polymer flooding reservoir interference well testing includes the following steps:

[0075] ① Establish fluid seepage control equations, including oil-water two-phase continuity equation, polymer continuity equation, oil-water two-phase seepage velocity equation, and polymer diffusion velocity equation;

[0076] The oil phase continuity equation is:

[0077] Where φ is the reservoir porosity, a decimal; b o is the reciprocal of the oil phase volume coefficient; S o is the oil phase saturation, decimal; v o is the oil phase formation flow rate, in m 3 / s;q o is the oil phase wellbore production, in m 3 / s;

[0078] The water phase continuity equation is:

[0079] Where φ is the reservoir porosity, a decimal; b w is the inverse of the volume coefficient of the water phase; S w is the water phase saturation, decimal; v w is the water phase formation flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s;

[0080] The polymer continuity equation is:

[0081] Where φ is the reservoir porosity, a decimal; f p is the accessible pore volume coefficient of the polymer, a decimal; b w is the inverse of the volume coefficient of the water phase; S w is the water phase saturation, decimal; C p is the polymer concentration, in g / L; ρ r is the rock density of the formation, in kg / m 3 ; is the adsorption concentration of the polymer in the rock pores, in g / L; v w is the water phase formation flow rate, in m 3 / s;v d is the polymer diffusion flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s;

[0082] The oil phase seepage velocity equation is:

[0083] Among them, v o is the oil phase formation flow rate, in m 3 / s; K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase, decimal; S w is the water phase saturation, decimal; μ o is the oil phase viscosity, in mPa·s; p o is the oil phase formation pressure, in MPa; ρ o is the oil phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; z is the z-direction coordinate;

[0084] The water phase seepage velocity equation is:

[0085] Where K is the reservoir permeability, in μm 2 ;k rw is the relative permeability of water phase, decimal; S w is the water phase saturation, decimal; μ w is the viscosity of the water phase, in mPa·s; C p is the polymer concentration, in g / L; v w is the water phase formation flow rate, in m 3 / s; R k is the permeability reduction coefficient, dimensionless; C p is the polymer concentration, in g / L; p w is the water phase formation pressure; ρ w is the water phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; z is the z-direction coordinate;

[0086] The polymer diffusion rate equation is:

[0087] v d =-D pφf p S w (▽C p ), where D p is the diffusion coefficient, in m 2 / s; φ is the reservoir porosity, a decimal; f p is the accessible pore volume coefficient of the polymer, a decimal; S w is the water phase saturation, decimal; C p is the polymer concentration, in g / L;

[0088] ② Given the initial condition equations of the mathematical model of the polymer flooding reservoir interference well test, including the initial condition equations of pressure, saturation and concentration;

[0089] The pressure initial condition equation is:

[0090] p o (x,y,z,0)=p i , where p o is the oil phase formation pressure, p i is the initial formation pressure, in MPa;

[0091] The water saturation initial condition equation is:

[0092] S w (x,y,z,0)=S wi (x,y,z), where S w is the water phase saturation, decimal; S wi is the initial saturation of water phase, decimal;

[0093] The polymer concentration initial condition equation is:

[0094] C p (x,y,z,0)=C pi (x,y,z), where C p is the polymer concentration, g / L; C pi is the initial polymer concentration, g / L;

[0095] The initial condition equation for oil saturation is:

[0096] S o (x,y,z,0)=S oi (x,y,z), where S o S is the oil phase saturation, decimal; oi is the initial saturation of the oil phase, a decimal.

[0097] ③ Given the boundary condition equations of the mathematical model of polymer flooding reservoir interference well testing, including the inner boundary condition equations and the outer boundary condition equations.

[0098] The inner boundary condition equation is:

[0099] Among them, Q α is the oil phase or water phase wellbore production or injection volume, in m 3 / s;λ α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); h is the formation thickness, in m; b α is the reciprocal of the volume coefficient of the oil phase or water phase, a decimal; r e is the equivalent radius of the wellbore grid, in m; r w is the wellbore radius, in meters; S is the skin factor, in decimals; p wf is the bottom hole flowing pressure, in MPa; p α is the oil phase or water phase formation pressure, in MPa; α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); C is the wellbore storage coefficient, in m 3 / MPa; t is time, unit is s;

[0100] Among them, λ o is the fluidity of the single-layer oil phase, in μm 2 / (mPa·s);λ w is the single-layer water phase fluidity, in μm 2 / (mPa·s); K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase, a decimal; k rw is the relative permeability of water phase, decimal; μ o is the oil phase viscosity, in mPa·s; μ w is the viscosity of the water phase, in mPa·s; R k is the permeability reduction coefficient, dimensionless;

[0101] The outer boundary condition equation is:

[0102]

[0103] Among them, p w is the water phase formation pressure; x, y, z are coordinates in different directions.

[0104] In the step 3), solving the mathematical model of polymer flooding reservoir interference well testing includes: dividing the space and time grids, establishing finite difference flow equations, processing boundaries and initial conditions, and on this basis solving the pressure, saturation and polymer concentration difference equations by fully implicit Newton iteration.

[0105] In step 4), the formation and fluid parameters are mainly near-well permeability, far-well permeability, composite radius, polymer concentration and other parameters.

[0106] In step 5), the inter-well connectivity can be calculated by the following formula:

[0107]

[0108] Wherein, μ is the average viscosity of each phase fluid, in mPa·s; C t is the comprehensive compression coefficient, in MPa -1 ; K is the reservoir permeability, in μm 2 ; φ is the reservoir porosity, a decimal.

[0109] The present invention adopts the above technical solution, which has the following advantages:

[0110] The present invention improves the stability of the numerical solution by performing full implicit solutions for pressure, saturation and polymer concentration;

[0111] The polymer flooding reservoir interference well test mathematical model established by the present invention can be used for single-phase or two-phase model interpretation, is applicable to single-layer or multi-layer reservoirs, and can also be used for water-flooding reservoirs, and has a wide range of applications;

[0112] The polymer flooding reservoir interference well test analysis method proposed in the present invention makes up for the deficiency that the current interference well test technology research is based on water flooding reservoirs, and provides strong technical support for the improvement of polymer flooding reservoir well test methods.

[0113] Embodiment 1

[0114] This embodiment provides a three-layer polymer flooding reservoir interference well test analysis method, according to the method of the above embodiment, including the following steps (the symbols in the following formulas have the same meanings as in the embodiment):

[0115] Step S11, considering polymer shear thinning, diffusion, convection, adsorption and retention, and the difference in flow capacity between the near-well and far-well zones, a physical model of interference well testing of a three-layer polymer flooding reservoir is established, such as Figure 1 As shown;

[0116] Step S12, establishing a mathematical model of the interference well test of a three-layer polymer flooding reservoir according to the physical model of the interference well test of the three-layer polymer flooding reservoir;

[0117] Step S13, according to the three-layer polymer flooding reservoir interference well test mathematical model, by fully implicitly solving the pressure, saturation and polymer concentration equations, a numerical solution for the bottom hole flowing pressure is obtained;

[0118] Step S14, obtaining the three-layer polymer flooding interference well test curve according to the bottom hole flowing pressure at different time steps. By adjusting the formation and fluid parameters, the three-layer polymer flooding interference well test theoretical curve chart under different parameter conditions can be obtained.

[0119] Step S15, fitting the three-layer polymer flooding interference well test theoretical curve chart with the field measured curve to obtain parameters such as near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity.

[0120] In step S11 of this embodiment, the physical model of the three-layer polymer flooding reservoir interference well test is three-dimensional, such as Figure 1 As shown;

[0121] Step S12 of this embodiment is to establish a mathematical model of the three-layer polymer flooding reservoir interference well testing based on the three-layer polymer flooding reservoir interference well testing physical model, specifically including:

[0122] ① Establish fluid seepage control equations, including oil-water two-phase continuity equation, polymer continuity equation, oil-water two-phase seepage velocity equation, and polymer diffusion velocity equation;

[0123] The oil phase continuity equation is:

[0124]

[0125] The water phase continuity equation is:

[0126]

[0127] The polymer continuity equation is:

[0128]

[0129] The oil phase seepage velocity equation is:

[0130]

[0131] The water phase seepage velocity equation is:

[0132]

[0133] The polymer diffusion rate equation is:

[0134]

[0135] ② Given the initial condition equations of the mathematical model of the polymer flooding reservoir interference well test, including the initial condition equations of pressure, saturation and concentration;

[0136] The pressure initial condition equation is:

[0137] p o(x,y,z,0)=p i

[0138] The water saturation initial condition equation is:

[0139] S w (x,y,z,0)=S wi (x,y,z)

[0140] The initial condition equation for polymer concentration is:

[0141] C p (x,y,z,0)=C pi (x,y,z)

[0142] The initial condition equation for oil saturation is:

[0143] S o (x,y,z,0)=S oi (x,y,z)

[0144] ③ Given the boundary condition equations of the mathematical model of polymer flooding reservoir interference well testing, including the inner boundary condition equations and the outer boundary condition equations.

[0145] The inner boundary condition equation is:

[0146]

[0147]

[0148] The outer boundary condition equation is:

[0149]

[0150] In step S13 of this embodiment, according to the three-layer polymer flooding reservoir interference well test mathematical model, the numerical solution of the bottom hole flowing pressure is obtained by fully implicitly solving the pressure, saturation and polymer concentration equations. The process is as follows: Figure 2 Specifically including:

[0151] This model uses a uniform rectangular grid and a gradually increasing variable time step. The finite volume method is used to differentially discretize the seepage equation, and the divergence and gradient based on the polyhedral grid are introduced. The divergence of the grid flow is expressed as the difference between the flow of the outflow and the flow of the inflow fluid in the grid:

[0152]

[0153] The pressure gradient between the grids is as follows:

[0154] grad(p)[f]=p[C2(f)]-p[C1(f)] (4-19)

[0155] Where c is a grid, dimensionless; f is a face, dimensionless; C1 and C2 are two adjacent grids that make up a face, dimensionless; C1(f) and C2(f) are two adjacent grids C1 and C2 that make up face f, dimensionless; F is the set of faces that make up the grid, dimensionless; F(c) is the set of all faces that make up grid c, dimensionless; v is the formation flow vector, m 3 / s; v[f] is the flow rate on surface f, m 3 / s; is the flow rate in the direction of C1(f) (outflow) on surface f, m 3 / s; Flow rate in the direction of C2(f) (inflow) on surface f, m 3 / s; div(v)[c] is the flow divergence of grid c, m 3 / s; p[C1(f)] is the pressure vector in the direction of C1(f) on surface f, in MPa; p[C2(f)] is the pressure vector in the direction of C2(f) on surface f, in MPa; grad(p)[f] is the pressure gradient on surface f, in MPa.

[0156] Using α to represent the oil phase or the water phase, the residual form of the fully implicit discrete control equation is expressed as:

[0157]

[0158]

[0159] Where n is the number of time steps; l is the number of iteration steps; is the residual of the oil phase or water phase control equation corresponding to the 1st iteration step in the n+1 time step; is the residual of the polymer control equation corresponding to the lth iteration step in the n+1 time step; φ is the reservoir porosity, a decimal; b α It is the reciprocal of the volume coefficient of the oil phase or water phase, a decimal; S α is the oil phase or water phase saturation, decimal; v α is the oil phase or water phase formation flow rate, m 3 / s;Q α is the oil phase or water phase wellbore production or injection volume, m 3 / s;b w is the reciprocal of the water phase volume coefficient, a decimal; S w is the water phase saturation, decimal; C p is the polymer concentration, g / L; v w is the water phase formation flow rate, m 3 / s;v d is the polymer diffusion flow rate, m 3 / s;Q w is the water phase wellbore injection volume, m 3 / s.

[0160] The fully implicit discrete form of the oil or water phase formation flow is expressed as:

[0161]

[0162] in, is the oil or water phase formation flow rate corresponding to the lth iteration step in the n+1 time step, m 3 / s; K is the reservoir permeability, μm 2 ; is the relative permeability of the oil phase or water phase corresponding to the 1st iteration step in the n+1 time step, a decimal; A is the flow cross-sectional area, m 2 ;μ α is the viscosity of the oil phase or water phase fluid, mPa·s; ——The oil or water phase pressure gradient corresponding to the 1st iteration in the n+1 time step; g is the gravitational acceleration, m / s 2 ; is the density of the oil phase or water phase corresponding to the 1st iteration in the n+1 time step, kg / m 3 ; grad(z) is the vertical height difference corresponding to the middle of the oil layer, m.

[0163] The fully implicit discretized form of the wellbore equation is as follows:

[0164]

[0165]

[0166] in, is the oil phase or water phase wellbore flow rate corresponding to the lth iteration step in the n+1 time step, m 3 / s; is the fluidity of the single-layer oil or water phase corresponding to the lth iteration step in the n+1 time step, μm 2 / (mPa·s); It is the reciprocal of the volume coefficient of the oil phase or water phase corresponding to the 1st iteration step in the n+1 time step, a decimal; is the bottom hole flowing pressure corresponding to the 1st iteration step in the n+1 time step, MPa; is the oil phase or water phase formation pressure corresponding to the 1st iteration step in the n+1 time step, MPa; is the bottom hole flowing pressure corresponding to time step n, MPa; is the residual of the total wellbore flow equation corresponding to the lth iteration step in the n+1 time step. The number of equations is equal to the number of wells in the reservoir. m 3 / s; is the sum of the oil and water flow rates of the wellbore corresponding to time n+1, m 3 / s; is the oil phase wellbore flow rate corresponding to the lth iteration step in the n+1 time step, m 3 / s; is the water phase wellbore flow rate corresponding to the lth iteration step in the n+1 time step, m 3 / s.

[0167] All residual equations are summarized as follows:

[0168]

[0169]

[0170] Among them, R n+1.l (X n+1,l ) is the transposition of the residual equations of oil, water, polymer and wellbore after combination in the n+1 time step and the 1st iteration step; X n+1,l is the column vector of the unknown independent variable combination at the lth iteration step in the n+1 time step;

[0171] ——Residual equations for oil, water, polymer and wellbore at 1 iteration step in n+1 time step;

[0172] ——column vector of water phase formation pressure, water saturation, polymer concentration and bottom hole flowing pressure at the 1st iteration step in the n+1 time step;

[0173] Finally, the nonlinear equation is solved by Newton iteration:

[0174]

[0175] The unknown independent variables after each iteration can be updated by the following equation:

[0176] X n+1,l+1 =X n+1,l +ΔX n+1,l (4-28)

[0177] In the formula, ——In the n+1 time step, at the 1st iteration step, all residual equations are differentiated with respect to all independent variables;

[0178] ΔX n+1,l ——A column vector of the increments of all unknown independent variables at the lth iteration in the n+1 time step;

[0179] -R n+1.l (X n+1,l )——column vector consisting of the values ​​of oil, water, polymer and wellbore residual equations at the lth iteration in the n+1 time step; X n+1,l+1 ——The column vector of unknown independent variable combinations at the l+1 iteration step in the n+1 time step;

[0180] In the solution module compiled by MATLAB, the above formula is used to perform specific matrix iterative solution, as shown in the following solution process, to obtain the bottom hole flowing pressure at different time steps.

[0181]

[0182] Where \ is the inverse division method, GMRES is the generalized minimum residual method, and The derivatives of the oil phase residual equation with respect to the water phase formation pressure, water saturation, polymer concentration and bottom hole flowing pressure are obtained respectively; and Derivatives of the water phase excess equation with respect to water phase formation pressure, water saturation, polymer concentration and bottom hole flowing pressure are obtained respectively; and The polymer excess equation is derived with respect to water phase formation pressure, water saturation, polymer concentration and bottom hole flowing pressure respectively; and are the derivatives of the wellbore excess equation with respect to water phase formation pressure, water saturation, polymer concentration and bottom hole flowing pressure; δp w1 ...δp wN For each iteration step, the water phase formation pressure increment of each grid; δS w1 ...δS wN For each iteration step, the water saturation increment of each grid; δC p1 ...δC pN For each iteration step, the polymer concentration of each grid is incremented; δp wf1 ...δp wfm For each iteration step, the bottom hole pressure increment of each wellbore; R o1 ...R oN is the value of the oil phase residual equation for each grid, R w1 ...R wN is the value of the water phase excess equation for each grid, R p1 ...R pN is the value of the polymer excess equation for each grid, R q1 ...R qm is the value of each wellbore margin equation.

[0183] In step S14 of this embodiment, the three-layer polymer flooding interference well test curve is obtained according to the bottom hole flow pressure at different time steps, and it is compared with the water flooding interference well test curve, such as Figure 3 At the same time, by adjusting the formation and fluid parameters, the theoretical curve chart of the three-layer polymer flooding interference well test under different parameter conditions can be obtained.

[0184] Figure 4The interference well test curves of different composite radii in the three-layer polymer flooding reservoir are shown in Figure 2. Figure 5 Interference test curves of different far-well permeabilities for interference test in a three-layer polymer flooding reservoir.

[0185] In step S15 of this embodiment, the three-layer polymer flooding interference well test theoretical curve chart is fitted with the field measured curve to obtain parameters such as near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity.

[0186] Embodiment 2

[0187] This embodiment is an application example of performing interference well test interpretation on a water injection well in an oil field according to the specific application process provided in the first embodiment. In this embodiment, the polymer flooding reservoir interference well test model described in the first embodiment is selected. Since the water injection well is interpreted, the concentration of the polymer is set to 0. The test data of the example well and the fitting curve of the theoretical plate are as follows: Figure 6 The obtained interpretation data are shown in Table 1, and compared with the interpretation results of the mature commercial software Ecrin, the permeability coincidence rate reached 99%, proving the reliability of the interference well test interpretation method for polymer flooding reservoirs.

[0188] Table 1 Interference well test module and Ecrin well test interpretation results of polymer flooding reservoir

[0189]

[0190] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprises" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprises a..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0191] The above embodiments are only used to illustrate the present invention, in which the components and devices of the embodiments can be changed, and each implementation method can be combined or deleted as needed. Not all components in the drawings are necessary. The general principles defined in this document can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to the embodiments described herein, and all equivalent changes and improvements based on the technical solution of the present invention should not be excluded from the protection scope of the present invention.

Claims

1. A method for analyzing well testing interference in polymer flooding reservoirs, characterized in that: The method comprises the following steps: Step S11, establishing a physical model of polymer flooding reservoir interference well testing; Step S12, establishing a polymer flooding reservoir interference well test mathematical model according to the polymer flooding reservoir interference well physical model; Step S13, according to the polymer flooding reservoir interference well test mathematical model, by fully implicitly solving the pressure, saturation and polymer concentration equations, a numerical solution for the bottom hole flowing pressure is obtained; Step S14, obtaining a polymer flooding interference well test curve according to the bottom hole flowing pressure at different time steps; and obtaining a polymer flooding interference well test theoretical curve chart under different parameter conditions by adjusting formation and fluid parameters; Step S15, fitting the polymer flooding interference well test theoretical curve chart with the field measured curve to obtain near and far well permeability, well storage coefficient, skin coefficient, composite radius, and well connectivity parameters; Establishing the polymer flooding reservoir interference well testing mathematical model in step S12 includes the following steps: ① Establish fluid seepage control equations, including oil-water two-phase continuity equation, polymer continuity equation, oil-water two-phase seepage velocity equation, and polymer diffusion velocity equation; ② giving the initial condition equations of the mathematical model of the polymer flooding reservoir interference well test, including the pressure initial condition equation, the saturation initial condition equation, and the concentration initial condition equation; ③ Giving boundary condition equations of the polymer flooding reservoir interference well test mathematical model, including inner boundary condition equations and outer boundary condition equations; In step S12, The oil phase continuity equation is: Where, φ is the reservoir porosity; b o is the reciprocal of the oil phase volume coefficient; S o is the oil phase saturation; v o is the oil phase formation flow rate, in m 3 / s;q o is the oil phase wellbore production, in m 3 / s; The continuity equation for the water phase is: Where, φ is the reservoir porosity; b w is the inverse of the volume coefficient of the water phase; S w is the water phase saturation; v w is the water phase formation flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s; The continuity equation for polymers is: Where, φ is the reservoir porosity; f p is the accessible pore volume coefficient of the polymer; b w is the inverse of the volume coefficient of the water phase; S w is the water phase saturation; C p is the polymer concentration, in g / L; ρ r is the rock density of the formation, in kg / m 3 ; is the adsorption concentration of the polymer in the rock pores, in g / L; v w is the water phase formation flow rate, in m 3 / s;v d is the polymer diffusion flow rate, in m 3 / s;q w is the water phase wellbore injection volume, in m 3 / s; The oil phase seepage velocity equation is: Among them, v o is the oil phase formation flow rate, in m 3 / s; K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase; S w is the water phase saturation; μ o is the oil phase viscosity, in mPa·s; p o is the oil phase formation pressure, in MPa; ρ o is the oil phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; z is the z-direction coordinate; The water phase seepage velocity equation is: Where K is the reservoir permeability, in μm 2 ;k rw is the relative permeability of water phase; S w is the water phase saturation; μ w is the viscosity of the water phase, in mPa·s; C p is the polymer concentration in g / L; v w is the water phase formation flow rate, in m 3 / s; R k is the permeability reduction coefficient, dimensionless; C p is the polymer concentration, in g / L; p w is the water phase formation pressure; ρ w is the water phase density, in kg / m 3 ; g is the acceleration due to gravity, in m / s 2 ; z is the z-direction coordinate; The polymer diffusion rate equation is: Among them, D p is the diffusion coefficient, in m 2 / s; φ is the reservoir porosity; f p is the accessible pore volume coefficient of the polymer; S w is the water phase saturation; C p is the polymer concentration, in g / L; The pressure initial condition equation is: p o (x,y,z,0)=p i , where p o is the oil phase formation pressure, p i is the initial formation pressure, in MPa; The initial condition equation for water saturation is: Sw(x,y,z,0)=Swi(x,y,z), where S w is the water phase saturation; S wi is the initial saturation of water phase; The initial condition equation for polymer concentration is: Cp(x,y,z,0)=Cpi(x,y,z), where, C p is the polymer concentration, g / L; C pi is the initial polymer concentration, in g / L; The initial condition equation for oil saturation is: S o (x,y,z,0)=S oi (x,y,z), where S o is the oil phase saturation; S oi is the initial saturation of the oil phase.

2. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: The inner boundary condition equation is: Among them, Q α is the oil phase or water phase wellbore production or injection volume, in m 3 / s;λ α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); h is the formation thickness, in m; b α is the reciprocal of the volume coefficient of the oil phase or water phase; r e is the equivalent radius of the wellbore grid, in m; r w is the wellbore radius, in meters; S is the skin factor; p wf is the bottom hole flowing pressure, in MPa; p α is the oil phase or water phase formation pressure, in MPa; α is the fluidity of a single layer of oil or water phase, in μm 2 / (mPa·s); C is the wellbore storage coefficient, in m 3 / MPa; t is time, unit is s; Among them, λ o is the fluidity of the single-layer oil phase, in μm 2 / (mPa·s);λ w is the single-layer water phase fluidity, in μm 2 / (mPa·s); K is the reservoir permeability, in μm 2 ;k ro is the relative permeability of the oil phase; k rw is the relative permeability of water phase; μ o is the oil phase viscosity, in mPa·s; μ w is the viscosity of the water phase, in mPa·s; R k is the permeability reduction coefficient, dimensionless; The outer boundary condition equation is: Among them, p w is the water phase formation pressure; x, y, z are coordinates in different directions.

3. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: In step S13, solving the mathematical model of polymer flooding reservoir interference well testing includes: dividing the space and time grids, establishing finite difference flow equations, processing boundaries and initial conditions, and on this basis performing full implicit Newton iteration to solve the pressure, saturation and polymer concentration difference equations.

4. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: In step S11, the physical model established includes the following factors: ① Shear thinning, diffusion, convection and adsorption of polymers; ② Differences in flow capacity between the near-wellbore and far-wellbore zones; ③Influence of reservoir boundary.

5. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: In step S14, the formation and fluid parameters include near-well permeability, far-well permeability, composite radius, and polymer concentration.

6. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: In step S15, the well connectivity is calculated by the following formula: Wherein, μ is the average viscosity of each phase fluid, in mPa·s; C t is the comprehensive compression coefficient, in MPa -1 ; K is the reservoir permeability, in μm 2 ; φ is the reservoir porosity.

7. The polymer flooding reservoir interference well test analysis method according to claim 1, characterized in that: In step S11, the physical model established can be used for single-phase or two-phase model interpretation. The physical model is three-dimensional and is applicable to single-layer, two-layer or three-layer oil layers.

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