Non-Newtonian fluid displacement front calculation method considering gravity action and electronic equipment

Abstract

The invention relates to the technical field of oil and gas field development, and provides a non-Newtonian fluid displacement front calculation method considering a gravity effect and electronic equipment. Establishing a shunt equation considering the non-Newtonian fluid shear rate related viscosity and the gravity number; calculating the shunt equation by using a characteristic line method to obtain a Beckley-Levilt expansion equation, and obtaining an implicit solution of the leading edge position through integral transformation; calculating a nonlinear equation of the front edge position by using a Lanbert W function, performing approximate estimation on the value of the Lanbert W function in combination with a Wenniz analytic solution function, and explicitly calculating the front edge position; and according to the calculation result of the analytical solution, determining the front edge position of non-Newtonian fluid displacement under different apparent viscosities and different reservoir dip angles. The analytical solution has guiding significance for solving the gravity effect problem in the two-phase flow, and the change condition of the front edge position can be predicted through the model, so that a more effective development scheme is formulated, and the sweep efficiency and the crude oil recovery rate are improved.

Description

Technical Field

[0001] The present application relates to the technical field of oil and gas field development, and in particular to a method and electronic equipment for calculating the displacement front of a non-Newtonian fluid taking gravity into account. Background Art

[0002] Non-Newtonian fluid displacement technology is an important method for enhancing oil recovery. As its application continues to expand, our understanding of its displacement mechanisms is also deepening. While the traditional Berkeley-Levert theory provides a theoretical basis for two-phase flow, its assumptions (such as neglecting gravity effects) have limitations in practical application. In tilted reservoirs, gravity differentiation causes the injected fluid to preferentially advance along the reservoir bottom, creating a coning phenomenon that reduces vertical sweep efficiency and limits effective oil displacement.

[0003] Therefore, analyzing the displacement problem of non-Newtonian fluids under the influence of gravity is helpful for the efficient development of oil reservoirs. Summary of the Invention

[0004] In view of this, the embodiments of the present application provide a non-Newtonian fluid displacement front calculation method and electronic equipment that takes into account the effect of gravity, which can predict the changes in the front position, accurately describe the two-phase seepage behavior in the reservoir, and provide a theoretical method for optimizing reservoir development strategies.

[0005] A first aspect of an embodiment of the present application provides a method for calculating a non-Newtonian fluid displacement front taking into account gravity, comprising:

[0006] Establish a partial flow equation that considers the shear rate-dependent viscosity and gravity number of non-Newtonian fluids;

[0007] The flow split equation is calculated using a characteristic line method to obtain a Berkeley-Levert expanded equation, and an implicit solution of the leading edge position is obtained through integral transformation;

[0008] The nonlinear equation for calculating the leading edge position is calculated using the Lambert W function, and the value of the Lambert W function is approximately estimated in combination with the Winnitsky analytical solution function to explicitly calculate the leading edge position;

[0009] Based on the results of analytical solution, the front position of non-Newtonian fluid displacement under different apparent viscosities and reservoir inclinations is determined.

[0010] A second aspect of an embodiment of the present application provides a non-Newtonian fluid displacement front calculation device taking into account gravity, comprising:

[0011] a first calculation unit for establishing a partial flow equation considering the shear rate-dependent viscosity and gravity number of the non-Newtonian fluid;

[0012] a second calculation unit, configured to calculate the flow separation equation using a characteristic line method to obtain a Berkeley-Levert expanded equation, and obtain an implicit solution for the leading edge position by integral transformation;

[0013] a third calculation unit, configured to calculate a nonlinear equation for a leading edge position using a Lambert W function, and to perform an approximate estimation of a value of the Lambert W function in combination with a Winnitsky analytical solution function, thereby explicitly calculating the leading edge position;

[0014] The fourth calculation unit is used to determine the front position of non-Newtonian fluid displacement under different apparent viscosities and different reservoir inclinations based on the calculation results of the analytical solution.

[0015] A third aspect of an embodiment of the present application provides an electronic device, comprising a processor, a memory, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, the electronic device implements the non-Newtonian fluid displacement front calculation method considering gravity as provided in the first aspect of the embodiment of the present application.

[0016] A fourth aspect of the embodiments of the present application provides a computer program product, including a computer program. When the computer program is executed, the method according to the first aspect of the embodiments of the present application is executed.

[0017] The first aspect of the embodiment of the present application provides a method for calculating the displacement front of a non-Newtonian fluid taking into account the effect of gravity. The method establishes a flow equation that considers the viscosity and gravity number related to the shear rate of the non-Newtonian fluid; the characteristic line method is used to calculate the flow equation to obtain the Berkeley-Levert expansion equation, and the implicit solution of the front position is obtained by integral transformation; the nonlinear equation of the front position is calculated using the Lambert W function, and the value of the Lambert W function is approximated in combination with the Winnitsky analytical solution function to explicitly calculate the front position; based on the results of the analytical solution, the front position of the non-Newtonian fluid displacement under different apparent viscosities and different reservoir inclinations is determined. This analytical solution is of guiding significance for solving the problem of gravity effect in two-phase flow. Through this model, the position change of the displacement front can be predicted, thereby formulating a more effective development plan and improving the sweep efficiency and crude oil recovery rate.

[0018] It can be understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments or descriptions of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0020] Figure 1 This is a flow chart of a method for calculating a non-Newtonian fluid displacement front taking into account gravity provided in one embodiment of the present application;

[0021] Figure 2 This is a comparison chart of the saturation distribution results of the analytical solution model and the numerical simulation model of the present application;

[0022] Figure 3 Schematic diagram of the split flow and its derivative in one embodiment of the present application;

[0023] Figure 4 Schematic diagram of breakthrough time under different apparent viscosities of non-Newtonian fluids in one embodiment of the present application;

[0024] Figure 5 This is a schematic cross-sectional diagram of displacement saturation distribution at different reservoir inclination angles in an embodiment of the present application;

[0025] Figure 6 Schematic diagram of a curve showing the change of the leading edge position over time at different gravity numbers in an embodiment of the present application;

[0026] Figure 7 2 is a schematic diagram of a non-Newtonian fluid displacement front calculation device taking into account gravity provided in an embodiment of the present application;

[0027] Figure 8 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0028] In the following description, specific details such as specific system structures and techniques are provided for purposes of illustration rather than limitation to facilitate a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid obscuring the description of the present application with unnecessary detail.

[0029] It should be understood that when used in the present specification and the appended claims, the term "comprising" indicates the presence of described features, integers, steps, operations, elements and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or collections thereof.

[0030] References to "one embodiment" or "some embodiments" in this specification mean that a particular feature, structure, or characteristic described in conjunction with that embodiment is included in one or more embodiments of the present application. Thus, phrases such as "in one embodiment," "in some embodiments," "in other embodiments," and "in other embodiments" appearing in various places in this specification do not necessarily refer to the same embodiment, but rather mean "one or more but not all embodiments," unless otherwise specifically emphasized. The terms "including," "comprising," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0031] like Figure 1 As shown, the method for calculating the displacement front of a non-Newtonian fluid considering gravity provided in an embodiment of the present application includes the following steps S101 to S104:

[0032] Step S101: Establish a flow rate equation that takes into account the viscosity and gravity number related to the shear rate of the non-Newtonian fluid.

[0033] In application, the shear viscosity at different shear rates is determined based on rheological experimental data, and the shear rate-related viscosity of non-Newtonian fluids and the fractional flow rate including the gravity number are obtained through relevant data such as the phase permeation curve.

[0034] Step S102 : Calculate the flow separation equation using the characteristic line method to obtain the Berkeley-Levert expansion equation, and obtain the implicit solution of the leading edge position through integral transformation.

[0035] In the application, the flow rate equation solved by the characteristic line method is combined with the expression of saturation change to obtain the leading edge propulsion velocity. By integrating the solution, the implicit solution of the leading edge position related to saturation and time is obtained.

[0036] Step S103 : Using the Lambert W function to calculate the nonlinear equation of the leading edge position, the value of the Lambert W function is approximately estimated in combination with the Winnitsky analytical solution function, and the leading edge position is explicitly calculated.

[0037] In this application, the leading edge velocity is integrated to obtain expressions for the time and breakthrough time. The Lambert W function is introduced for calculation, and the method proposed by Winitzky is used to calculate an approximate solution for the Lambert W function. Substituting the estimated result into the leading edge position equation, the leading edge position is explicitly estimated.

[0038] Step S104: Determine the front position of the non-Newtonian fluid displacement under different apparent viscosities and different reservoir inclinations based on the analytical solution calculation results.

[0039] In the application, the front position of the non-Newtonian fluid displacement under different apparent viscosities and different reservoir inclinations is determined based on the results of analytical solution calculations. The value of the Lambert W function can be estimated based on the different shear rate-dependent viscosities obtained from the Carreau model and the influence of the reservoir inclination on the fractional flow rate function containing the gravity number. Combined with the improved Berkeley-Levert equation, the front position of the non-Newtonian fluid displacement can be explicitly solved.

[0040] In the application, based on the solved front position of non-Newtonian fluid displacement, the shear viscosity at different shear rates, the breakthrough time changes under different reservoir inclinations and different gravity numbers, the saturation distribution and the change of the front position over time can be plotted.

[0041] The embodiment of the present application establishes a partial flow equation that takes into account the viscosity and gravity effects related to the shear rate of non-Newtonian fluids; combines the characteristic line method to calculate the partial flow equation, obtains an improved Berkeley-Levert expansion equation, and calculates the implicit solution of the front position through integral transformation; uses the Lambert W function to calculate the nonlinear equation of the front position, and uses the Winnitsky analytical solution function to approximate the value of the Lambert W function and explicitly calculate the front position; combines the improved Berkeley-Levert equation to determine the front position under different apparent viscosities and different reservoir inclinations. It can predict the change of the front position, accurately describe the two-phase flow behavior in the reservoir, and provide a theoretical method for optimizing reservoir development strategies. The analytical solution model in this method uses the Carreau model to describe non-Newtonian fluids and takes into account the effect of gravity. The partial flow equation is combined with the characteristic line method (MOC) for calculation, and an improved Berkeley-Levert equation is proposed. It solves the limitations of the traditional Berkeley-Levert equation and is suitable for non-Newtonian fluid displacement and inclined reservoirs. Implicit and explicit solutions are proposed to predict the front position and sweep efficiency, providing an important theoretical approach for understanding the two-phase flow laws in complex reservoir environments.

[0042] In one embodiment, the flow equation for a non-Newtonian fluid that takes into account the shear rate-dependent viscosity and gravity number is:

[0043]

[0044] Among them, N G is the gravity number, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, S NNf is the saturation of non-Newtonian fluid, and M is the mobility ratio of the non-Newtonian fluid phase to the oil phase.

[0045] In the application, based on the oil-water two-phase motion equation, a flow equation is established that takes into account the shear rate-related viscosity of non-Newtonian fluids and the gravity number:

[0046] The Carreau model that exhibits shear rate-dependent viscosity is:

[0047]

[0048] Where: μ NNf is the apparent viscosity of the non-Newtonian fluid, in mPa·s; μ ∞ is the infinite shear viscosity, unit is mPa·s;

[0049] μ o is the zero shear viscosity, in mPa·s;

[0050] is the shear rate, unit is s -1 ;

[0051] τ is the relaxation time, unit is s;

[0052] n is the power law exponent, dimensionless.

[0053] The fluidity of the oil phase is:

[0054]

[0055] Where: o is the oil phase fluidity, unit is m 2 / cp;

[0056] K is the absolute permeability, in mD;

[0057] K ro is the relative permeability of the oil phase, dimensionless;

[0058] μ o It is the viscosity of the oil phase, in mPa·s.

[0059] The fluidity of a non-Newtonian fluid is:

[0060]

[0061] Where: NNf is the fluidity of the non-Newtonian fluid phase, unit is m 2 / cp;

[0062] K rNNf is the relative permeability of the non-Newtonian fluid phase, dimensionless;

[0063] μ NNf is the apparent viscosity of the non-Newtonian fluid, in mPa·s.

[0064] The mobility ratio is:

[0065]

[0066] Where: M is the mobility ratio of the non-Newtonian fluid phase to the oil phase.

[0067] The equation of motion for the oil phase is:

[0068]

[0069] Where: V o is the oil phase velocity, unit is m / s;

[0070] P o is the oil phase pressure, unit: MPa;

[0071] ρ o is the oil phase density, unit is kg / m 3 ;

[0072] g is the acceleration due to gravity, unit is m / s 2 ;

[0073] θ is the reservoir inclination, unit: °.

[0074] The equation of motion for the non-Newtonian fluid phase is:

[0075]

[0076] Where: V NNf is the non-Newtonian fluid phase velocity, unit is m / s;

[0077] P NNf is the non-Newtonian fluid phase pressure, unit: MPa;

[0078] ρ NNf is the density of the non-Newtonian fluid phase, in kg / m 3 .

[0079] The total formation velocity equation is:

[0080] V t =V o +V NNf (7)

[0081] Where: V t is the total speed in m / s.

[0082] The difference between the density of the oil phase and the density of the non-Newtonian fluid phase is:

[0083] Δρ=ρ o -ρ NNf (8)

[0084] Where: Δρ is the difference between the density of the oil phase and the density of the non-Newtonian fluid phase, unit: kg / m 3 .

[0085] Under constant pressure conditions, assuming the capillary force is zero (Po =P NNf ). Combining the above equations, the flow rate equation considering the shear rate-related viscosity and reservoir inclination of non-Newtonian fluid is obtained as follows:

[0086]

[0087] Where: F NNf is the fractional flow rate of the non-Newtonian fluid phase in the fluid, dimensionless.

[0088] The gravity number is defined as:

[0089]

[0090] Where: N G is the gravity number, dimensionless.

[0091] Combining equations (9) and (10), the flow rate equation including the gravity number is obtained as follows:

[0092]

[0093] In one embodiment, the partial flow equation considering the shear rate-dependent viscosity and gravity number of the non-Newtonian fluid is calculated based on the partial flow equation considering the shear rate-dependent viscosity and reservoir inclination of the non-Newtonian fluid and the gravity number;

[0094] The flow rate equation considering the shear rate-dependent viscosity and reservoir inclination of non-Newtonian fluid is:

[0095]

[0096] The formula for calculating the gravity number is:

[0097]

[0098] Among them, N G is the gravity number, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, S NNf is the saturation of non-Newtonian fluid, M is the mobility ratio of non-Newtonian fluid phase and oil phase, V NNf is the phase velocity of the non-Newtonian fluid, V t is the total velocity, Δρ is the density difference between the oil phase and the non-Newtonian fluid phase, K is the absolute permeability, K ro is the relative permeability of the oil phase, μ o is the oil phase viscosity, θ is the reservoir inclination, P is the total pressure, and g is the acceleration of gravity.

[0099] In one embodiment, the characteristic line method is used to calculate the split flow equation, and the resulting Berkeley-Levert expanded equation is:

[0100]

[0101] Among them, S NNf is the saturation of non-Newtonian fluid, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, Φ is the porosity, x is the distance, and t is the time.

[0102] In one embodiment, the implicit solution to the Berkeley-Levert extended equation is:

[0103]

[0104] Among them, S NNf is the saturation of non-Newtonian fluid, x is the distance, t is the time, f′ NNf (S NNf ) is the flow rate derivative related to the saturation of non-Newtonian fluid, f′ NNf (S NNff ) is the derivative of the time-division flow rate of the non-Newtonian fluid front saturation, f′ NNf is the derivative of the fractional flow, Φ is the porosity, V t (t) is the total flow rate, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, x f is the leading edge position, and α1, α2, β1, and β2 are constant terms in the leading edge velocity formula.

[0105] In one embodiment, the leading edge velocity is calculated based on the leading edge propulsion velocity and the total velocity. The leading edge velocity formula is:

[0106]

[0107] in, is the front velocity, ΔP is the pressure difference between the injection pressure and the outlet pressure, ε1 and ε2 are the constant terms in the calculation formula of the pressure difference ΔP between the injection pressure and the outlet pressure, g is the acceleration of gravity, θ is the reservoir inclination, L is the reservoir length, and ρ o is the oil phase density, K is the absolute permeability, K ro is the relative permeability of the oil phase, μ o is the oil phase viscosity.

[0108] In one embodiment, the pressure difference ΔP between the injection pressure and the outlet pressure is calculated as follows:

[0109]

[0110] Among them, λ o is the oil phase mobility, λ NNf is the non-Newtonian fluid phase mobility, ρ NNf is the density of the non-Newtonian fluid phase.

[0111] In application, the flow separation function is solved using the characteristic line method, and the one-dimensional Berkeley-Levitra equation can be written as:

[0112]

[0113] Where: S NNf is the saturation of non-Newtonian fluid, dimensionless;

[0114] Φ is the porosity, dimensionless;

[0115] x is the distance in meters;

[0116] t is time, unit is s.

[0117] Saturation is a binary function of time and position, so the expression for saturation change can be written as:

[0118]

[0119] When x = 0, the saturation of the non-Newtonian fluid is constant, and the total differential of the saturation can be written as:

[0120]

[0121] From equations (12), (13) and (14), the leading edge propulsion speed can be obtained as:

[0122]

[0123] Integrating formula (15) yields:

[0124]

[0125] Where: f′ NNf is the derivative of the partial flow, dimensionless.

[0126] The integral of the total flow rate over time can be written as:

[0127] Q t =∫0 t V t (t)dt (17) Where: Q t It is the integral of total flow velocity over time, in m.

[0128] Since f′ NNf (S NNf ) is a monotonically increasing function, so formula (16) is transformed into:

[0129]

[0130] By using equations (17) and (18), we can get the leading edge position (xf )for:

[0131]

[0132] Where: x f is the position of the leading edge, in m;

[0133] S NNff is the front saturation of non-Newtonian fluid, dimensionless.

[0134] f′ NNf (S NNff ) is the derivative of the time-dimensioned flow rate of the non-Newtonian fluid front saturation, which is dimensionless.

[0135] From formula (7), the expression of pressure gradient can be written as:

[0136]

[0137] Where: P is the total pressure, unit is MPa.

[0138] Transform (20) from 0 to x f and x from x f By integrating the two parts up to L, the pressure difference between the injection pressure and the outlet pressure can be obtained as:

[0139]

[0140] Where: ΔP is the pressure difference between injection pressure and outlet pressure, unit: MPa;

[0141] L is the reservoir length, in m.

[0142] From formula (19), we can get:

[0143]

[0144] Where: f″ NNf (S NNff ) is the second derivative of the time-divisional flow rate of the non-Newtonian fluid front saturation, dimensionless;

[0145] S or is the residual oil saturation, dimensionless.

[0146] Before the leading edge, the saturation of the non-Newtonian fluid is the initial saturation, so λ NNf = 0, behind the leading edge (i.e. x f Solving the integral from (to part L), we can get:

[0147]

[0148] The integral terms in formula (23) are constants, which can be expressed as:

[0149]

[0150] Where: ε1 is the integral term in equation (23), unit: kg / ms;

[0151] ε2 is the integral term in equation (23), unit: kg / m 3 .

[0152] Known λ NNf =0, defined by formula (19) The value of V t Can be written as:

[0153]

[0154] From equations (15) and (25), the front velocity (the speed at which the isosaturation surface moves in the formation) can be obtained as:

[0155] The constant term in equation (26) is written as:

[0156]

[0157] Where: α1 is the constant term in equation (26), unit: kg / ms 2 ;

[0158] α2 is the constant term in formula (26), unit is kg / m 2 s;

[0159] β1 is the constant term in formula (26), unit is kg / ms 2 ;

[0160] β2 is the constant term in formula (26), unit is kg / s.

[0161] From equations (16) and (26), the implicit solution of the leading edge position related to saturation and time is:

[0162]

[0163] In one embodiment, the leading edge position is explicitly solved as:

[0164]

[0165] Where x is the distance, α1, α2, β1, and β2 are constants in the leading edge velocity formula, ξ is the input variable of the Lambert W function, W(ξ) is the solution that satisfies the Lambert W function, and f′ NNf (S NNf ) is the flow rate derivative related to the saturation of non-Newtonian fluid, f′NNf (S NNff ) is the derivative of the time-domain flow rate of the non-Newtonian fluid front saturation, ξ0 is the input variable of the Lambert W function at t = 0, W(ξ0) is the solution that satisfies the Lambert W function at t = 0, and t is time.

[0166] In application, using the terms in Equation (27), integrating Equation (26) from 0 to the leading edge position, we can obtain:

[0167]

[0168] Integrating formula (29) yields:

[0169]

[0170] At the time of breakthrough, the leading edge position (x f ) should be equal to the reservoir length (L), so the breakthrough time can be obtained from formula (30) as:

[0171]

[0172] Where: t BT is the leading edge breakthrough time, unit is h.

[0173] The Lambert W function is defined as:

[0174] ξ=W(ξ)×e W(ξ) (32)

[0175] Where: ξ is the input variable of Lambert W function, dimensionless;

[0176] W(ξ) is the solution that satisfies equation (32); it is dimensionless.

[0177] make:

[0178]

[0179] Substituting t in formula (30) into formula (33), formula (33) can be written as:

[0180]

[0181] Expressing equation (34) using the Lambert W equation, we can obtain W(ξ) as:

[0182]

[0183] According to formula (33), t can be expressed by ξ as:

[0184]

[0185] The leading edge position is written using the Lambert W function:

[0186]

[0187] Using the terms in equation (27) and replacing the leading edge position in equation (25) with equation (37), we can obtain V t (t) is:

[0188]

[0189] Position x when the water drive front breaks through f Equal to the reservoir length L, when t=0:

[0190]

[0191] Where: ξ0 is the input variable of the Lambert W function at t = 0, dimensionless;

[0192] W(ξ0) is the solution that satisfies equation (32) when t=0; it is dimensionless.

[0193] According to formula (38), formula (28) can be solved as follows:

[0194]

[0195] In one embodiment, the value of the Lambert W function is approximately estimated by combining the Winnitsky analytical solution function to explicitly calculate the leading edge position, including:

[0196] By formula Calculate the value of ξ and determine the range of ξ;

[0197] Based on the range of ξ, the approximate value of W(ξ) is calculated using the corresponding Winnitsky analytical solution function;

[0198] Substituting the approximate value of W(ξ) into the explicit solution of the leading edge position, the leading edge position x is calculated. f .

[0199] In the application, the approximate solution of W(ξ) in equation (40) is calculated using the method proposed by Winitsky, and the relative error is less than 10 -2 , with higher precision, is calculated as follows:

[0200]

[0201] The analytical function developed by Winicki to calculate the approximate value of W(ξ) is as follows:

[0202] When ξ∈(0,+∞),

[0203]

[0204] At this time, the relative error of the approximate solution of W(ξ) is less than 0.01.

[0205] when hour,

[0206]

[0207] At this time, the relative error of the approximate solution of W(ξ) is less than 0.001.

[0208] In the application, step S104 is specifically as follows:

[0209] Based on the analytical calculation results, the location of the non-Newtonian fluid displacement front under different apparent viscosities and reservoir inclinations can be determined. This can be done by estimating the Lambert W function using the Carreau model for different shear rate-dependent viscosities and the fractional flow function that includes the gravity number due to reservoir inclination. This function is then combined with the modified Berkeley-Levert equation to explicitly solve for the non-Newtonian fluid displacement front. Based on the solved non-Newtonian fluid displacement front, the shear viscosity at different shear rates, the breakthrough time under different reservoir inclinations, and the saturation distribution and temporal evolution of the front position are plotted.

[0210] In one embodiment, a mechanism model is established for the method proposed in the embodiment of the present application to verify the analytical solution model. The grid system of the established model is 100*1*1, DX is 1m, DY is 1m, and DZ is 20m. In order to verify the analysis results, the breakthrough of the numerical model at different times is simulated when the permeability is 160mD, the porosity is 0.186, and the reservoir dip is 30°. Please refer to Figure 2 , where the solid line is the analytical model solution calculation result, and the dotted line is the numerical simulation estimation result. The key parameters of the analytical solution model calculation are shown in Table 1:

[0211]

[0212]

[0213] Depend on Figure 2 The analytical solution and the numerical simulation results show a good fit. However, due to the discretization of the grid size, the numerical simulation results have a slight deviation at the shock front. The saturation distribution of the analytical solution is compared with the numerical simulation, verifying the correctness of the analytical solution model.

[0214] In a specific application, the method for determining the water flooding front of the present invention is described as follows:

[0215] Step S101: Figure 3As shown, the reservoir block data is sorted out to obtain the apparent viscosity of the non-Newtonian fluid. Through the processed phase permeability data and the required reservoir rock and fluid data, the flow equation considering the shear rate-related viscosity of the non-Newtonian fluid and the gravity number is obtained. The gravity acceleration is taken as 9.8m / s 2 , the oil phase viscosity is 13.083 mPa·s, and the density difference between the oil phase and the non-Newtonian fluid phase is 0.15. The fractional flow rate can be expressed as:

[0216]

[0217] The derivative of the calculated partial flow can be obtained by differentiating the partial flow, which is used for subsequent calculations.

[0218] Step S102: Figure 4 As shown, according to the reservoir displacement using non-Newtonian fluids with apparent viscosities of 0.6 mPa·s, 3 mPa·s, 6 mPa·s, 9 mPa·s, 12 mPa·s, and 16 mPa·s, the reservoir inclination θ is 30°. The corresponding parameters are substituted into the fractional flow equation solved by the characteristic line method. Combined with the expression of saturation change, the front advancement velocity is obtained. By integral solution, the implicit solution of the front position related to saturation and time at different apparent viscosities is obtained, and the change of displacement breakthrough time at different apparent viscosities is obtained.

[0219] Step S103: Figure 5 As shown in the figure, for reservoir inclinations of 30° and 60°, the front velocity is integrated based on the fractional flow rate results, and expressions for the Lambert W function calculation time and breakthrough time are introduced. The approximate solution of the Lambert W function is calculated using the method proposed by Winitsky. The explicit estimation of the front position is obtained. Combined with the expression for saturation change, the displacement saturation distribution profile corresponding to different reservoir inclinations at 6000 hours of displacement can be obtained.

[0220] Step S104: According to the above steps, the corresponding breakthrough time under different apparent viscosities and the saturation distribution curves at different reservoir inclinations at 6000h are obtained. Figure 4 It can be seen that with the increase of the apparent viscosity of the non-Newtonian fluid, the breakthrough time is prolonged and the macro displacement efficiency is increased. Figure 5 It can be seen that as the reservoir inclination increases, the front advance distance becomes shorter, resulting in a decrease in microscopic displacement efficiency. According to the calculated flow distribution when the gravity number is 0.1 and 0.5, the corresponding front position changes with time are obtained, see Figure 6 .Depend on Figure 6 It can be seen that as the gravity number increases, the breakthrough time decreases and the front edge advances faster. As the displacement progresses, when the fluid flow capacity increases, the front edge advances faster.

[0221] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0222] The present application also provides a device for calculating a non-Newtonian fluid displacement front taking into account gravity, configured to execute the steps of the aforementioned method for calculating a non-Newtonian fluid displacement front taking into account gravity. The device for calculating a non-Newtonian fluid displacement front taking into account gravity can be a virtual appliance within an electronic device, executed by a processor within the electronic device, or can be the electronic device itself.

[0223] like Figure 7 As shown, the non-Newtonian fluid displacement front calculation device 100 considering gravity provided in an embodiment of the present application includes:

[0224] a first calculation unit for establishing a partial flow equation considering the shear rate-dependent viscosity and gravity number of the non-Newtonian fluid;

[0225] a second calculation unit, configured to calculate the flow separation equation using a characteristic line method to obtain a Berkeley-Levert expansion equation, and obtain an implicit solution for the leading edge position by integral transformation;

[0226] a third calculation unit, configured to calculate an explicit solution of the leading edge position using a Lambert W function, and to perform an approximate estimation of a value of the Lambert W function in combination with a Winnitsky analytical solution function, to calculate a value of the leading edge position;

[0227] The fourth calculation unit is used to determine the front position of non-Newtonian fluid displacement under different apparent viscosities and different reservoir inclinations based on the calculation results of the analytical solution.

[0228] In applications, each module in the non-Newtonian fluid displacement front calculation device considering gravity can be a software program module, or can be implemented by different logic circuits integrated in a processor, or can be implemented by multiple distributed processors.

[0229] like Figure 8 As shown, the embodiment of the present application further provides an electronic device 200, including: at least one processor 201 ( Figure 8 Only one processor is shown in the figure), a memory 202, and a computer program 203 stored in the memory 202 and executable on at least one processor 201. When the processor 201 executes the computer program 203, the steps in the above-mentioned various method embodiments are implemented.

[0230] In applications, electronic devices may include, but are not limited to, processors and memories. Those skilled in the art will appreciate that Figure 8 The electronic device is merely an example and does not limit the electronic device. The electronic device may include more or fewer components than shown in the figure, or may include a combination of certain components or different components.

[0231] In applications, the processor may be a central processing unit (CPU), other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor, etc.

[0232] In applications, in some embodiments, the memory can be an internal storage unit of an electronic device, such as a hard disk or memory of the electronic device. In other embodiments, the memory can also be an external storage device of the electronic device, such as a plug-in hard disk equipped on the electronic device, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card, etc. Furthermore, the memory can also include both an internal storage unit of the electronic device and an external storage device. The memory is used to store an operating system, application programs, a boot loader (BootLoader), data, and other programs, such as the program code of a computer program. The memory can also be used to temporarily store data that has been output or is about to be output.

[0233] It should be noted that the information interaction, execution process, etc. between the above-mentioned devices / units are based on the same concept as the method embodiment of this application. Their specific functions and technical effects can be found in the method embodiment section and will not be repeated here.

[0234] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In actual applications, the above-mentioned functions can be distributed and completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated into one processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, and will not be repeated here.

[0235] An embodiment of the present application further provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments can be implemented.

[0236] An embodiment of the present application provides a computer program product, including a computer program. When the computer program product runs on an electronic device, the electronic device can implement the steps in the above-mentioned various method embodiments when executing the computer program product.

[0237] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the processes in the above-mentioned embodiment method, which can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and when the computer program is executed by the processor, it can implement the steps of the above-mentioned various method embodiments. Among them, the computer program includes computer program code, which can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may at least include: any entity or device that can carry the computer program code to the device / electronic device, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electric carrier signal, a telecommunication signal and a software distribution medium. For example, a USB flash drive, a mobile hard disk, a magnetic disk or an optical disk. In some jurisdictions, according to legislation and patent practice, a computer-readable medium cannot be an electric carrier signal or a telecommunication signal.

[0238] In the above embodiments, the description of each embodiment has its own focus. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant description of other embodiments.

[0239] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0240] In the embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of modules or units is only a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0241] Units described as separate components may or may not be physically separate, and components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0242] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A method for calculating the displacement front of a non-Newtonian fluid considering gravity, characterized in that: include: Establish a partial flow equation that considers the shear rate-dependent viscosity and gravity number of non-Newtonian fluids; The flow split equation is calculated using a characteristic line method to obtain a Berkeley-Levert expanded equation, and an implicit solution of the leading edge position is obtained through integral transformation; The nonlinear equation for calculating the leading edge position is calculated using the Lambert W function, and the value of the Lambert W function is approximately estimated in combination with the Winnitsky analytical solution function to explicitly calculate the leading edge position; Based on the results of analytical solution, the front position of non-Newtonian fluid displacement under different apparent viscosities and reservoir inclinations is determined.

2. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 1, characterized in that: The flow rate equation considering the viscosity and gravity number related to the shear rate of non-Newtonian fluid is: Among them, N G is the gravity number, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, S NNf is the saturation of non-Newtonian fluid, and M is the mobility ratio of the non-Newtonian fluid phase to the oil phase.

3. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 1, characterized in that: The partial flow equation considering the viscosity and gravity number related to the shear rate of the non-Newtonian fluid is calculated based on the partial flow equation considering the viscosity and reservoir inclination related to the shear rate of the non-Newtonian fluid and the gravity number; The flow rate equation considering the non-Newtonian fluid shear rate-dependent viscosity and reservoir inclination is: The calculation formula of the gravity number is: Among them, N G is the gravity number, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, S NNf is the saturation of non-Newtonian fluid, M is the mobility ratio of non-Newtonian fluid phase and oil phase, V NNf is the phase velocity of the non-Newtonian fluid, V t is the total velocity, Δρ is the density difference between the oil phase and the non-Newtonian fluid phase, K is the absolute permeability, K ro is the relative permeability of the oil phase, μ o is the oil phase viscosity, θ is the reservoir inclination, P is the total pressure, and g is the acceleration of gravity.

4. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 1, characterized in that: The Berkeley-Levert expanded equation obtained by calculating the flow split equation using the characteristic line method is: Among them, S NNf is the saturation of non-Newtonian fluid, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, Φ is the porosity, x is the distance, and t is the time.

5. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 1, wherein: The nonlinear equation for calculating the implicit solution of the leading edge position is: Among them, S NNf is the saturation of non-Newtonian fluid, x is the distance, t is the time, f′ NNf (S NNf ) is the flow rate derivative related to the saturation of non-Newtonian fluid, f′ NNf (S NNff ) is the derivative of the time-division flow rate of the non-Newtonian fluid front saturation, f′ NNf is the derivative of the fractional flow, φ is the porosity, V t (t) is the total flow rate, f NNf is the fractional flow of the non-Newtonian fluid phase in the fluid, x f is the leading edge position, and α1, α2, β1, and β2 are constant terms in the leading edge velocity formula.

6. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 5, characterized in that: The leading edge speed is calculated based on the leading edge propulsion speed and the total speed. The leading edge speed formula is: in, is the front velocity, ΔP is the pressure difference between the injection pressure and the outlet pressure, ε1 and ε2 are the constant terms in the calculation formula of the pressure difference ΔP between the injection pressure and the outlet pressure, g is the acceleration of gravity, θ is the reservoir inclination, L is the reservoir length, ρ o is the oil phase density, K is the absolute permeability, K ro is the relative permeability of the oil phase, μ o is the oil phase viscosity.

7. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 6, characterized in that: The calculation formula for the pressure difference ΔP between the injection pressure and the outlet pressure is: Among them, λ o is the oil phase mobility, λ NNf is the non-Newtonian fluid phase mobility, ρ NNf is the density of the non-Newtonian fluid phase.

8. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 1, characterized in that: The explicit solution for the leading edge position is: Where x is the distance, α1, α2, β1, and β2 are constants in the leading edge velocity formula, ξ is the input variable of the Lambert W function, W(ξ) is the solution that satisfies the Lambert W function, and f′ NNf (S NNf ) is the flow rate derivative related to the saturation of non-Newtonian fluid, f′ NNf (S NNff ) is the derivative of the time-domain flow rate of the non-Newtonian fluid front saturation, ξ0 is the input variable of the Lambert W function at t = 0, W(ξ0) is the solution that satisfies the Lambert W function at t = 0, and t is time.

9. The method for calculating the displacement front of a non-Newtonian fluid considering gravity according to claim 8, characterized in that: The method of approximating the value of the Lambert W function by combining the Winnitsky analytical solution function and explicitly calculating the leading edge position includes: By formula Calculate the value of ξ and determine the range of ξ; Based on the range of ξ, the approximate value of W(ξ) is calculated using the corresponding Winnitsky analytical solution function; Substitute the approximate value of W(ξ) into the explicit solution of the leading edge position to calculate the leading edge position x f .

10. An electronic device, characterized in that: The electronic device comprises a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the electronic device implements the method according to any one of claims 1 to 9.

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