A numerical simulation method for calculating the effective viscosity of polymers under high temperature conditions

Abstract

The present invention relates to numerical simulation of oil reservoirs, and in particular to a numerical simulation method for calculating the effective viscosity of polymers under high temperature conditions. The method comprises: step 1. performing a thermal degradation experiment on a polymer, and fitting a first-order degradation equation according to the experimental results; step 2. establishing a polymer effective concentration decay equation, and determining the decay coefficient of the polymer effective concentration; step 3. establishing a polymer effective concentration equation; step 4. solving the equation in step 3 to obtain the effective concentration of the polymer, and performing interpolation calculation according to the effective concentration and the polymer concentration-viscosity relationship curve data obtained by the test. The present invention comprehensively reflects the influence of high-temperature thermal degradation on polymer viscosity under the combined action of static and flow states by establishing a polymer effective concentration equation. All parameters and data can be obtained by indoor experiments. The equation conforms to basic physical laws and is easy to solve, and can be accurately and quickly applied to oil reservoir numerical simulation software.

Description

Technical Field

[0001] The invention relates to numerical simulation of oil reservoirs, and in particular to a numerical simulation method for calculating effective viscosity of polymers under high temperature conditions. Background Art

[0002] Polymer flooding is one of the leading technologies for chemical flooding to enhance oil recovery in my country, and is the most mature and effective among various tertiary oil recovery technologies. The main mechanism of polymer flooding technology is to add high-viscosity polymers to the water injected into the reservoir to increase the viscosity of the displacement phase, reduce the mobility ratio of the displacement fluid to the displaced fluid, and thus expand the swept volume. A considerable portion of the oil reservoirs in my country where polymer flooding is carried out are high-temperature and high-salinity reservoirs with temperatures above 75°C, such as Shengli Oilfield and Henan Oilfield. After the polymer is injected into the oil layer, it will undergo thermal degradation under high temperature conditions. This degradation will cause the polymer molecular chain to break and degrade into a small molecular structure, resulting in a decrease in the viscosity of the polymer solution.

[0003] Lu Xiangan, Jiang Hanqiao, Li Junjian, Zhao Lin and others established a partial differential description equation for polymer viscosity change for numerical simulation of polymer thermal stability, and simulated the thermal degradation process of polymer in reservoir flow ([1] Lu Xiangan, Jiang Hanqiao, Luo Hongxia, et al. Numerical simulation of polymer thermal degradation based on viscosity correction model [J]. Daqing Petroleum Geology and Development, 2015, 34(6): 95-99. [2] Li Junjian, Jiang Hanqiao, Lu Xiangan, et al. New exploration of mathematical model of polymer solution aging under reservoir conditions [J]. Petroleum Drilling and Production Technology, 2016, 38(4): 499-544.)

[0004] Lin Chunyang, Zhang Xiansong, Liu Huiqing and others proposed the concept of "time flux" for the numerical simulation of polymer thermal stability, and established a numerical reservoir model that takes into account the effect of polymer aging. The main idea is to determine the equivalent aging time of mixed polymers in the grid of reservoir numerical simulation. ([3] Lin Chunyang, Zhang Xiansong, Liu Huiqing. Research on numerical model of polymer solution aging effect [J]. Journal of Oil and Gas, 2012, 34(12): 143-147. [4] Lin Chunyang, Xue Xinsheng, Zhu Yuejun, et al. Aging law and application of polymer solution under reservoir flow conditions [J]. Petroleum Geology and Recovery, 2013, 20(1): 77-80.).

[0005] In the mathematical model description of reservoir numerical simulation software, in addition to the shear effect during the flow process, the change in polymer viscosity is generally reflected by the change in polymer concentration. However, during high-temperature degradation, the concentration of the polymer does not change, but only degrades from large molecules to small molecules. Conventional reservoir numerical simulation models do not consider the influence of temperature. Therefore, the current reservoir numerical simulation software cannot reflect the thermal degradation mechanism of the polymer, and thus cannot accurately calculate the effective viscosity of the polymer under high temperature conditions in the reservoir. As a result, the prediction indicators of the scheme based on the numerical simulation calculation results are more optimistic than the actual situation, which makes it difficult to form effective guidance for the actual development of the mine.

[0006] Some of the previously published relevant literature either focuses on the study of the static thermal stability of polymers under high temperature conditions, where the viscosity changes with time, without considering the complex effects of polymer flow and diffusion under reservoir conditions, especially the effects of polymer inflow, outflow and thermal degradation at different times in the numerical simulation grid on the viscosity of the polymer mixture in the grid; or adopts some equivalent models that do not satisfy the conservation law or cannot be verified by experiments, which are difficult to be effectively implemented in numerical simulation software. For example, the convection-diffusion equation of viscosity established in literature [1-2] does not satisfy the physical conservation law, and its physical meaning needs further demonstration. The conservation of the total amount of aging time in literature [3-4] is difficult to be verified by experiments. Summary of the invention

[0007] The main purpose of the present invention is to provide a numerical simulation method for calculating the effective viscosity of a polymer under high temperature conditions. The method of the present invention solves the problem of not only considering the change in thermal stability of the polymer under a high temperature static state, but also reflecting the change in viscosity at different times and positions of the polymer under a flowing state. At the same time, the mathematical model satisfies the law of conservation of mass, and relevant parameters can be obtained through indoor experimental test results, which is easy to implement in existing reservoir numerical simulation software.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] The present invention provides a numerical simulation method for calculating the effective viscosity of a polymer under high temperature conditions, the method comprising:

[0010] Step 1. Conduct a thermal degradation experiment on the polymer and obtain a first-order degradation equation based on the experimental results;

[0011] Step 2. Establish a polymer effective concentration decay equation and determine the decay coefficient of the polymer effective concentration;

[0012] Step 3. Establishing the polymer effective concentration equation;

[0013] Step 4. Solve the equation in step 3 to obtain the effective concentration of the polymer, and perform interpolation calculation based on the effective concentration and the polymer concentration-viscosity relationship curve data obtained from the test.

[0014] Preferably, in step 1, the polymer is placed in a high temperature environment indoors, the viscosity of the polymer is measured at different time periods, a time-viscosity curve of the polymer solution is plotted, a first-order thermal degradation equation of the polymer viscosity is obtained by curve regression, and the thermal degradation coefficient of the viscosity is determined.

[0015] Further preferably, the first-order thermal degradation equation of polymer viscosity can be expressed as:

[0016]

[0017] Preferably, the analytical solution of equation (1) is expressed as:

[0018]

[0019] Where μ represents the viscosity of the polymer solution, μ0 represents the viscosity of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, and λ represents the thermal degradation coefficient of the polymer.

[0020] Preferably, in step 2, the polymer concentration-viscosity relationship curve and the viscosity degradation equation in step 1 are obtained based on indoor experimental tests, the viscosity change caused by thermal degradation of the polymer is equivalent to the attenuation of the effective concentration of the polymer, and the decay equation and decay coefficient of the effective concentration of the polymer are determined.

[0021] Further preferably, the effective concentration decay equation of the polymer solution can be expressed as:

[0022]

[0023] The analytical solution of equation (3) is expressed as:

[0024]

[0025] Among them C p represents the effective concentration of the polymer solution, C p0 represents the concentration of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, λ p The decay coefficient representing the effective concentration of the polymer.

[0026] Preferably, in step 3, a polymer effective concentration equation is established in the following form:

[0027]

[0028] Where φ represents the porosity, ρ pDenotes the density of the polymer, D p is the diffusion coefficient, v w represents the flow rate of the water phase, Q p It is the source and sink term.

[0029] Preferably, the equation in step 3 is solved using a finite difference algorithm to obtain the effective concentration of the polymer at each time and each spatial position, and then interpolation calculations are performed based on this effective concentration and the polymer concentration-viscosity curve data obtained from the indoor experimental test in step 2 to obtain the effective viscosity after polymer flow, diffusion and high-temperature thermal degradation.

[0030] The numerical simulation method for calculating the effective viscosity of polymer under high temperature conditions in the present invention not only takes into account the variation law of polymer viscosity over time in a static state, but also takes into account the composite influence of the flow and diffusion of polymer at different times and spatial positions on the viscosity of polymer solution. At the same time, the original polymer concentration calculation result is not changed, and only a polymer effective concentration equation is added to reflect the influence of various comprehensive factors on the effective viscosity of polymer. In addition, all formula parameters or data can be obtained by regression or interpolation of indoor experimental test data. The polymer effective concentration equation is a common convection-diffusion equation in chemical flooding numerical simulation, and can be calculated by applying mature solution methods. It has good technical application prospects and supporting role for quickly realizing corresponding simulation functions in existing reservoir numerical simulation software, effectively supporting the prediction of development effects and the optimization of development plans.

[0031] Compared with the prior art, the present invention has the following excellent effects:

[0032] The present invention establishes a polymer effective concentration equation to comprehensively reflect the influence of high-temperature thermal degradation on polymer viscosity under the combined action of static and flow states. All parameters and data can be obtained from indoor experiments. The equation conforms to basic physical laws and is easy to solve. It can be accurately and quickly applied to reservoir numerical simulation software. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0034] Figure 1 is a graph showing the change of polymer viscosity with thermal degradation time in a specific embodiment of the present invention;

[0035] Figure 2 is a polymer concentration-viscosity experimental test curve diagram in a specific embodiment of the present invention;

[0036] Figure 3is a graph of the decay curve of the effective concentration of a polymer in a specific embodiment of the present invention;

[0037] Figure 4 It is a comparison diagram of the influence of different polymer thermal degradation coefficients on chemical flooding simulation results in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0038] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0039] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations and / or combinations thereof.

[0040] In order to enable those skilled in the art to more clearly understand the technical solution of the present invention, the technical solution of the present invention will be described in detail below in conjunction with specific embodiments.

[0041] Terminology explanation:

[0042] Effective polymer concentration: After thermal degradation, the actual concentration of the polymer solution does not change. The change in viscosity is due to the high temperature causing the polymer molecular weight to decrease. Therefore, it can be equivalently regarded as a change in the effective components of the polymer that affect the viscosity of the solution. The concentration of this effective component of the polymer is called the effective polymer concentration.

[0043] Embodiment A numerical simulation method for calculating the effective viscosity of a polymer under high temperature conditions

[0044] The method comprises:

[0045] Step 1. Conduct a thermal degradation experiment on the polymer and fit the first-order degradation equation based on the experimental results: place the polymer in a high-temperature environment indoors, measure the viscosity of the polymer at different time periods, draw a time-viscosity curve of the polymer solution, obtain the first-order thermal degradation equation of the polymer viscosity through curve regression, and determine the thermal degradation coefficient of the viscosity.

[0046] The first-order thermal degradation equation of polymer viscosity can be expressed as:

[0047]

[0048] The analytical solution of equation (1) is expressed as:

[0049]

[0050] Where μ represents the viscosity of the polymer solution, μ0 represents the viscosity of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, and λ represents the thermal degradation coefficient of the polymer. Figure 1 is the curve of polymer viscosity changing with thermal degradation time. Figure 1 The results show that the thermal degradation coefficient of the viscosity of the polymer at 85°C is 0.011.

[0051] Step 2. Establish a decay equation for the effective concentration of the polymer and determine the decay coefficient of the effective concentration of the polymer: Based on the polymer concentration-viscosity relationship curve obtained from indoor experimental tests and the viscosity degradation equation in step 1, the viscosity change caused by thermal degradation of the polymer is equivalent to the attenuation of the effective concentration of the polymer, and the decay equation and decay coefficient of the effective concentration of the polymer are determined.

[0052] The effective concentration decay equation of polymer solution can be expressed as:

[0053]

[0054] The analytical solution of equation (3) is expressed as:

[0055]

[0056] Among them C p represents the effective concentration of the polymer solution, C p0 represents the concentration of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, λ p Decay coefficient representing the effective concentration of the polymer.

[0057] Step 3. Establishing the polymer effective concentration equation: Combining the polymer effective concentration decay equation (3) in step 2 with the law of conservation of mass, establish the polymer effective concentration equation in the following form:

[0058]

[0059] Where φ represents the porosity, ρ p Denotes the density of the polymer, D p is the diffusion coefficient, v w represents the flow rate of the water phase, Q p It is the source and sink term.

[0060] Figure 2 It is the polymer concentration-viscosity experimental test curve, according to Figure 1 and Figure 2 The decay curve of the effective concentration of the polymer over time can be obtained by two-dimensional interpolation, such as Figure 3, and can be based on Figure 3 The decay equation of the effective concentration of the polymer is regressed out from the data points, Figure 3 It can be seen that the decay coefficient of the effective concentration of the polymer is 0.009.

[0061] Step 4. Use the finite difference algorithm to solve equation (5) in step 3 to obtain the effective concentration of the polymer at each time and each spatial position. Then, based on this effective concentration and the polymer concentration-viscosity curve data obtained from the indoor experimental test in step 2, interpolation calculation is performed to obtain the effective viscosity after polymer flow, diffusion and high-temperature thermal degradation.

[0062] A reservoir conceptual model was established, with a grid step size of 5m×5m×5m in the x, y, and z directions and a grid size of 20×20×1. The plane permeability is 2μm 2 There are two wells, one for injection and one for production. Well I1 is a quantitative injection well with a grid coordinate of (1,1) and a daily injection volume of 20m 3 Well P1 is a fixed-liquid production well, with grid coordinates of (20,20) and an injection-production ratio of 1:1. The simulation time is 3000 days, and the injection slug is set as follows: from 1650 days to 2000 days, a polymer with a concentration of 1000 mg / L and a surfactant with a concentration of 0.2% are injected, and water flooding is used for the rest of the time.

[0063] Figure 4 The numerical simulation results corresponding to the thermal degradation coefficients of different polymer viscosities calculated based on the conceptual model are shown below. Under the conditions where the thermal degradation coefficients of polymer viscosities are 0, 0.0012, and 0.011, respectively, the width and depth of the funnel containing water are quite different. At this time, according to the method in step 2, the corresponding polymer effective concentration decay coefficients can be obtained to be 0, 0.001, and 0.009, respectively. Figure 4 It can be seen that the larger the polymer viscosity thermal degradation coefficient, the smaller the width and depth of the comprehensive water-containing funnel, especially when the polymer thermal degradation reaches Figure 1 When the degradation coefficient is 0.011, the viscosity of the polymer decreases rapidly in about 90 days. In addition, various shearing effects on the polymer in the wellbore and reservoir show that this type of polymer can hardly be used for oil recovery in numerical simulations. This shows that this method can effectively reflect the effect of thermal degradation of polymers under high temperature conditions on the viscosity of the displacement phase, thereby effectively reflecting the effect of high-temperature thermal degradation on oil recovery effects and oil recovery indicators, and can provide necessary technical means for the prediction and optimization of development plans, and even for the evaluation and screening of polymer properties.

[0064] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A numerical simulation method for calculating the effective viscosity of a polymer under high temperature conditions, characterized in that: The method comprises: Step 1: Performing a thermal degradation experiment on the polymer, and fitting a first-order degradation equation of the polymer viscosity according to the experimental results; Step 2: Establishing a polymer effective concentration decay equation and determining a polymer effective concentration decay coefficient; Step 3: Establishing the polymer effective concentration equation; Step 4: Solving the equation in step 3 to obtain the effective concentration of the polymer, and interpolating the effective concentration and the polymer concentration-viscosity relationship curve data obtained from indoor experimental tests to obtain the effective viscosity after the polymer flows, diffuses and undergoes high-temperature thermal degradation; In step 1, the polymer is placed in a high temperature environment indoors, the viscosity of the polymer is measured at different time periods, a time-viscosity curve of the polymer solution is plotted, a first-order thermal degradation equation of the polymer viscosity is obtained by curve regression, and a thermal degradation coefficient of the viscosity is determined; The first-order thermal degradation equation for polymer viscosity is expressed as: The analytical solution of equation (1) is expressed as: Where μ represents the viscosity of the polymer solution, μ0 represents the viscosity of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, and λ represents the thermal degradation coefficient of the polymer; In step 2, based on the polymer concentration-viscosity relationship curve obtained from indoor experimental tests and the first-order degradation equation of polymer viscosity in step 1, the viscosity change caused by polymer thermal degradation is equivalent to the attenuation of polymer effective concentration, and the decay equation and decay coefficient of polymer effective concentration are determined; The effective concentration decay equation of the polymer solution is expressed as: The analytical solution of equation (3) is expressed as: Among them C p represents the effective concentration of the polymer solution, C p0 represents the concentration of the polymer solution at the initial moment, t represents time, t0 represents the time at the initial moment, λ p The decay coefficient representing the effective concentration of the polymer; According to the polymer effective concentration decay equation in step 2 and the law of conservation of mass, the polymer effective concentration equation is established in the following form: Where φ represents the porosity, ρ p Denotes the density of the polymer, D p is the diffusion coefficient, v w represents the flow rate of the water phase, Q p It is the source and sink term.

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