A method for predicting the interfacial tension of CO2-crude oil-formation water system based on ACE theory

Abstract

The present invention provides a method for predicting the interfacial tension of a CO2-crude oil-formation water system based on ACE theory, comprising: step 1, analyzing the influencing factors affecting the interfacial tension of the CO2-formation water system; step 2, analyzing the correlation of the parameters affecting the interfacial tension of the CO2-formation water system; step 3, establishing a calculation model for predicting the interfacial tension of the CO2-formation water system using the ACE model; step 4, verifying and evaluating the calculation model for predicting the interfacial tension of the CO2-formation water system; step 5, establishing an isotonic volume correction model for the equilibrium interfacial tension of the CO2-crude oil system; step 6, verifying and evaluating the isotonic volume correction model for the equilibrium interfacial tension of the CO2-crude oil system. The method analyzes the relationship between the interfacial tension of the CO2-crude oil system and the density difference between the two phases, and improves the isotonic volume model for predicting the interfacial tension of the CO2-crude oil.

Description

Technical Field

[0001] The present invention relates to the technical field of oilfield development, and in particular to a method for predicting the interfacial tension of a CO2-crude oil-formation water system based on ACE theory. Background Art

[0002] Since the last century, rapid economic development and the resulting surge in demand for fossil fuels have led to a gradual increase in atmospheric concentrations of greenhouse gases such as CO2. Large amounts of CO2 emissions are causing global warming, posing a threat to human survival and socioeconomic development. As one of the most valuable areas of CO2 research, tertiary oil recovery (TER) through CO2 flooding in oil fields not only improves crude oil recovery and stores CO2, but also aligns with national energy conservation and emission reduction policies, achieving both economic and environmental benefits. In EOR (Energy Recovery), CO2 is injected into the oil reservoir as an oilfield injection agent, increasing the reservoir's permeability and reducing crude oil viscosity. Compared to conventional water flooding, EOR can increase oil recovery by 10% to 15%, boosting global oil production by 50%.

[0003] The CO2 flooding process is generally divided into immiscible and miscible flooding. During immiscible flooding, the injected gas interacts with the reservoir fluid, reducing the viscosity of the crude oil, expanding its volume, improving the mobility ratio between the displacing and displaced phases, and reducing interfacial tension, thereby increasing the capillary number, reducing residual oil saturation, and enhancing oil recovery. In miscible flooding, the interfacial tension between the injected gas and the crude oil is zero, the capillary number increases to infinity, and a miscible phase forms between the displacing and displaced phases, achieving optimal displacement. Clearly, during CO2 flooding, the interfacial interactions between reservoir fluids and between reservoir fluids and rock control the flow characteristics of the formation fluid during CO2 flooding and influence the ultimate oil recovery.

[0004] However, there is currently little research on the interfacial tension data and influencing factors of the supercritical CO2-crude oil-formation water system under high temperature and high pressure conditions. At the same time, there are few prediction models for the interfacial tension of the supercritical CO2-crude oil-formation water system, and most models are only empirical relationships with poor portability. Therefore, studying the influence of supercritical CO2 on crude oil properties and providing corresponding quantitative relationships is of great significance for my country's current efficient utilization of CO2 for oil recovery and achieving the organic unity of the social benefits of CO2 emission reduction and the economic benefits of increased recovery.

[0005] In the Chinese patent application with application number 201911397801.5, a method for calculating the solid deformation interface taking into account the surface tension of the liquid is involved. This invention provides a method for calculating the solid deformation interface taking into account the surface tension of the liquid, directly considering the displacement-surface force decoupling numerical method, using cubic spline curves to fit the discrete points of the fluid-solid boundary surface in the finite element model, calculating the curvature of each point, and obtaining the overall curvature data of the liquid-solid interface, solving the fluid-solid coupling load problem with surface tension. Compared with the present invention, this patent does not involve the calculation formula of the interfacial tension between CO2 and liquid, and only considers the calculation formula of the interfacial tension between liquid and solid.

[0006] In the Chinese patent application with application number 201610566723.7, an oil-gas interfacial tension measuring device based on the hanging drop method is involved. This invention controls the volume of the oil droplet injection through the pressure difference injection of the crude oil supply unit, so that a stable droplet is formed at the probe, thereby achieving the purpose of quantitative and stable injection. The pre-filled oil and gas balance method is adopted to make the experimental conditions and the formation conditions closer, so that the interfacial tension test results closer to the formation conditions can be obtained. Compared with this patent, the operation is simple and easy to observe. However, it is easily affected by the environment. When the temperature and pressure of the system change, the lighter components in the crude oil will evaporate into the high-temperature and high-pressure hanging drop chamber, resulting in a gas-liquid phase change process, which affects the continued observation of the hanging drop during the experiment and the accuracy of the experimental results.

[0007] Chinese patent application number CN201110312917.1 describes a device and method for measuring the variation of oil-water interfacial tension during CO2 flooding, a method used in oil and gas field development. The method first measures the oil-water interfacial tension at different pressures during water flooding. Then, maintaining reservoir conditions, the method switches to CO2 flooding. The oil-water interfacial tension at different pressures during CO2 flooding is then measured. Finally, the two measured oil-water interfacial tensions are compared to determine the variation of oil-water interfacial tension during CO2 injection. Compared to this patent, this patent better simulates real-world mine operations. However, it primarily explores the relationship between pressure and oil-water interfacial tension, and other factors that significantly influence the process are not considered.

[0008] The above existing technologies are significantly different from the present invention and fail to solve the technical problems we want to solve. To this end, we have invented a new method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory, which solves the above technical problems. Summary of the Invention

[0009] The purpose of the present invention is to provide a CO2-formation water interfacial tension model that comprehensively considers formation pressure, temperature, formation water salinity and injected gas composition, and to establish a CO2-crude oil-formation water system interfacial tension prediction method based on ACE theory.

[0010] The object of the present invention can be achieved by the following technical measures: a method for predicting the interfacial tension of the CO2-crude oil-formation water system is established based on the ACE theory, and the method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory includes:

[0011] Step 1: Analyze the factors affecting the interfacial tension of the CO2-formation water system;

[0012] Step 2: Analyze the correlation of parameters affecting the interfacial tension of the CO2-formation water system;

[0013] Step 3: Using the ACE model, a calculation model for predicting the interfacial tension of the CO2-formation water system is established;

[0014] Step 4: Verify and evaluate the calculation model for predicting the interfacial tension of the CO2-formation water system;

[0015] Step 5, establishing an isotonic volume correction model for the equilibrium interfacial tension of the CO2-crude oil system;

[0016] Step 6: Verify and evaluate the isotonic volume correction model of the equilibrium interfacial tension of the CO2-crude oil system.

[0017] The purpose of the present invention can also be achieved by the following technical measures:

[0018] In step 1, the factors affecting the interfacial tension of the CO2-formation water system include pressure, temperature, salinity of the formation water, and the composition of the injected CO2 gas.

[0019] In step 1, the interfacial tension data is screened based on the above-mentioned influencing factors, and the screening criteria are:

[0020] (1) All interfacial tension values ​​of CO2-formation water systems were measured using the dynamic pendant drop method;

[0021] (2) The interfacial tension value measured experimentally is the equilibrium interfacial tension value after the CO2-formation water system reaches equilibrium;

[0022] (3) The interfacial tensions of the CO2-formation water system measured experimentally are independent of each other.

[0023] In step 2, the factors that affect the interfacial tension of the CO2-formation water system are: reservoir pressure, reservoir temperature, concentration of monovalent cations in formation water (Na + +K +), divalent cation concentration in formation water (Ca 2+ +Mg 2+ ), N2 mole fraction and CH4 mole fraction in the injected gas.

[0024] In step 2, the Spearman correlation coefficient was used to analyze the correlation between the influencing factors and the interfacial tension. It was found that except for the negative correlation between reservoir pressure and interfacial tension, the other parameters were all positively correlated with the interfacial tension; and the reservoir pressure had the greatest impact on the interfacial tension; the order of influence of other parameters on the interfacial tension of the CO2-formation water system was: divalent cation concentration > CH4 mole fraction > N2 mole fraction > monovalent cation concentration > reservoir temperature.

[0025] In step 3, the ACE model is used to establish the basic relationship for predicting the interfacial tension of the CO2-formation water system as follows:

[0026]

[0027] Where, σ is the interfacial tension of CO2-formation water system, mN / m; p is the reservoir pressure, MPa; T is the reservoir temperature, °C; x(N2) is the mole fraction of N2 in the injected gas, mol%; x(CH4) is the mole fraction of CH4, mol%; y(Na + +K + ) is Na in formation water + and K + Equivalent monovalent cation content, mol / kg; y(Ca 2+ +Mg 2+ ) is Ca in formation water 2+ +Mg 2+ Equal divalent cation content mol / kg; θ is a function of the causal variable σ; is the original independent variable X i function.

[0028] In step 3, the inverse transformation of equation (8) is performed to obtain the calculation model for predicting the interfacial tension of the CO2-formation water system:

[0029]

[0030] In step 4, the accuracy of the prediction results is analyzed using the relative error ARE, average relative error AARE, and standard deviation SD indicators to verify the model:

[0031]

[0032]

[0033]

[0034] Where, ρ oil and ρ co2 is the density of the oil layer and carbon dioxide.

[0035] In step 4, in order to further verify the accuracy of the model prediction, the calculation model for predicting the interfacial tension of the CO2-formation water system is compared with the existing prediction relationship to verify the prediction accuracy of the model.

[0036] In step 4, multiple groups of CO2-formation water system interfacial tension values ​​are used as verification data, and the interfacial tension value of the system is calculated using the prediction model for the interfacial tension of the CO2-formation water system to verify the experimental data.

[0037] In step 5, the isotonic volume correction model for calculating the equilibrium interfacial tension of the CO2-crude oil system is:

[0038]

[0039] The modified isotonic volume model is mainly divided into two parts. The first part is the equilibrium value σ0 to which the equilibrium interfacial tension gradually approaches when the system pressure is high; the second part is the isotonic volume model of a single pure substance; ρ oil and ρ co2 is the density of the oil layer and carbon dioxide.

[0040] In step 6, the CO2-crude oil interfacial tension value is predicted using the improved isotonic volume correction model of the CO2-crude oil system equilibrium interfacial tension, and the predicted value is compared with the experimental value to verify the model.

[0041] In step 6, in order to further verify the accuracy of the model prediction, the isotonic volume correction model of the equilibrium interfacial tension of the CO2-crude oil system is compared with the existing prediction relationship to verify the prediction accuracy of the model.

[0042] Existing methods for predicting the interfacial tension of CO2-crude oil-formation water systems consider few influencing factors, and some interfacial tension prediction models are only applicable to specific experimental temperatures. However, the interfacial tension prediction model for the CO2-crude oil-formation water system based on the ACE algorithm takes into account reservoir pressure, reservoir temperature, and the concentration of monovalent cations in formation water (Na + +K + ), divalent cation concentration in formation water (Ca 2+ +Mg 2+), the influence of the N2 mole fraction and CH4 mole fraction in the injected gas on the interfacial tension, and as the influencing factors increase, the accuracy of the interfacial tension prediction model is higher. At the same time, the interfacial tension model established based on the ACE algorithm can solve the nonlinear problem between the influencing factors and the interfacial tension, and there is no need to pre-assume the relationship function between the influencing factors and the interfacial tension. Therefore, the CO2-formation water interfacial tension model established based on the ACE algorithm has high calculation accuracy, a wide range of applications, and a small absolute error in the predicted value. The present invention uses the CO2-formation water interfacial tension model established by ACE theory, which comprehensively considers formation pressure, temperature, formation water salinity and injected gas composition, to analyze the relationship between the interfacial tension of the CO2-crude oil system and the density difference between the two phases, and improves the isotonic volume model for predicting the CO2-crude oil interfacial tension. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 Schematic diagram of the correlation analysis of factors affecting the interfacial tension of the CO2-formation water system in a specific embodiment of the present invention;

[0044] Figure 2 This is a flow chart of the prediction model for the CO2-formation water system in the present invention;

[0045] Figure 3 A diagram showing the relationship between various parameters and the ACE optimal transformation function in a specific embodiment of the present invention;

[0046] Figure 4 A diagram showing the relationship between the optimal transformation function of interfacial tension and the optimal transformation functions of various variables in a specific embodiment of the present invention;

[0047] Figure 5 A diagram showing the relationship between the optimal conversion function of interfacial tension and experimentally measured interfacial tension in a specific embodiment of the present invention;

[0048] Figure 6 Schematic diagram of comparison between calculated and experimental interfacial tension of CO2-formation water system in a specific embodiment of the present invention (learning sample);

[0049] Figure 7 Schematic diagram of the absolute error distribution diagram (learning sample) of the interfacial tension prediction of the CO2-formation water system in a specific embodiment of the present invention;

[0050] Figure 8 Schematic diagram showing a comparison between the calculated and experimental interfacial tension values ​​of the CO2-formation water system in a specific embodiment of the present invention (validation sample);

[0051] Figure 9 Schematic diagram of the absolute error distribution diagram of the interfacial tension prediction of the CO2-formation water system (validation sample) in a specific embodiment of the present invention;

[0052] Figure 10 A comparison chart of the calculated and experimental interfacial tensions of the CO2-pure water system under different models in a specific embodiment of the present invention;

[0053] Figure 11 A comparison chart of the calculated and experimental interfacial tensions of the CO2-formation water system under different models in a specific embodiment of the present invention;

[0054] Figure 12 A comparison chart of the calculated and experimental interfacial tension values ​​of the CO2-formation water system in a specific embodiment of the present invention;

[0055] Figure 13 Graph showing the relationship between the CO2-crude oil equilibrium interfacial tension and the CO2-crude oil density difference in a specific embodiment of the present invention;

[0056] Figure 14 A comparison chart of the calculated and experimental CO2-crude oil interfacial tension values ​​in a specific embodiment of the present invention;

[0057] Figure 15 This is a distribution diagram of the absolute error of CO2-crude oil interfacial tension prediction in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0058] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used in the present invention have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0059] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations and / or combinations thereof.

[0060] like Figure 2 As shown, the method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory of the present invention includes the following steps:

[0061] Step 1: Analyze the factors affecting the interfacial tension of the CO2-formation water system;

[0062] Through literature research, it was found that the main factors affecting the interfacial tension of the CO2-formation water system are pressure, temperature, salinity of the formation water, and the composition of the injected CO2 gas. Based on the above factors, the interfacial tension data in the literature were screened, and the screening criteria were as follows:

[0063] (1) All interfacial tension values ​​of CO2-formation water systems were measured using the dynamic pendant drop method;

[0064] (2) The interfacial tension value measured experimentally is the equilibrium interfacial tension value after the CO2-formation water system reaches equilibrium;

[0065] (3) The interfacial tensions of the CO2-formation water system measured experimentally are independent of each other.

[0066] Step 2: Analyze the correlation of parameters

[0067] The factors that affect the interfacial tension of the CO2-formation water system considered in this invention include: reservoir pressure, reservoir temperature, concentration of monovalent cations in formation water (Na + +K + ), divalent cation concentration in formation water (Ca 2+ +Mg 2+ ), N2 mole fraction, and CH4 mole fraction in the injected gas. The Spearman correlation coefficient was used to analyze the correlations between influencing factors and interfacial tension. It was found that, with the exception of reservoir pressure, which showed a negative correlation, all other parameters were positively correlated with interfacial tension. Reservoir pressure had the greatest impact on interfacial tension. The order of influence of other parameters on the interfacial tension of the CO2-formation water system was: divalent cation concentration > CH4 mole fraction > N2 mole fraction > monovalent cation concentration > reservoir temperature.

[0068] Step 3: Use the ACE model to establish the basic relationship for predicting the interfacial tension of the CO2-formation water system as follows:

[0069]

[0070] Where, σ is the interfacial tension of CO2-formation water system, mN / m; p is the reservoir pressure, MPa; T is the reservoir temperature, °C; x(N2) is the mole fraction of N2 in the injected gas, mol%; x(CH4) is the mole fraction of CH4, mol%; y(Na + +K + ) is Na in formation water + and K + Equivalent monovalent cation content, mol / kg; y(Ca 2+ +Mg 2+ ) is Ca in formation water 2+ +Mg 2+ Equal divalent cation content mol / kg. Taking the inverse transformation of formula (8) to obtain the interfacial tension calculation model:

[0071]

[0072] Step 4: Verify and evaluate the model

[0073] (1) Model Verification

[0074] The accuracy of the prediction results is analyzed using indicators such as relative error (ARE), average relative error (AARE) and standard deviation (SD):

[0075]

[0076]

[0077]

[0078] (2) Model comparison

[0079] In order to further verify the accuracy of the model prediction, the model proposed in the present invention is compared with the prediction relationship in the current literature to verify the prediction accuracy of the model.

[0080] (3) Experimental data verification

[0081] Multiple groups of CO2-formation water system interfacial tension values ​​are used as verification data, and the interfacial tension value of the system is calculated using the ACE model proposed in the present invention.

[0082] Step 5: Establish an isotonic volume correction model for the equilibrium interfacial tension of the CO2-crude oil system.

[0083] The isotonic volume model shows that the equilibrium interfacial tension of the CO2-crude oil system is closely related to the CO2-crude oil density difference. The equilibrium interfacial tension of the CO2-crude oil system increases exponentially with the increase in the density difference, with a Spearman correlation coefficient of 0.9881, indicating that the equilibrium interfacial tension of the CO2-crude oil system is mainly affected by the density difference. If the density difference between the two phases reaches a very small value, the equilibrium interfacial tension of the CO2-crude oil system will approach 0. At this point, the CO2-crude oil system will achieve a miscible state, forming a CO2 miscible flooding, which greatly improves the oil recovery efficiency of CO2-EOR.

[0084] The isotonic volume model proposed by Macleod and Sudgen is only applicable to the prediction of interfacial tension of a single pure substance and is not applicable to the prediction of interfacial tension of the CO2-heavy oil system in the present invention. In order to better predict the equilibrium interfacial tension of the CO2-heavy oil system in the present invention, the crude oil is regarded as a pseudo-component for the CO2-crude oil system, and a modified isotonic volume model for calculating the equilibrium interfacial tension of the CO2-crude oil system can be obtained:

[0085]

[0086] The modified isotonic volume model is mainly divided into two parts. The first part is the equilibrium value to which the equilibrium interfacial tension gradually approaches when the system pressure is high; the second part is the isotonic volume model of a single pure substance.

[0087] Step 6: Verify and evaluate the model

[0088] The CO2-crude oil interfacial tension was predicted using an improved isotonic-volumetric correction model for the equilibrium interfacial tension of the CO2-crude oil system. The predicted values ​​were compared with experimental values ​​to validate the model. To further verify the accuracy of the model predictions, the proposed model was compared with prediction equations in the literature.

[0089] The following are several specific embodiments of the present invention.

[0090] Example 1

[0091] In a specific embodiment 1 of the present invention, the following steps are included:

[0092] Establishing a prediction model for CO2-formation water interfacial tension

[0093] Step 1: Analyze influencing factors

[0094] Through literature research, it was found that the main factors affecting the interfacial tension of the CO2-formation water system are pressure, temperature, salinity of the formation water, and the composition of the injected CO2 gas. Based on the above factors, the interfacial tension data in the literature were screened, and the screening criteria were as follows:

[0095] (1) All interfacial tension values ​​of CO2-formation water systems were measured using the dynamic pendant drop method;

[0096] (2) The interfacial tension value measured experimentally is the equilibrium interfacial tension value after the CO2-formation water system reaches equilibrium;

[0097] (3) The interfacial tensions of the CO2-formation water system measured experimentally are independent of each other.

[0098] A total of 1,609 independent data sample points were screened according to the above data screening criteria. The literature sources and experimental conditions of the data are shown in Table 2. To facilitate the establishment and verification of the prediction model, the 1,609 data points were randomly divided into two parts: one part for model establishment (learning sample), totaling 805 data points; the other part for model verification (validation sample), totaling 804 data points.

[0099] Table 2 Sample data of interfacial tension of CO2-formation water system

[0100]

[0101] Step 2: Analyze the correlation of parameters

[0102] The factors that affect the interfacial tension of the CO2-formation water system considered in this invention include: reservoir pressure, reservoir temperature, concentration of monovalent cations in formation water (Na + +K + ), divalent cation concentration in formation water (Ca 2+ +Mg 2+ ), N2 mole fraction and CH4 mole fraction in the injected gas. The Spearman correlation coefficient was used to analyze the correlation between the influencing factors and the interfacial tension. Figure 1 The Spearman correlation coefficients between various influencing factors and interfacial tension are given. It can be seen that except for the negative correlation between reservoir pressure and interfacial tension, the other parameters are positively correlated with interfacial tension; and reservoir pressure has the greatest impact on interfacial tension, with a Spearman correlation coefficient of -0.80; the order of influence of other parameters on the interfacial tension of the CO2-formation water system is: divalent cation concentration > CH4 mole fraction > N2 mole fraction > monovalent cation concentration > reservoir temperature.

[0103] Step 3: Build the model

[0104] The Alternating Conditional Expectation Transformation (ACE) is a multivariate nonlinear regression method for finding the optimal transformation, first proposed by Breiman and Friedman in 1985. The conventional multivariate linear regression model is:

[0105]

[0106] Where Y is the dependent variable; X i are independent variables; β0 and β i is the regression coefficient; n is the number of variables; ε is the error term. The multiple linear regression model assumes that the dependent variable Y is a linear correlation function of n independent variables. This method combines the dependent variable Y and the independent variable X. i are considered as θ functions and The function's independent variable:

[0107]

[0108] Where θ is a function of the cause variable Y; is the original independent variable X i Function. By using formula (2), the original dependent variable Y and independent variable X i n dimensions between (X=X1,X2,X3,…,X n )The nonlinear regression problem is transformed into the problem of finding n+1 one-dimensional optimal functions. The error judgment condition of the multivariate nonlinear regression of formula (2) is:

[0109]

[0110] Where E is the conditional expectation, when the square of the error term ε 2 When the minimum is reached, the optimal transformation function can be obtained. In order to minimize the square of the error term, the constraints need to be met:

[0111]

[0112] Under the constraints, by calculating the minimum value of formula (3), the optimal transformation form of the function can be obtained:

[0113]

[0114]

[0115] Substitute equations (5) and (6) into (2) and perform inverse transformation to obtain the dependent variable Y and the independent variable X. i The relationship between:

[0116]

[0117] The ACE multivariate nonlinear regression method has the following advantages: (1) It does not require the assumption of the relationship function between the independent variable and the dependent variable and the form of the transformation function; (2) It can be used for the regression of nonlinear relationships between multiple variables and dependent variables; (3) The optimal transformation function can be found in the transformation space; (4) It is easy to program and convenient to apply.

[0118] The basic relationship for predicting the interfacial tension of the CO2-formation water system using the ACE model is as follows:

[0119]

[0120] Where, σ is the interfacial tension of CO2-formation water system, mN / m; p is the reservoir pressure, MPa; T is the reservoir temperature, °C; x(N2) is the mole fraction of N2 in the injected gas, mol%; x(CH4) is the mole fraction of CH4, mol%; y(Na + +K + ) is Na in formation water + and K + Equivalent monovalent cation content, mol / kg; y(Ca 2+ +Mg 2+ ) is Ca in formation water 2+ +Mg 2+ Equal divalent cation content mol / kg. Taking the inverse transformation of formula (8) to obtain the interfacial tension calculation model:

[0121]

[0122] The flow chart of CO2-formation water system interfacial tension model program design is as follows Figure 2 . Figure 3 The relationship between each influencing factor and its corresponding ACE optimal transformation function is given. Figure 3 (e) and (f) show that the slope of the divalent cation line is basically twice that of the monovalent cation line, which is basically consistent with the influence of cations on interfacial tension proposed by previous researchers, thus verifying the feasibility of using the ACE method to establish a prediction model.

[0123] Figure 4 is the relationship diagram between the optimal transformation function of interfacial tension and the sum of the optimal transformation functions of each variable. According to expression (8), the two must be equal for the established prediction model to be valid. Figure 5 It can be seen that there is a basically linear relationship between the two, and they are mainly distributed around the 45° line, so the prediction model established by the present invention is valid.

[0124] Taking into account the formation temperature, pressure, formation water salinity and injected gas composition, the interfacial tension model of the CO2-formation water system was established as follows:

[0125] σ=40.59259+11.41295S-0.81418S 2 +0.21986S 3 (10)

[0126]

[0127] Where a ij are the fitting parameters, see Table 3.

[0128] Table 3 Prediction model parameter data table

[0129]

[0130] Step 4: Verify and evaluate the model

[0131] (1) Model Verification

[0132] The accuracy of the prediction results is analyzed using indicators such as relative error (ARE), average relative error (AARE) and standard deviation (SD):

[0133]

[0134]

[0135]

[0136] Figure 6The comparison chart of the interfacial tension of CO2-formation water system calculated and the experimental values ​​for 805 data points of the learning sample is shown in the figure. Figure 6 It can be seen that the predicted value is basically equal to the experimental value. Figure 7 The distribution relationship diagram of absolute error is given by Figure 7 (a) and (b) show that the absolute error between the calculated value and the experimental value is basically distributed within the range of ±5mN / m. In order to verify the accuracy of the model, Figure 8 A comparison chart of the calculated and experimental values ​​of the CO2-formation water interfacial tension for 804 data points of the validation sample is given. It can be seen from the chart that the prediction accuracy is higher at points with smaller interfacial tension. When the interfacial tension is greater than 60mN / m, the predicted value is slightly larger than the experimental value. Figure 9 The distribution of absolute errors is given, and the absolute errors are mainly within the range of ±5mN / m. Table 4 shows the statistical error analysis results of the prediction model. The average relative error of the prediction of the learning sample is 7.62%, with a standard deviation of 11.04%; the average relative error of the validation sample is 8.65%, with a standard deviation of 12.75%.

[0137] Table 4 Statistical error analysis of prediction model

[0138] Data Sample Number of data points AARE (%) SD (%) Study Sample 805 7.62 11.04 Validation Sample 804 8.65 12.75

[0139] (2) Model comparison

[0140] To further verify the accuracy of the model's predictions, the model proposed in this paper was compared with prediction equations in current literature. Massoudi and King, Hebach et al., Bachu and Bennion, and Georgiadis et al., respectively, proposed equations for predicting the interfacial tension of CO2-pure water systems. Chalbaud et al. and Li et al., based on extensive experiments, proposed prediction formulas for the CO2-formation water interfacial tension that take into account formation water salinity. The expression and applicable scope of each prediction formula are shown in Table 5. As can be seen from the table, there is currently no prediction model for the CO2-formation water interfacial tension that comprehensively considers formation temperature, pressure, formation water salinity, and the composition of the injected gas.

[0141] Table 5 Prediction formula for CO2-formation water system

[0142]

[0143] For the pure CO2-pure water system, in order to compare the accuracy of calculating interfacial tension between the method determined in this study and the previous prediction model, the interfacial tension of 27 sample data was calculated and compared. Figure 9 The interfacial tension of CO2-pure water system of 27 samples predicted by this method and four previous methods are compared with the experimental results. Figure 10 It can be seen that different calculation methods vary significantly, and the ACE model proposed in this paper has higher prediction accuracy. The statistical error analysis of the prediction results of different prediction models is shown in Table 6. As can be seen from the table, compared with other models, the ACE model has improved prediction accuracy and a wider range of applicability, with an average relative error of 12.45% and a standard deviation of 18.57%.

[0144] Table 6 Statistical error analysis of prediction results of different prediction models

[0145] Prediction Model Number of data points AARE (%) SD (%) ACE Model 27 12.45 18.57 Massoudi and King 9 104.02 123.02 Hebach et al. 27 14.50 18.80 Bachu and Bennion 27 14.35 18.17 Georgiadis et al. 27 12.21 17.65

[0146] Figure 11 The interfacial tension of CO2-formation water system of 107 samples predicted by ACE model and two previous methods is compared with the experimental results. Figure 10 It can be seen that the ACE model has a high prediction accuracy, and the prediction accuracy of different prediction methods varies greatly. The statistical error analysis of the prediction results of different prediction models is shown in Table 7. As can be seen from the table, the ACE model has a high prediction accuracy, with an average relative error of 10.19% and a standard deviation of 13.16%.

[0147] Table 7 Statistical error analysis of prediction results of different prediction models

[0148] Prediction Model Number of data points AARE (%) SD (%) ACE Model 107 10.19 13.16 Chalbaud et al. 107 15.46 22.94 Li et al. 107 14.76 17.20

[0149] (3) Experimental data verification

[0150] 60 sets of CO2-formation water system interfacial tension values ​​were used as verification data, and the interfacial tension values ​​of the system were calculated using the ACE model proposed in this invention. The calculation results are as follows: Figure 12 As shown, the prediction accuracy is high when the interfacial tension is greater than 40 mN / m. When the interfacial tension is less than 40 mN / m, the model's predictions decrease. This is mainly due to the fact that at high pressures, CO2 becomes supercritical, and the CO2-formation water interface interacts strongly, resulting in a decrease in experimental measurement accuracy. The ACE model's predictions show an average relative error of 12.50% and a standard deviation of 20.31%.

[0151] Example 2

[0152] In a specific embodiment 2 of the present invention, the following steps are included:

[0153] Establishment of prediction model for CO2-crude oil interfacial tension

[0154] Step 1: Establish an isotonic volume model

[0155] From the isotonic volume model, we know that the equilibrium interfacial tension of CO2-crude oil system is closely related to the density difference between CO2 and crude oil. Based on the experimental data of CO2-crude oil interfacial tension, the relationship between the equilibrium interfacial tension of CO2-crude oil and the density difference is shown in the figure below: Figure 13 As shown, the equilibrium interfacial tension of the CO2-crude oil system increases exponentially with increasing density differentials, with a Spearman correlation coefficient of 0.9881, indicating that the equilibrium interfacial tension of the CO2-crude oil system is primarily influenced by the density differential. If the density differential between the two phases is very small, the equilibrium interfacial tension of the CO2-crude oil system approaches zero, at which point the CO2-crude oil system becomes miscible, forming a miscible CO2 flooding, which greatly improves the recovery efficiency of CO2-EOR.

[0156] The isotonic volume model proposed by Macleod and Sudgen is only applicable to the prediction of interfacial tension of a single pure substance and is not applicable to the prediction of interfacial tension of the CO2-heavy oil system in the present invention. In order to better predict the equilibrium interfacial tension of the CO2-heavy oil system in the present invention, the crude oil is regarded as a pseudo-component for the CO2-crude oil system, and a modified isotonic volume model for calculating the equilibrium interfacial tension of the CO2-crude oil system can be obtained:

[0157]

[0158] The modified isotonic volume model is mainly divided into two parts. The first part is the equilibrium value σ0 = 5.50 mN / m that the equilibrium interfacial tension gradually approaches when the system pressure is high. The second part is the isotonic volume model of a single pure substance, in which the isotonic volume parameter applicable to the crude oil system is P ch =31.43, index n=5.32.

[0159] Step 2: Verify and evaluate the model

[0160] The CO2-crude oil interfacial tension values ​​predicted by the improved isotonic volume model are basically the same as the experimental values, with an absolute error distribution within the range of ±3mN / m. The average relative error is 6.63% and the standard deviation is 9.1%. Figure 14 shown.

[0161] like Figure 15As shown, in order to further verify the accuracy of the model prediction, the model proposed in this invention is compared with the prediction relationship in the current literature. Massoudi and King, Hebach et al., Bachu and Bennion, and Georgiadis et al. respectively proposed relationship formulas for predicting the interfacial tension of the CO2-pure water system; Chalbaud et al. and Li et al. proposed a prediction formula for the CO2-formation water interfacial tension that takes into account the salinity of the formation water based on a large number of experiments. The expression form and applicable scope of each prediction formula are shown in Table 1. As can be seen from the table, there is currently no prediction model for the CO2-formation water interfacial tension that comprehensively considers the formation temperature, pressure, formation water salinity, and the composition of the injected gas.

[0162] Table 1 Prediction formula for CO2-formation water system

[0163]

[0164]

[0165] The ACE model developed in this paper for predicting CO₂-formation water interfacial tension has high computational accuracy and a wide range of applications, with an absolute error of ±5 mN / m, an average relative error of 7.62%, and a standard deviation of 11.04%. The improved isotonic volume model of this paper can effectively predict CO₂-crude oil interfacial tension, with an absolute error of ±3 mN / m, an average relative error of 6.63%, and a standard deviation of 9.1%.

[0166] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features therein. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

[0167] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A method for predicting the interfacial tension of the CO2-crude oil-formation water system is established based on the ACE theory, which is characterized by: The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory includes: Step 1: Analyze the factors affecting the interfacial tension of the CO2-formation water system; Step 2: Analyze the correlation of parameters affecting the interfacial tension of the CO2-formation water system; Step 3: Using the ACE model, a calculation model for predicting the interfacial tension of the CO2-formation water system is established; Step 4: Verify and evaluate the calculation model for predicting the interfacial tension of the CO2-formation water system; Step 5, establishing an isotonic volume correction model for the equilibrium interfacial tension of the CO2-crude oil system; Step 6, verifying and evaluating the isotonic volume correction model of the equilibrium interfacial tension of the CO2-crude oil system; In step 1, the factors affecting the interfacial tension of the CO2-formation water system include pressure, temperature, salinity of the formation water, and the composition of the injected CO2 gas; In step 2, the factors that affect the interfacial tension of the CO2-formation water system are: reservoir pressure, reservoir temperature, concentration of monovalent cations in formation water (Na + +K + ), divalent cation concentration in formation water (Ca 2+ +Mg 2+ ), N2 mole fraction and CH4 mole fraction in the injected gas; The Spearman correlation coefficient was used to analyze the correlation between influencing factors and interfacial tension. It was found that except for the negative correlation between reservoir pressure and interfacial tension, the other parameters were positively correlated with interfacial tension; and reservoir pressure had the greatest impact on interfacial tension; the order of influence of other parameters on the interfacial tension of the CO2-formation water system was: divalent cation concentration > CH4 mole fraction > N2 mole fraction > monovalent cation concentration > reservoir temperature.

2. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 1, the interfacial tension data is screened based on the above-mentioned influencing factors, and the screening criteria are: (1) All interfacial tension values ​​of CO2-formation water systems were measured using the dynamic pendant drop method; (2) The interfacial tension value measured experimentally is the equilibrium interfacial tension value after the CO2-formation water system reaches equilibrium; (3) The interfacial tensions of the CO2-formation water system measured experimentally are independent of each other.

3. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 3, the ACE model is used to establish the basic relationship for predicting the interfacial tension of the CO2-formation water system as follows: Where, σ is the interfacial tension of CO2-formation water system, mN / m; p is the reservoir pressure, MPa; T is the reservoir temperature, °C; x(N2) is the N2 mole fraction in the injected gas, mol%; x(CH4) is the CH4 mole fraction, mol%; y(Na + +K + ) is Na in formation water + and K + Equivalent monovalent cation content, mol / kg; y(Ca 2+ +Mg 2+ ) is Ca in formation water 2+ +Mg 2+ Equal divalent cation content mol / k; θ is a function of the causal variable σ; is the original independent variable X i function.

4. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 3, characterized in that: In step 3, the inverse transformation of equation (8) is performed to obtain the calculation model for predicting the interfacial tension of the CO2-formation water system:

5. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 4, the accuracy of the prediction results is analyzed using the relative error ARE, average relative error AARE, and standard deviation SD indicators to verify the model: Where, IFT exp,i is the experimental value of interfacial tension of CO2-formation water system, IFT cal,i is the calculated value of the interfacial tension of the CO2-formation water system.

6. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 4, in order to further verify the accuracy of the model prediction, the calculation model for predicting the interfacial tension of the CO2-formation water system is compared with the existing prediction relationship to verify the prediction accuracy of the model.

7. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 4, multiple groups of CO2-formation water system interfacial tension values ​​are used as verification data, and the interfacial tension value of the system is calculated using the prediction model for the interfacial tension of the CO2-formation water system to verify the experimental data.

8. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 5, the isotonic volume correction model for calculating the equilibrium interfacial tension of the CO2-crude oil system is: The modified isotonic volume model is mainly divided into two parts. The first part is the equilibrium value σ0 to which the equilibrium interfacial tension gradually approaches when the system pressure is high; the second part is the isotonic volume model of a single pure substance; ρ oil and ρ co2 is the density of the oil layer and carbon dioxide.

9. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 6, the CO2-crude oil interfacial tension value is predicted using the improved isotonic volume correction model of the CO2-crude oil system equilibrium interfacial tension, and the predicted value is compared with the experimental value to verify the model.

10. The method for predicting the interfacial tension of the CO2-crude oil-formation water system based on the ACE theory according to claim 1, characterized in that: In step 6, in order to further verify the accuracy of the model prediction, the isotonic volume correction model of the equilibrium interfacial tension of the CO2-crude oil system is compared with the existing prediction relationship to verify the prediction accuracy of the model.

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