A method for characterizing rheological impedance characteristics of a polymer used for oil displacement based on an equivalent circuit method

Abstract

The application relates to a polymer rheological impedance characteristic representation method for oil displacement based on an equivalent circuit method, which comprises the following steps: obtaining total rheological impedance and phase angles of the polymer for oil displacement under different shearing rates, constructing and dividing polymer rheological impedance characteristic representation data sets under shearing effects; constructing a series equivalent model representing the rheological impedance characteristics of the polymer for oil displacement; constructing a parallel equivalent model representing the rheological impedance characteristics of the polymer for oil displacement; constructing a composite equivalent model representing the rheological impedance characteristics of the polymer for oil displacement; introducing a grey wolf algorithm, preferably selecting applicable limits of the equivalent model under different shearing rates based on the data sets representing the rheological impedance characteristics of the polymer for oil displacement under shearing effects, and realizing quantitative representation of the rheological impedance characteristics of the polymer for oil displacement. The application quantifies the rheological impedance of the polymer for oil displacement under shearing effects, guarantees quantitative and scientific representation of the rheological impedance characteristics in the polymer rheological performance evaluation process.

Description

TECHNICAL FIELD

[0001] The application relates to a rheological resistance characteristic representation technology for polymer flooding in a polymer flooding enhanced oil recovery process, in particular to a rheological resistance characteristic representation method for polymer flooding based on an equivalent circuit method. BACKGROUND

[0002] Polymer flooding has been proved to be the most mature and widely used process in tertiary oil recovery through polymer flooding enhanced oil recovery practices at home and abroad, and has become an important measure for stabilizing and increasing production of old oilfields. Taking the largest-scale, most efficient and most advanced polymer flooding tertiary oil production base in the world, Daqing Oilfield, as an example, since the industrial application in 1996, the annual oil production of polymer flooding has exceeded 10 million tons for more than 20 years, and the recovery rate is increased by about 13% compared with water flooding. With the wide application of polymer flooding, various types of oil displacement polymers have been derived, such as amphiphilic polymers and super-high molecular polymers. Polymer flooding increases the viscosity of injected water by adding a certain amount of high molecular polymer into the injected water, and improves the oil-water mobility ratio. Based on the viscoelasticity of the polymer, the oil-water mobility ratio is changed, the sweep efficiency of the polymer in the low-permeability area of small pores is improved, the "pulling and dragging" effect is exerted on the oil droplets and oil films remaining in the dead ends or corners after water flooding, the carrying capacity is enhanced, and the micro oil displacement efficiency is improved, so that the old oilfield can be rejuvenated.

[0003] However, the polymer solution is affected by the variable shear seepage field in the near wellbore and the formation pore migration process, which often leads to the destruction of the molecular structure, the degradation of the solution, the loss of viscosity, and the decrease of the molecular weight, greatly weakening the polymer flooding effect. Therefore, when preparing and evaluating the physical parameters and rheological properties of the polymer for oil displacement, the stability characteristics under the condition of variable shear rate need to be considered, that is, the rheological impedance reflecting the stability of the polymer for oil displacement needs to be mastered. In addition, with the long-term development and utilization of conventional oil reservoirs, high-temperature and high-salt oil reservoirs have become an important target for replacing conventional oil and gas energy and supporting the oil and gas revolution. Such oil reservoirs have the characteristics of high temperature, high salinity, high divalent ion content, and high shear degree, which puts forward more stringent requirements for the temperature resistance, salt resistance, and shear stability of the polymer for oil displacement. The traditional polymer represented by partially hydrolyzed polyacrylamide (HPAM) has low viscosity and poor stability under the conditions of high temperature and high salinity in the oil reservoir, which has significantly affected the oil displacement effect. Therefore, it is urgent to develop a polymer with more excellent performance for high-temperature and high-salt oil reservoirs. In addition, during the preparation of the temperature-resistant and salt-resistant polymer, the injection performance needs to be evaluated according to the parameters such as the injection pressure gradient and the resistance coefficient of the oil reservoir, and the viscoelasticity, temperature resistance, shear resistance, and rheological impedance characteristics need to be determined to investigate the adaptability of the polymer in the deep and complex oil reservoir environment. Therefore, determining the rheological impedance characteristics of the polymer for oil displacement under the shear effect has become the key to the preparation and evaluation of the polymer, and is the fundamental solution to the stability of the polymer in the complex pore conditions. However, the existing understanding is based on the rheological test results under shear effect, which reflects the changes of viscosity, yield stress, and thixotropy related to time. Although such test results can reflect the physical parameters and rheological properties of the polymer for oil displacement to some extent, they cannot solve the problem of quantitative characterization of the rheological impedance characteristics under the condition of differential shear effect, which directly affects the stability of the polymer in the deep and high-temperature and high-salt oil reservoir environment. Therefore, it is necessary to design a method for characterizing the rheological impedance characteristics of the polymer for oil displacement based on the rheological behavior of the polymer for oil displacement in the performance evaluation process, break through the traditional single evaluation mode, and especially solve the limitations and problems caused by the difficulty in characterizing the rheological impedance caused by the charge transfer transition. SUMMARY

[0004] The purpose of the present application is to provide a rheological impedance characterization method for a polymer for oil displacement based on an equivalent circuit method, which is used to solve the rheological properties and stability evaluation of the polymer for oil displacement under the conditions of high temperature and high salinity in the oil reservoir, especially to solve the problem that the rheological impedance characteristics of the polymer for oil displacement are difficult to quantitatively characterize due to the interference of external charge transfer transition and other behaviors, and the current method is only limited to qualitative description and has not realized quantitative characterization.

[0005] The technical solution adopted by this invention to solve its technical problem is as follows: This method for characterizing the rheological impedance characteristics of polymers used for oil displacement based on the equivalent circuit method includes the following steps:

[0006] (i) Based on the rheological property test results of the polymer for oil displacement, the total rheological impedance Z and phase angle of the polymer for oil displacement under different shear rates were obtained. Construct and segment a dataset characterizing polymer rheological impedance properties under shear effects;

[0007] (II) Constructing a series equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement, introducing the rheological impedance of the phase angle element to simulate the double-layer capacitance phenomenon near the interface between the test electrode and the polymer, and replacing the rheological impedance of the polymer with pure resistance; at the same time, considering the rheological impedance of the measuring electrode and the wires connected to it, as well as the inductance phenomenon caused by high frequency, they are regarded as pure resistance and pure inductance; by combining the pure resistance representing the rheological impedance of the polymer, the rheological impedance of the phase angle element representing the double-layer capacitance phenomenon, and the pure resistance and inductance of the rheological impedance of the measuring electrode and the wires connected to it, an equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement can be constructed.

[0008] (III) Constructing a parallel equivalent model to characterize the rheological impedance properties of polymers used for oil displacement;

[0009] (iv) Construct a composite equivalent model to characterize the rheological resistance properties of polymers used for oil displacement;

[0010] (v) The Grey Wolf algorithm is introduced to construct a dataset that characterizes the rheological impedance properties of polymers used for oil displacement under shear effects. The applicability limits of the equivalent model under different shear rates are optimized to achieve quantitative characterization of the rheological impedance properties of polymers used for oil displacement.

[0011] The series equivalent circuit model characterizing the rheological impedance properties of the polymer used for oil displacement in Scheme (II) above is as follows:

[0012] Z C =Z * +Z L =R p +[A0(jω) ψ ] -1 +R2+jωL (12)

[0013] In the formula, Z C Z represents the rheological impedance of the series equivalent circuit model. * The total rheological impedance is in complex form; j is the imaginary unit. Z LR2 is the resistance of the measuring electrode and the lead wire connected thereto; L is the inductance of the measuring electrode and the lead wire connected thereto; ψ is the conductivity; A0 is a constant; ω is the angular frequency; R p is the resistance of the equivalent polymer rheological impedance.

[0014] In the above scheme (three), the parallel equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement is constructed by connecting the rheological impedance of the polymer in parallel with the rheological impedance of the phase angle element, constructing a parallel equivalent circuit, and summing the rheological impedance under the parallel equivalent condition and the rheological impedance of the measuring electrode and the lead wire connected thereto, to obtain the parallel equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement as follows:

[0015]

[0016] In the formula, Z B is the rheological impedance of the parallel equivalent model;

[0017] In the above scheme (four), the complex equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement is constructed by connecting the rheological impedance of the polymer in parallel with a virtual capacitor, and then connecting the impedance of the phase angle element and the rheological impedance of the measuring electrode and the lead wire connected thereto in series, constructing a complex equivalent circuit model, and summing the rheological impedance under the complex equivalent condition and the rheological impedance of the measuring electrode and the lead wire connected thereto, to construct the complex equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement as follows:

[0018]

[0019] In the formula, Z F is the rheological impedance of the complex equivalent model; C1 is a virtual capacitor connected in parallel with the rheological impedance of the polymer.

[0020] The above scheme (two) constructs a series equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement:

[0021] Based on the generalized Ohm's law, the total rheological impedance Z of the experimental test is calculated:

[0022]

[0023] In the formula, Z is the total rheological impedance; U is the input voltage; I is the input current; |U| is the output voltage amplitude; |I| is the input current amplitude; |Z| is the modulus of the total rheological impedance; ω is the angular frequency; t is the time; is the phase angle;

[0024] Based on the Euler formula, the total rheological impedance Z is converted into a vector form:

[0025]

[0026] In the formula, Z * is the total rheological impedance in complex form, Ω; j is the imaginary unit, Z' is the real part of the total rheological impedance in complex form; Z" is the imaginary part of the total rheological impedance in complex form; R is the equivalent resistance of the total rheological impedance, Ω; C is the capacitance, F;

[0027] Based on the generalized Ohm's law of the equivalent circuit, when the angular frequency tends to 0 or infinity, the values of the real part and the imaginary part of the total rheological impedance are as follows:

[0028] When ω→0, Z'| ω→0 = R, Z"| ω→0 = R; when ω→∞, Z'| ω→∞ = 0, Z"| ω→∞ = 0.

[0029] Meanwhile, Z' and Z" also satisfy the following equation:

[0030] (Z'-R / 2) 2 + Z" 2 = (R / 2) 2 (5)

[0031] In the rheological impedance characteristic test of the polymer for oil displacement, the total rheological impedance value is regarded as the total resistance of the equivalent circuit, i.e. the circuit is decomposed into the polymer resistance, the phase angle element resistance and the resistance and inductance generated by the measuring electrode and the wire connected thereto; when the resistance R p of the equivalent polymer rheological impedance and the connection of the phase angle element CPE are in series connection, based on the generalized Ohm's law and the current flow rule of the series circuit, they are regarded as a series equivalent circuit model; under the condition of the series equivalent circuit, the current flowing through both is the same, at this time, the rheological impedance Z CPE of the phase angle element is:

[0032]

[0033] In the formula: ψ is the conductivity, S; A0 is a constant. When ψ = 0, the CPE is a pure resistance; when ψ = 1, the CPE is a pure capacitance; when ω = 0, the imaginary part is zero, the phase angle element is regarded as an ideal resistance; when ω = 1, the real part becomes zero, the phase angle element is regarded as an ideal capacitance;

[0034] Under the condition of the series equivalent model, the total impedance value of the polymer and the phase angle element is the sum of their resistances, i.e.:

[0035] Z * = R p+ [A0(jω) ψ ] -1 (7)

[0036]

[0037] wherein R p is the resistance of the equivalent polymer rheological impedance, Ω;

[0038] Meanwhile, Z' and Z" also satisfy the following equation:

[0039]

[0040] In addition, there is also a rheological impedance in the series equivalent circuit produced by the measuring electrode and the wire connected thereto, that is:

[0041] Z L = R2 + jωL (11)

[0042] wherein Z L is the rheological impedance produced by the measuring electrode and the wire connected thereto; R2 is the resistance of the measuring electrode and the wire connected thereto, Ω; and L is the inductance of the measuring electrode and the wire connected thereto;

[0043] The rheological impedance produced by the polymer and the phase angle element is summed with the rheological impedance produced by the measuring electrode and the wire connected thereto, that is, the series equivalent circuit model representing the rheological impedance characteristics of the polymer used for oil displacement is constructed.

[0044] The method for constructing the parallel equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement in the above-mentioned scheme (three) is:

[0045] During the test of the rheological impedance characteristics of the polymer, the rheological impedance of the polymer is connected in parallel with the rheological impedance of the phase angle element based on the generalized Ohm's law and the current flow rule of the parallel circuit, a parallel equivalent circuit is constructed, and the rheological impedance under the parallel equivalent condition is obtained according to the generalized Ohm's law, that is:

[0046]

[0047] wherein,

[0048] Similarly, Z' and Z" satisfy the following equation, that is:

[0049]

[0050] The rheological impedance under the parallel equivalent condition is summed with the rheological impedance produced by the measuring electrode and the wire connected thereto, that is, the parallel equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement is constructed.

[0051] The method for constructing the complex equivalent model representing the rheological impedance characteristics of the polymer for oil displacement in the above scheme (four) is as follows:

[0052] During the rheological impedance test of the polymer for oil displacement, the rheological impedance of the polymer is connected in parallel with a virtual capacitor, and then the impedance of a phase angle element and the rheological impedance of the measuring electrode and the wire connected thereto are connected in series, and then a complex equivalent circuit model is constructed, and the specific process is as follows:

[0053]

[0054]

[0055] In the formula, C1 is a virtual capacitor connected in parallel with the rheological impedance of the polymer.

[0056] Therefore, the complex rheological impedance of the polymer and the phase angle element is written as:

[0057]

[0058] The rheological impedance under the complex equivalent condition and the rheological impedance of the measuring electrode and the wire connected thereto are summed up, and the complex equivalent model representing the rheological impedance characteristics of the polymer for oil displacement is constructed.

[0059] Beneficial effects:

[0060] (1) The characterization of the rheological impedance characteristics of the polymer for oil displacement in the present application is based on the test results of the rheological impedance device, a phase angle element is introduced to describe the abnormal relationship between the polymer and the test environment, and based on the obtained rheological impedance and phase angle, the mechanical interaction of bound charges and mobile charges in the polymer system is considered, and a series and parallel equivalent circuit containing resistance, inductance and capacitance is constructed. This can not only match the conductivity of the polymer, but also help to decompose the rheological impedance from the perspective of the equivalent circuit, and then quantify the rheological impedance of the polymer for oil displacement under shear effect, so as to ensure the quantitative and scientific characterization of the rheological impedance characteristics in the polymer rheological performance evaluation process.

[0061] (2) The present application fully considers the charge transfer transition behavior between the test electrode and the polymer during the evaluation process of the polymer for oil displacement, and starts from the impedance analogy relationship, and splits the rheological impedance into the rheological impedance of the polymer for oil displacement, the rheological impedance of the phase angle element, the rheological impedance of the charge transfer and the inductance and resistance of the wire. According to the distribution mode of the equivalent rheological impedance of the polymer and the equivalent rheological impedance of the phase angle element, the applicable limits of the equivalent circuit model under the action of different shear rates are optimized, the error caused by the additional impedance is eliminated, and an important foundation is formed for the effective evaluation of the rheological performance of the polymer, so that the quantitative characterization of the rheological impedance characteristics of the polymer under shear effect is extended from the traditional qualitative to the quantitative.

[0062] (Three) The evaluation of the rheological impedance characteristics of the polymer for oil displacement in the application not only focuses on the non-Newtonian flow behavior, charge transfer transition and double-layer capacitance interface dynamics of the polymer related to conductivity, but also takes into account the complex electrochemical processes reflected by the charge transfer and electron transport and diffusion effects under different frequency ranges, avoids the lack of key impedance parameters in the rheological performance evaluation and quantitative characterization of the polymer, and further ensures the accuracy of the equivalent model construction of the rheological impedance characteristics of the polymer for oil displacement, which is beneficial to the reliable application of the temperature-resistant and salt-resistant polymer in the deep high-temperature and high-salt complex reservoir environment.

[0063] (Four) The application is based on the generalized Ohm's law, which is the essence of the equivalent circuit, and describes the superposition effect of the effects of frequency, concentration and shear rate on the rheological performance of the polymer by rheological impedance, excavates the potential crosslinking behavior of the polymer system, and quantitatively characterizes the rheological impedance characteristics of the polymer by taking the equivalent polymer impedance resistance as the final index. The principle is clear and feasible, the method is scientific and reliable, and it can break through the limitations of traditional qualitative description of the rheological impedance characteristics of the polymer, effectively provide a method for quantitatively characterizing the rheological impedance characteristics of the polymer for oil displacement, and has strong scientificity, operability and practicality. It can not only provide a beneficial scientific method for the evaluation and deep revelation of the rheological performance of the temperature-resistant and salt-resistant polymer, but also enrich and expand the preparation and evaluation methods of new polymers, and also provide theoretical means and basis for accelerating the green and efficient development of oilfields and the effective development of oil and gas resources in deep complex reservoir environments.

[0064] (Five) The application solves the technical problems of the rheological performance and characteristic description of the polymer for oil displacement under different shear effects, especially the rheological impedance characteristics of the polymer for oil displacement in the preparation and physical property parameter determination process. The application is used to solve the rheological performance and stability evaluation of the polymer for oil displacement under high-temperature and high-salt reservoir conditions, especially to solve the problem that the rheological impedance characteristics of the polymer for oil displacement are difficult to quantitatively characterize due to the interference of external charge transfer transition and other behaviors. At present, it is only limited to qualitative description and has not realized quantitative characterization.

[0065] (Six) The application breaks through the traditional single evaluation mode of the rheological performance of the polymer for oil displacement, especially the limitations and problems caused by the difficulty in characterization of the rheological impedance caused by the charge transfer transition. The application provides a reliable means and scientific method for the quantitative characterization of the rheological impedance characteristics of any new polymer for oil displacement, and has a positive effect on promoting the popularization and application of polymer flooding enhanced oil recovery technology in oilfields, solving the problem of conventional polymer efficiency oil displacement in high-temperature and high-salt complex reservoir environments, and driving the orderly implementation of oil and gas resource exploration and development plans under the "deep engineering" goal. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 The figure is a schematic diagram of the principle of the method of the application;

[0067] Figure 2 This is a schematic diagram of the gray wolf algorithm introduced in the method of this invention.

[0068] 1. Rheological impedance test tank 2. Polymer for oil displacement 3. Test electrode 4. Wire 5. Double layer capacitor 6. Polarized charge 7. Series equivalent circuit model 8. Rheological impedance generated by measuring electrode and connected wire 9. Rheological impedance of phase angle element 10. Rheological impedance of polymer 11. Parallel equivalent circuit model 12. Composite equivalent circuit model 13. Virtual capacitor in parallel with polymer rheological impedance 14. α wolf 15. Random direction vector of α wolf 16. Distance between ω wolf and α wolf 17. β wolf 18. Random direction vector of β wolf 19. Distance between ω wolf and β wolf 20. δ wolf 21. Random direction vector of δ wolf 22. Distance between ω wolf and δ wolf 23. ω wolf 24. Prey. Detailed implementation method:

[0069] The invention will be further described below with reference to the accompanying drawings:

[0070] like Figure 1 As shown, in the rheological impedance test cell 1 used to test the rheological impedance characteristics of the polymer used for oil displacement, the polymer 2 and the test electrode 3 form a double-layer capacitance 5 phenomenon caused by the mechanical interaction of polarization charges 6. Furthermore, as the test cycle extends, the wire 4 connected to the test electrode also forms rheological impedance induced by inductance and resistance. Therefore, to quantitatively characterize the rheological impedance characteristics of the polymer used for oil displacement, the polymer's rheological impedance 10 is introduced to represent the rheological impedance 10 generated by the polymer in the rheological impedance test cell 1. The phase angle element's rheological impedance 9 represents the double-layer capacitance 5 phenomenon and the transfer and transition behavior of polarization charges 6 in the rheological impedance test cell 1. The measurement electrode and the connected wire's rheological impedance 8 represent the rheological impedance generated by the test electrode 3 and the wire 4 in the rheological impedance test cell 1. Based on the distribution patterns of the polymer's rheological impedance 10 and the phase angle element's rheological impedance 9, and based on the generalized Ohm's law, a series equivalent circuit model 7, a parallel equivalent circuit model 11, and a composite equivalent circuit model 12 are constructed. In the composite equivalent circuit model, a virtual capacitor 13 is introduced in parallel with the polymer rheological impedance to simulate the mechanical behavior of charge transfer transition at the interface between the test electrode 3 and the oil displacement polymer 2, thereby eliminating interference from external factors and realizing quantitative characterization of the rheological impedance characteristics of the oil displacement polymer.

[0071] Figure 2is a schematic diagram of the grey wolf algorithm introduced in the method for determining the applicable limits of the equivalent model characterizing the rheological impedance characteristics of the polymer used for oil displacement, aiming to optimize the applicable limits of the series equivalent circuit model 7, the parallel equivalent circuit model 11 and the composite equivalent circuit model 12 under different shear rate conditions. According to the social status of the wolf pack and the fitness of the three types of equivalent models, the grey wolf algorithm is divided into alpha wolves 14, beta wolves 17, delta wolves 20 and omega wolves 23 from top to bottom. According to the strengthening of the wolf pack's encirclement of the prey 24, the random direction vectors of the alpha wolves 14, beta wolves 17 and delta wolves 20 are updated, i.e. the random direction vector 15 of the alpha wolf, the random direction vector 18 of the beta wolf and the random direction vector 21 of the delta wolf. At the same time, the distances between the alpha wolves 14, beta wolves 17, delta wolves 20 and omega wolves 23 are also updated, i.e. the distance 16 between the omega wolf and the alpha wolf, the distance 19 between the omega wolf and the beta wolf and the distance 22 between the omega wolf and the delta wolf. Then, the positions of the alpha wolves 14, beta wolves 17, delta wolves 20 and omega wolves 23 are updated, and it is determined whether the updated results are the optimal applicable limits of the series equivalent circuit model 7, the parallel equivalent circuit model 11 and the composite equivalent circuit model 12. If the optimal use limit condition is not met, the above steps need to be repeated until the optimal applicable limits of the series equivalent circuit model 7, the parallel equivalent circuit model 11 and the composite equivalent circuit model 12 are determined.

[0072] This method for characterizing the rheological impedance characteristics of the polymer used for oil displacement based on the equivalent circuit method:

[0073] (I) Based on the rheological impedance device, the total rheological impedance (Z) and phase angle of the polymer under different shear rate conditions are designed and tested The rheological impedance characterization data set of the polymer used for oil displacement under shear effect is constructed. The data set is randomly divided into training set, validation set and test set in a certain proportion by leave-one-out method, and the proportion of the training set, validation set and test set is 8:1:1.

[0074] Thus, the division of the rheological impedance characterization data set of the polymer used for oil displacement under shear effect is completed.

[0075] This step can be repeated to construct another data set for rheological impedance characterization of the polymer used for oil displacement with another property and structure.

[0076] (II) For the evaluation of the rheological properties and impedance characteristics of the polymer used for oil displacement, the rheological impedance 9 of the phase angle element simulates the test electrode and the double-layer capacitance phenomenon near the interface of the polymer used for oil displacement, and the rheological impedance 10 of the polymer is replaced by a pure resistance. At the same time, considering the rheological impedance 8 of the measuring electrode and the wire connected thereto and the inductance phenomenon caused by high frequency, they are regarded as pure resistance and pure inductance. The pure resistance representing the rheological impedance 10 of the polymer, the rheological impedance 9 of the phase angle element of the double-layer capacitance phenomenon, and the pure resistance and inductance of the rheological impedance 8 of the measuring electrode and the wire connected thereto are combined, that is, the equivalent model representing the rheological impedance characteristics of the polymer used for oil displacement is constructed. Based on the generalized Ohm's law, the total rheological impedance Z of the experimental test can be calculated:

[0077]

[0078] In the formula, Z is the total rheological impedance, Ω; U is the input voltage, V; I is the input current, A; |U| is the output voltage amplitude, V; |I| is the input current amplitude, A; |Z| is the modulus of the total rheological impedance, Ω; ω is the angular frequency, rad / s; t is the time, s; is the phase angle, °.

[0079] Based on the Euler formula, the total rheological impedance Z is converted into a vector form:

[0080]

[0081]

[0082] In the formula, Z * is the total rheological impedance in complex form, Ω; j is the imaginary unit, Z' is the real part of the total rheological impedance in complex form; Z" is the imaginary part of the total rheological impedance in complex form; R is the equivalent resistance of the total rheological impedance, Ω; C is the capacitance, F.

[0083] Based on the generalized Ohm's law of the equivalent circuit, when the angular frequency tends to 0 or infinity, the values of the real part and the imaginary part of the total rheological impedance are as follows:

[0084] When ω→0, Z'| ω→0 =R, Z"| ω→0 =R; when ω→∞, Z'| ω→∞ =0, Z"| ω→∞ =0.

[0085] At the same time, Z' and Z" also satisfy the following equation:

[0086] (Z'-R / 2) 2 +Z” 2 =(R / 2) 2 (5)

[0087] In the rheological impedance test of the polymer used for oil displacement, the total rheological impedance value is regarded as the total resistance of the equivalent circuit, i.e. the circuit is decomposed into the polymer resistance, the phase angle element resistance and the rheological impedance 8 produced by the measuring electrode and the wire connected thereto. When the resistance R p of the equivalent polymer rheological impedance 10 is greater than the resistance R CPE of the phase angle element (CPE), the connection between the polymer and the phase angle element is a series connection, and the phase angle element can be regarded as a series equivalent circuit model based on the generalized Ohm's law and the current flow rule of the series circuit. Under the condition of the series equivalent circuit, the current flowing through the two is the same, at this time, the rheological impedance (Z CPE ) of the phase angle element can be written as:

[0088]

[0089] In the formula, ψ is the conductivity, S; A0 is a constant. When ψ = 0, the CPE is a pure resistance; when ψ = 1, the CPE is a pure capacitance. When ω = 0, the imaginary part is zero, the phase angle element is regarded as an ideal resistance; when ω = 1, the real part becomes zero, the phase angle element is regarded as an ideal capacitance.

[0090] Then, under the condition of the series equivalent model, the total impedance value of the polymer and the phase angle element can be regarded as the sum of their resistances, i.e.:

[0091] Z * = R p + [A0(jω) ψ ] -1 (7)

[0092]

[0093] In the formula, R p is the resistance of the equivalent polymer rheological impedance 10, Ω.

[0094] At the same time, Z' and Z" also satisfy the following equation:

[0095]

[0096] In addition, there is also a rheological impedance 8 produced by the measuring electrode and the wire connected thereto in the series equivalent circuit, which is specifically expressed as:

[0097] Z L = R2+jωL (11)

[0098] In the formula, Z L is the rheological impedance 8 produced by the measuring electrode and the wire connected thereto, Ω; R2 is the resistance produced by the measuring electrode and the wire connected thereto, Ω; L is the inductance produced by the measuring electrode and the wire connected thereto, H.

[0099] Summing up the rheological impedance of the polymer and the phase angle element and the rheological impedance 8 of the measuring electrode and the wire connected thereto, i.e. constructing a series equivalent circuit model 7 representing the rheological impedance characteristics of the polymer for oil displacement, is as follows:

[0100] Z C = Z * + Z L = R p + [A0(jω) ψ ] -1 + R2+jωL (12)

[0101] In the formula, Z C is the rheological impedance of the series equivalent circuit model, Ω.

[0102] Thus, the construction of the series equivalent model representing the rheological impedance characteristics of the polymer for oil displacement is completed.

[0103] Repeating the step, the series equivalent model of the rheological impedance characteristics of another property and structure of the polymer for oil displacement can be constructed.

[0104] (Three) During the test of the rheological impedance characteristics of the polymer, based on the generalized Ohm's law and the current flow law of the parallel circuit, the rheological impedance of the polymer is connected in parallel with the rheological impedance 9 of the phase angle element, and a parallel equivalent circuit is constructed. Based on this, the rheological impedance under the parallel equivalent condition is obtained according to the generalized Ohm's law, i.e.

[0105]

[0106] In the formula,

[0107] Similarly, Z' and Z" satisfy the following equation, i.e.

[0108]

[0109] Summing up the rheological impedance under the parallel equivalent condition and the rheological impedance 8 of the measuring electrode and the wire connected thereto, i.e. constructing a parallel equivalent model 11 representing the rheological impedance characteristics of the polymer for oil displacement, is as follows:

[0110]

[0111] In the formula, Z B is the rheological impedance of the parallel equivalent model, Ω.

[0112] Thus, the construction of the parallel equivalent model representing the rheological impedance characteristics of the polymer for oil displacement is completed.

[0113] Repeating the step, the parallel equivalent model of the rheological impedance characteristics of another property and structure of the polymer for oil displacement can be constructed.

[0114] (IV) In the rheological impedance test of the polymer for oil displacement, to meet the applicability requirements of different shear rates, the rheological impedance 10 of the polymer is connected in parallel with a virtual capacitor, and then connected in series with the rheological impedance 9 of the phase angle element and the rheological impedance 8 of the measuring electrode and the wire connected thereto, thereby constructing a composite equivalent circuit model. Compared with the series and parallel equivalent circuit models, the composite equivalent circuit model takes into account the rheological impedance induced by the test environment, thereby enhancing the accuracy of the rheological impedance characterization of the polymer for oil displacement at a certain shear rate. Specifically:

[0115]

[0116] In the formula, C1 is a virtual capacitor 13 connected in parallel with the polymer rheological impedance, F.

[0117] Therefore, the composite rheological impedance of the polymer and the phase angle element can be written as:

[0118]

[0119] In summary, the rheological impedance under the composite equivalent condition is summed with the rheological impedance 8 of the measuring electrode and the wire connected thereto, thereby constructing a composite equivalent model 14 for characterizing the rheological impedance of the polymer for oil displacement, specifically as follows:

[0120]

[0121] In the formula, Z F is the rheological impedance of the composite equivalent model, Ω.

[0122] Thus, the construction of the composite equivalent model for characterizing the rheological impedance of the polymer for oil displacement is completed.

[0123] By repeating this step, a composite equivalent model for characterizing the rheological impedance of another property and structure of the polymer for oil displacement can be constructed.

[0124] (V) To determine the applicable limits of the equivalent model for characterizing the rheological impedance of the polymer for oil displacement at different shear rates, a grey wolf algorithm is introduced to optimize the applicable limits of the equivalent model. In the grey wolf algorithm, the social structure of the wolf pack is divided into four levels: alpha, beta, delta, and omega. The alpha wolf 14 serves as the leader, representing the optimal equivalent circuit model at the current shear rate; the beta wolf 17 serves as the assistant, supporting the decision of the alpha wolf 14, representing the suboptimal solution; the delta wolf 20 follows the commands of the alpha and beta wolves, representing the third optimal solution; and the omega wolf 23 is at the bottom of the hierarchy, obeying the commands of the alpha, beta, and delta wolves. The hunting behavior of the wolf pack is divided into two steps: surrounding the prey 24 and hunting.

[0125] In the first step, after the wolf pack discovers the prey 24, the wolf pack surrounds the prey 24, and the distance D between each omega wolf 23 and the prey 24 and the updated position vector X(t+1) of the omega wolf 23 are respectively as follows:

[0126] D = |C X p (t) - X(t) | (21)

[0127] X(t+1) = X p (t) - A D (22)

[0128] In the formula, t is the current iteration number; X(t) is the position vector of the current omega wolf 23; X p (t) is the position vector of the prey 24; A and C are random direction vectors, and have

[0129] A = a (2r1-1) (23)

[0130] C = 2r2 (24)

[0131]

[0132] In the formula, r1 and r2 are random vectors in [0, 1]; a is a decay factor, which linearly decreases from 2 to 0 as the iteration number increases; and T is the total iteration number.

[0133] In the second step, after the wolf pack simulation completes the surrounding behavior of the prey 24, the alpha wolf, the beta wolf, and the delta wolf jointly lead the entire wolf pack to gradually reduce the surrounding range of the prey 24, and then achieve the purpose of predation. The specific process is as follows:

[0134]

[0135] In the formula, X α , X β , and X δ are the position vectors of the alpha wolf, the beta wolf, and the delta wolf respectively; X α (t), X β (t), and X δ (t) are the position vectors of the alpha wolf, the beta wolf, and the delta wolf in the tth iteration respectively; D α , D β , and D δ are the distances between the alpha wolf, the beta wolf, and the delta wolf and the omega wolf respectively; A1, A2, A3, and C1, C2, C3 are random direction vectors; X1, X2, and X3 are the updated position vectors of the omega wolf according to the positions of the alpha wolf, the beta wolf, and the delta wolf respectively; and X'(t+1) is the final updated position vector of the omega wolf after the tth iteration.

[0136] After each round of iteration, the fitness value of all wolves 23 is recalculated, the new a, b and d wolves are determined by comparison, and the next round of iteration is carried out, gradually approaching the global optimal solution. At this time, the equivalent circuit model type represented by the a wolf 14 with the highest fitness value is the equivalent model that best matches the shear rate condition, and thus the applicable range of the three types of equivalent circuit models under different shear rates can be determined.

[0137] To ensure the accuracy of the determination of the rheological impedance characterization equivalent model applicable range of the polymer used for oil displacement under shear effect, considering that the random direction vector A changes with the change of the attenuation factor a, the size of which is closely related to the global search and local search ability of the algorithm, which will cause the deviation of the rheological impedance characterization equivalent model applicable range. Therefore, on the basis of the algorithm, the nonlinear attenuation factor a * is introduced to enhance the accuracy of the prediction of the equivalent model applicable range, and the updated attenuation factor a * is as follows:

[0138]

[0139] where t max is the maximum number of iterations.

[0140] To speed up the convergence speed of the global search stage, the grey wolf algorithm is improved combined with prior knowledge, so that the initialization population distribution is more uniform. For the determination of the rheological impedance characterization equivalent model applicable range of the polymer used for oil displacement under shear effect, the rectangular range of the wolf pack hunting prey 24 is set as LxW, and the global coordinate system is established with the lower left corner as the origin. According to the prey radius r a and the hunting area length L, k = |L / (2r a ) | reference lines are generated, and the reference line y k represents

[0141] y k : x = r a + i(2r a ), (i = 0, 2,..., k-1) (30)

[0142] When the population is initialized, the prey 24 random coordinates are guided, and n coordinates are set. Unlike the random initialization of the prey 24 coordinate values, |n / k| prey 24 random coordinates are randomly generated on each reference line, that is, these prey 24 random coordinates x are fixed in batches, and their y coordinates are randomly set. If there is a remainder, n-|n / k| prey random initialization distribution is distributed.

[0143] In the grey wolf optimization algorithm, the alpha wolf 14, the beta wolf 17 and the delta wolf 20 guide the omega wolf 23 to search for optimization, and the first three wolves have a consistent guiding effect on the omega wolf 23. However, in each iteration process, the alpha wolf 14, the beta wolf 17 and the delta wolf 20 are assumed by the three wolves with the highest fitness value, and the fitness value of the alpha wolf 14 is the highest, that is, the alpha wolf 14 is closer to the prey 24. Therefore, by increasing the proportion of the alpha wolf 14 in the guiding process of the three head wolves, the effect of guiding the omega wolf 23 to more effectively approach the prey 24 is achieved. In addition, as the iteration optimization proceeds, the alpha wolf 14 of different iteration numbers is closer to the position of the prey 24, and the fitness difference between the beta wolf 17 and the delta wolf 20 and the alpha wolf 14 is also gradually reduced, at this time, the guiding effect of the beta wolf 17 and the delta wolf 20 is gradually increased. Specifically, as the iteration number proceeds, the weight of the alpha wolf 14 is dynamically increased in the first half, and the guiding proportion of the beta wolf 17 and the delta wolf 20 is gradually increased under the condition that the fitness value difference between the alpha wolf 14, the beta wolf 17 and the delta wolf 20 is gradually reduced. The improvement of the mathematical expression of the next generation position of the omega wolf 23 is as follows:

[0144]

[0145] In the formula, ζ and are adjustment factors, used to adjust the proportion of the additional guiding effect of the alpha wolf 14 in the early and late stages of iteration optimization.

[0146] Thus, the determination of the applicable limit of the equivalent model representing the rheological impedance characteristics of the polymer for oil displacement is completed.

[0147] The steps (two), (three), (four) and (five) are repeated, and the applicable limit of the equivalent model representing the rheological impedance characteristics of another property and structure of the polymer for oil displacement can be determined.

[0148] The total rheological impedance (Z) of the polymer for oil displacement under the shear effect is obtained by using the automatic balance bridge method and the radio frequency I-V method; the phase angle of the rheological impedance of the polymer for oil displacement under the shear effect is obtained by using the electrochemical impedance spectroscopy method; the value range of the shear rate is 0-10 3 s -1 ; the initial value of the attenuation factor a is 2; the initial values of the adjustment factors ζ and are 0.5 and 0.28, respectively.

[0149] The application is mainly a five-step method, that is, the rheological impedance characterization dataset of the polymer used for oil displacement under shear effect is divided, the series equivalent model for characterizing the rheological impedance characteristics of the polymer used for oil displacement is constructed, the parallel equivalent model for characterizing the rheological impedance characteristics of the polymer used for oil displacement is constructed, the composite equivalent model for characterizing the rheological impedance characteristics of the polymer used for oil displacement is constructed, and the applicable limits of the equivalent model for characterizing the rheological impedance characteristics of the polymer used for oil displacement are determined. The first step is to construct and divide the rheological impedance characteristic dataset of the polymer used for oil displacement under shear effect according to the rheological performance test results of the polymer used for oil displacement. The second, third and fourth steps are to break through the error caused by the charge transfer transition behavior and the double-layer effect in the rheological performance test of the polymer used for oil displacement, establish the series, parallel and composite equivalent circuit models for characterizing the rheological impedance characteristics of the polymer used for oil displacement, and extract the equivalent resistance of the polymer rheological impedance according to the equivalent model, which is also the key to quantitatively characterize the rheological impedance characteristics of the polymer used for oil displacement. The fifth step is to introduce the grey wolf algorithm, optimize the applicable limits of the equivalent model under different shear rates based on the dataset for characterizing the rheological impedance characteristics of the polymer used for oil displacement under shear effect, and form the quantitative characterization of the rheological impedance characteristics of the polymer used for oil displacement. Thus, a reliable means and scientific method are provided for the quantitative characterization of the rheological impedance characteristics of any new polymer used for oil displacement. Meanwhile, the method has a positive effect on promoting the popularization and application of the polymer flooding enhanced oil recovery process in oilfields, solving the problem of conventional polymer efficiency in complex high-temperature and high-salt reservoir environments, and driving the orderly implementation of oil and gas resource exploration and development plans under the "deep earth engineering" target.

Claims

1. A method for characterizing the rheological impedance properties of polymers used for oil displacement based on the equivalent circuit method, characterized in that... Includes the following steps: (i) Based on the rheological property test results of the polymer for oil displacement, the total rheological impedance of the polymer for oil displacement under different shear rates was obtained. Z and phase angle φ We constructed and segmented a dataset characterizing the rheological impedance properties of polymers under shear effects. (II) Constructing a series equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement, introducing the rheological impedance of the phase angle element to simulate the double-layer capacitance phenomenon near the interface between the test electrode and the polymer, and replacing the rheological impedance of the polymer with pure resistance; at the same time, considering the rheological impedance of the measuring electrode and the wires connected to it, as well as the inductance phenomenon caused by high frequency, they are regarded as pure resistance and pure inductance; by combining the pure resistance representing the rheological impedance of the polymer, the rheological impedance of the phase angle element representing the double-layer capacitance phenomenon, and the pure resistance and inductance of the rheological impedance of the measuring electrode and the wires connected to it, an equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement can be constructed. Calculate the total rheological impedance based on the generalized Ohm's law. Z : （1） In the formula, Z 1) Total rheological impedance; U Input voltage; I For input current; | U | represents the output voltage amplitude; | I | represents the input current amplitude; | Z | represents the magnitude of the total rheological impedance; ω Angular frequency; t For time; φ The phase angle; Based on Euler's formula, the total rheological impedance Z Convert to vector form: （2） （3） （4） In the formula, Z * The total rheological impedance is in complex form, in Ω; j The imaginary unit, ; Z' The real part of the total rheological impedance in complex form; Z'' This represents the imaginary part of the total rheological impedance in complex form. R The equivalent resistance of the total rheological impedance is given in Ω. C Capacitance, F; Based on the generalized Ohm's law of equivalent circuits, the real and imaginary parts of the total rheological impedance are as follows when the angular frequency approaches 0 or infinity: when ω →0, , ;when ω As we approach infinity, , ; at the same time, Z' , Z'' It also satisfies the following equation: （5） When testing the rheological impedance characteristics of polymers used for oil displacement, the total rheological impedance value is considered as the total resistance of the equivalent circuit. This means the circuit is decomposed into the polymer resistance, the phase angle element resistance, and the resistance and inductance generated by the measuring electrodes and connected wires. When the resistance of the equivalent polymer rheological impedance... R p When the phase angle element CPE is connected in series, based on generalized Ohm's law and the current flow law of series circuits, it is regarded as a series equivalent circuit model. Under the condition of series equivalent circuit, the current flowing through both is the same. At this time, the rheological impedance of the phase angle element is... Z CPE for: （6） In the formula: ψ S represents electrical conductivity. A 0 is a constant; when ψ When = 0, CPE is a pure resistor; when ψ When =1, CPE is a pure capacitor; when ω When = 0, the imaginary part is zero. The phase angle element is considered as an ideal resistor; when ω When =1, the real part becomes zero. The phase angle element is considered as an ideal capacitor; Under the series equivalent model conditions, the total impedance of the polymer and the phase angle element is the sum of their resistances, i.e.: （7） （8） （9） In the formula, R p The resistance is the equivalent polymer rheological impedance, in Ω; at the same time, Z' and Z'' It also satisfies the following equation: （10） In addition, the series equivalent circuit also contains rheological resistance generated by the measuring electrodes and the wires connected to them, namely: （11） In the formula, Z L The rheological impedance generated by the measuring electrodes and the wires connected to them; R 2 represents the resistance generated by the measuring electrode and the wires connected to it, in Ω; L The inductance generated by the measuring electrodes and the wires connected to them; The series equivalent circuit model characterizing the rheological impedance of the polymer for oil displacement is constructed by summing the rheological impedance generated by the polymer and the phase angle element with the rheological impedance generated by the measuring electrode and the wire connected to it. Construct a parallel equivalent model to characterize the rheological impedance properties of polymers used for oil displacement; When testing the rheological impedance characteristics of polymers, based on generalized Ohm's law and the current flow law of parallel circuits, the rheological impedance is connected in parallel with the rheological impedance of the phase angle element to construct a parallel equivalent circuit. The rheological impedance under the parallel equivalent condition is then obtained according to generalized Ohm's law, i.e.: （13） In the formula, ; Similarly, Z' and Z'' It satisfies the following equation, namely: （14） （15） The rheological impedance under parallel equivalent conditions is summed with the rheological impedance generated by the measuring electrode and the wire connected to it, thus completing the construction of a parallel equivalent model characterizing the rheological impedance properties of the polymer used for oil displacement. (iv) Constructing a composite equivalent model to characterize the rheological impedance properties of polymers used for oil displacement; (v) Introducing the Grey Wolf algorithm, based on the construction of a dataset characterizing the rheological impedance properties of polymers used for oil displacement under shear effects, the applicability limits of the equivalent model under different shear rates are optimized to achieve quantitative characterization of the rheological impedance properties of polymers used for oil displacement.

2. The method for characterizing the rheological impedance properties of polymers used for oil displacement based on the equivalent circuit method according to claim 1, characterized in that: The series equivalent circuit model characterizing the rheological impedance properties of the polymer used for oil displacement in (ii) is as follows: （12） In the formula, Z C The rheological impedance is the value of the series equivalent circuit model. Z * The total rheological impedance is in complex form. j The imaginary unit, ; Z L The rheological impedance generated by the measuring electrodes and the wires connected to them; R 2 represents the resistance generated by the measuring electrodes and the wires connected to them; L The inductance generated by the measuring electrodes and the wires connected to them; ψ Electrical conductivity; A 0 is a constant; ω Angular frequency; R p The resistance is the equivalent polymer rheological impedance.

3. The method for characterizing the rheological impedance properties of polymers used for oil displacement based on the equivalent circuit method according to claim 2, characterized in that: In section (iii), when constructing the parallel equivalent model characterizing the rheological impedance characteristics of the polymer used for oil displacement, the polymer rheological impedance is connected in parallel with the rheological impedance of the phase angle element to construct a parallel equivalent circuit. The rheological impedance under the parallel equivalent condition is summed with the rheological impedance generated by the measuring electrode and the wire connected to it to obtain the parallel equivalent model characterizing the rheological impedance characteristics of the polymer used for oil displacement as follows. （16） In the formula: Z B The rheological impedance of the parallel equivalent model; .

4. The method for characterizing the rheological impedance properties of polymers used for oil displacement based on the equivalent circuit method according to claim 3, characterized in that: In section (iv), when constructing the composite equivalent model characterizing the rheological impedance properties of the polymer used for oil displacement, the rheological impedance of the polymer is connected in parallel with the virtual capacitor, and then the impedance of the phase angle element and the rheological impedance generated by the measuring electrode and the wires connected to it are connected in series to construct the composite equivalent circuit model. The rheological impedance under the composite equivalent conditions is summed with the rheological impedance generated by the measuring electrode and the wires connected to it to construct the composite equivalent model characterizing the rheological impedance properties of the polymer used for oil displacement, as follows: （20） In the formula, Z F The rheological impedance of the composite equivalent model; C 1 represents the virtual capacitance connected in parallel with the polymer rheological impedance.

5. The method for characterizing the rheological impedance properties of polymers used for oil displacement based on the equivalent circuit method according to claim 4, characterized in that: The method described in section (iv) for constructing a composite equivalent model characterizing the rheological resistance properties of polymers used for oil displacement is as follows: When testing the rheological impedance of polymers used for oil displacement, the rheological impedance of the polymer is connected in parallel with a virtual capacitor, and then connected in series with the impedance of a phase angle element and the rheological impedance generated by the measuring electrode and the wires connected to it, thereby constructing a composite equivalent circuit model, as follows: （17） （18） In the formula, C 1 represents the virtual capacitance connected in parallel with the polymer rheological impedance; Therefore, the composite rheological impedance of the polymer and the phase angle element is written as: （19） The composite equivalent model characterizing the rheological impedance of polymers used for oil displacement is constructed by summing the rheological impedance under the composite equivalent conditions with the rheological impedance generated by the measuring electrode and the wires connected to it.

Images