Oil displacement polymer rheological impedance characteristic characterization method based on equivalent circuit method

Abstract

The invention relates to an oil displacement polymer rheological impedance characteristic characterization method based on an equivalent circuit method, which comprises the following steps: obtaining the total rheological impedance and phase angle of an oil displacement polymer under different shear rate conditions, and constructing and dividing a polymer rheological impedance characteristic characterization data set under a shear effect; constructing a series equivalent model for representing the rheological impedance characteristics of the polymer for oil displacement; constructing a parallel equivalent model for representing the rheological impedance characteristics of the polymer for oil displacement; constructing a composite equivalent model for representing the rheological impedance characteristics of the polymer for oil displacement; a grey wolf algorithm is introduced, on the basis of constructing a data set representing the rheological impedance characteristics of the polymer for oil displacement under the shear effect, the application limit of the equivalent model at different shear rates is optimized, and quantitative representation of the rheological impedance characteristics of the polymer for oil displacement is achieved. According to the method, the rheological impedance of the polymer for oil displacement under the shear effect is quantified, and quantitative and scientific characterization of the rheological impedance characteristic in the rheological property evaluation process of the polymer is ensured.

Description

Technical field:

[0001] The present invention relates to a rheological impedance characteristic characterization technology for oil displacement polymers in a polymer flooding enhanced oil recovery process, in particular to a rheological impedance characteristic characterization method for oil displacement polymers based on an equivalent circuit method. Background technology:

[0002] Polymer flooding for enhanced oil recovery (ERR) has proven to be the most mature and widely used tertiary oil recovery (TER) process, becoming a crucial measure for stabilizing and increasing production in mature oilfields. For example, Daqing Oilfield, the world's largest, most profitable, and most technologically advanced TERR production base for polymer flooding, has consistently produced over 10 million tons of oil annually for more than two decades since its industrial application in 1996. Its recovery rate is approximately 13% higher than that of water flooding, an average of which is higher. With the widespread application of polymer flooding, a variety of polymers for oil recovery have emerged, including amphiphilic polymers and ultrahigh molecular weight polymers. Polymer flooding involves adding a certain amount of high-molecular-weight polymer to the injected water to increase its viscosity and improve the oil-water mobility ratio. By leveraging the polymer's viscoelastic properties, this modifies the oil-water mobility ratio, enhancing its sweep in small, low-permeability areas. This "pulling" effect exerts a "drag" on oil droplets and oil films trapped at blind ends or edges after water flooding, enhancing their carrying capacity and improving microscopic oil recovery efficiency, thereby revitalizing mature oilfields.

[0003] However, polymer solutions are subject to the variable shear flow field during migration near the wellbore and within formation pores, often leading to molecular structure destruction, solution degradation, viscosity loss, and molecular weight reduction, significantly impairing polymer flooding effectiveness. Therefore, when preparing and evaluating the physical properties and rheological performance of oil-displacement polymers, it is crucial to consider their stability characteristics under variable shear rates. In other words, understanding the rheological impedance, which reflects the stability of the oil-displacement polymer, is crucial. Furthermore, with the long-term development and utilization of conventional oil reservoirs, high-temperature, high-salinity reservoirs have become a key target for replacing conventional oil and gas energy sources and supporting the oil and gas revolution. These reservoirs, characterized by high temperatures, high salinity, high divalent ion content, and high shear stress, place even more stringent requirements on the temperature and salt resistance and shear stability of oil-displacement polymers. Conventional polymers, such as partially hydrolyzed polyacrylamide (HPAM), suffer from low viscosity and poor stability in high-temperature, high-salinity reservoirs, significantly impacting oil-displacement effectiveness. The development of polymers with superior performance for these reservoirs is urgently needed. In addition, in the process of preparing heat-resistant and salt-resistant polymers, it is also necessary to evaluate their injection performance based on parameters such as the reservoir injection pressure gradient and resistance coefficient, and determine indicators such as viscoelasticity, heat and shear resistance, and rheological impedance characteristics to examine their adaptability in deep and complex reservoir environments. Therefore, determining the rheological impedance characteristics of oil-displacement polymers under shear effects has become the key to polymer preparation and evaluation, and is the fundamental solution to their stability under complex pore conditions. However, the existing understanding is based on indoor rheological experimental test results that reflect the time-related changes in viscosity, yield stress, and thixotropy under shear effects. Although such test results can reflect the physical parameters and rheological properties of oil-displacement polymers to a certain extent, they cannot solve the problem of quantitative characterization of rheological impedance characteristics when there are differentiated shear effects, which directly affects the stability of polymers in deep, high-temperature, and high-salt reservoir environments. This raises the scientific problem of designing a method to characterize the rheological impedance characteristics in the form of an equivalent circuit during the performance evaluation process based on the rheological behavior of oil-displacement polymers, breaking through the traditional single evaluation model, especially the various limitations and difficulties brought about by the difficulty in characterizing the rheological impedance caused by charge transfer transitions. It is particularly necessary to scientifically design a method to characterize the rheological impedance characteristics of oil-displacement polymers during the evaluation process. Summary of the invention:

[0004] The purpose of the present invention is to provide a method for characterizing the rheological impedance characteristics of oil-displacement polymers based on the equivalent circuit method. This method for characterizing the rheological impedance characteristics of oil-displacement polymers based on the equivalent circuit method is used to solve the rheological performance and stability evaluation of oil-displacement polymers under high-temperature and high-salinity reservoir conditions, especially to solve the problem that the rheological impedance characteristics of oil-displacement polymers are difficult to quantitatively characterize due to interference from external charge transfer transitions and other behaviors, and are currently limited to qualitative description but not quantitative characterization.

[0005] The technical solution adopted by the present invention to solve the technical problem is: the method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method comprises the following steps:

[0006] (1) Based on the rheological properties test results of oil displacement polymers, the total rheological impedance Z and phase angle of oil displacement polymers under different shear rate conditions are obtained Construct and partition the data set for characterizing the rheological impedance characteristics of polymers under shear effects;

[0007] (2) Constructing a series equivalent model to characterize the rheological impedance characteristics of polymers 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 a pure resistance; at the same time, considering the rheological impedance of the measuring electrode and the wire connected thereto, as well as the inductance phenomenon caused by high frequency, they are regarded as pure resistance and pure inductance; combining the pure resistance representing the rheological impedance of the polymer, the rheological impedance of the phase angle element of the double-layer capacitance phenomenon, and the pure resistance and inductance of the rheological impedance of the measuring electrode and the wire connected thereto, an equivalent model to characterize the rheological impedance characteristics of polymers for oil displacement can be constructed;

[0008] (3) Constructing a parallel equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement;

[0009] (4) Constructing a composite equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement;

[0010] (5) The Grey Wolf algorithm is introduced to construct a data set for characterizing the rheological impedance characteristics of polymers for oil displacement under shear effects, and the applicable limits of the equivalent model at different shear rates are optimized to achieve quantitative characterization of the rheological impedance characteristics of polymers for oil displacement.

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

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

[0013] Where Z C is the rheological impedance of the series equivalent circuit model; Z * is the total rheological impedance in complex form; j is the imaginary unit, Z Lis the rheological impedance generated by the measuring electrode and the wire connected to it; R2 is the resistance generated by the measuring electrode and the wire connected to it; L is the inductance generated by the measuring electrode and the wire connected to it; 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] When constructing a parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement in the above scheme (iii), the rheological impedance of the polymer 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 thereto. The parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement is obtained as follows;

[0015]

[0016] Where: Z B is the rheological impedance of the parallel equivalent model;

[0017] When constructing a composite equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement in the above scheme (IV), 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 wire connected thereto are connected in series to construct a composite equivalent circuit model. The rheological impedance under the composite equivalent conditions and the rheological impedance generated by the measuring electrode and the wire connected thereto are summed to construct a composite equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement, as follows:

[0018]

[0019] Where Z F is the rheological impedance of the composite equivalent model; C1 is the virtual capacitor in parallel with the rheological impedance of the polymer.

[0020] In the above scheme (II), the method for constructing a series equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement is as follows:

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

[0022]

[0023] Where 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 time; is the phase angle;

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

[0025]

[0026] Where 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 approaches 0 or infinity, the values ​​of the real and imaginary parts 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] At the same time, Z' and Z" also satisfy the following equations:

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

[0031] When testing the rheological impedance characteristics of polymers used for oil displacement, the total rheological impedance value is regarded as the total resistance of the equivalent circuit, that is, the circuit is decomposed into the resistance of the polymer, the resistance of the phase angle element, and the resistance and inductance generated by the measuring electrode and the wire connected to it; when the resistance R of the equivalent polymer rheological impedance is p When the connection with the phase angle element CPE is in series, it is regarded as a series equivalent circuit model based on the generalized Ohm's law and the current flow law of the series circuit. Under the series equivalent circuit condition, the current flowing through the two is the same. At this time, the rheological impedance Z of the phase angle element CPE for:

[0032]

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

[0034] The total impedance of the polymer and phase angle element under the series equivalent model condition is the sum of their resistances, that is:

[0035] Z * =R p+[A0(jω) ψ ] -1 (7)

[0036]

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

[0038] At the same time, Z' and Z" also satisfy the following equations:

[0039]

[0040] In addition, the series equivalent circuit also contains the rheological impedance generated by the measuring electrodes and the wires connected to them, namely:

[0041] Z L =R2+jωL(11)

[0042] Where Z L is the rheological impedance generated by the measuring electrode and the wire connected to it; R2 is the resistance generated by the measuring electrode and the wire connected to it, Ω; L is the inductance generated by the measuring electrode and the wire connected to it;

[0043] The rheological impedance generated by the polymer and the phase angle element is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus constructing a series equivalent circuit model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

[0044] In the above scheme (3), the method for constructing a parallel equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement is as follows:

[0045] When testing the rheological impedance characteristics of polymers, based on the generalized Ohm's law and the current flow law of parallel circuits, its rheological impedance is connected in parallel with the rheological impedance of the phase angle element to construct a parallel equivalent circuit. According to the generalized Ohm's law, the rheological impedance under parallel equivalent conditions is obtained, that is:

[0046]

[0047] Where,

[0048] Similarly, Z' and Z" satisfy the following equations, namely:

[0049]

[0050] The rheological impedance under the parallel equivalent condition is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus completing the construction of a parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

[0051] In the above scheme (IV), the method for constructing a composite equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement is as follows:

[0052] When testing the rheological impedance of a polymer for oil displacement, the rheological impedance of the polymer is connected in parallel with a virtual capacitor. Then, the impedance of the phase angle element and the rheological impedance generated by the measuring electrode and the wire connected to it are connected in series to construct a composite equivalent circuit model, as follows:

[0053]

[0054]

[0055] Where C1 is the virtual capacitor in parallel with the rheological impedance of the polymer;

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

[0057]

[0058] The rheological impedance under the composite equivalent conditions is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus completing the construction of a composite equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

[0059] Beneficial effects:

[0060] (1) The characterization of the rheological impedance characteristics of the polymer for oil displacement in the present invention is based on the test results of the rheological impedance device, and a phase angle element is introduced to describe the abnormal connection between the polymer and the test environment. Based on the obtained rheological impedance and phase angle, the mechanical interaction between bound charges and mobile charges in the polymer system is considered, and series and parallel equivalent circuits including resistors, inductors, and capacitors are constructed. This is consistent with the conductivity of the polymer and is beneficial for decomposing the rheological impedance from the perspective of the equivalent circuit, thereby quantifying the rheological impedance of the polymer for oil displacement under the shear effect, ensuring the quantitative and scientific characterization of the rheological impedance characteristics in the process of evaluating the rheological properties of the polymer.

[0061] (2) The present invention fully considers the charge transfer transition behavior between the test electrode and the polymer during the evaluation of oil displacement polymers. Starting from the impedance analogy relationship, the rheological impedance is divided into the rheological impedance of the oil displacement polymer, the rheological impedance of the phase angle element, and the rheological impedance of charge transfer and the inductance and resistance of the conductor. Based on the distribution pattern of the equivalent rheological impedance of the polymer and the equivalent rheological impedance of the phase angle element, the applicable limit of the equivalent circuit model under different shear rates is optimized, eliminating the error caused by the additional impedance, forming an important foundation for the effective evaluation of the rheological properties of the polymer, and making it possible to extend the quantitative characterization of the rheological impedance characteristics under the shear effect from the traditional qualitative to the quantitative.

[0062] (3) The present invention evaluates the rheological impedance characteristics of polymers for oil recovery, focusing on the non-Newtonian flow behavior, charge transfer transitions and double-layer capacitance interface dynamics related to the conductivity of the polymer, while taking into account the complex electrochemical processes reflected by charge transfer, electron transport and diffusion effects in different frequency ranges, avoiding the loss of key impedance parameters in the evaluation and quantitative characterization of the rheological properties of polymers, thereby ensuring the accuracy of the construction of an equivalent model for characterizing the rheological impedance characteristics of polymers for oil recovery, which is beneficial to the reliable application of temperature-resistant and salt-resistant polymers in deep, high-temperature and high-salt complex reservoir environments.

[0063] (IV) The present invention is based on the essence of the generalized Ohm's law being an equivalent circuit, and uses rheological impedance to describe the superimposed effect of the effects of frequency, concentration and shear rate on the rheological properties of polymers, explores the potential cross-linking behavior of the polymer system, and uses the equivalent polymer impedance resistance as the final indicator to quantitatively characterize the rheological impedance characteristics of the polymer. The principle is clear and feasible, the method is scientific and reliable, and it can break through the limitation of the traditional qualitative description of the rheological impedance characteristics of polymers, and effectively provide a method for quantitatively characterizing the rheological impedance characteristics of polymers for oil displacement. It is scientific, operable and practical, and can provide a useful scientific method for the evaluation and profound revelation of the rheological properties of heat-resistant and salt-resistant polymers, and can enrich and expand the preparation and evaluation methods of new polymers. At the same time, it also provides theoretical means and basis for accelerating the green and efficient development of oil fields and the effective utilization of oil and gas resources in deep and complex oil reservoir environments.

[0064] (5) The present invention solves the technical difficulties of rheological properties and characteristic descriptions under different shear effects during the preparation and physical property parameter determination of oil recovery polymers, especially the characterization of rheological impedance characteristics of oil recovery polymers; the present invention is used to solve the rheological properties and stability evaluation of oil recovery polymers under high-temperature and high-salt oil reservoir conditions, especially to solve the problem that the rheological impedance characteristics of oil recovery polymers are difficult to quantitatively characterize due to interference from external charge transfer transitions and other behaviors, and are currently limited to qualitative descriptions but not quantitative characterizations.

[0065] (6) The present invention breaks through the traditional single evaluation model for the rheological properties of oil-displacement polymers, especially the limitations and difficulties caused by the difficulty in characterizing the rheological impedance caused by charge transfer transitions. It provides a reliable means and scientific method for quantitatively characterizing the rheological impedance characteristics of new oil-displacement polymers of any nature and structure. At the same time, it has a positive effect on promoting the promotion and application of polymer flooding enhanced oil recovery technology in oil fields and solving the problem of conventional polymer enhanced oil recovery in complex reservoir environments with high temperature and high salinity. It also has a driving effect on the orderly implementation of oil and gas resource exploration and development plans under the goal of "deep earth engineering." Description of the drawings:

[0066] Figure 1 Schematic diagram of the principle of the method of the present invention;

[0067] Figure 2 Schematic diagram of the grey wolf algorithm introduced in the method of the present invention.

[0068] 1 Rheological impedance test tank 2 Polymer for oil displacement 3 Test electrode 4 Wire 5 Double-layer capacitance 6 Polarization charge 7 Series equivalent circuit model 8 Rheological impedance generated by the measuring electrode and the wire connected to it 9 Rheological impedance of the phase angle element 10 Rheological impedance of the polymer 11 Parallel equivalent circuit model 12 Composite equivalent circuit model 13 Virtual capacitance in parallel with the rheological impedance of the polymer 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. Specific implementation method:

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

[0070] like Figure 1 As shown, in a rheological impedance test cell 1 used to test the rheological impedance characteristics of an oil-displacement polymer, the oil-displacement polymer 2 and the test electrode 3 form a double-layer capacitance 5 phenomenon caused by the mechanical interaction of polarized charges 6. Furthermore, as the test period increases, the wire 4 connected to the test electrode also forms a rheological impedance induced by inductance and resistance. Therefore, to quantitatively characterize the rheological impedance characteristics of the oil-displacement polymer, the polymer rheological impedance 10 is introduced to represent the rheological impedance 10 generated by the oil-displacement polymer in the rheological impedance test cell 1. The rheological impedance 9 of the phase angle element represents the double-layer capacitance 5 phenomenon and the transfer transition behavior of polarized charges 6 in the rheological impedance test cell 1. The rheological impedance 8 generated by the measuring electrode and the wire connected to it represents the rheological impedance generated by the test electrode 3 and wire 4 in the rheological impedance test cell 1. Based on the distribution patterns of the polymer rheological impedance 10 and the rheological impedance 9 of the phase angle element, and based on 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. Among them, for the composite equivalent circuit model, a virtual capacitor 13 in parallel with the polymer rheological impedance is introduced to simulate the mechanical behavior of the charge transfer transition at the interface between the test electrode 3 and the oil displacement polymer 2, eliminate the interference of external factors, and realize the quantitative characterization of the rheological impedance characteristics of the oil displacement polymer.

[0071] Figure 2This is a schematic diagram of the Gray Wolf algorithm introduced in this method to determine the applicability limits of equivalent models used to characterize the rheological impedance characteristics of oil displacement polymers. This algorithm aims to optimize the applicability 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. The Gray Wolf algorithm is divided, from top to bottom, into α-wolves 14, β-wolves 17, δ-wolves 20, and ω-wolves 23, based on the wolf pack's social status and fitness with the three equivalent models. As the pack strengthens its encirclement of prey 24, the algorithm updates the random direction vectors of α-wolves 14, β-wolves 17, and δ-wolves 20 (i.e., random direction vector 15 for α-wolves, random direction vector 18 for β-wolves, and random direction vector 21 for δ-wolves). It also updates the distances between α-wolves 14, β-wolves 17, δ-wolves 20 and ω-wolves 23 (i.e., distance 16 between ω-wolf and α-wolves, distance 19 between ω-wolf and β-wolves, and distance 22 between ω-wolf and δ-wolves). Next, the positions of α wolf 14, β wolf 17, δ wolf 20 and ω wolf 23 are updated, and it is determined whether the updated result is the optimal applicable limit of the series equivalent circuit model 7, the parallel equivalent circuit model 11 and the composite equivalent circuit model 12. If the optimal usage limit conditions are 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 based on the equivalent circuit method to characterize the rheological impedance characteristics of polymers for oil displacement:

[0073] (1) 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 A dataset for polymer rheological impedance characterization under shear was constructed. The dataset was randomly divided into training, validation, and test sets using a holdout method, with a ratio of 8:1:1.

[0074] This completes the division of the data set for polymer rheological impedance characterization for oil displacement under shear effect.

[0075] Repeat this step to construct another data set for characterizing the rheological impedance of polymers used for property and structural oil displacement.

[0076] (2) For the evaluation of the rheological properties and impedance characteristics of polymers for oil displacement, the rheological impedance 9 of the phase angle element is introduced to simulate the double-layer capacitance phenomenon near the interface between the test electrode and the polymer for oil displacement, while the rheological impedance 10 of the polymer is replaced by pure resistance. At the same time, the rheological impedance 8 of the measuring electrode and the wire connected to it, as well as the inductance phenomenon caused by high frequency, are considered and regarded as pure resistance and pure inductance. By combining 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 to it, an equivalent model characterizing the rheological impedance characteristics of polymers for oil displacement can be constructed. Based on the generalized Ohm's law, the total rheological impedance Z of the experimental test can be calculated:

[0077]

[0078] Where 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 Euler's formula, the total rheological impedance Z is converted into a vector form:

[0080]

[0081]

[0082] Where 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 approaches 0 or infinity, the values ​​of the real and imaginary parts 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 equations:

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

[0087] When testing the rheological impedance characteristics of polymers used for oil displacement, the total rheological impedance value is regarded as the total resistance of the equivalent circuit, that is, the circuit is decomposed into the polymer resistance, the phase angle element resistance and the rheological impedance 8 generated by the measuring electrode and the wire connected thereto. When the resistance R of the equivalent polymer rheological impedance 10 p When the connection with the phase angle element (CPE) is in series, it can be regarded as a series equivalent circuit model based on the generalized Ohm's law and the current flow law of the series circuit. Under the series equivalent circuit conditions, the current flowing through the two is the same. In this case, the rheological impedance (Z CPE ) can be written as:

[0088]

[0089] Where: ψ is the conductivity, S; A0 is a constant. When ψ = 0, CPE is a pure resistor; when ψ = 1, CPE is a pure capacitor. When ω = 0, the imaginary part is zero, The phase angle element is regarded as an ideal resistor; when ω = 1, the real part becomes zero, The phase angle elements are considered as ideal capacitors.

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

[0091] Z * =R p +[A0(jω) ψ ] -1 (7)

[0092]

[0093] Where 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 equations:

[0095]

[0096] In addition, the series equivalent circuit also contains the rheological impedance 8 generated by the measuring electrodes and the wires connected to them, which can be expressed as:

[0097] Z L =R2+jωL (11)

[0098] Where Z L is the rheological impedance 8, Ω generated by the measuring electrode and the wire connected to it; R2 is the resistance generated by the measuring electrode and the wire connected to it, Ω; L is the inductance generated by the measuring electrode and the wire connected to it, H.

[0099] In summary, the rheological impedance generated by the polymer and the phase angle element is summed with the rheological impedance 8 generated by the measuring electrode and the wire connected thereto, that is, a series equivalent circuit model 7 is constructed to characterize the rheological impedance characteristics of the polymer for oil displacement, namely

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

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

[0102] This completes the construction of a series equivalent model for characterizing the rheological impedance characteristics of polymers used for oil displacement.

[0103] By repeating this step, a series equivalent model of the rheological impedance characteristics of another polymer for oil displacement with different properties and structures can be constructed.

[0104] (III) When testing the rheological impedance characteristics of polymers, based on the generalized Ohm's law and the current flow law of parallel circuits, its rheological impedance is connected in parallel with the rheological impedance of the phase angle element 9 to construct a parallel equivalent circuit. Based on this, the rheological impedance under the parallel equivalent condition is obtained according to the generalized Ohm's law, that is,

[0105]

[0106] Where,

[0107] Similarly, Z' and Z" satisfy the following equations, namely

[0108]

[0109] In summary, the rheological impedance under the parallel equivalent condition is summed with the rheological impedance 8 generated by the measuring electrode and the wire connected thereto, that is, a parallel equivalent model 11 characterizing the rheological impedance characteristics of the oil displacement polymer is constructed, which is as follows:

[0110]

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

[0112] This completes the construction of a parallel equivalent model for characterizing the rheological impedance characteristics of polymers used for oil displacement.

[0113] By repeating this step, a parallel equivalent model of the rheological impedance characteristics of another polymer for oil displacement with different properties and structures can be constructed.

[0114] (IV) When testing the rheological impedance of polymers for oil displacement, in order to meet the applicability requirements under different shear rate conditions, the rheological impedance 10 of the polymer is connected in parallel with the virtual capacitor, and then the rheological impedance 9 of the phase angle element and the rheological impedance 8 generated by the measuring electrode and the wire connected thereto are connected in series, thereby constructing a composite equivalent circuit model. Compared with the series and parallel equivalent circuit models, this composite equivalent circuit model incorporates the rheological impedance induced by the test environment, thereby enhancing the accuracy of the characterization of the rheological impedance characteristics of polymers for oil displacement at a certain shear rate. The details are as follows:

[0115]

[0116] Where C1 is the virtual capacitor 13F connected in parallel with the rheological impedance of the polymer.

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

[0118]

[0119] In summary, by summing the rheological impedance under the composite equivalent conditions and the rheological impedance 8 generated by the measuring electrode and the wire connected thereto, a composite equivalent model 14 for characterizing the rheological impedance characteristics of the oil displacement polymer can be constructed, as follows:

[0120]

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

[0122] This completes the construction of a composite equivalent model for characterizing the rheological impedance characteristics of polymers used for oil displacement.

[0123] By repeating this step, a composite equivalent model of the rheological impedance characteristics of another polymer for oil displacement with different properties and structures can be constructed.

[0124] (V) In order to determine the applicable limits of the equivalent model for characterizing the rheological impedance characteristics of polymers used for oil displacement at different shear rates, the 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: α, β, δ, and ω. α wolf 14, as the leader, represents the optimal equivalent circuit model at the current shear rate; β wolf 17, as the assistant, supports the decision of α wolf 14 and represents the suboptimal solution; δ wolf 20 follows the command of α and β wolves and represents the third optimal solution; and ω wolf 23 is at the bottom of the hierarchy and obeys the command of α, β, and δ wolves. The hunting behavior of the wolf pack is divided into two steps: surrounding the prey 24 and hunting.

[0125] Step 1: After finding the prey 24, the wolf pack surrounds the prey 24. The distance D between each ω wolf 23 and the prey 24 and the updated position vector X(t+1) of the ω wolf 23 are respectively:

[0126] D=|C·X p (t)-X(t)| (21)

[0127] X(t+1)=X p (t)-A·D (22)

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

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

[0130] C=2r2 (24)

[0131]

[0132] Where r1 and r2 are random vectors in [0,1]; a is the attenuation factor, which decreases linearly from 2 to 0 as the number of iterations increases; T is the total number of iterations.

[0133] In step 2, after the wolf pack simulates the encirclement of prey 24, wolf α, wolf β, and wolf δ jointly lead the entire wolf pack to gradually narrow the encirclement of prey 24, thereby achieving the goal of predation. The details are as follows:

[0134]

[0135] Where, X α 、X β 、X δ are the position vectors of α, β and δ wolves respectively; X α (t), X β (t), X δ (t) are the position vectors of wolves α, β and δ in the tth iteration respectively; D α 、D β 、D δ are the distances between α, β and δ wolves and ω wolf respectively; A1, A2, A3 and C1, C2, C3 are all random direction vectors; X1, X2, X3 are the updated position vectors generated by ω wolf according to the positions of α, β and δ wolves respectively; X'(t+1) is the final updated position vector of ω wolf after the end of the tth round of iteration.

[0136] After each iteration, the fitness values ​​of all ω wolves 23 are recalculated, compared, and new α, β, and δ wolves are determined. The next iteration is then repeated, gradually approaching the global optimal solution. At this point, the equivalent circuit model type represented by the α wolves 14 with the highest fitness value is the equivalent model that best matches the shear rate condition. This allows the applicability limits of the three types of equivalent circuit models at different shear rates to be determined.

[0137] In order to ensure the accuracy of the applicable limit of the equivalent model of polymer rheological impedance characteristics for oil displacement under shear effect, considering that the random direction vector A changes with the change of attenuation factor a, its size is closely related to the global search and local search capabilities of the algorithm, which will cause deviation in the applicable limit of the equivalent model of rheological impedance characteristics. Therefore, based on the algorithm, a nonlinear attenuation factor a is introduced. * , enhance the accuracy of the prediction of the applicable limit of the equivalent model, the updated attenuation factor a * as follows:

[0138]

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

[0140] In order to speed up the convergence of the global search phase, the gray wolf algorithm is improved by combining prior knowledge to make the initial population distribution more uniform. In order to determine the applicable limit of the equivalent model for the rheological impedance characteristics of polymers used for oil displacement under shear effect, the rectangular range of the wolf pack encircling the prey 24 is set to L×W, and the global coordinate system is established with the lower left corner as the origin. According to the prey radius r a and the length of the capture zone L, generating k=|L / (2r a )| baseline, baseline y k express

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

[0142] When the population is initialized, the random coordinates of the prey 24 are guided, and n coordinates are set. Different from the randomly initialized coordinate values ​​of the prey 24, it is stipulated that |n / k| random coordinates of the prey 24 are randomly generated on each baseline, that is, the random coordinates x of these prey 24 are fixed in batches, and their y coordinates are randomly set. If there are any surpluses, n-|n / k| prey are randomly initialized and distributed.

[0143] In the gray wolf optimization algorithm, α wolf 14, β wolf 17, and δ wolf 20 guide ω wolf 23 in its search for optimal results. The guidance provided by the first three wolves to ω wolf 23 is consistent. However, during each iteration, α wolf 14, β wolf 17, and δ wolf 20 are assigned to the three wolves with the highest fitness values. Among them, α wolf 14 has the highest fitness value, meaning that α wolf 14 is closer to prey 24. Therefore, by increasing the weight of α wolf 14 in the guidance process among the three leading wolves, ω wolf 23 is guided more effectively towards prey 24. Furthermore, as the iterative optimization progresses, α wolf 14 approaches prey 24 closer and closer at different iterations. At the same time, the fitness differences between β wolf 17 and δ wolf 20 and α wolf 14 gradually decrease. At this point, the guidance role of β wolf 17 and δ wolf 20 is gradually strengthened. Specifically, as the number of iterations progresses, the weight of α wolf 14 is dynamically and evenly increased in the first half. In the second half, as the fitness gap between α wolf 14, β wolf 17, and δ wolf 20 gradually narrows, the guiding weight of β wolf 17 and δ wolf 20 is gradually increased. The mathematical expression for the next generation position of ω wolf 23 is improved as follows:

[0144]

[0145] Where ζ and It is an adjustment factor used to adjust the proportion of additional guidance given to alpha wolf 14 in the early and late stages of iterative optimization.

[0146] This completes the determination of the applicability limit of the equivalent model for characterizing the rheological impedance characteristics of polymers used for oil displacement.

[0147] By repeating steps (2), (3), (4) and (5), the applicable limit of the equivalent model for characterizing the rheological impedance characteristics of polymers with other properties and structures for oil displacement can be determined.

[0148] The total rheological impedance (Z) of the polymer for oil displacement under shear effect of the present invention is obtained by automatic balanced bridge method and radio frequency IV method; the phase angle of the rheological impedance of the polymer for oil displacement under shear effect is The shear rate range is 0 to 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] This invention mainly consists of a five-step method, namely, the division of the data set for characterizing the rheological impedance of polymers for oil displacement under shear effect, the construction of a series equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement, the construction of a parallel equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement, the construction of a composite equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement, and the determination of the applicable limit of the equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement. The first step is to construct and divide the data set for characterizing the rheological impedance characteristics of polymers for oil displacement under shear effect according to the rheological performance test results of polymers for oil displacement; the second, third and fourth steps are to break through the rheological impedance characteristics of polymers for oil displacement. To address the errors caused by charge transfer transitions and double-layer effects in rheological performance testing, we established series, parallel, and composite equivalent circuit models for characterizing the rheological impedance of oil-displacement polymers. Furthermore, we extracted the equivalent resistance of the polymer rheological impedance based on these equivalent models, which is crucial for quantitatively characterizing the rheological impedance of oil-displacement polymers. The fifth step involves introducing the Grey Wolf algorithm. Based on a dataset constructed to characterize the rheological impedance of oil-displacement polymers under shear effects, we optimize the applicable limits of the equivalent model at different shear rates, thereby forming a quantitative characterization of the rheological impedance of oil-displacement polymers. This provides a reliable and scientific method for quantitatively characterizing the rheological impedance of new oil-displacement polymers of any properties and structures. This approach has a positive impact on promoting the widespread application of polymer flooding in oilfields, addressing the challenges of conventional polymer enhanced oil recovery in complex reservoir environments with high temperature and high salinity, and driving the orderly implementation of oil and gas resource exploration and development plans under the "Deep Earth Engineering" initiative.

Claims

1. A method for characterizing the rheological impedance characteristics of polymers for oil displacement based on an equivalent circuit method, characterized in that The steps include: (1) Based on the rheological properties test results of oil displacement polymers, the total rheological impedance Z and phase angle of oil displacement polymers under different shear rate conditions are obtained Construct and partition the data set for characterizing the rheological impedance characteristics of polymers under shear effects; (2) Constructing a series equivalent model to characterize the rheological impedance characteristics of polymers 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 a pure resistance; at the same time, considering the rheological impedance of the measuring electrode and the wire connected thereto, as well as the inductance phenomenon caused by high frequency, they are regarded as pure resistance and pure inductance; combining the pure resistance representing the rheological impedance of the polymer, the rheological impedance of the phase angle element of the double-layer capacitance phenomenon, and the pure resistance and inductance of the rheological impedance of the measuring electrode and the wire connected thereto, an equivalent model to characterize the rheological impedance characteristics of polymers for oil displacement can be constructed; (3) Constructing a parallel equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement; (4) Constructing a composite equivalent model to characterize the rheological impedance characteristics of polymers used for oil displacement; (5) The Grey Wolf algorithm is introduced to construct a data set for characterizing the rheological impedance characteristics of polymers for oil displacement under shear effects, and the applicable limits of the equivalent model at different shear rates are optimized to achieve quantitative characterization of the rheological impedance characteristics of polymers for oil displacement.

2. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 1, wherein: The series equivalent circuit model for characterizing the rheological impedance characteristics of the oil displacement polymer in (II) is as follows: WITH C =Z * +Z L =R p +[A0(jω) ψ ] -1 +R2+jωL(12) Where Z C is the rheological impedance of the series equivalent circuit model; Z * is the total rheological impedance in complex form; j is the imaginary unit, Z L is the rheological impedance generated by the measuring electrode and the wire connected to it; R2 is the resistance generated by the measuring electrode and the wire connected to it; L is the inductance generated by the measuring electrode and the wire connected to it; ψ is the conductivity; A0 is a constant; ω is the angular frequency; R p is the resistance of the equivalent polymer rheological impedance.

3. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 2, wherein: When constructing the parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement in (III), the rheological impedance of the polymer 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 thereto, and the parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement is obtained as follows; Where: Z B is the rheological impedance of the parallel equivalent model; 4. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 3, wherein: When constructing the composite equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement in (IV), 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 wire connected thereto are connected in series to construct a composite equivalent circuit model. The rheological impedance under the composite equivalent conditions and the rheological impedance generated by the measuring electrode and the wire connected thereto are summed to construct a composite equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement, as follows: Where Z F is the rheological impedance of the composite equivalent model; C1 is the virtual capacitor in parallel with the rheological impedance of the polymer.

5. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 4, wherein: The method (2) for constructing a series equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement: Based on the generalized Ohm's law, the total rheological impedance Z of the experimental test is calculated as: Where 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; Based on Euler's formula, the total rheological impedance Z is converted into a vector form: Where 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; Based on the generalized Ohm's law of the equivalent circuit, when the angular frequency approaches 0 or infinity, the values ​​of the real and imaginary parts of the total rheological impedance are as follows: When ω→0, Z'| ω→0 =R, Z"| ω→0 =R; when ω→∞, Z'| ω→∞ =0, Z"| ω→∞ =0; At the same time, Z' and Z" also satisfy the following equations: (Z'-R / 2) 2 +Z” 2 =(R / 2) 2 (5) When testing the rheological impedance characteristics of polymers used for oil displacement, the total rheological impedance value is regarded as the total resistance of the equivalent circuit, that is, the circuit is decomposed into the resistance of the polymer, the resistance of the phase angle element, and the resistance and inductance generated by the measuring electrode and the wire connected to it; when the resistance R of the equivalent polymer rheological impedance is p When the connection with the phase angle element CPE is in series, it is regarded as a series equivalent circuit model based on the generalized Ohm's law and the current flow law 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 of the phase angle element CPE for: Where: ψ is the conductivity, S; A0 is a constant. When ψ = 0, CPE is a pure resistor; when ψ = 1, CPE is a pure capacitor; when ω = 0, the imaginary part is zero, The phase angle element is regarded as an ideal resistor; when ω = 1, the real part becomes zero, The phase angle element is regarded as an ideal capacitor; The total impedance of the polymer and phase angle element under the series equivalent model condition is the sum of their resistances, that is: Where R p is the resistance of the equivalent polymer rheological impedance, Ω; At the same time, Z' and Z" also satisfy the following equations: In addition, the series equivalent circuit also contains the rheological impedance generated by the measuring electrodes and the wires connected to them, namely: WITH L =R2+jωL(11) Where Z L is the rheological impedance generated by the measuring electrode and the wire connected to it; R2 is the resistance generated by the measuring electrode and the wire connected to it, Ω; L is the inductance generated by the measuring electrode and the wire connected to it; The rheological impedance generated by the polymer and the phase angle element is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus constructing a series equivalent circuit model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

6. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 5, characterized in that: The method of constructing a parallel equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement (III): When testing the rheological impedance characteristics of polymers, based on the generalized Ohm's law and the current flow law of parallel circuits, its rheological impedance is connected in parallel with the rheological impedance of the phase angle element to construct a parallel equivalent circuit. According to the generalized Ohm's law, the rheological impedance under parallel equivalent conditions is obtained, that is: Where, Similarly, Z' and Z" satisfy the following equations, namely: The rheological impedance under the parallel equivalent condition is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus completing the construction of a parallel equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

7. The method for characterizing the rheological impedance characteristics of polymers for oil displacement based on the equivalent circuit method according to claim 6, wherein: The method (IV) for constructing a composite equivalent model for characterizing the rheological impedance characteristics of polymers for oil displacement: When testing the rheological impedance of a polymer for oil displacement, the rheological impedance of the polymer is connected in parallel with a virtual capacitor. Then, the impedance of the phase angle element and the rheological impedance generated by the measuring electrode and the wire connected to it are connected in series to construct a composite equivalent circuit model, as follows: Where C1 is the virtual capacitor in parallel with the rheological impedance of the polymer; Therefore, the composite rheological impedance of the polymer and the phase angle element is written as: The rheological impedance under the composite equivalent conditions is summed with the rheological impedance generated by the measuring electrode and the wire connected thereto, thus completing the construction of a composite equivalent model for characterizing the rheological impedance characteristics of the polymer for oil displacement.

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