A method for predicting rheological properties of a polymer solution based on fusion of physical information and machine learning

Abstract

This invention discloses a method for predicting the rheological properties of polymer solutions based on the fusion of physical information and machine learning. First, a dataset for training the machine learning model is constructed, including experimental condition data and rheological property data, where the rheological property data is the viscosity of the polymer solution. The experimental condition data is processed using the Carreau-Yasuda equation and the Arrhenius equation to obtain Carreau-Yasuda equation parameters, temperature displacement factor, and theoretically predicted viscosity values. A machine learning model is selected, trained, and optimized to obtain a polymer solution rheological property prediction model. Based on the input polymer type, polymer concentration, temperature, inorganic salt type, inorganic salt concentration, and shear rate, the viscosity of the polymer solution is predicted. This invention establishes a polymer solution rheological property prediction model and method based on the fusion of physical information and machine learning, solving the problems of insufficient generalization ability of purely data-driven models and low accuracy in predicting conditions exceeding the training data range.

Description

Technical Field

[0001] This invention belongs to the field of polymer material application technology, specifically a method for predicting the rheological properties of polymer solutions based on the fusion of physical models and machine learning. Background Technology

[0002] Polymer solutions are viscoelastic, non-Newtonian fluids formed when polymer materials are dissolved in a solvent. This viscoelastic rheological property ensures the widespread application of polymer solutions in human society. In the oil and gas extraction field, polymer solutions are used in fracturing, drilling, and oil displacement. For example, during fracturing operations, the high viscosity of polymer solutions ensures the high dispersion of the proppant used to support formation fractures, preventing fracturing failure due to proppant blockage. The rheological properties of polymer solutions are core indicators that directly determine their adaptability and effectiveness in practical engineering applications. For instance, in tertiary oil recovery, the viscosity stability of polymer solutions directly affects oil displacement efficiency and swept volume; in water treatment flocculation processes, their rheological behavior is closely related to floc formation efficiency and sedimentation performance.

[0003] The rheological properties of polymer solutions are influenced by environmental factors, process formulations, and polymer structure. For example, increasing temperature leads to a decrease in solution viscosity, while increasing polymer concentration increases viscosity. Existing theoretical models have established constitutive equations for the macroscopic rheological behavior of polymer solutions and influencing factors; for instance, the Carreau-Yasuda model describes the relationship between rheological properties and shear rate, the Arrhenius equation describes the relationship between rheological properties and temperature, and the Mark-Houwink equation describes the relationship between polymer concentration and rheological properties. However, these theoretical models can only quantify the relationship between a single factor and rheological properties, and cannot simultaneously correlate multiple experimental factors (such as polymer concentration, polymer molecular weight, temperature, and shear rate) with rheological properties, resulting in an inability to accurately predict the rheological properties of polymer solutions. Nevertheless, a precise method for predicting the rheological properties of polymer solutions has significant theoretical and engineering value for guiding solution formulation optimization, process parameter control, and application expansion.

[0004] With the rapid development of computer science and data analysis technologies, the integration of machine learning techniques with traditional materials science has gradually become a research hotspot. Machine learning, with its powerful data mining and nonlinear fitting capabilities, provides a novel approach to predicting material properties. However, existing machine learning models rely on purely data-driven approaches, resulting in insufficient generalization ability. When prediction conditions exceed the scope covered by the training data, the models are prone to significant biases.

[0005] The key to solving the above problems lies in breaking through the limitations of purely data-driven approaches and integrating knowledge from the physical domain into machine learning models to construct performance prediction models embedded with physical information. Establishing a method for predicting the rheological properties of polymer solutions based on the fusion of physical information and machine learning is of great significance for accurately predicting the response of solutions to rheological properties under complex environments and optimizing polymer solution formulation process parameters. Summary of the Invention

[0006] To address the aforementioned problems in existing technologies, this invention provides a method for predicting the rheological properties of polymer solutions based on the fusion of physical information and machine learning. A prediction model for the rheological properties of polymer solutions based on the fusion of physical information and machine learning is established to solve the problems of insufficient generalization ability of purely data-driven models and low accuracy in predicting conditions exceeding the training data range, thereby achieving accurate prediction of the rheological response of polymer solutions.

[0007] This invention is achieved through the following technical solution: A method for predicting the rheological properties of polymer solutions based on the fusion of physical information and machine learning includes the following steps: (1) Constructing the dataset used to train the machine learning model A dataset is constructed that includes experimental condition data and rheological performance data, wherein the rheological performance data is the viscosity data of the polymer solution, i.e., the experimentally tested viscosity value.

[0008] Select polymers and design rheological property testing experimental conditions, including polymer concentration, polymer type, inorganic salt concentration, inorganic salt type, temperature, and shear rate; prepare a series of polymer solutions, set different polymer and inorganic salt concentrations in the polymer solutions, and use a rheometer to conduct rheological property testing experiments on each polymer solution at different temperatures and shear rates to obtain experimental viscosity values ​​and rheological curves under different experimental conditions.

[0009] (2) Data processing and partitioning The Carreau-Yasuda and Arrhenius equations are the most reliable physical equations describing the relationship between shear rate and temperature and the viscosity of polymer solutions, respectively. This invention embeds the Carreau-Yasuda and Arrhenius equations into a machine learning rheological property prediction model to improve the model's accuracy in predicting changes in rheological properties caused by variations in temperature and shear rate. A dataset is constructed using obtained rheological curve data and experimental condition data. The experimental condition data in the dataset is then processed using the Carreau-Yasuda and Arrhenius equations to fit the model parameters of the Carreau-Yasuda equation, yielding the model parameters, temperature displacement factor, and theoretically predicted viscosity value.

[0010] The Carreau-Yasuda equation is expressed as follows: , in η 0 represents zero shear viscosity. Let λ represent infinite shear viscosity, λ be the relaxation time, n be the power-law exponent, and m represent the Yasuda exponent. η 0、 λ, n, and m are collectively referred to as the model parameters of the Carreau-Yasuda equation.

[0011] The Arrhenius equation is expressed as follows: , in Let A be the solution viscosity, E be the activation energy of viscous flow, R = 8.314 J / (mol·K), and T be the absolute temperature.

[0012] The residual viscosity data (residual viscosity = theoretical predicted viscosity value - experimental tested viscosity value) between the theoretical predicted viscosity value and the experimental tested viscosity value under the same experimental conditions is used as a new dataset. The residual viscosity data is normalized and divided into training set and test set. The training set is used to train the machine learning model to obtain the optimal parameters, and the test set is used to evaluate the model's predictive performance.

[0013] (3) Constructing a rheological performance prediction model The machine learning model is trained using the following input features: inorganic salt type, inorganic salt concentration, polymer concentration, polymer type, shear rate, temperature displacement factor, theoretically predicted viscosity value, and the product of shear rate and temperature displacement factor. The residual viscosity between the theoretically predicted viscosity value and the experimentally tested viscosity value is used as the output feature. The machine learning model is trained using the training set data and tested using the test set; the coefficient of determination is used. R 2 To evaluate the performance of the model, R 2 The calculation formula is:

[0014] In the formula, η i This is expressed as the viscosity value obtained from experimental testing; Predict viscosity values ​​for the model; This represents the average viscosity measured in the experiments. i This is the sample index value.

[0015] The model performance was further optimized by adjusting the hyperparameters; the optimized machine learning model was then used as a prediction model for the rheological properties of polymer solutions. This model can predict the viscosity of polymer solutions based on the input polymer type, polymer concentration, temperature, inorganic salt type, inorganic salt concentration, and shear rate.

[0016] Further, step (2) involves processing experimental data using the Carreau-Yasuda equation as follows: Data are grouped according to the same polymer concentration, polymer type, inorganic salt concentration, and inorganic salt type. A reference temperature is selected for each formulation group (chosen from the multiple experimental temperatures in step 1). Only the viscosity-shear rate curve at this reference temperature is used to fit the model parameters of the Carreau-Yasuda equation and saved as the "reference parameters" for that formulation group. When the effective measurement points at the reference temperature are insufficient to support nonlinear fitting, heuristic initial values ​​based on the upper and lower bounds of observation are used as fallback parameters to ensure the program runs normally.

[0017] The theoretical viscosity prediction data is calculated as follows: For each formulation group (same polymer concentration, same polymer type, same inorganic salt concentration, same inorganic salt type, different shear rates), find the Carreau-Yasuda model parameters fitted to the formulation group at the reference temperature; calculate the temperature displacement factor between the temperature at which the viscosity to be predicted is set for the formulation group and the selected reference temperature using the Arrhenius equation. The expression of the temperature displacement factor calculated by the Arrhenius equation is as follows:

[0018] in It is the temperature displacement factor, T and T ref These are the temperature at which the viscosity is to be predicted and the reference temperature, respectively.

[0019] The temperature displacement factor is multiplied by the Carreau-Yasuda model parameters at the reference temperature to scale the Carreau-Yasuda model parameters at the temperature at which the viscosity of the formulation group is to be predicted. The scaled model parameters are then substituted into the Carreau-Yasuda equation to obtain the theoretical predicted viscosity of the polymer solution at the set temperature of the formulation group.

[0020] Further, the polymer in step (1) is a polyacrylamide compound, specifically acrylamide combined with sodium acrylate, sodium 2-acrylamido-2-methylpropanesulfonate, methacryloyloxyethyltrimethylammonium chloride, etc. N A copolymer of any one of (3-dimethylaminopropyl)methacrylamide, sodium styrene sulfonate, or a homopolymer of polyacrylamide.

[0021] Preferably, the molar ratio of acrylamide structural units in the polyacrylamide compound structure is 0 to 100 mol.

[0022] Furthermore, the machine learning model selected in step (3) is one of the following: random forest, support vector regression, decision tree, extreme gradient boosting, Gaussian regression, or deep learning algorithm.

[0023] Furthermore, the specific method for further optimizing the model performance by adjusting the model hyperparameters in step (3) is to adjust the model hyperparameters using existing hyperparameter adjustment methods; preferably, the model hyperparameter adjustment method is at least one of particle swarm optimization, naive Bayes, grid search algorithm and random search algorithm.

[0024] Further, in step (2), the data values ​​of the residual viscosity data after normalization are transformed to the range of [0, 1]; then 80% of the residual viscosity data is divided into the training set and 20% into the test set.

[0025] Furthermore, the above method also includes using a trained model to predict the rheological properties of a polymer solution system under designed experimental conditions, and comparing the model-predicted viscosity value with the experimentally tested viscosity value (true value) to evaluate the accuracy of the model prediction.

[0026] Compared with the prior art, the present invention has the following beneficial effects: (1) Traditional mathematical models can only predict the rheological properties of polymer solutions under single experimental conditions, but cannot accurately predict the rheological properties of polymer solutions under the combined effects of multiple experimental factors. The method proposed in this invention, which integrates physical knowledge based on machine learning, incorporates physical knowledge describing shear rate and solution viscosity, as well as the relationship between temperature and solution viscosity, into the machine learning model to construct a polymer solution rheological property prediction model embedded with physical information. The machine learning model compensates for the error between the physical formula prediction and the actual measurement results, and establishes a polymer solution rheological property prediction method based on the integration of physical information and machine learning. This method can accurately predict the response of solution rheological properties under complex environments, optimize polymer solution formulation and process parameters, and solve the problem of accurately predicting the rheological response of polymer solutions under complex environments.

[0027] (2) This invention utilizes the ability of machine learning technology to process high-dimensional data, fully considers the main factors affecting rheological performance, and solves the problem of large prediction errors caused by the difficulty of a single mathematical model in handling the relationship between multiple variables and rheological performance. This method does not require directly establishing a complex functional relationship between experimental conditions and rheological performance, reducing modeling time and improving performance prediction efficiency.

[0028] (3) By establishing a prediction model for the rheological properties of polymer solutions based on machine learning technology, this invention is of great help in understanding the evolution of the rheological properties of polymer solutions under changes in environmental factors, and can guide the optimization of process parameters according to the actual application environment of polymer solutions.

[0029] (4) This invention integrates machine learning technology with polymer physics knowledge to establish a method for predicting the rheological properties of polymer solutions, providing a reference for the development of machine learning in the field of materials and promoting the integration of computer science and materials science. Attached Figure Description

[0030] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a graph showing the performance prediction results of the machine learning model. Figure 3 A comparison graph showing the viscosity values ​​predicted by the machine learning model and the experimentally tested viscosity values ​​(true viscosity). Detailed Implementation

[0031] The specific embodiments of the present invention will be further described below with reference to implementation examples. These embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0032] Example 1 This embodiment takes the prediction of the rheological properties of a specific polymer solution system under varying shear rates as an example. The specific implementation steps are as follows: (1) Constructing the dataset used to train the machine learning model Polymers were selected and rheological property testing conditions were designed, including polymer concentration, polymer type, inorganic salt concentration, inorganic salt type, temperature, and shear rate. A series of acrylamide and sodium 2-acrylamido-2-methylpropanesulfonate copolymer solution samples were prepared according to the designed experimental conditions. Rheological property tests were conducted on the samples at different temperatures and shear rates using a rheometer, obtaining experimental viscosity values ​​and true rheological curves under different experimental conditions.

[0033] (2) Data processing and partitioning A dataset was constructed using real rheological curve data and designed experimental condition parameters. The experimental condition data of the obtained dataset were processed using the Carreau-Yasuda equation and the Arrhenius equation to obtain Carreau-Yasuda equation parameters, temperature displacement factor, and theoretically predicted viscosity data (the specific processing method is the same as in the invention description section).

[0034] The Carreau-Yasuda equation is expressed as follows: , in η 0 represents zero shear viscosity. Let λ represent infinite shear viscosity, λ be the relaxation time, n be the power-law exponent, and m represent the Yasuda exponent. η 0、 λ, n, and m are collectively referred to as the model parameters of the Carreau-Yasuda equation.

[0035] The Arrhenius equation is expressed as follows: , Where is the solution viscosity, A is the pre-factor, E is the activation energy of viscous flow of the solution, R = 8.314 J / (mol·K), and T is the absolute temperature.

[0036] The method for processing experimental data using the Carreau-Yasuda equation is as follows: Data are grouped according to the same polymer concentration, polymer type, inorganic salt concentration, and inorganic salt type. A reference temperature is selected for each formulation group (chosen from the multiple experimental temperatures in step 1). Only the viscosity-shear rate curve at this reference temperature is used to fit the model parameters of the Carreau-Yasuda equation and saved as the "reference parameters" for that formulation group. When the effective measurement points at the reference temperature are insufficient to support nonlinear fitting, heuristic initial values ​​based on observational upper and lower bounds are used as fallback parameters to ensure the program runs correctly.

[0037] The theoretical viscosity prediction data is calculated as follows: For each formulation group (same polymer concentration, same polymer type, same inorganic salt concentration, same inorganic salt type, different shear rates), find the Carreau-Yasuda model parameters fitted to the formulation group at the reference temperature; calculate the temperature displacement factor between the temperature at which the viscosity to be predicted is set for the formulation group and the selected reference temperature using the Arrhenius equation. The expression of the temperature displacement factor calculated by the Arrhenius equation is as follows: , in It is the temperature displacement factor, T and T ref These are the temperature at which the viscosity is to be predicted and the reference temperature, respectively.

[0038] The temperature displacement factor is multiplied by the Carreau-Yasuda model parameters at the reference temperature to scale the Carreau-Yasuda model parameters at the temperature at which the viscosity of the formulation group is to be predicted. The scaled model parameters are then substituted into the Carreau-Yasuda equation to obtain the theoretical predicted viscosity of the polymer solution at the set temperature of the formulation group.

[0039] (3) Constructing a rheological performance prediction model The residual viscosity data between theoretically predicted viscosity values ​​and experimentally tested viscosity values ​​under the same experimental conditions is used as a new dataset. The inorganic salt type, inorganic salt concentration, polymer concentration, polymer type, shear rate, temperature displacement factor, theoretically predicted viscosity, and the product of shear rate and temperature displacement factor are used as input features, and the residual viscosity is used as the output feature.

[0040] The new residual viscosity dataset was normalized to the [0, 1] interval. 80% of the new dataset was divided into a training set and 20% into a test set. The training set was used to train the model and obtain optimal parameters, while the test set was used to evaluate the model's predictive performance. A random forest algorithm was selected, and the model was trained using the training set and tested using the test set. The particle swarm optimization algorithm was used to adjust the model's hyperparameters. The coefficient of determination was used... R 2 Evaluate the model's performance. R 2 The higher the value, the higher the model's predictive accuracy. For example... Figure 2 As shown. R 2 The calculation formula is:

[0041] In the formula, n i This is expressed as the viscosity value obtained from experimental testing; Predict viscosity for the model; This represents the average viscosity measured in the experiments. i This is the sample index value.

[0042] (4) The rheological properties of the polymer solution system under the designed experimental conditions were predicted using the trained model. The designed experimental conditions were: an experimental temperature of 80℃, sodium chloride as the inorganic salt with a concentration of 1.0 M, a polymer concentration of 50 mM, and a copolymer of acrylamide-2-acrylamido-2-methylpropanesulfonate with a molar content of 80% of the acrylamide-corresponding unit structure. The shear rate range was 0.01–1000 1 / s. The comparison results between the viscosity data predicted by the machine learning model and the viscosity data tested in the actual experiment are as follows: Figure 3 As shown, the viscosity values ​​of the polymer solution predicted by the machine learning model are in high agreement with the experimentally tested viscosity values, indicating that the machine learning model incorporating physical information proposed in this patent can accurately predict the rheological properties of polymer solutions.

Claims

1. A method for predicting the rheological properties of polymer solutions based on the fusion of physical information and machine learning, comprising the following steps: (1) Constructing the dataset used to train the machine learning model A dataset is constructed that includes experimental condition data and rheological performance data, wherein the rheological performance data is the viscosity data of the polymer solution, i.e., the experimentally tested viscosity value; Select polymers and design rheological property testing experimental conditions, including polymer concentration, polymer type, inorganic salt concentration, inorganic salt type, temperature, and shear rate; prepare a series of polymer solutions, set different polymer concentrations and inorganic salt concentrations in the polymer solutions, and use a rheometer to conduct rheological property testing experiments on each polymer solution at different temperatures and shear rates to obtain experimental viscosity values ​​and rheological curves under different experimental conditions; (2) Data processing and partitioning A dataset was constructed using the obtained rheological curve data and experimental condition data. The experimental condition data of the dataset was processed using the Carreau-Yasuda equation and the Arrhenius equation to obtain the Carreau-Yasuda equation model parameters, temperature displacement factor and theoretically predicted viscosity value. The Carreau-Yasuda equation is expressed as follows: ， in η 0 represents zero shear viscosity. The viscosity is infinite shear, λ is the relaxation time, n is the power law exponent, and m represents the Yasuda exponent. η 0、 λ, n, and m are all model parameters of the Carreau-Yasuda equation; The Arrhenius equation is expressed as follows: ， in Let A be the solution viscosity, E be the activation energy of viscous flow, R = 8.314 J / (mol·K), and T be the absolute temperature. The residual viscosity data between the theoretically predicted viscosity value and the experimentally tested viscosity value under the same experimental conditions is used as a new dataset; the residual viscosity data is normalized and the dataset is divided into training set and test set; (3) Constructing a rheological performance prediction model The machine learning model is trained using the following input features: inorganic salt type, inorganic salt concentration, polymer concentration, polymer type, shear rate, temperature displacement factor, theoretically predicted viscosity, and the product of shear rate and temperature displacement factor. The residual viscosity between the theoretically predicted viscosity and the experimentally tested viscosity is used as the output feature. The machine learning model is trained using the training set data and tested using the test set. The coefficient of determination is used. R 2 Evaluate the model's performance. R 2 The calculation formula is: ， In the formula, η i This is expressed as the viscosity value obtained from experimental testing; Predict viscosity values ​​for the model; This represents the average viscosity measured in the experiments. i This is the sample index value; The model performance was further optimized by adjusting the model hyperparameters; the optimized machine learning model was then used as a prediction model for the rheological properties of polymer solutions.

2. The method according to claim 1, characterized in that, Step (2) involves processing the experimental condition data of the dataset using the Carreau-Yasuda equation and the Arrhenius equation as follows: Data were grouped according to the same polymer concentration, polymer type, inorganic salt concentration, and inorganic salt type, and a reference temperature was selected for each formulation group; the viscosity-shear rate curve at the reference temperature was used only to fit the model parameters of the Carreau-Yasuda equation; when the effective measurement points at the reference temperature were insufficient to support nonlinear fitting, heuristic initial values ​​based on the upper and lower bounds of observation were used as fallback parameters. For each formulation group, find the Carreau-Yasuda model parameters fitted to the formulation group at the reference temperature; calculate the temperature displacement factor between the temperature at which the viscosity to be predicted for the formulation group is set and the selected reference temperature using the Arrhenius equation; multiply the temperature displacement factor by the Carreau-Yasuda model parameters at the reference temperature to scale the Carreau-Yasuda model parameters at the temperature at which the viscosity to be predicted for the formulation group is set, and substitute the scaled model parameters into the Carreau-Yasuda equation to obtain the theoretical predicted viscosity of the polymer solution at the set temperature for the formulation group.

3. The method according to claim 1, characterized in that, The temperature displacement factor calculated using the Arrhenius equation is expressed as follows: ， in It is the temperature displacement factor, T and T ref These are the temperature at which the viscosity is to be predicted and the reference temperature, respectively.

4. The method according to claim 1, characterized in that, The polymer in step (1) is a polyacrylamide compound, which is acrylamide, sodium acrylate, sodium 2-acrylamido-2-methylpropanesulfonate, methacryloyloxyethyltrimethylammonium chloride, etc. N A copolymer of any one of (3-dimethylaminopropyl)methacrylamide, sodium styrene sulfonate, or a homopolymer of polyacrylamide.

5. The method according to claim 1, characterized in that, The molar ratio of acrylamide structural units in the polyacrylamide compound structure is 0 ~ 100 mol.

6. The method according to claim 1, characterized in that, The machine learning model mentioned in step (3) is one of the following algorithms: random forest, support vector regression, decision tree, extreme gradient boosting, Gaussian regression, or deep learning.

7. The method according to claim 1, characterized in that, Step (3) further optimizes the model performance by adjusting the model hyperparameters by using the hyperparameter adjustment method to adjust the model hyperparameters.

8. The method according to claim 7, characterized in that, The method for adjusting the model hyperparameters is one of the following: particle swarm optimization, naive Bayes, grid search, and random search.

9. The method according to claim 1, characterized in that, In step 2, after normalizing the residual viscosity data, the data values ​​are transformed to the [0, 1] interval; then, 80% of the residual viscosity data is divided into the training set and 20% into the test set.

10. The method according to claim 1, characterized in that, The trained model is used to predict the rheological properties of polymer solution systems under designed experimental conditions, and the predicted viscosity values ​​are compared with the experimentally tested viscosity values ​​(true values) to evaluate the accuracy of the model prediction.

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