Method for predicting liquid phase viscosity of fluid based on free volume theory

Abstract

The invention discloses a method for predicting fluid liquid phase viscosity based on a free volume theory, and relates to the technical field of fluid thermophysical property theoretical calculation, and the method comprises the following steps: step 1, obtaining material parameters related to a to-be-measured fluid, and establishing a corresponding free volume theoretical viscosity model; 2, improving the free volume theoretical viscosity model to obtain a correction model; and 3, fitting the correction model and the material parameters, and calculating the viscosity of the fluid to be measured. The method can effectively reduce the calculation deviation of the viscosity.

Description

Technical Field

[0001] This invention relates to the field of fluid thermal property theory calculation technology, and more specifically to a method for predicting the viscosity of a fluid liquid phase based on free volume theory. Background Technology

[0002] Viscosity is one of the fundamental parameters of the fluid momentum conservation equation, and it also characterizes the heat and mass transfer potential of fluid molecules under non-equilibrium thermodynamic conditions. Experimental measurement of viscosity is limited by experimental conditions; obtaining high-precision experimental data is often extremely costly. Furthermore, while existing experimental viscosity measurement methods are highly accurate, their experimental range is typically limited. Therefore, accurate theoretical estimation methods for viscosity are particularly important.

[0003] Traditional viscosity models are categorized into theoretical models, semi-theoretical models, and empirical models. Theoretical models, based on relatively complete low-pressure gas dynamics theory, offer highly accurate predictions for rarefied gases. However, when dealing with liquid viscosity, the complex interactions between liquid molecules and the lack of a unified theory of liquid molecules mean that there are virtually no widely accepted theoretical prediction models for liquid viscosity. Empirical models, through analyzing viscosity data patterns or fluid molecular composition, empirically determine the relationship between viscosity and temperature (and pressure), but these methods exhibit errors under high-pressure conditions. Semi-theoretical models, including free volume theory viscosity models, friction theory viscosity models, and absolute velocity theory models, can generally be used to calculate fluid viscosity over a wide temperature and pressure range.

[0004] The absolute rate theory, based on the velocity of molecular motion, provides a relatively accurate description of gases, but its complexity makes the calculation process cumbersome. Friction theory primarily focuses on intermolecular forces and is suitable for describing high-viscosity fluids, but its applicability to the gas phase is weaker. The free volume viscosity model is one of the most successful viscosity models currently available, demonstrating high accuracy in calculating the viscosity of both gases and liquids, including various pure fluids such as alkanes, aromatics, refrigerants, and ionic liquids. It has the advantages of simple form, few parameters, and the ability to be applied to both gas and liquid phase viscosity calculations.

[0005] Establishing a free volume viscosity model requires the introduction of an additional equation of state to calculate the density at a given temperature and pressure. The PR equation is considered one of the best two-constant cubic equations suitable for calculating the thermodynamic properties of gas-liquid equilibrium (VLE) and mixtures, offering advantages such as simple structure and the ability to obtain fluid thermodynamic properties only requiring critical parameters. However, while the PR equation provides high accuracy for gas-phase calculations, its accuracy for liquid-phase calculations is limited. This can lead to significant deviations in the viscosity calculation model.

[0006] In summary, a method is needed to improve the accuracy of density calculation in the liquid phase region using the PR equation, thereby reducing the bias in viscosity calculation models. Summary of the Invention

[0007] In view of this, the present invention provides a method for predicting the viscosity of fluid liquid phase based on free volume theory, which can effectively reduce the deviation of viscosity calculation model.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting the viscosity of a fluid liquid phase based on free volume theory, comprising: Step 1: Obtain the relevant material parameters of the fluid to be tested and establish the corresponding free volume theoretical viscosity model; Step 2: Improve the free volume theoretical viscosity model to obtain the modified model; Step 3: Fit the modified model and material parameters to calculate the viscosity of the fluid to be tested.

[0009] Preferably, the material parameters in step 1 include: temperature, pressure, density, viscosity, gas constant, amount of substance M, eccentricity factor w, critical temperature, and critical pressure.

[0010] Preferably, the free volume theoretical viscosity model in step 2 includes a rarefied gas viscosity term and a dense fluid viscosity correction term; the rarefied gas viscosity term and the dense fluid viscosity correction term are corrected respectively to obtain the corrected model.

[0011] Preferably, the process of correcting the viscosity term of rarefied gases includes: A correction factor F is introduced into the viscosity term of the rarefied gas. c By modifying the molecular polarity, the model can be applied to predict the viscosity of low-pressure gases from polyatomic, polar, and hydrogen-based substances. The expression for the modified model is as follows: ; ; ; ; ; In the formula: η represents the viscosity value; η0 and Δ η These are the viscosity terms for rarefied gases and the viscosity correction terms for dense fluids, respectively. For collision integrals; It is 1.2593 times the comparison temperature; B represents the superposition of free volumes; αρ is the energy barrier that molecular diffusion needs to overcome; R is the universal gas constant; F c The correction factor is related to the dipole moment and the eccentricity factor; w is the eccentricity factor; μr is the dimensionless dipole moment; κ is the correction factor for strongly polar substances; μ is the contrast dipole moment; V c T c These are the critical specific volume and critical temperature, respectively; α, l κ and κ are parameters to be determined.

[0012] Preferably, the undetermined parameter α of the rarefied gas viscosity term... l The superposition of κ and the free volume B was obtained by fitting the experimental data of overloaded refrigerant.

[0013] Preferably, the process of correcting the viscosity correction term of the dense fluid includes: By adding a volume translation term to the PR equation and using the α function of the generalized Twu form to improve the accuracy of density calculation, the improved volume translation PR equation is obtained as follows: ; ; ; ; ; ; ; In the formula: Tr = T / Tc; T, v, p, R, and w represent Kelvin temperature, specific volume, pressure, gas constant, and eccentricity factor, respectively; the subscript c indicates the critical state, C vt d represents the volume translation term; d, e, f, and g are the parameters to be fitted.

[0014] Preferably, the experimental density values ​​of the fluid under test at a certain temperature and pressure are substituted into the improved volume translation PR equation to obtain the model parameters C. vt And d, e, f, g; then substitute the viscosity value η of the fluid under a certain temperature and pressure into the volume shift PR-viscosity model for fitting to obtain the model parameters α, B, l and κ.

[0015] As can be seen from the above technical solution, compared with the prior art, the present invention discloses a method for predicting the viscosity of a fluid liquid phase based on the free volume theory, with the following beneficial effects: Taking R1234yf refrigerant as an example, the calculation results show that the average relative deviation and maximum relative deviation of the original PR equation in calculating the liquid phase density are 1.39% and 6.96%, respectively, while the average relative deviation and maximum relative deviation of the improved volume translation PR equation in calculating the liquid phase density are 0.05% and 0.33%, respectively. The improved density calculation accuracy nearly halve the calculation deviation of the viscosity model. The average relative deviation and maximum relative deviation of the viscosity calculation model using the original PR equation are 1.17% and 6.59%, respectively, while the improved model has average relative deviations and maximum relative deviations of 0.74% and 2.98%, respectively. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0017] Figure 1 The method flowchart provided by the present invention.

[0018] Figure 2 A comparison chart showing the deviation between the calculated density and experimental values ​​of the original PR and volume translation PR equations provided for this invention.

[0019] Figure 3 The graph shows the deviation between the calculated viscosity and the experimental value of the original PR-viscosity calculation model provided by this invention.

[0020] Figure 4 The deviation diagram between the calculated viscosity and the experimental value of the volume translation PR-viscosity calculation model provided by this invention is shown. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] like Figure 1 As shown, this invention discloses a method for predicting the viscosity of a fluid liquid phase based on free volume theory, comprising: include: Step 1: Obtain the relevant material parameters of the fluid to be tested and establish the corresponding free volume theoretical viscosity model; Step 2: Improve the free volume theoretical viscosity model to obtain the modified model; Step 3: Fit the modified model and material parameters to calculate the viscosity of the fluid to be tested.

[0023] Specifically, the material parameters in step 1 include: temperature, pressure, density, viscosity, gas constant, amount of substance M, eccentricity factor w, critical temperature, and critical pressure.

[0024] Specifically, the free volume theoretical viscosity model in step 2 includes a rarefied gas viscosity term and a dense fluid viscosity correction term; the rarefied gas viscosity term and the dense fluid viscosity correction term are corrected respectively to obtain the corrected model.

[0025] Specifically, the process of correcting the viscosity term for rarefied gases includes: A correction factor F is introduced into the viscosity term of the rarefied gas. c To correct for molecular polarity, a correction factor F is introduced into the viscosity term of rarefied gases. c By modifying the molecular polarity, the model can be applied to predict the viscosity of low-pressure gases from polyatomic, polar, and hydrogen-based substances. The expression for the modified model is as follows: ; ; ; ; ; In the formula: η represents the viscosity value; η0 and Δ η These are the viscosity terms for rarefied gases and the viscosity correction terms for dense fluids, respectively. For collision integrals; It is 1.2593 times the comparison temperature; B represents the superposition of free volumes; αρ is the energy barrier that molecular diffusion needs to overcome; R is the universal gas constant; F c The correction factor is related to the dipole moment and the eccentricity factor; w is the eccentricity factor; μ r is the dimensionless dipole moment; κ is the correction factor for strongly polar substances; μ is the contrast dipole moment; V c T c These are the critical specific volume and critical temperature, respectively; α, l κ and κ are parameters to be determined.

[0026] Specifically, the undetermined parameter α of the rarefied gas viscosity term... l The superposition of κ and the free volume B was obtained by fitting the experimental data of overloaded refrigerant.

[0027] In a specific embodiment of the present invention, for nonpolar molecules, F c Only the first two terms are considered; for polar molecules, all four terms are considered. This makes the viscosity model more widely applicable when calculating the viscosity of ideal gases.

[0028] Specifically, the process of correcting the viscosity correction term of the dense fluid includes: By adding a volume translation term to the PR equation and using the α function of the generalized Twu form to improve the accuracy of density calculation, the improved volume translation PR equation is obtained as follows: ; ; ; ; ; ; ; In the formula: Tr = T / Tc; T, v, p, R, and w represent Kelvin temperature, specific volume, pressure, gas constant, and eccentricity factor, respectively; the subscript c indicates the critical state, C vt d represents the volume translation term; d, e, f, and g are the parameters to be fitted.

[0029] Specifically, the experimental density values ​​of the fluid under test at a certain temperature and pressure are substituted into the improved volume translation PR equation for fitting to obtain the model parameters C. vt And d, e, f, g; then substitute the viscosity value η of the fluid under a certain temperature and pressure into the volume shift PR-viscosity model for fitting to obtain the model parameters α, B, l and κ.

[0030] The goal of viscosity models is to obtain the viscosity under corresponding conditions using easily measurable quantities such as temperature and pressure. Therefore, it is necessary to introduce a state equation to calculate the density at a certain temperature and pressure. In this equation, v and density are reciprocals of each other, that is, their product is 1.

[0031] In one specific embodiment of the present invention, this is the result obtained by fitting data using R1234yf. Figures 2-4 They all take R1234yf as the research object.

[0032] The first step in fitting is to write code based on temperature, pressure, density, and relevant formulas of the equation of state, and use nonlinear fitting (lsqnonlin) in MATLAB to minimize the sum of the squares of the calculated density and the input density.

[0033] Why is it necessary to fit the equation of state instead of using density data directly? Because the resulting density data is ultimately fragmented. In this embodiment, to obtain the density at any temperature and pressure, it is necessary to fit the data using these fragmented data points.

[0034] The second step is to introduce the fitted state equation into the viscosity calculation model code. First, calculate the density using the state equation, then substitute the calculated density into the viscosity formula to obtain the calculated viscosity. Then, use nonlinear fitting (lsqnonlin) to minimize the sum of the squares of the calculated viscosity and the input viscosity to obtain the parameters to be fitted in the viscosity model.

[0035] As shown in Table 1, the improved PR equation fitting parameters are as follows: Table 1. PR Equation Fitting Parameters

[0036] The viscosity model fitting parameters are shown in Table 2.

[0037] The experimental density values ​​of the fluid under test at certain temperature and pressure are substituted into the improved volume translation PR equation presented in this paper for fitting to obtain the model parameters C. vt And d, e, f, g. Figure 2 The figure shown is a comparison of the deviations between the density calculated by the PR equation and the experimental values ​​before and after the improvement.

[0038] The experimental viscosity values ​​of the fluid under test at a certain temperature and pressure are substituted into the volume-shifted PR-viscosity model for fitting to obtain the model parameters α, B, l and κ. Figure 3 , Figure 4 The figure shows the deviation between the viscosity calculated by the viscosity calculation model before and after the improvement and the experimental value.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0040] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting the viscosity of a fluid liquid phase based on free volume theory, characterized in that, include: Step 1: Obtain the relevant material parameters of the fluid to be tested and establish the corresponding free volume theoretical viscosity model; Step 2: Improve the free volume theoretical viscosity model to obtain the modified model; Step 3: Fit the modified model and material parameters to calculate the viscosity of the fluid to be tested.

2. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 1, characterized in that, The material parameters in step 1 include: temperature, pressure, density, viscosity, gas constant, amount of substance M, eccentricity factor w, critical temperature, and critical pressure.

3. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 1, characterized in that, The free volume theoretical viscosity model in step 2 includes a rarefied gas viscosity term and a dense fluid viscosity correction term; the rarefied gas viscosity term and the dense fluid viscosity correction term are corrected respectively to obtain the corrected model.

4. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 3, characterized in that, The process of correcting the viscosity term for rarefied gases includes: A correction factor F is introduced into the viscosity term of the rarefied gas. c By modifying the molecular polarity, the model can be applied to predict the viscosity of low-pressure gases from polyatomic, polar, and hydrogen-based substances. The expression for the modified model is as follows: ； ； ； ； ； In the formula: η represents the viscosity value; η0 and Δ η These are the viscosity terms for rarefied gases and the viscosity correction terms for dense fluids, respectively. For collision integrals; It is 1.2593 times the comparison temperature; B represents the superposition of free volumes; αρ is the energy barrier that molecular diffusion needs to overcome; R is the universal gas constant; F c The correction factor is related to the dipole moment and the eccentricity factor; w is the eccentricity factor; μ r is the dimensionless dipole moment; κ is the correction factor for strongly polar substances; μ is the contrast dipole moment; V c T c These are the critical specific volume and critical temperature, respectively; α, l κ and κ are parameters to be determined.

5. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 4, characterized in that, The undetermined parameter α of the rarefied gas viscosity term, l、 The superposition of κ and the free volume B was obtained by fitting the experimental data of overloaded refrigerant.

6. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 4, characterized in that, The process of correcting the viscosity correction term of the dense fluid includes: By adding a volume translation term to the PR equation and using the α function of the generalized Twu form to improve the accuracy of density calculation, the improved volume translation PR equation is obtained as follows: ； ； ； ； ； ； ； In the formula: Tr = T / Tc; T, v, p, R, and w represent Kelvin temperature, specific volume, pressure, gas constant, and eccentricity factor, respectively; the subscript c indicates the critical state, C vt d represents the volume translation term; d, e, f, and g are the parameters to be fitted.

7. The method for predicting the viscosity of a fluid liquid phase based on free volume theory according to claim 6, characterized in that, The experimental density values ​​of the fluid under test at a certain temperature and pressure are substituted into the improved volume translation PR equation for fitting to obtain the model parameters C. vt And d, e, f, g; Then, the viscosity value η of the fluid under test at a certain temperature and pressure is substituted into the volume shift PR-viscosity model for fitting to obtain the model parameters α, B, and C. l and κ.

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