Method for calculating the swelling force of a polymer slurry

Abstract

The application discloses a kind of high polymer slurry expansion force calculation methods, including steps: according to slurry each component allocation ratio initialization relevant variable;By Runge-Kutta algorithm solving high polymer slurry chemical reaction kinetics equation, obtain the conversion rate change of isocyanate and polyol in current time step;Solving energy balance equation, get slurry temperature change, cumulative current slurry temperature;Combining ideal gas state equation solves slurry volume and determines slurry expansion stage;Slurry is not filled with slurry chamber stage, set fixed slurry confining pressure as atmospheric pressure, slurry volume free expansion;After slurry fills slurry chamber, fixed slurry volume, calculate slurry expansion force;According to the calculation result, update density, volume, pressure, temperature parameter, promote time step;The application can solve the change process of high polymer slurry expansion force with time in real time, lays the foundation for in-depth study high polymer expansion diffusion mechanism, slurry-ground interaction mechanism.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of hydraulic engineering, in particular to a calculation method of the expansion force of a polymer slurry. BACKGROUND

[0002] The polymer material has the characteristics of rapid chemical reaction, large volume expansion rate, good durability and environmental protection safety, and the polymer grouting technology is widely used in highway, tunnel, dam and bridge engineering and other civil and hydraulic engineering because of its small damage to the structure, rapid reaction and other characteristics, and the research on the characteristics of the polymer grouting material is the focus of the polymer material research, and understanding the expansion characteristics of the polymer helps to better understand the reaction process of the polymer material, so that the polymer grouting material can be better used in engineering.

[0003] The principle of the polymer grouting is to inject two-component polymer slurry into the medium, utilize the characteristics that the volume of the slurry rapidly expands and solidifies after the reaction, and achieve the purposes of filling the gap, splitting and compacting the soil body, lifting the upper structure, plugging the leakage channel and reinforcing the rock mass. Accurately mastering the change rule of the expansion force of the polymer slurry with time in the diffusion process is the key to the research on the repair and reinforcement mechanism of the polymer grouting.

[0004] The carbon dioxide gas generated by the foaming reaction and the physical foaming agent gasification are the main reasons for the expansion of the polymer slurry. The reaction heat of the foaming reaction and the gel reaction promotes the vaporization of the physical foaming agent and the increase of the gas volume, so the expansion of the polymer slurry is the result of the joint action of the chemical reaction and the physical foaming agent. When the expansion process of the polymer slurry is constrained, the extrusion pressure is generated on the surrounding medium.

[0005] At present, the research on the expansion performance of the polymer slurry is still relatively insufficient. Based on the empirical expression of the slurry density-expansion force obtained through the test, although the expansion force of the polymer slurry can be determined to some extent, the final expansion force corresponding to the specific slurry density can be obtained, the time change of the expansion force and the density in the reaction process of the polymer cannot be reflected, the accuracy of the calculation and analysis is restricted, and it is difficult to provide guidance for the accurate grouting under the complex pressure environment. Since the expansion force of the polymer is closely related to the chemical reaction process of the slurry, the constraint conditions of the surrounding medium and other factors, under a certain grouting environment, the expansion pressure of the polymer slurry on the surrounding medium changes with time, and the diffusion behavior is closely related to the evolution process of the expansion pressure. At present, there is still lack of effective calculation method for accurately calculating the expansion force of the polymer slurry at different times. SUMMARY

[0006] The application aims to provide a calculation method of high polymer slurry expansion force, solve the problem that current technology can only obtain final expansion force corresponding to specific slurry density, cannot reflect time change of expansion force and density in high polymer reaction process, restricts accuracy of calculation analysis, and is difficult to provide guidance for accurate grouting under complex pressure environment, and lack effective calculation method for accurately calculating expansion force of high polymer slurry at different time.

[0007] The application is implemented as follows: a calculation method of high polymer slurry expansion force, the calculation method comprises the following steps:

[0008] Step one: initialize variables including pressure, slurry temperature, density and molar density according to volume fixed boundary condition and slurry component distribution ratio;

[0009] Step two: obtain change amount of conversion rate of isocyanate and polyol by solving high polymer slurry chemical reaction kinetics equation in current time step through Runge-Kutta algorithm;

[0010] Step three: obtain change amount of slurry temperature by solving energy balance equation, and accumulate to obtain current slurry temperature;

[0011] Step four: solve slurry volume through ideal gas state equation, so as to judge slurry expansion stage;

[0012] Step five: select different boundary conditions and calculation formula according to different slurry expansion stages: set fixed slurry confining pressure as 0.1 MPa and slurry volume freely expands in the stage that slurry does not fill slurry chamber; and fix slurry volume and calculate slurry expansion force in the stage that slurry fills slurry chamber;

[0013] Step six: update parameters including density, volume, pressure, temperature and conversion rate of isocyanate and polyol component reaction according to new calculation result;

[0014] Step seven: time step is advanced, and steps two to six are repeated.

[0015] A further technical scheme of the application is that the high polymer slurry chemical reaction kinetics equation of step two comprises polyurethane high polymer slurry gelation reaction rate equation and slurry foaming reaction rate equation, and the polyurethane high polymer slurry gelation reaction rate equation is as follows:

[0016]

[0017] The slurry foaming reaction rate equation is as follows:

[0018]

[0019] Wherein, ci,0 and X i Let A represent the initial concentration and conversion rate of component i, respectively. When i takes the values ​​of W, OH, and NCO, it represents water, polyol, and isocyanate, respectively. OH and A W E represents the pre-exponential factor for the gelation reaction and the foaming reaction, respectively. OH and E W These are the activation energies of the two reactions, r. W r represents the mass fraction of water. BL ρ is the mass fraction of the liquid physical foaming agent. BL ρ is the density of the physical foaming agent. W ρ is the density of water. P The density of polyurethane, R is the ideal gas constant, and T is the slurry temperature.

[0020] A further technical solution of the present invention is: the Runge-Kutta algorithm in step two uses a fourth-order Runge-Kutta algorithm to solve the chemical reaction kinetic equation. For ordinary differential equations of the form y'=f(x,y), the mathematical description of the fourth-order Runge-Kutta algorithm is as follows:

[0021]

[0022] k1=f(x n ,y n )

[0023]

[0024]

[0025] k4=f(x n +h,y n +hk3)

[0026] Where: h represents the time step selected in the calculation process, which is 0.1s in the program; the independent variable x is the time step; the dependent variable y is the conversion rate of hydroxyl groups or water in the chemical reaction; and k1 represents x. n The slope at the point; k2 represents the x obtained using k1. n The slope at point +h / 2; k3 represents the x obtained using k2. n The slope at point +h / 2; k4 represents the x obtained using k3. n The slope at point +h. The higher the order of the Runge-Kutta algorithm, the more accurate the calculation results.

[0027] The conversion rate of the components can be obtained by solving the above kinetic equations.

[0028] A further technical solution of the present application is that the conversion rates of hydroxyl and water obtained according to the Runge-Kutta algorithm are substituted into the energy balance equation, the energy balance equation is solved, the slurry temperature change is obtained, and the current slurry temperature is accumulated.

[0029]

[0030] Wherein: C P is the heat capacity of the polymer slurry, is the heat capacity of carbon dioxide, C W is the heat capacity of water, C BG is the heat capacity of the gaseous physical foaming agent, C BL is the heat capacity of the liquid physical foaming agent, is the mass fraction of carbon dioxide, r W is the mass fraction of water, r BG is the mass fraction of the gaseous physical foaming agent, ΔH OH is the gel reaction heat, ΔH W is the foaming reaction heat, and λ is the evaporation heat absorption of the physical foaming agent.

[0031] A further technical solution of the present application is that the slurry volume is solved by the ideal gas state equation in the step four: the initial stage is the free expansion stage of the slurry, the fixed slurry confining pressure is set to 0.1 MPa, and the slurry volume is calculated; the slurry expansion stage is judged by the slurry volume: when the slurry volume is less than the cavity volume, it is the stage that the slurry has not filled the slurry cavity; and when the slurry volume is greater than or equal to the cavity volume, the slurry has filled the cavity.

[0032] A further technical solution of the present application is that the amount of carbon dioxide gas generated in the chemical reaction process is:

[0033]

[0034]

[0035] Wherein, m0 is the total mass of the polymer slurry, is the molar mass of carbon dioxide, is the initial mass fraction of carbon dioxide;

[0036] The amount of physical foaming agent gasification in the chemical reaction process is:

[0037]

[0038] r BG = r BL,0 -r BL

[0039] Wherein, r BL,0M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent;

[0040] According to the ideal gas law pV = nRT, under constant pressure, the volume occupied by the gas is:

[0041] V = (n CO2 +n BG The slurry volume can be obtained by comparing the gas volume with the original slurry volume.

[0042] A further technical solution of the present invention is: in step five, the amount of carbon dioxide gas generated during the chemical reaction is:

[0043]

[0044]

[0045] Where m0 is the total mass of the polymer slurry. The molar mass of carbon dioxide, This represents the initial mass fraction of carbon dioxide.

[0046] Amount of physical foaming agent vaporized during the chemical reaction:

[0047]

[0048] r BG =r BL,0 -r BL

[0049] Where, r BL,0 M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent;

[0050] According to the ideal gas law pV = nRT, the pressure generated by the gas under a constant volume is:

[0051] The expansion force of the polymer slurry can then be obtained.

[0052] The carbon dioxide gas produced by the foaming reaction and the vaporization of the physical foaming agent are the main reasons for the expansion of the polymer slurry. The heat of reaction in the foaming and gelation reactions promotes the vaporization of the physical foaming agent and the increase in gas volume. Therefore, the expansion of the polymer slurry is the result of the combined effect of the chemical reaction and the physical foaming agent. When the expansion process of the polymer slurry is constrained, it generates compressive force on the surrounding medium.

[0053] The beneficial effects of this invention are as follows: Based on the principle of energy conservation and considering the mechanism of slurry polymerization reaction, this invention uses the Runge-Kutta method to solve the chemical reaction kinetic equation describing the reaction process of polymer slurry, and combines it with the ideal gas law, which improves the accuracy of calculating the expansion force of polymer slurry. It can solve the process of polymer slurry expansion force changing with time in real time, laying the foundation for in-depth research on the expansion and diffusion mechanism of polymers and the interaction mechanism between slurry and formation under different conditions.

[0054] The carbon dioxide gas produced by the foaming reaction and the vaporization of the physical foaming agent are the main reasons for the expansion of the polymer slurry. The heat of reaction in the foaming and gelation reactions promotes the vaporization of the physical foaming agent and the increase in gas volume. Therefore, the expansion of the polymer slurry is the result of the combined effects of the chemical reaction and the physical foaming agent. When the expansion process of the polymer slurry is constrained, the compressive force exerted on the surrounding medium is called the polymer slurry expansion force.

[0055] The initial stage is the free expansion stage of the slurry. The confining pressure of the slurry is set to 0.1 MPa, and the slurry volume is calculated using the ideal gas law. The expansion stage of the slurry is determined by the slurry volume: when the slurry volume is less than the cavity volume, the slurry cavity is not filled; when the slurry volume is greater than or equal to the cavity volume, the slurry cavity is filled. The slurry volume is fixed, and the slurry expansion force is calculated. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating a method for calculating the expansion force of polymer slurry.

[0057] Figure 2 The density of the slurry is 375 kg·m³. -3 Comparison chart of calculated expansion force and experimental values;

[0058] Figure 3 The slurry density is 500 kg·m³. -3 Comparison chart of calculated expansion force and experimental values;

[0059] Figure 4 The slurry density is 625 kg·m³. -3 Comparison chart of calculated expansion force and experimental values;

[0060] Figure 5 The slurry density is 750 kg·m³. -3 Comparison chart of calculated expansion force and experimental values;

[0061] Figure 6 The calculated final density of the slurry is 800 kg·m³. -3 850kg·m -3 900kg·m -3 and 950 kg·m -3The time-history curve of the expansion force of the slurry. Detailed Implementation

[0062] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0063] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings are merely for illustrative purposes to aid those skilled in the art and to facilitate understanding and reading. They are not intended to limit the scope of the invention and therefore have no substantial technical significance. Any modifications to the structure, changes in proportions, or adjustments to size, without affecting the effectiveness and purpose of the invention, should still fall within the scope of the technical content disclosed herein. Furthermore, the terms "upper," "lower," "left," "right," "middle," and "one" used in this specification are merely for clarity and not intended to limit the scope of the invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the invention.

[0064] Example 1:

[0065] The polymer slurry used in the experiment contained two components, A and B. Component A was isocyanate (PAPI), and component B was a mixture of polyol, triethyl phosphate, physical blowing agent, amine catalyst, and other additives. The mass percentage of each component relative to the polyol mixture is shown in Table 1.

[0066] Table 1. Distribution ratio of component B

[0067]

[0068] This invention is achieved through the following technical solution:

[0069] A method for calculating the swelling force of polymer slurry considering chemical reactions, such as Figure 1 The process includes the following steps:

[0070] Step 1: Initialize all variables, such as pressure, slurry temperature, density, and molar density, based on the fixed volume boundary conditions and the distribution ratio of each component in the slurry.

[0071] The boundary condition is a fixed volume, with an initial cavity volume of 3.33 × 10⁻⁶. -4 m 3 The initial density of the polyurethane polymer slurry is 1140 kg / m³.3 The initial temperature was set to 305.15K.

[0072] Step 2: Solve the polymer slurry chemical reaction kinetic equation within the current time step using the fourth-order Runge-Kutta algorithm to obtain the change in conversion rate of isocyanate and polyol components.

[0073] The rate equation for the gelation reaction of polyurethane polymer slurry is:

[0074]

[0075] The rate equation for the foaming reaction of slurry is:

[0076]

[0077] Among them, c i,0 and X i These represent the initial concentration and conversion rate of component i, respectively. When i takes the values ​​of W, OH, and NCO, it represents water, polyol, and isocyanate, respectively. The pre-exponential factor A of the slurry. OH It is 2.6460m 3 ·s -1 ·mol -1 A W It is 27.457m 3 ·s -1 ·mol -1 Activation energy E OH It is 35552.47 J·mol -1 ·K -1 E W 40175.42 J·mol -1 ·K -1 r W r represents the mass fraction of water. BL ρ is the mass fraction of the liquid physical foaming agent. BL ρ is the density of the physical foaming agent. W 1000 kg / m 3 , ρ P It is 1140 kg / m 3 R is 8.314 J / (mol·K), and the initial concentration of the polyol is c. OH,0 2692.0 mol·m -3 isocyanate concentration c NCO,0 10430 mol·m -3 ;

[0078] Step 3: Solve the energy equation to obtain the change in slurry temperature, and sum them up to obtain the current slurry temperature.

[0079] The energy balance equation for self-expanding polymer slurry under adiabatic conditions is:

[0080]

[0081] Among them: the specific heat C of polyurethane P 1800 J·kg -1 ·K -1 heat capacity of carbon dioxide 1800 J·kg -1 ·K -1 The heat capacity of water, C W 4200 J·kg -1 ·K -1 Specific heat C of gaseous physical foaming agent BG 1000 J·kg -1 ·K -1 Specific heat C of liquid physical foaming agent BL 1159 J·kg -1 ·K -1 , r represents the mass fraction of carbon dioxide. W r represents the mass fraction of water. BG The mass fraction of the gaseous physical blowing agent, and the heat of reaction (-ΔH) of the polyol. OH It is 7.075×10 4 J / g equiv, ΔH W The heat of vaporization λ of the physical foaming agent is 206.8 kJ·kg⁻¹, which is the heat of the foaming reaction. -1 Initial polyol concentration 2692.0 mol·m -3 The conversion rate of hydroxyl groups and water obtained by the Runge-Kutta algorithm can be substituted into the energy equation to obtain the slurry temperature at different times.

[0082] Step 4: Solve for the slurry volume using the ideal gas law to determine the slurry expansion stage;

[0083] The initial stage is the free expansion stage of the slurry. The fixed confining pressure of the slurry is set to 0.1 MPa, and the slurry volume is calculated by the ideal gas law. The expansion stage of the slurry is determined by the slurry volume: when the slurry volume is less than the cavity volume, the slurry cavity is not filled; when the slurry volume is greater than or equal to the cavity volume, the slurry cavity is filled.

[0084] Specifically, the amount of carbon dioxide gas generated during a chemical reaction:

[0085]

[0086]

[0087] Where m0 is the total mass of the polymer slurry. The molar mass of carbon dioxide, This represents the initial mass fraction of carbon dioxide.

[0088] Amount of physical foaming agent vaporized during the chemical reaction:

[0089]

[0090] r BG =r BL,0 -r BL

[0091] Where, r BL,0 M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent;

[0092] According to the ideal gas law pV = nRT, under constant pressure, P = 0.1 MPa, the volume occupied by the gas is:

[0093] V = (n CO2 +n BG )RT / p

[0094] The volume of the slurry can be obtained by comparing the gas volume with the original volume of the slurry.

[0095] Step 5: Select different boundary conditions and calculation formulas according to different slurry expansion stages: When the slurry does not fill the slurry cavity, set the fixed slurry confining pressure to 0.1MPa and allow the slurry volume to expand freely; after the slurry fills the slurry cavity, fix the slurry volume and calculate the slurry expansion force; that is, after the slurry fills the slurry cavity, the pressure generated by the gas is the polymer slurry expansion force.

[0096] Amount of carbon dioxide gas generated during a chemical reaction:

[0097]

[0098]

[0099] Where m0 is the total mass of the polymer slurry. The molar mass of carbon dioxide, This represents the initial mass fraction of carbon dioxide.

[0100] Amount of physical foaming agent vaporized during the chemical reaction:

[0101]

[0102] r BG =r BL,0 -r BL

[0103] Where, r BL,0 M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent;

[0104] According to the ideal gas law pV = nRT, the pressure generated by the gas under a constant volume is:

[0105]

[0106] Where T is the temperature of the slurry at this moment, and V is the volume of the cavity (3.33 × 10⁻⁶). -4 m 3 .

[0107] Step Six: Based on the new calculation results, update the density, volume, pressure, temperature, and the conversion rate of the isocyanate and polyol components. Proceed with the time step and repeat steps Two through Five. This will yield the slurry expansion force at different times.

[0108] The following assumptions are made when solving the above calculation method:

[0109] (1) The polymer slurry reacts quickly. Assuming that its expansion process is in an adiabatic environment and does not exchange heat with the outside, the influence of heat conduction is ignored.

[0110] (2) The reaction rate and density of each part of the slurry are the same.

[0111] Analysis of calculation results:

[0112] Figures 2-5 The calculated density of the slurry under constant volume conditions is 375 kg·m³. -3 500kg·m -3 625 kg·m -3 and 750 kg·m -3 A comparison chart of the calculated and experimental expansion force values ​​is shown. The calculated final expansion force values ​​for the slurry under four working conditions are 0.358 MPa, 0.587 MPa, 0.916 MPa, and 1.456 MPa, respectively, while the experimental values ​​are 0.365 MPa, 0.581 MPa, 0.898 MPa, and 1.420 MPa, respectively. The relative errors between the two are 1.92%, 1.03%, 2.00%, and 2.53%, respectively. It can be seen that the calculated slurry expansion force over time under different working conditions matches the experimental results well, and the final expansion force values ​​are basically equal, demonstrating the accuracy and effectiveness of the calculation method described in this invention.

[0113] Figure 6 Under the condition of a fixed volume, the calculated density of the slurry is 800 kg·m³. -3 850kg·m-3 900kg·m -3 and 950 kg·m -3 The curve showing the change of its expansion force over time.

[0114] Depend on Figure 6 It can be seen that the expansion force of slurries with different densities has a basically the same trend. During the expansion process of the slurry, the expansion force changes slowly at first and then quickly, eventually slowing down and approaching zero. At the same time, the expansion force of the slurry increases with the increase of density. The greater the density, the greater the increase in expansion force per unit density.

[0115] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for calculating the swelling force of polymer slurry, characterized in that: The calculation method includes the following steps: Step 1: Initialize variables based on the fixed volume boundary conditions and the distribution ratio of each component in the slurry. The variables include pressure, slurry temperature, density, and molar density. Step 2: Solve the chemical reaction kinetic equation of the polymer slurry in the current time step using the Runge-Kutta algorithm to obtain the change in the conversion rate of isocyanate and polyol; Step 3: Solve the energy balance equation to obtain the change in slurry temperature, and sum them up to obtain the current slurry temperature; Step 4: Solve for the slurry volume using the ideal gas law to determine the slurry expansion stage; Step 5: Select different boundary conditions and calculation formulas according to different grout expansion stages: When the grout does not fill the grout cavity, set the fixed grout confining pressure to 0.1MPa and allow the grout volume to expand freely; after the grout fills the grout cavity, fix the grout volume and calculate the grout expansion force. Step 6: Update the parameters based on the new calculation results. The parameters include density, volume, pressure, temperature, and the conversion rate of isocyanate to polyol component. Step 7: Proceed with the time step, repeating steps 2 to 6 to obtain the change of expansion force over time.

2. The method for calculating the swelling force of polymer slurry according to claim 1, characterized in that, The chemical reaction kinetic equations for the polymer slurry in step two include the gelation reaction rate equation for the polyurethane polymer slurry and the foaming reaction rate equation for the slurry. The gelation reaction rate equation for the polyurethane polymer slurry is as follows: The equation for the foaming reaction rate of the slurry is: Among them, c i,0 and X i Let A represent the initial concentration and conversion rate of component i, respectively. When i takes the values ​​of W, OH, and NCO, it represents water, polyol, and isocyanate, respectively. OH and A W E represents the pre-exponential factor for the gelation reaction and the foaming reaction, respectively. OH and E W These are the activation energies of the two reactions, r. W r represents the mass fraction of water. BL ρ is the mass fraction of the liquid physical foaming agent. BL ρ is the density of the physical foaming agent. W ρ is the density of water. P The density of polyurethane, R is the ideal gas constant, and T is the slurry temperature.

3. The method for calculating the swelling force of a polymer slurry according to claim 1 or 2, characterized in that, Step two, the Runge-Kutta algorithm, uses a fourth-order Runge-Kutta algorithm to solve the chemical reaction rate equation. For ordinary differential equations of the form y'=f(x,y), the mathematical description of the fourth-order Runge-Kutta algorithm is as follows: k1=f(x n ,y n ) k4=f(x n +h,y n +hk3) Where: h represents the time step selected in the calculation process, and the independent variable x n Let y be the start time of the nth time step, y be the conversion rate of hydroxyl groups or water in the chemical reaction, and k1 represent x. n The slope at the point; k2 represents the x obtained using k1. n The slope at point +h / 2; k3 represents the x obtained using k2. n The slope at point +h / 2; k4 represents the x obtained using k3. n The slope at point +h.

4. The method for calculating the swelling force of a polymer slurry according to claim 1 or 2, characterized in that, In step three, the energy balance equation for the self-expanding polymer slurry under adiabatic conditions is: Where: C P The heat capacity of the polymer slurry, For the heat capacity of carbon dioxide, C W For the heat capacity of water, C BG The heat capacity of the gaseous physical foaming agent, C BL The heat capacity of a liquid physical foaming agent. r represents the mass fraction of carbon dioxide. W r represents the mass fraction of water. BG ΔH represents the mass fraction of the gaseous physical foaming agent. OH The heat of gelation reaction, ΔH W λ is the heat of the foaming reaction, and λ is the heat of absorption during the evaporation of the physical foaming agent. The conversion rates of hydroxyl groups and water obtained from the Runge-Kutta algorithm can be substituted into the energy balance equation to obtain the slurry temperature at different times.

5. A method for calculating the swelling force of a polymer slurry according to claim 1 or 2, characterized in that, In step four, the slurry volume is calculated using the ideal gas law: the initial stage is the free expansion stage of the slurry, and a fixed slurry confining pressure of 0.1 MPa is set to calculate the slurry volume; the slurry expansion stage is determined by the slurry volume: when the slurry volume is less than the cavity volume, the slurry cavity is not filled; when the slurry volume is greater than or equal to the cavity volume, the slurry cavity is filled.

6. The method for calculating the swelling force of polymer slurry according to claim 5, characterized in that, Amount of carbon dioxide gas generated during a chemical reaction: Where m0 is the total mass of the polymer slurry. The molar mass of carbon dioxide, This represents the initial mass fraction of carbon dioxide. Amount of physical foaming agent vaporized during the chemical reaction: r BG ＝r BL,0 -r BL Where, r BL,0 M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent; According to the ideal gas law pV = nRT, under constant pressure, the volume occupied by the gas is: V=(n CO2 +n BG )RT / p The volume of the slurry can then be obtained.

7. A method for calculating the swelling force of a polymer slurry according to claim 1 or 2, characterized in that, In step five, the amount of carbon dioxide gas generated during the chemical reaction is as follows: Where m0 is the total mass of the polymer slurry. The molar mass of carbon dioxide, This represents the initial mass fraction of carbon dioxide. Amount of physical foaming agent vaporized during the chemical reaction: r BG ＝r BL,0 -r BL Where, r BL,0 M represents the initial mass fraction of the liquid physical foaming agent. B Indicates the molar mass of the physical foaming agent; According to the ideal gas law pV = nRT, the pressure generated by the gas under a constant volume is: The expansion force of the polymer slurry can then be obtained.

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