A low-temperature liquid storage tank pressure prediction method based on a non-thermal equilibrium model

Abstract

A method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model aims to improve the calculation speed of pressure evolution laws and reduce the time required to predict tank pressure. First, pressure sensors, temperature sensors, and level gauges are used to collect data on the current temperature of the gas and liquid phases, the pressure inside the tank, the vacuum degree of the insulation layer, and the real-time liquid level. Second, the signal data obtained from the sensors are transmitted to a processor, and the density, latent heat of phase change, and thermodynamic energy of the gas and liquid phases inside the tank are retrieved using REFPROP software. Finally, a three-dimensional model of the tank and its heat transfer parameters are established. Mass transfer relationships are analyzed to assess the heat transfer of the gas and liquid phases within the storage tank. Next, based on the established 3D model and the heat transfer analysis results, energy analysis is performed on the gas phase region, liquid phase region, and gas-liquid interface within the tank. An appropriate time step is selected for iterative calculations to ensure the accuracy of each step. The calculation results from the previous step are then saved, and the thermodynamic parameters for the next time step are retrieved using REFPROP software based on the calculated parameters. Finally, the safe storage time of the tank under the current liquid filling volume and insulation performance is calculated to ensure the safe operation of the tank.

Description

Technical Field

[0001] This invention relates to the field of cryogenic liquid storage and transportation, and is a technology for predicting the pressure evolution of cryogenic liquid storage tanks based on a non-thermal equilibrium model. It is mainly applied to the storage and transportation of cryogenic media such as liquid hydrogen, liquid oxygen, and liquefied natural gas. Background Technology

[0002] In today's environmentally conscious world, low-loss storage of cryogenic media such as liquid hydrogen, liquid oxygen, and liquefied natural gas (LNG) has become an important research topic. Although modern super-insulated containers have reduced the apparent thermal conductivity to 10... -5 While the pressure-time relationship can be measured in W / (m·K), eliminating the bulk-occurrence loss (BOG) of cryogenic liquids remains impossible. Therefore, rapidly and accurately predicting the pressure-time relationship during the storage of these cryogenic media is crucial for their effective storage and transportation.

[0003] For predicting BOG (Body Pressure) and tank pressure, current methods employ computational fluid dynamics (CFD) coupled with the volume fraction interface tracking (VOF) method and the Lee model (interface evaporation model). Numerical solutions are then obtained using the finite element method (FEM) to determine the relationship between tank pressure, temperature, and other physical quantities and time. This method is relatively accurate and widely used, but its problems are also significant. First, it requires enormous computational resources, making it virtually impossible for large-scale calculations with long prediction times. Numerous domestic and international publications document cases where months of computation were required to simulate evaporation processes lasting only a few hours. Second, this method places specific demands on mesh generation and time step selection. Insufficient mesh quality or excessively long time steps can negatively impact computational stability and even prevent convergence. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model, thereby improving the calculation speed of pressure evolution laws and reducing the time required to predict tank pressure.

[0005] This invention is a method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model, the steps of which are as follows: Step (1) Use pressure sensors, temperature sensors and level gauges to collect the current temperature of the gas phase and liquid phase zones of the cryogenic liquid storage tank, the pressure inside the tank, the vacuum degree of the insulation layer and the real-time liquid level; Step (2) transmit the signal data obtained by the sensor to the processor, and use REFPROP software to retrieve the density, latent heat of phase change, and thermodynamic energy of the gas and liquid phases in the storage tank; Step (3) Establish a three-dimensional model of the storage tank and the heat and mass transfer relationship, and conduct heat transfer analysis on the gas and liquid media in the storage tank; Step (4) Based on the established three-dimensional model and heat transfer analysis results, perform energy analysis on the gas phase region, liquid phase region and gas-liquid interface in the storage tank, select an appropriate time step for iterative calculation, and ensure the calculation accuracy of each step. Step (5) Save the calculation results of the previous step, and use the calculated parameters to retrieve the thermodynamic parameters of the next time step using REFPROP software; Step (6) calculates the safe storage time of the tank under the current liquid filling volume and insulation performance to ensure the safe operation of the tank.

[0006] The beneficial effects of this invention are as follows: The calculation method based on non-thermal equilibrium described in this invention can quickly calculate the pressure evolution of various storage tanks. This method can predict the pressure evolution of storage tanks with different forms, insulation properties, media, liquid filling volumes, volume sizes, and those with buffer containers, and obtain pressure-time curves. The entire process can be completed in just a few hours, significantly improving prediction efficiency compared to CFD methods, and ensuring the safe operation of cryogenic liquid storage tanks within the plant area. Even in the event of insulation failure, this method can still predict the pressure evolution of storage tanks, providing a basis for emergency response. Attached Figure Description

[0007] Figure 1 This is a flowchart of the calculation process of the present invention. Detailed Implementation

[0008] like Figure 1 As shown, this invention is a method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model, comprising the following steps: Step (1) Use pressure sensors, temperature sensors and level gauges to collect the current temperature of the gas phase and liquid phase zones of the cryogenic liquid storage tank, the pressure inside the tank, the vacuum degree of the insulation layer and the real-time liquid level; Step (2) transmit the signal data obtained by the sensor to the processor, and use REFPROP software to retrieve the density, latent heat of phase change, and thermodynamic energy of the gas and liquid phases in the storage tank; Step (3) Establish a three-dimensional model of the storage tank and the heat and mass transfer relationship, and conduct heat transfer analysis and energy analysis on the gas and liquid phase media in the storage tank; Step (4) Based on the established three-dimensional model and the heat transfer analysis and energy analysis results of the two-phase region, perform energy analysis on the gas-liquid interface in the storage tank; Step (5) Select an appropriate time step for iterative calculation to ensure the accuracy of each step. Save the calculation results. Use the calculated parameters to retrieve the thermodynamic parameters for the next time step using REFPROP software. Step (6) calculates the safe storage time of the tank under the current liquid filling volume and insulation performance to ensure the safe operation of the tank.

[0009] The above method, in step (3), establishes a three-dimensional model of the storage tank, uses MATLAB software to mathematically model the three-dimensional structure of the storage tank, and determines the energy transfer relationship between the gas phase region, liquid phase region and gas-liquid interface in the storage tank according to the actual form, support structure and insulation performance of the storage tank.

[0010] For the gas phase region, the energy relationship is as follows: (1); in, The mass of the gas in the gas phase space is expressed in kg. The change in specific thermodynamic energy of a gas in the gas phase space over one time step, expressed in J / kg; is the heat transfer rate between the gas phase and the gas-liquid interface, W; p is the pressure of the gas phase space, Pa; denoted as mass transfer rate between the gas-liquid interface and the gas phase space, in kg / s; It is the mass flow rate of the gas discharged from inside the container when the pressure relief device is activated, in kg / s; is the specific enthalpy of saturated vapor corresponding to pressure p in the gas phase space, in J / kg; is the specific enthalpy of the gas under superheated conditions, in J / kg; Let m be the volume of the gas phase space. 3 ; Let be the time step, in seconds; For the liquid phase region, the energy relationship is as follows: (2) In the formula: The mass of the liquid is expressed in kg. It is the change in specific internal energy of a liquid within a time step, expressed in J / kg. W represents the heat transferred from the container wall to the liquid per unit time. Let W be the heat transfer rate at the liquid-gas-liquid interface in the liquid space. denoted as the mass transfer rate between the liquid and vapor-liquid interfaces, in kg / s; , where p is the specific enthalpy of the liquid in saturated state corresponding to the internal pressure p in the storage tank, in J / kg; It is the volume of the liquid in the liquid, m 3 ; For the gas-liquid interface, the energy relationship is as follows: (3) In the energy equations (1), (2), and (3), the heat transfer in the gas phase region, the liquid phase region, and the gas-liquid interface is determined as follows.

[0011] The wall heat transfer equation in the gas phase region is: (4) In the formula, The natural convection heat transfer coefficient of the gas is W / (m³). 2 ·K); The temperature of the wall in the gas phase region is K; The volume average temperature of the gas phase region is K; The wall area of ​​the gas phase region is m. 2 ; ν is the thermal conductivity of the solid wall surface, W / (m·K); Let p be the saturation temperature, in K. The width of the heat-affected zone of the solid wall near the interface, in meters; Let m be the cross-sectional area of ​​the solid wall. 2 ; is the apparent thermal conductivity of the insulation layer, W / (m·K); The ambient temperature, in K; The thickness of the insulation layer is in meters (m). The wall heat transfer equation in the liquid phase region is: (5); In the formula, The natural convection heat transfer coefficient of the liquid is W / (m³). 2 ·K); The temperature of the wall within the liquid phase region is K; Let m be the wall area of ​​the liquid phase region. 2 .

[0012] In the heat transfer equations (4) and (5), the convective heat transfer coefficient in the gas phase or liquid phase is... The relationship conforms to the following system of equations (6); In the formula, Where is the Rayleigh number for the gas or liquid phase; g is the acceleration due to gravity, m / s². 2 ; K is the coefficient of volumetric expansion of the gas or liquid phase. -1 ; The average Nusselt number for the gas or liquid phase; The contact height between the gas or liquid phase and the vertical inner wall of the inner container, in meters (m). The kinematic viscosity coefficient of the gas or liquid phase, m 2 / s; For the gas or liquid phase, the Prandtl number is used. is the thermal conductivity of the gas or liquid phase, W / (m·K); The actual heat transferred into the bulk gas region is: (7); In the formula The vertical wall area of ​​the gas phase region is m. 2 ; The area of ​​the wall at the top of the gas phase region is m. 2 .

[0013] The actual heat transferred to the bulk liquid region is: (8); In the formula The vertical wall area of ​​the liquid phase region is m. 2 ; The area of ​​the wall at the bottom of the liquid phase region is m. 2 , The convective heat transfer coefficient at the bottom of the liquid phase region is W / (m²). 2 ·K). For It can be obtained from the following equation. (9); is the isobaric specific heat of the low-temperature gas, J / (kg·K); The density of the low-temperature gas is expressed in kg / m³. ρ is the dynamic viscosity coefficient of the gas, in Pa·s.

[0014] The method described above, in step (4), calculates the heat and mass transfer at the gas-liquid interface based on the thermal analysis results of the gas phase and liquid phase obtained in step (3). For the gas phase side of the gas-liquid interface, the heat transferred into the interface can be determined by the following set of equations: (10); (11); in, The convective heat transfer coefficient between the interface and the gas is W / (m²). 2 ·K). ν is the thermal conductivity of the gas, W / (m⋅K). is the volume expansion coefficient of the gas, 1 / K; m is the kinematic viscosity coefficient of the gas. 2 / s; m is the thermal diffusivity of the low-temperature gas. 2 / s; The Rayleigh number is the low-temperature gas on the gas phase side of the interface. The Nusselt number is the low-temperature gas on the gas phase side of the interface. For the gas phase side of the gas-liquid interface, the heat transferred into the interface can be determined by the following set of equations: (12) (13); in, The convective heat transfer coefficient between the interface and the liquid is W / (m). 2 ·K). ν is the thermal conductivity of the liquid, W / (m⋅K). is the coefficient of volumetric expansion of the liquid, 1 / K; m is the kinematic viscosity coefficient of the liquid. 2 / s; m is the thermal diffusivity of the cryogenic liquid. 2 / s; The Rayleigh number is the low-temperature liquid on the liquid phase side of the interface. The Nusselt number is the cryogenic liquid on the liquid phase side of the interface. The flow states of gas and liquid near the gas-liquid interface inside the storage tank differ under varying pressures and insulation properties. Therefore, the constant remains constant under different pressures and insulation properties. , as well as , The value will also be different.

[0015] According to research, the gauge pressure of the storage tank is in the range of 0~0.7 MPa, and the vacuum degree of the insulation layer is less than 10. 3 Under the condition of Pa: (14); The gauge pressure of the storage tank is in the range of 1.5~3.5 MPa, and the vacuum degree of the insulation layer is less than 10. 3 Under the condition of Pa: (15); If the gas phase temperature ,but If the liquid phase temperature ,but .

[0016] The method described above, in step (4), after obtaining the heat transfer between the interface and the wall, calculates the phase change mass within one time step according to the following equation. (16); After obtaining the phase change mass, the gas-liquid phase masses can be updated. Based on the liquid density, the new liquid level can be calculated, and the new gas density can be obtained. Finally, the pressure P can be obtained using PEFPROP software. i+1 .

[0017] In the method described above, step (5) involves substituting the state parameters measured in steps (1) and (2) and the heat and mass transfer rates calculated in steps (3) and (4) into the energy equations (1), (2), and (3). If the error limit is not reached, the calculated internal energy value is used to recalculate the two-phase region temperature according to the following set of equations and then brought back to step (4). (17); By selecting an appropriate time step and performing iterative calculations until the specified error limits are met, the thermodynamic energy of the two-phase region within one time step can be obtained. Using the calculated thermodynamic energy and pressure values ​​obtained through REFPROP software, the thermodynamic parameters for the next time step can be retrieved.

[0018] The method described above, in step (6), involves plotting a pressure-time curve based on the data obtained at each time step, and stopping the calculation after reaching the predetermined termination time or termination pressure, thereby obtaining the pressure evolution law of the cryogenic liquid storage tank.

Claims

1. A method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model, characterized in that, The steps are as follows: Step (1) Use pressure sensors, temperature sensors and level gauges to collect the current temperature of the gas phase zone and liquid phase zone of the cryogenic liquid storage tank, the pressure inside the tank, the vacuum degree of the insulation layer and the real-time liquid level; Step (2) transmit the signal data obtained by the sensor to the processor, and use REFPROP software to retrieve the density, latent heat of phase change, and thermodynamic energy of the gas and liquid phases in the storage tank; Step (3) Establish a three-dimensional model of the storage tank and the heat and mass transfer relationship, and conduct heat transfer analysis on the gas and liquid media in the storage tank; Step (4) Based on the established three-dimensional model and heat transfer analysis results, perform energy analysis on the gas phase region, liquid phase region and gas-liquid interface in the storage tank, select an appropriate time step for iterative calculation, and ensure the calculation accuracy of each step. Step (5) Save the calculation results from the previous step; use the results to retrieve the thermodynamic parameters for the next time step in the REFPROP software; Step (6) calculates the safe and undamaged storage time of the storage tank under the current liquid filling volume and insulation performance, ensuring the safe operation of the storage tank; As described in step (3), the energy relationship in the gas phase region follows formula (1): （1）； in, The mass of the gas in the gas phase space is expressed in kg. The change in specific thermodynamic energy of a gas in the gas phase space over one time step, expressed in J / kg; is the heat transfer rate between the gas phase and the gas-liquid interface, W; p is the pressure of the gas phase space, Pa; denoted as mass transfer rate between the gas-liquid interface and the gas phase space, in kg / s; It is the mass flow rate of the gas discharged from inside the container when the pressure relief device is activated, in kg / s; is the specific enthalpy of saturated vapor corresponding to pressure p in the gas phase space, in J / kg; is the specific enthalpy of the gas under superheated conditions, in J / kg; Let m be the volume of the gas phase space. 3 ; Let be the time step, in seconds; The energy relationship in the liquid phase region follows formula (2): (2)； in, The mass of the liquid is expressed in kg. It is the change in specific internal energy of a liquid within a time step, expressed in J / kg. W represents the heat transferred from the container wall to the liquid per unit time. Let W be the heat transfer rate at the liquid-gas-liquid interface in the liquid space. denoted as the mass transfer rate between the liquid and vapor-liquid interfaces, in kg / s; , where p is the specific enthalpy of the liquid in saturated state corresponding to the internal pressure p in the storage tank, in J / kg; It is the volume of the liquid in the liquid, m 3 ; The energy relationship at the gas-liquid interface follows formula (3): （3）； As described in step (3), the wall heat transfer relationship in the gas phase region follows formula (4): （4）; in, The natural convection heat transfer coefficient of the gas is W / (m³). 2 ·K); The temperature of the wall in the gas phase region is K; The volume average temperature of the gas phase region is K; The wall area of ​​the gas phase region is m. 2 ; ν is the thermal conductivity of the solid wall surface, W / (m·K); Let p be the saturation temperature, in K. The width of the heat-affected zone of the solid wall near the interface, in meters; Let m be the cross-sectional area of ​​the solid wall. 2 ; is the apparent thermal conductivity of the insulation layer, W / (m·K); The ambient temperature, in K; The thickness of the insulation layer is in meters (m). The heat transfer relationship at the wall in the liquid phase region follows the formula: (5)； In the formula, The natural convection heat transfer coefficient of the liquid is W / (m³). 2 ·K); The temperature of the wall within the liquid phase region is K; Let m be the wall area of ​​the liquid phase region. 2 ; As described in step (4), the heat transfer on both sides of the gas-liquid interface is convective heat transfer, and the heat transfer law on the gas phase side follows the form of formulas (6) and (7): (6)； （7）； in, The convective heat transfer coefficient between the interface and the gas is W / (m²). 2 ·K); Where is the thermal conductivity of the gas, W / (m⋅K); is the volume expansion coefficient of the gas, 1 / K; m is the kinematic viscosity coefficient of the gas. 2 / s; m is the thermal diffusivity of the low-temperature gas. 2 / s; The Rayleigh number is the low-temperature gas on the gas phase side of the interface. The Nusselt number of the cryogenic gas on the gas-phase side of the interface; a constant. and It needs to be determined based on the current pressure and insulation performance of the storage tank; The heat transfer law on the liquid side follows the form of formulas (8) and (9): （8）; (9)； in, The convective heat transfer coefficient between the interface and the liquid is W / (m). 2 ·K); is the thermal conductivity of the liquid, W / (m⋅K); is the coefficient of volumetric expansion of the liquid, 1 / K; m is the kinematic viscosity coefficient of the liquid. 2 / s; m is the thermal diffusivity of the cryogenic liquid. 2 / s; The Rayleigh number is the low-temperature liquid on the liquid phase side of the interface. The Nusselt number of the cryogenic liquid on the liquid phase side of the interface; a constant. and It needs to be determined based on the current pressure and insulation performance of the storage tank.

2. The method for predicting the pressure of cryogenic liquid storage tanks based on a non-thermal equilibrium model according to claim 1, characterized in that: The gauge pressure of the storage tank is in the range of 0~0.7 MPa, and the vacuum degree of the insulation layer is less than 10. 3 Under the condition of Pa: (10)； The gauge pressure of the storage tank is in the range of 1.5~3.5 MPa, and the vacuum degree of the insulation layer is less than 10. 3 Under the condition of Pa: (11)； When the gas phase temperature hour, When the liquid phase temperature hour, .

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