Low-temperature liquid storage tank pressure prediction method based on non-thermal equilibrium state model

Abstract

The invention discloses a low-temperature liquid storage tank pressure prediction method based on a non-thermal equilibrium state model, and aims to improve the calculation speed of a pressure evolution law so as to reduce the time required for predicting the pressure of a storage tank. The method comprises the steps that firstly, a pressure sensor, a temperature sensor and a liquid level meter are used for collecting the temperature of a current gas phase and liquid phase area of the low-temperature liquid storage tank, the pressure in the storage tank, the vacuum degree of a heat insulation layer and the real-time liquid level; secondly, transmitting signal data obtained by monitoring of the sensor to a processor, and checking the density, phase change latent heat and thermodynamic energy of gas and liquid phases in the storage tank through REFPROP software; then establishing a three-dimensional model and a heat and mass transfer relationship of the storage tank, and performing heat transfer analysis on gas-phase and liquid-phase media in the storage tank; secondly, performing energy analysis on a gas phase region, a liquid phase region and a gas-liquid interface in the storage tank according to the established three-dimensional model and a heat transfer analysis result, and selecting a proper time step to perform iterative calculation so as to ensure the calculation precision of each step; storing the calculation result of the previous step, and searching and taking thermodynamic parameters of the next time step through REFPROP software according to the parameters obtained through calculation; finally, the safe storage time of the storage tank under the current liquid filling volume and the heat insulation performance is calculated, and safe work of the storage tank is guaranteed.

Description

Technical Field

[0001] The present invention relates to the field of cryogenic liquid storage and transportation. It is a technology that predicts the pressure evolution law of cryogenic liquid storage tanks based on a non-thermal equilibrium model. It is mainly used in the storage and transportation of cryogenic media such as liquid hydrogen, liquid oxygen, and liquefied natural gas. Background Art

[0002] In today’s world where environmental protection is a priority, low-loss storage of cryogenic media such as liquid hydrogen, liquid oxygen, and liquefied natural gas (LNG) has gradually become an important research topic. Although today’s super-insulated containers have reduced the apparent thermal conductivity to 10 -5 W / (m·K), but it is still impossible to eliminate the evaporation loss (BOG) of cryogenic liquids. Therefore, quickly and accurately predicting the relationship between pressure and time during the storage of these cryogenic media is a crucial task in the storage and transportation of cryogenic media.

[0003] The current method for predicting BOG and tank pressure uses computational fluid dynamics (CFD) coupled with the volume fraction interface tracking method (VOF) and the Lee model (interface evaporation model). Finite element methods are then used to numerically solve the relationship between physical quantities such as pressure and temperature within the tank and time. This method is relatively accurate and widely used, but it also has significant drawbacks. First, the computational resources required are enormous, making it nearly impossible to implement for large-scale and long-time prediction cases. Domestic and international literature abounds with examples where simulations of evaporation processes lasting only a few hours required months of calculations. Second, this method imposes certain requirements on the meshing method and time step selection. Poor mesh quality or excessively long time steps can compromise computational stability and even prevent convergence. Summary of the Invention

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

[0005] The present invention is a method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model, the steps of which are as follows: Step (1) using a pressure sensor, a temperature sensor and a liquid level gauge to collect the temperature of the current gas phase and liquid phase of the cryogenic liquid storage tank, the pressure inside the storage tank, the vacuum degree of the insulation layer, and the real-time liquid level; Step (2) transmitting the signal data obtained by the sensor monitoring to the processor, and checking the density, phase change latent heat, and thermodynamic energy of the gas and liquid phases in the storage tank through REFPROP software; Step (3) establishing a three-dimensional model of the storage tank and the heat and mass transfer relationship, and performing 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, liquid phase, and gas-liquid interface in the 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 query the thermodynamic parameters of the next time step through 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 present invention has the following beneficial effects: The non-thermal equilibrium calculation method described herein can rapidly calculate the pressure evolution patterns of various storage tanks. This method can predict the pressure evolution patterns of storage tanks of varying types, insulation properties, media, liquid filling volumes, dimensions, and those with buffer containers, and generate 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 a plant. In the event of insulation failure, this method can also predict the pressure evolution patterns of storage tanks, providing a basis for emergency response. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Figure 1 It is a calculation flow chart of the present invention. DETAILED DESCRIPTION

[0008] like Figure 1 As shown, the present invention is a method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model, which consists of the following steps: Step (1) using a pressure sensor, a temperature sensor and a liquid level gauge to collect the temperature of the current gas phase and liquid phase of the cryogenic liquid storage tank, the pressure inside the storage tank, the vacuum degree of the insulation layer, and the real-time liquid level; Step (2) transmitting the signal data obtained by the sensor monitoring to the processor, and checking the density, phase change latent heat, and thermodynamic energy of the gas and liquid phases in the storage tank through REFPROP software; Step (3) establishing a three-dimensional model of the storage tank and the heat and mass transfer relationship, and performing heat transfer analysis and energy analysis on the gas and liquid media in the storage tank; Step (4) performing energy analysis on the gas-liquid interface in the storage tank based on the established three-dimensional model and the results of heat transfer analysis and energy analysis of the two-phase region; 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 query the thermodynamic parameters of the next time step through 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] In the above method, as described in step (3), a three-dimensional model of the storage tank is established, and the three-dimensional structure of the storage tank is mathematically modeled using MATLAB software. According to the actual form, support structure, and thermal insulation performance of the storage tank, the energy transfer relationship between the gas phase region, liquid phase region, and gas-liquid interface in the storage tank is determined.

[0010] For the gas phase, the energy relationship is: (1); in, is the mass of the gas in the gas phase space, kg; is the change in specific thermodynamic energy of gas in the gas phase space in one time step, 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; is the mass transfer rate between the gas-liquid interface and the gas phase space, kg / s; is the mass flow rate of gas discharged from the interior of the container when the pressure relief device is activated, kg / s; is the specific enthalpy of saturated vapor corresponding to the pressure p in the gas phase space, J / kg; is the specific enthalpy of the gas in the superheated state, J / kg; is the volume of the gas phase space, m 3 ; is the time step, s; For the liquid phase, the energy relationship is: (2) Where: is the mass of the liquid, kg; is the change in specific internal energy of the liquid in one time step, J / kg; is the heat transferred from the container wall to the liquid per unit time, W; is the heat transfer rate between the liquid in the liquid space and the gas-liquid interface, W; is the mass transfer rate between the liquid and the vapor-liquid interface, kg / s; is the specific enthalpy of the liquid in the saturated state corresponding to the internal pressure p in the tank, J / kg; is the volume of liquid in liquid, m 3 ; For the gas-liquid interface, the energy relationship is: (3) In the energy equations (1), (2), and (3), the heat transfer in the gas phase, liquid phase, and gas-liquid interface is determined as follows.

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

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

[0013] The actual heat transferred into the main liquid phase area is: (8); In the formula is the vertical wall area of ​​the liquid phase region, m 2 ; is the wall area at the bottom of the liquid phase region, m 2 , is the convection heat transfer coefficient at the bottom of the liquid phase, W / (m 2 K). For It can be obtained by the following equation (9); is the constant-pressure specific heat of the cryogenic gas, J / (kg·K); is the density of cryogenic gas, kg / m3; is the dynamic viscosity coefficient of the gas, Pa·s.

[0014] In the above method, as described in step (4), based on the thermal analysis results of the gas phase region and the liquid phase region obtained in step (3), the heat and mass transfer at the gas-liquid interface are calculated. For the gas phase side of the gas-liquid interface, the heat transferred into the interface can be determined by the following equations: (10); (11); in, is the convection heat transfer coefficient between the interface and the gas, W / (m 2 ·K). is the thermal conductivity of the gas, W / (m⋅K). is the volume expansion coefficient of the gas, 1 / K; is the kinematic viscosity coefficient of the gas, m 2 / s; is the thermal diffusion coefficient of low-temperature gas, m 2 / s; is the Rayleigh number of the low-temperature gas on the gas phase side of the interface; is the Nusselt number of 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 equations: (12) (13); in, is the convection heat transfer coefficient between the interface and the liquid, W / (m 2 ·K). is the thermal conductivity of the liquid, W / (m⋅K). is the volume expansion coefficient of the liquid, 1 / K; is the kinematic viscosity coefficient of the liquid, m 2 / s; is the thermal diffusivity of the cryogenic liquid, m 2 / s; is the Rayleigh number of the low-temperature liquid on the liquid side of the interface; is the Nusselt number of the cryogenic liquid on the liquid side of the interface; When the pressure and thermal insulation performance are different, the flow state of gas and liquid near the gas-liquid interface in the tank is also different. Therefore, under different pressure and thermal insulation performance, the constant 、 as well as 、 The value of will also be different.

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

[0016] In the above method, as described in step (4), after obtaining the heat transfer of the interface and wall, the phase change mass within one time step is calculated according to the following equation: (16); After the phase change mass is obtained, the gas-liquid phase mass can be updated, and the new liquid level can be calculated according to the liquid density to obtain the new gas phase density. Finally, the next pressure P can be obtained through the PEFPROP software. i+1 .

[0017] In the above method, as described in step (5), the state parameters measured in steps (1) and (2) and the heat and mass transfer rates calculated in steps (3) and (4) are substituted into the energy equations (1), (2), and (3). If the error limit is not reached, the calculated internal energy value is recalculated according to the following equations to calculate the two-phase region temperature and then brought back to step (4): (17); By selecting an appropriate time step and iterating the calculation until the specified error limit is met, the thermodynamic energy in the two-phase region within one time step can be obtained. Using the calculated thermodynamic energy and pressure values, the thermodynamic parameters for the next time step can be retrieved using the REFPROP software.

[0018] In the above method, as described in step (6), a pressure-time curve is drawn based on the data obtained at each time step. After reaching the predetermined end time or end pressure, the calculation stops and the pressure evolution law of the cryogenic liquid storage tank is obtained.

Claims

1. A method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model, characterized in that: The steps are: Step (1) using a pressure sensor, a temperature sensor and a liquid level gauge to collect the temperature of the current gas phase and liquid phase of the cryogenic liquid storage tank, the pressure inside the storage tank, the vacuum degree of the insulation layer, and the real-time liquid level; Step (2) transmitting the signal data obtained by the sensor monitoring to the processor, and checking the density, phase change latent heat, and thermodynamic energy of the gas and liquid phases in the storage tank through REFPROP software; Step (3) establishing a three-dimensional model of the storage tank and the heat and mass transfer relationship, and performing 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, liquid phase, and gas-liquid interface in the 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 query the thermodynamic parameters of the next time step through REFPROP software; Step (6) calculates the safe and lossless storage time of the tank under the current liquid filling volume and insulation performance to ensure the safe operation of the tank.

2. The method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model according to claim 1, characterized in that: As described in step (3), the energy relationship in the gas phase follows formula (1): （1）； in, is the mass of the gas in the gas phase space, kg; is the change in specific thermodynamic energy of gas in the gas phase space in one time step, 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; is the mass transfer rate between the gas-liquid interface and the gas phase space, kg / s; is the mass flow rate of gas discharged from the interior of the container when the pressure relief device is activated, kg / s; is the specific enthalpy of saturated vapor corresponding to the pressure p in the gas phase space, J / kg; is the specific enthalpy of the gas in the superheated state, J / kg; is the volume of the gas phase space, m 3 ; is the time step, s; The energy relationship in the liquid phase follows formula (2): (2)； in, is the mass of the liquid, kg; is the change in specific internal energy of the liquid in one time step, J / kg; is the heat transferred from the container wall to the liquid per unit time, W; is the heat transfer rate between the liquid in the liquid space and the gas-liquid interface, W; is the mass transfer rate between the liquid and the vapor-liquid interface, kg / s; is the specific enthalpy of the liquid in the saturated state corresponding to the internal pressure p in the tank, J / kg; is the volume of liquid in liquid, m 3 ; The energy relationship at the gas-liquid interface follows formula (3): （3）。 3. The method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model according to claim 1, wherein: As described in step (3), the wall heat transfer relationship in the gas phase region follows formula (4): （4）; in, is the natural convection heat transfer coefficient of the gas, W / (m 2 K); is the wall temperature in the gas phase region, K; is the volume average temperature of the gas phase region, K; is the wall area of ​​the gas phase region, m 2 ; is the thermal conductivity of the solid wall, W / (m·K); is the saturation temperature corresponding to pressure p, K; is the width of the heat-affected zone of the solid wall near the interface, m; is the cross-sectional area of ​​the solid wall, m 2 ; is the apparent thermal conductivity of the insulation layer, W / (m·K); is the external ambient temperature, K; is the thickness of the insulation layer, m; The wall heat transfer relationship in the liquid phase region follows the formula: (5)； Where, is the natural convection heat transfer coefficient of the liquid, W / (m 2 K); is the wall temperature in the liquid phase region, K; is the wall area of ​​the liquid phase region, m 2 .

4. The method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model according to claim 1, wherein: 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 formula (6) and (7): (6)； （7）； in, is the convection heat transfer coefficient between the interface and the gas, W / (m 2 K); is the thermal conductivity of the gas, W / (m⋅K); is the volume expansion coefficient of the gas, 1 / K; is the kinematic viscosity coefficient of the gas, m 2 / s; is the thermal diffusion coefficient of low-temperature gas, m 2 / s; is the Rayleigh number of the low-temperature gas on the gas phase side of the interface; is the Nusselt number of the low-temperature gas on the gas phase side of the interface; 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 formula (8) (9): （8）; (9)； in, is the convection heat transfer coefficient between the interface and the liquid, W / (m 2 K); is the thermal conductivity of the liquid, W / (m⋅K); is the volume expansion coefficient of the liquid, 1 / K; is the kinematic viscosity coefficient of the liquid, m 2 / s; is the thermal diffusivity of the cryogenic liquid, m 2 / s; is the Rayleigh number of the low-temperature liquid on the liquid side of the interface; is the Nusselt number of the cryogenic liquid on the liquid side of the interface; constant and It needs to be determined based on the current pressure and insulation performance of the tank.

5. The method for predicting the pressure of a cryogenic liquid storage tank based on a non-thermal equilibrium model according to claim 4, characterized in that: The gauge pressure of the storage tank is within the range of 0~0.7 MPa, and the vacuum degree of the insulation layer is less than 10 3 Under the conditions of Pa: (10)； The gauge pressure of the storage tank is within the range of 1.5~3.5 MPa, and the vacuum degree of the insulation layer is less than 10 3 Under the conditions of Pa: (11)； When the gas phase temperature hour, When the liquidus temperature hour, .

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