A simulation method and device for low-temperature rectification separation of helium isotopes

Abstract

The application provides a simulation calculation method and device for low-temperature rectification separation of helium isotopes, and the method comprises the following steps: establishing a mathematical model of a low-temperature rectification tower of helium isotopes, and determining initial parameters, wherein the initial parameters comprise initial values of temperature, initial values of phase equilibrium constants and initial values of gas phase flow rates; based on the initial parameters, a three-diagonal matrix method is used to solve a component material balance equation set and a phase equilibrium equation set of each component to obtain liquid phase component concentrations of each component on each tower plate; according to the liquid phase component concentrations of each component on each tower plate, a mole fraction addition equation set is used to correct temperature, and a heat balance equation set is used to correct the gas phase flow rate, so that the component concentration, temperature, gas-liquid phase flow rate of the helium isotopes in the rectification tower and the heat load of a tower top condenser and a tower bottom reboiler are finally simulated.

Description

Technical Field

[0001] This invention relates to the field of cryogenic distillation technology, and in particular to a simulation calculation method and apparatus for separating helium isotopes by cryogenic distillation. Background Technology

[0002] Helium-3 and helium-4, as the main stable helium isotopes, often exist in the form of mixtures. The separation of helium-3 and helium-4, i.e., the separation of helium isotopes, has important applications in the medical, nuclear, and aerospace industries. Since the 1950s, scientists have been researching methods for separating helium isotopes. Among these, thermal flushing and super-leakage methods utilize the superfluidity of helium-4 at Tλ (2.17 K), thus the separation temperature must be lowered below Tλ. Thermal flushing has been gradually phased out due to its low separation efficiency. While membrane separation can avoid separation below liquid helium temperature, membrane technology for helium isotope separation is not yet mature. Cryogenic distillation, as a mature and simple separation method, utilizes the different boiling points of helium isotopes to achieve efficient separation.

[0003] It is not difficult to find research reports on the low-temperature distillation of helium isotopes since the beginning of the 21st century. In particular, due to the high price and scarcity of helium-3, conducting experiments on the low-temperature distillation of helium isotopes has become extremely difficult, making low-temperature distillation simulation particularly important. However, as the gases with the lowest boiling points currently known (helium-4 boiling point 4.2K and helium-3 boiling point 3.19K), the physical properties of helium isotopes at low temperatures are difficult to describe uniformly using equations of state, and vapor-liquid equilibrium data are especially lacking. It is difficult to achieve simulation of helium isotope distillation using commercially available chemical process simulation software (Aspen Plus, Chemcad, etc.). Summary of the Invention

[0004] This invention provides a simulation calculation method and apparatus for the separation of helium isotopes by low-temperature distillation, which solves the problem that it is difficult to simulate the distillation of helium isotopes in the prior art.

[0005] This invention provides a simulation calculation method for the separation of helium isotopes by low-temperature distillation, comprising:

[0006] A mathematical model of a helium isotope cryogenic distillation column is established, which is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that the gas and liquid phases can quickly reach equilibrium after contact on each plate, that is, the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is assumed that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature and composition; the helium isotope cryogenic distillation column contains N plates and M components, with each plate serving as an equilibrium stage in the mathematical model; the mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for the N equilibrium stages.

[0007] Determine the initial parameters, which include the initial value of temperature, the initial value of phase equilibrium constant, and the initial value of gas phase flow rate;

[0008] Based on the initial parameters, the material balance equations and phase equilibrium equations for each component are solved using the tridiagonal matrix method to obtain the liquid phase concentration of each component on each tray.

[0009] Based on the liquid phase component concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas phase flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid phase flow rate, and heat load of the top condenser and bottom reboiler in the distillation column are simulated.

[0010] According to a simulation calculation method provided by the present invention, determining initial parameters includes:

[0011] The initial temperature values ​​of each tray are obtained by linear interpolation of the bubble point temperature of the mixture generated on the top tray and the dew point temperature of the mixture generated on the bottom tray.

[0012] The initial value of the phase equilibrium constant is calculated based on the ideal K-model equation;

[0013] The initial value of the gas phase flow rate is determined based on the constant molar flow assumption and the heat balance equations, wherein the constant molar flow assumption means that the rising steam molar flow rates in the rectifying section and the stripping section are equal.

[0014] According to a simulation calculation method provided by the present invention, the initial value of the phase equilibrium constant is calculated based on the ideal K-model equation, including:

[0015]

[0016] in, ρ is the saturated vapor pressure of component i, and p is the total pressure;

[0017] The components include helium-3 and helium-4. The saturated vapor pressures of helium-3 and helium-4 are calculated using the following formula:

[0018] The formula for the saturated vapor pressure of helium-4 is:

[0019]

[0020]

[0021]

[0022] The formula for the saturated vapor pressure of helium-3 is:

[0023]

[0024] Where p represents, p c It means, a k T represents, T c Let θ represent , and b represent .

[0025] According to a simulation calculation method provided by the present invention, the component material balance equations are realized by the following formulas:

[0026] L j-1 x i,j-1 +V j+1 y i,j+1 +F j z i,j -(L j +U j )x i,j -(V j +W j )y i,j =0

[0027] Among them, L j V is the liquid flow rate on the j-th tray; j x is the gas flow rate on the j-th tray; i,j Let y be the liquid phase concentration of component i on the j-th tray; i,j Let F be the gas phase concentration of component i on the j-th tray; j U is the feed flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j Let $\frac{j}{j}$ be the gas flow rate sampled from the side stream on the $j$-th tray.

[0028] The phase equilibrium equations are achieved through the following formulas:

[0029] y i,j -K i,j x i,j =0

[0030] Among them, K i,jLet be the phase equilibrium constant of component i on the j-th tray.

[0031] According to a simulation calculation method provided by the present invention, temperature is corrected using the mole fraction summation equations based on the liquid phase component concentration of each component on each tray, including:

[0032] Substitute the calculated liquid phase concentrations of each component on each tray into the set of equations for summing the mole fractions, and determine whether the sum of the mole fractions of the liquid phase components on each tray is equal to 1.

[0033] If the sum of the mole fractions of the liquid phase components in each plate is not equal to 1, the calculated liquid phase component concentration is normalized using the normalization equation, and then the phase equilibrium plate temperature and phase equilibrium constant are recalculated using the normalized liquid phase component concentration.

[0034] Based on the recalculated phase equilibrium tray temperature and phase equilibrium constant, the gas phase component concentration of each component on each tray is calculated using the phase equilibrium equation set. The gas phase component concentration of each component on each tray is substituted into the mole fraction summation equation set. The mole fraction summation equation set is used to determine whether the sum of the mole fractions of the gas phase components on each tray is equal to 1.

[0035] If it is not equal to 1, continue to calculate the phase equilibrium plate temperature and phase equilibrium constant, and use the phase equilibrium equations to calculate the gas phase component concentration of each component on each plate until the sum of the mole fractions of the gas phase components on each plate is equal to 1.

[0036] Update the phase equilibrium constant, re-execute the calculation of the liquid phase concentration of each component on each tray, substitute the calculated liquid phase concentration of each component on each tray into the mole fraction summation equation system, and determine whether the sum of the liquid phase mole fractions of each tray is equal to 1, until the sum of the liquid phase mole fractions of each tray is equal to 1.

[0037] According to a simulation calculation method provided by the present invention, the mole fraction summation equation system is used to determine whether the sum of the mole fractions of the gas phase components in each stage of the plate is equal to the following:

[0038]

[0039]

[0040] Where, x i,j Let y be the liquid phase concentration of component i on the j-th tray; i,j Let be the concentration of the gas phase component of component i on the j-th tray.

[0041] According to a simulation calculation method provided by the present invention, the gas phase flow rate is corrected using the heat balance equations, including:

[0042]

[0043] Among them, h Lj h is the liquid phase enthalpy of the mixture on the j-th tray; Fj h is the feed enthalpy on the j-th tray; Vj Q is the vapor enthalpy of the mixture on the j-th tray; j Let L be the heat load on the j-th tray; j V is the liquid flow rate on the j-th tray; j U is the gas flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j F represents the gas flow rate extracted from the side stream of the j-th tray; j Let be the feed flow rate on the j-th tray.

[0044] The present invention also provides a simulation computing device for the separation of helium isotopes by cryogenic distillation, comprising:

[0045] A model unit is established to build a mathematical model of a helium isotope cryogenic distillation column. This mathematical model is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that on each plate, the gas and liquid phases reach equilibrium rapidly after contact, meaning the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is also assumed that the liquid on each plate and the gas between plates are completely mixed and have uniform pressure, temperature, and composition. The helium isotope cryogenic distillation column comprises N plates and M components, with each plate serving as an equilibrium stage in the mathematical model. The mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for the N equilibrium stages.

[0046] A parameter determination unit is used to determine initial parameters, wherein the initial parameters include initial values ​​of temperature, phase equilibrium constant, and gas phase flow rate;

[0047] The liquid phase determination unit is used to solve the component material balance equations and phase equilibrium equations for each component based on the initial parameters using the tridiagonal matrix method, so as to obtain the liquid phase component concentration of each component on each tray.

[0048] The simulation calculation unit is used to correct the temperature using the mole fraction summation equations and the gas flow rate using the heat balance equations, based on the liquid phase component concentration of each component on each tray, and finally simulate the concentration distribution, temperature distribution, and flow rate distribution of helium isotopes in the distillation column, as well as the heat load of the top condenser and bottom reboiler.

[0049] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the simulation calculation method for separating helium isotopes by cryogenic distillation as described above.

[0050] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the simulation calculation method for separating helium isotopes by cryogenic distillation as described above.

[0051] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the simulation calculation method for separating helium isotopes by cryogenic distillation as described above.

[0052] The present invention provides a simulation calculation method and apparatus for the separation of helium isotopes by cryogenic distillation. This method establishes a mathematical model of a cryogenic distillation column for helium isotopes, and then solves the model based on determined initial parameters to obtain the liquid phase concentration of each component on each tray. Based on the liquid phase concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas phase flow rate is corrected using the heat balance equations. Finally, the simulation results determine the component concentration, temperature, gas-liquid phase flow rate, and heat load of the top condenser and bottom reboiler of the helium isotopes within the distillation column. The simulation results provide important guidance for the selection of experimental parameters and the construction of the apparatus in the future. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in this 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 some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0054] Figure 1 This is one of the flowcharts illustrating the simulation calculation method for the low-temperature distillation separation of helium isotopes provided by the present invention;

[0055] Figure 2 This is a schematic diagram of a low-temperature distillation column model provided by the present invention;

[0056] Figure 3 This is the second schematic diagram of the simulation calculation method for low-temperature distillation separation of helium isotopes provided by the present invention;

[0057] Figure 4 This is the third flowchart of the simulation calculation method for low-temperature distillation separation of helium isotopes provided by the present invention;

[0058] Figure 5 This is the fourth flowchart of the simulation calculation method for low-temperature distillation separation of helium isotopes provided by the present invention;

[0059] Figure 6 This is a schematic diagram of the structure of the simulation computing device for low-temperature distillation separation of helium isotopes provided by the present invention;

[0060] Figure 7 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0062] This invention discloses a simulation calculation method for the separation of helium isotopes by cryogenic distillation. The method mainly includes solving the MESH mathematical model for cryogenic distillation and calculating the thermodynamic properties of helium isotopes. See also... Figure 1 ,include:

[0063] 101. Establish a mathematical model for a cryogenic distillation column for helium isotopes.

[0064] The mathematical model is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that on each plate, the gas and liquid phases can quickly reach equilibrium after contact, that is, the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is assumed that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature and composition.

[0065] In addition, the model needs to consider the following additional simplifying assumptions:

[0066] 1. The distillation column is insulated from the outside environment;

[0067] 2. Ignore the pressure drop inside the tower.

[0068] The helium isotope cryogenic distillation column contains N trays and M components, with each tray serving as an equilibrium stage in a mathematical model. The mathematical model includes a set of material balance equations M, a set of phase balance equations E, a set of mole fraction summation equations S, and a set of heat balance equations H for the N equilibrium stages.

[0069] Specifically, the M equation—the set of component material balance equations—is as follows (1):

[0070] L j-1 x i,j-1+V j+1 y i,j+1 +F j z i,j -(L j +U j )x i,j -(V j +W j )y i,j =0 (1)

[0071] Among them, L j V is the liquid flow rate on the j-th tray; j x is the gas flow rate on the j-th tray; i，j Let y be the liquid phase concentration of component i on the j-th tray; i，j Let F be the gas phase concentration of component i on the j-th tray; j U is the feed flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j Let be the gas flow rate extracted from the side stream of the j-th tray.

[0072] E equations—the phase equilibrium equations are as follows (2):

[0073] y i，j -K i，j x i，j =0 (2)

[0074] Among them, K i，j Let be the phase equilibrium constant of component i on the j-th tray, and the rest are the same as above.

[0075] The S-equation—the set of equations for the sum of mole fractions is given by equations (3) and (4):

[0076]

[0077]

[0078] The H equation—the heat balance equation system—is as follows (5):

[0079]

[0080] Among them, h Lj h is the liquid phase enthalpy of the mixture on the j-th tray; Fj h is the feed enthalpy on the j-th tray; Vj Q is the vapor enthalpy of the mixture on the j-th tray; j Let be the heat load on the j-th tray; the rest are the same as above.

[0081] In addition, the overall material balance formula for the device from stage 1 to stage j is as follows (6):

[0082]

[0083] Among them, F m U is the feed flow rate on the j-th tray; m W represents the liquid flow rate sampled from the side stream on the j-th tray; m L represents the gas flow rate extracted from the side stream of the j-th tray. j Vj is the liquid flow rate on the j-th tray; V1 is the gas flow rate on the 1-th tray. j+1 Let be the gas flow rate on the (j+1)th tray.

[0084] See Figure 2 , Figure 2 The diagram shown is a schematic of the cryogenic distillation column model in this embodiment. In the diagram: L j V is the liquid flow rate on the j-th tray; j x is the gas flow rate on the j-th tray; i,j Let y be the liquid phase concentration of component i on the j-th tray; i,j Let F be the gas phase concentration of component i on the j-th tray; j U is the feed flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j Q represents the gas flow rate extracted from the side stream of the j-th tray; j Let be the heat load on the j-th tray.

[0085] 102. Determine the initial parameters, wherein the initial parameters include the initial value of temperature, the initial value of phase equilibrium constant, and the initial value of gas phase flow rate.

[0086] In this embodiment, solving each set of equations requires determining appropriate initial values ​​for temperature, phase equilibrium constant, and gas flow rate. The quality of the initial values ​​directly affects the convergence speed of the program.

[0087] Specifically, see Figure 3 Step 102, determining the initial parameters, includes:

[0088] 301. The initial temperature values ​​of each tray are obtained by linear interpolation based on the bubble point temperature of the mixture generated on the top tray and the dew point temperature of the mixture generated on the bottom tray.

[0089] 302. The initial value of the phase equilibrium constant is calculated based on the ideal K-model equation.

[0090] Specifically, the initial value of the phase equilibrium constant is calculated based on the ideal K-model equation, including the following equation (7):

[0091]

[0092] in, ρ is the saturated vapor pressure of component i, and p is the total pressure;

[0093] The components include helium-3 and helium-4. The saturated vapor pressures of helium-3 and helium-4 are calculated using the following formula:

[0094] The saturated vapor pressure of helium-4 is given by equations (8) to (10):

[0095]

[0096]

[0097]

[0098] The saturated vapor pressure of helium-3 is given by the following formula (11):

[0099]

[0100] 303. Determine the initial value of the gas phase flow rate based on the constant molar flow assumption and the heat balance equations, wherein the constant molar flow assumption means that the rising steam molar flow rates in the rectifying section and the stripping section are equal.

[0101] The initial value of the vapor phase flow rate is determined based on the constant molar flow assumption, meaning that the rising vapor molar flow rates in the rectifying and stripping sections are equal. However, the vapor phase molar flow rates in the two sections are not necessarily equal, depending on the thermal condition of the feed. Therefore, it is necessary to determine the thermal condition of the feed based on the feed parameters. The steps for determining the thermal condition of the feed are determined based on the heat balance equations.

[0102] 103. Based on the initial parameters, the material balance equations and phase equilibrium equations for each component are solved using the tridiagonal matrix method to obtain the liquid phase concentration of each component on each tray.

[0103] The specific steps for solving the ME equations are as follows: Substituting the phase equilibrium equation (2) into the material balance equation (1) will eliminate y. i,j Substituting equation (6) into the equation, we can eliminate L. j After simplification, a system of multivariate linear equations is obtained, which can be easily written in matrix form. Then, the liquid phase composition x can be solved using the Gaussian elimination method. i,j .

[0104] 104. Based on the liquid phase component concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas phase flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid phase flow rate, and heat load of the top condenser and bottom reboiler of the distillation column are simulated.

[0105] Among them, the component concentration is obtained according to formulas (1) and (2), the temperature is obtained according to formulas (3) and (4), the gas-liquid phase flow rate is obtained according to formula (1), and the heat load is obtained according to formula (5).

[0106] The simulation method for separating helium isotopes by cryogenic distillation provided in this invention establishes a mathematical model of a cryogenic distillation column for helium isotopes. Then, based on predetermined initial parameters, the model is solved to obtain the liquid phase concentration of each component on each tray. Based on the liquid phase concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid flow rate, and heat load of the top condenser and bottom reboiler of the helium isotopes within the distillation column are simulated. The simulation results provide important guidance for the selection of experimental parameters and the construction of the apparatus in the future.

[0107] Specifically, see Figure 4 In step 104, the temperature is corrected using the mole fraction summation equations based on the liquid phase concentration of each component on each tray, including:

[0108] 401. Substitute the calculated concentrations of the liquid phase components on each tray into the equation system of mole fraction summation, and determine whether the sum of the mole fractions of the liquid phase components on each tray is equal to 1.

[0109] 402. If the sum of the mole fractions of the liquid phase components in each plate is not equal to 1, the calculated liquid phase component concentrations are normalized using the normalization equation. Then, the phase equilibrium plate temperature and phase equilibrium constant are recalculated using the normalized liquid phase component concentrations.

[0110] 403. Based on the recalculated phase equilibrium tray temperature and phase equilibrium constant, use the phase equilibrium equations to calculate the gaseous component concentration of each component on each tray. Substitute the gaseous component concentration of each component on each tray into the mole fraction summation equations and use the mole fraction summation equations to determine whether the sum of the mole fractions of the gaseous components on each tray is equal to 1.

[0111] 404. If it is not equal to 1, continue to calculate the phase equilibrium plate temperature and phase equilibrium constant, and use the phase equilibrium equations to calculate the gas phase component concentration of each component on each plate until the sum of the mole fractions of the gas phase components on each plate is equal to 1.

[0112] 405. Update the phase equilibrium constant, re-execute the calculation of the liquid phase concentration of each component on each tray, substitute the calculated liquid phase concentration of each component on each tray into the mole fraction summation equation system, and determine whether the sum of the liquid phase mole fractions of each tray is equal to 1, until the sum of the liquid phase mole fractions of each tray is equal to 1.

[0113] The normalization equation is given in equation (7):

[0114]

[0115] After correcting the temperature using the S equation, the next step is to correct the gas flow rate using the H equation, which is the gas flow rate correction using the heat balance equations in step 104.

[0116] First, the molar enthalpy of the mixture in both the gas and liquid phases on each tray needs to be calculated, as well as the enthalpy of the feed. Due to the special properties of helium, there is currently no well-defined equation of state to describe its thermodynamic properties at low temperatures. Directly using general SRK, PR, or BWM equations of state can easily cause iterative oscillations in the program, making convergence difficult. To address this, this embodiment of the invention uses the least squares method to fit the saturated gas-liquid enthalpy data of helium-3 within a temperature range into a function of temperature. Similarly, the saturated gas-liquid enthalpy of helium-4 is processed in the same way. However, since the superfluid helium transition temperature of helium-4 is 2.17 K, within the rectification temperature range, there will be a corresponding inflection point in its enthalpy when helium-4 transforms into superfluid helium. Therefore, this embodiment of the invention fits the enthalpy data of helium-4 before and after the superfluid helium transition in segments to ensure the accuracy of the fitted equation.

[0117] See Figure 5 , Figure 5 This invention discloses a simulation calculation method for the separation of helium isotopes by cryogenic distillation, comprising:

[0118] S1, Predefined F j -Feed flow rate of each tray, z i，j -Concentration of light components in the feed for each tray, and feed conditions (T) Fj -Feed temperature of each tray, P Fj - Feed pressure of each tray, or h Fj - Enthalpy of the feed mixture for each tray), P j -Pressure on each tray, U j - Liquid phase outflow rate on each tray, W j - Vapor extraction flow rate on each tray; Q j -Heat load on each tray except Q l -Heat load of the condenser (i.e., the first layer) and Q N- Heat load of the reboiler (i.e., the Nth layer); N - number of theoretical plates, R - reflux ratio, V1 - vapor phase outflow rate on the first plate (condenser).

[0119] The method in this embodiment requires solving the MESH equation, which necessitates determining suitable initial values ​​for temperature Tj and phase equilibrium constant K. i,j and the initial value of gas phase flow rate V j 0 The quality of the initial value selection directly affects the convergence speed of the program.

[0120] First, the initial values ​​of each tray temperature are obtained by linear interpolation of the bubble point temperature of the top product and the dew point temperature of the bottom product. Utilizing the properties of the bubble and dew points of the mixture, the steps for calculating the top bubble point temperature and the bottom dew point temperature are written as subroutines PB and PD, respectively. The recalculation of the tray temperature also uses the bubble point calculation method and is iteratively updated using Newton's interpolation method until the criteria are met. Second, due to the lack of gas-liquid phase equilibrium constants for Helium-3 and Helium-4, as well as available thermodynamic equations of state, the initial values ​​of the phase equilibrium constants are calculated using the ideal K-model equation, see formula (7). The steps for calculating the gas-liquid phase equilibrium constants of Helium-3 and Helium-4, i.e., formulas (8) to (11), are written into subroutine K34.

[0121] S2, Set initial temperature value T j And the initial value of gas phase flow rate V j 0 .

[0122] S3, Load the K34 program to calculate the initial value of the phase equilibrium constant K. i,j .

[0123] Once the initial parameters are determined, the MESH equations can be calculated.

[0124] A simulation calculation method for the separation of helium isotopes by cryogenic distillation is to group the MESH equations by type. Under certain initial values ​​of temperature and vapor flow rate, the ME equations for each component are solved using the tridiagonal matrix method. Then, the temperature is corrected by the S-equation and the vapor flow rate is corrected by the H-equation. Finally, the component concentration, temperature, flow rate and heat load of the helium isotope that meet the conditions are obtained.

[0125] The specific steps for solving the ME equations are as follows: Substituting the phase equilibrium equation (2) into the material equilibrium equation (1) will eliminate the concentration y of the gas phase component of component i on the j-th tray. i,j Substituting equation (6) into the equation, L can be eliminated. j After simplification, a system of multivariate linear equations is obtained, which can be easily written in matrix form. Then, the concentration x of liquid component i on the j-th tray can be solved using the Gaussian elimination method. i,jThe above solution steps x i，j Compile it into a subroutine and name it ME.

[0126] S4. Load the ME program to calculate the concentration of liquid phase components x. i，j .

[0127] S5. The liquid phase composition x of each plate is calculated using the ME subroutine. i，j Substitute into equation (4) of the S-phase to determine whether the sum of the mole fractions of the liquid phase components in each plate is equal to 1.

[0128] S6. If it is not equal to 1, then use the normalization equation (7) to calculate x. i，j Normalization is performed.

[0129] S7. Using the normalized x i，j Recalculate the phase equilibrium tray temperature Tj and the phase equilibrium constant K. i，j The step of calculating the phase equilibrium tray temperature has been written as a subroutine TB.

[0130] S8. Calculate the gas phase composition y of each plate using the E equation. i，j And use S equation (3) to determine whether the sum of the mole fractions of the gas phase components of each plate is equal to 1.

[0131] If it is not equal to 1, continue to step S7, calculate the phase equilibrium plate temperature and phase equilibrium constant, and use the phase equilibrium equations to calculate the gas phase component concentration of each component on each plate, until the sum of the mole fractions of the gas phase components on each plate is equal to 1.

[0132] S9. Update the phase equilibrium constant, re-execute the calculation of the liquid phase concentration of each component on each tray, substitute the calculated liquid phase concentration of each component on each tray into the mole fraction summation equation system, and determine whether the sum of the liquid phase mole fractions of each tray is equal to 1, until the sum of the liquid phase mole fractions of each tray is equal to 1.

[0133] After correcting the temperature using the S-equation, the next step is to correct the vapor flow rate using the H-equation. First, the molar enthalpy of the mixture in both the gas and liquid phases on each tray needs to be calculated, along with the enthalpy of the feed. Due to the unique properties of helium, there is currently no well-defined equation of state to describe its thermodynamic properties at low temperatures. Directly using general SRK, PR, or BWM equations of state can easily cause iterative oscillations in the program, making convergence difficult. To address this, this invention uses the least squares method to fit the saturated gas-liquid enthalpy data of helium-3 within the temperature range into a function of temperature. Similarly, the saturated gas-liquid enthalpy of helium-4 is handled in the same way. However, since the superfluid helium transition temperature of helium-4 is 2.17 K, within the distillation temperature range, there will be a corresponding inflection point in its enthalpy when helium-4 transitions to superfluid helium. Therefore, this invention fits the enthalpy data of helium-4 piecewise before and after the superfluid helium transition to ensure the accuracy of the fitted equation. The steps for calculating the molar enthalpy of the mixture in both the gas and liquid phases on each tray are written as a subroutine named Hmix. The step of calculating the feed enthalpy is written as a subroutine and named FeedH.

[0134] S10. Load FeedH and Hmix programs to calculate the feed enthalpy h. fj Liquid phase enthalpy h Lj and the vapor phase enthalpy h Vj .

[0135] S11. By solving equation H, the heat load Q1 of the top condenser and the heat load Q of the bottom reboiler can be obtained respectively. N And the gas flow rate V on the tray j (k) The steps for calculating the gas flow rate and heat load are written as a subroutine named VandQ. Finally, the liquid flow rate on the tray can be calculated accordingly using equation (6).

[0136] S12. Calculate whether the interval accuracy value of the gas phase flow rate is less than the set threshold. If yes, end directly. If no, update the gas phase flow rate value on each tray and start the next iteration calculation of steps S4 to S12.

[0137] Among them, the interval accuracy value of the gas phase flow rate is |(V j (k+1) -V j (k) ) / V j (k+1) |. In step S12, calculate |(V) j (k+1) -V j (k) ) / V j (k+1) Is the gas flow rate less than the set threshold e3? If not, update the gas flow rate value on each tray to V. j(k+1) =0.5(V) j (k+1) +V j (k) ).

[0138] Furthermore, the boundary conditions required for this method are shown in Table 1. Using this method, after inputting the boundary conditions, the component concentration, temperature, gas-liquid flow rate, and heat load in the condenser and reboiler of the helium isotope cryogenic distillation column can be simulated. The specific values ​​in Table 1 are for illustrative purposes only and can be modified accordingly for actual simulations.

[0139] Table 1 Setting Parameters

[0140]

[0141]

[0142] Helium isotopes, being the gases with the lowest boiling points (helium-4 at 4.2 K and helium-3 at 3.19 K), have physical properties at low temperatures that are difficult to describe uniformly using equations of state, especially given the lack of vapor-liquid equilibrium data. Commercially available chemical process simulation software (Aspen Plus, Chemcad, etc.) struggles to simulate the distillation of helium isotopes. This invention provides a simulation method for the low-temperature distillation separation of helium isotopes. It uses the least squares method to fit the thermodynamic data of helium isotopes at low temperatures into usable equations for program calls. The solution steps for the MESH equation are sequentially written into subroutines, and finally, the mathematical model of a low-temperature helium isotope distillation column can be successfully solved using the overall program. Using this calculation method, based on set boundary conditions, the concentration distribution, temperature distribution, and flow rate distribution of helium isotopes within the distillation column, as well as the heat load of the condenser and reboiler, can be simulated.

[0143] The following describes the simulation calculation device for the low-temperature distillation separation of helium isotopes provided by the present invention. The simulation calculation device for the low-temperature distillation separation of helium isotopes described below can be referred to in correspondence with the simulation calculation method for the low-temperature distillation separation of helium isotopes described above.

[0144] This invention discloses a simulation computing device for the low-temperature distillation separation of helium isotopes, see [link to relevant documentation]. Figure 6 ,include:

[0145] Model unit 601 is established to build a mathematical model of a helium isotope cryogenic distillation column. This mathematical model is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that on each plate, the gas and liquid phases can quickly reach equilibrium after contact, meaning the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is assumed that the liquid on each plate and the gas between plates are completely mixed and have uniform pressure, temperature, and composition; the helium isotope cryogenic distillation column contains N plates and M components, with each plate serving as an equilibrium stage in the mathematical model; the mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for the N equilibrium stages.

[0146] The parameter determination unit 602 is used to determine initial parameters, wherein the initial parameters include initial values ​​of temperature, phase equilibrium constant, and gas phase flow rate.

[0147] The liquid phase determination unit 603 is used to solve the component material balance equations and phase equilibrium equations for each component based on the initial parameters using the tridiagonal matrix method, so as to obtain the liquid phase component concentration of each component on each tray.

[0148] The simulation calculation unit 604 is used to correct the temperature using the mole fraction summation equations and the gas flow rate using the heat balance equations, based on the liquid phase component concentration of each component on each tray, and finally simulate the concentration distribution, temperature distribution, and flow rate distribution of helium isotopes in the distillation column, as well as the heat load of the top condenser and bottom reboiler.

[0149] Optionally, the parameter determination unit 602 is specifically used for:

[0150] The initial temperature values ​​of each tray are obtained by linear interpolation of the bubble point temperature of the mixture generated on the top tray and the dew point temperature of the mixture generated on the bottom tray.

[0151] The initial value of the phase equilibrium constant is calculated based on the ideal K-model equation;

[0152] The initial value of the gas phase flow rate is determined based on the constant molar flow assumption and the heat balance equations, wherein the constant molar flow assumption means that the rising steam molar flow rates in the rectifying section and the stripping section are equal.

[0153] Optionally, the simulation calculation unit 604 is specifically used for:

[0154] Substitute the calculated liquid phase concentrations of each component on each tray into the set of equations for summing the mole fractions, and determine whether the sum of the mole fractions of the liquid phase components on each tray is equal to 1.

[0155] If the sum of the mole fractions of the liquid phase components in each plate is not equal to 1, the calculated liquid phase component concentration is normalized using the normalization equation, and then the phase equilibrium plate temperature and phase equilibrium constant are recalculated using the normalized liquid phase component concentration.

[0156] Based on the recalculated phase equilibrium tray temperature and phase equilibrium constant, the gas phase component concentration of each component on each tray is calculated using the phase equilibrium equation set. The gas phase component concentration of each component on each tray is substituted into the mole fraction summation equation set. The mole fraction summation equation set is used to determine whether the sum of the mole fractions of the gas phase components on each tray is equal to 1.

[0157] If it is not equal to 1, continue to calculate the phase equilibrium plate temperature and phase equilibrium constant, and use the phase equilibrium equations to calculate the gas phase component concentration of each component on each plate until the sum of the mole fractions of the gas phase components on each plate is equal to 1.

[0158] Update the phase equilibrium constant, re-execute the calculation of the liquid phase concentration of each component on each tray, substitute the calculated liquid phase concentration of each component on each tray into the mole fraction summation equation system, and determine whether the sum of the liquid phase mole fractions of each tray is equal to 1, until the sum of the liquid phase mole fractions of each tray is equal to 1.

[0159] Figure 7 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 7As shown, the electronic device may include: a processor 710, a communication interface 720, a memory 730, and a communication bus 740, wherein the processor 710, the communication interface 720, and the memory 730 communicate with each other through the communication bus 740. The processor 710 can call logical instructions in the memory 730 to execute a simulation calculation method for the cryogenic distillation separation of helium isotopes, including: establishing a mathematical model of a helium isotope cryogenic distillation column, wherein the mathematical model is based on the assumptions of theoretical plates and fully mixed plates: assuming that on each plate, the gas and liquid phases can quickly reach equilibrium after contact, i.e., the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; assuming that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature, and composition; the helium isotope cryogenic distillation column contains N plates and M components, each plate serving as an equilibrium stage in the mathematical model; the mathematical model includes N equilibrium stages. The process involves establishing a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for each component. Initial parameters are determined, including initial values ​​for temperature, phase equilibrium constant, and gas flow rate. Based on these initial parameters, the tridiagonal matrix method is used to solve the component material balance equations and phase equilibrium equations for each component, obtaining the liquid phase concentration of each component on each tray. Based on the liquid phase concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas flow rate is corrected using the heat balance equations. Finally, the concentration of helium isotopes, temperature, gas-liquid flow rates, and heat load of the top condenser and bottom reboiler within the distillation column are simulated.

[0160] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, essentially, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0161] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the simulation calculation method for the low-temperature distillation separation of helium isotopes provided by the above methods, including: establishing a mathematical model of a helium isotope low-temperature distillation column, wherein the mathematical model is based on the assumptions of theoretical plates and fully mixed plates: assuming that on each plate, the gas and liquid phases can quickly reach equilibrium after contact, that is, the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; assuming that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature and composition; the helium isotope low-temperature distillation column includes N plates and M groups. Each tray serves as an equilibrium stage in the mathematical model. The mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for N equilibrium stages. Initial parameters are determined, including initial values ​​for temperature, phase equilibrium constant, and gas flow rate. Based on these initial parameters, the component material balance equations and phase equilibrium equations for each component are solved using the tridiagonal matrix method to obtain the liquid phase component concentration of each component on each tray. Based on the liquid phase component concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid flow rate, and heat load of the top condenser and bottom reboiler in the distillation column are simulated.

[0162] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a simulation calculation method for the cryogenic distillation separation of helium isotopes provided by the methods described above, including: establishing a mathematical model of a helium isotope cryogenic distillation column, wherein the mathematical model is based on the assumptions of theoretical plates and fully mixed plates: assuming that on each plate, the gas and liquid phases can quickly reach equilibrium after contact, i.e., the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; assuming that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature, and composition; the helium isotope cryogenic distillation column comprises N plates and M components, each plate serving as a component of the mathematical model. The mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for N equilibrium stages. Initial parameters are determined, including initial values ​​for temperature, phase equilibrium constant, and gas flow rate. Based on these initial parameters, the component material balance equations and phase equilibrium equations for each component are solved using the tridiagonal matrix method to obtain the liquid phase concentration of each component on each tray. According to the liquid phase concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid flow rate, and heat load of the top condenser and bottom reboiler in the distillation column are simulated.

[0163] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0164] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A simulation calculation method for the separation of helium isotopes by low-temperature distillation, characterized in that, include: A mathematical model of a helium isotope cryogenic distillation column is established, which is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that the gas and liquid phases can quickly reach equilibrium after contact on each plate, that is, the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is assumed that the liquid on each plate and the gas between the plates are completely mixed and have uniform pressure, temperature and composition; the helium isotope cryogenic distillation column contains N plates and M components, with each plate serving as an equilibrium stage in the mathematical model; the mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for the N equilibrium stages. Determine the initial parameters, which include the initial value of temperature, the initial value of phase equilibrium constant, and the initial value of gas phase flow rate; The initial values ​​of the phase equilibrium constants are calculated based on the ideal K-model equations, including: ； in, It is the saturated vapor pressure of component i. It is the total pressure; the components include helium-3 and helium-4. Based on the initial parameters, the material balance equations and phase equilibrium equations for each component are solved using the tridiagonal matrix method to obtain the liquid phase concentration of each component on each tray. Based on the liquid phase component concentration of each component on each tray, the temperature is corrected using the mole fraction summation equations, and the gas phase flow rate is corrected using the heat balance equations. Finally, the component concentration, temperature, gas-liquid phase flow rate, and heat load of the top condenser and bottom reboiler in the distillation column are simulated.

2. The simulation calculation method according to claim 1, characterized in that, Determine the initial parameters, including: The initial temperature values ​​of each tray are obtained by linear interpolation of the bubble point temperature of the mixture generated on the top tray and the dew point temperature of the mixture generated on the bottom tray. The initial value of the gas phase flow rate is determined based on the constant molar flow assumption and the heat balance equations, wherein the constant molar flow assumption means that the rising steam molar flow rates in the rectifying section and the stripping section are equal.

3. The simulation calculation method according to claim 2, characterized in that, The saturated vapor pressures of helium-3 and helium-4 are calculated using the following formula: The formula for the saturated vapor pressure of helium-4 is: ； ； ； The formula for the saturated vapor pressure of helium-3 is: ； in, This represents the saturated vapor pressure of helium-4 and helium-3. This indicates the critical pressure of helium-4. The coefficient used to calculate the saturated vapor pressure of helium-3. Indicates temperature. This indicates the critical temperature of helium-4. denoted by Tc, the dimensionless temperature number is used to establish the value, and b represents the coefficient for calculating the saturated vapor pressure of helium-3.

4. The simulation calculation method according to claim 1, characterized in that, The component material balance equations are achieved through the following formulas: ； Among them, L j V is the liquid flow rate on the j-th tray; j x is the gas flow rate on the j-th tray; i,j Let y be the liquid phase concentration of component i on the j-th tray; i,j Let F be the gas phase concentration of component i on the j-th tray; j U is the feed flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j Let be the gas flow rate extracted from the side stream of the j-th tray; The phase equilibrium equations are achieved through the following formulas: ； Among them, K i,j Let be the phase equilibrium constant of component i on the j-th tray.

5. The simulation calculation method according to claim 1, characterized in that, Temperature is corrected using the mole fraction summation equations based on the liquid phase concentration of each component on each tray, including: Substitute the calculated liquid phase concentrations of each component on each tray into the set of equations for summing the mole fractions, and determine whether the sum of the mole fractions of the liquid phase components on each tray is equal to 1. If the sum of the mole fractions of the liquid phase components in each plate is not equal to 1, the calculated liquid phase component concentration is normalized using the normalization equation, and then the phase equilibrium plate temperature and phase equilibrium constant are recalculated using the normalized liquid phase component concentration. Based on the recalculated phase equilibrium tray temperature and phase equilibrium constant, the gas phase component concentration of each component on each tray is calculated using the phase equilibrium equation set. The gas phase component concentration of each component on each tray is substituted into the mole fraction summation equation set. The mole fraction summation equation set is used to determine whether the sum of the mole fractions of the gas phase components on each tray is equal to 1. If it is not equal to 1, continue to calculate the phase equilibrium plate temperature and phase equilibrium constant, and use the phase equilibrium equations to calculate the gas phase component concentration of each component on each plate until the sum of the mole fractions of the gas phase components on each plate is equal to 1. Update the phase equilibrium constant, re-execute the calculation of the liquid phase concentration of each component on each tray, substitute the calculated liquid phase concentration of each component on each tray into the mole fraction summation equation system, and determine whether the sum of the liquid phase mole fractions of each tray is equal to 1, until the sum of the liquid phase mole fractions of each tray is equal to 1.

6. The simulation calculation method according to claim 5, characterized in that, The set of equations for summing mole fractions includes: (And)j= ; (Sx)j= ; in, Let y be the liquid phase concentration of component i on the j-th tray; i,j Let be the concentration of the gas phase component of component i on the j-th tray.

7. The simulation calculation method according to claim 1, characterized in that, Correcting the gas phase flow rate using the aforementioned heat balance equations includes: ； Among them, h Lj h is the liquid phase enthalpy of the mixture on the j-th tray; Fj h is the feed enthalpy on the j-th tray; Vj Q is the vapor enthalpy of the mixture on the j-th tray; j Let L be the heat load on the j-th tray; j V is the liquid flow rate on the j-th tray; j U is the gas flow rate on the j-th tray; j W represents the liquid flow rate sampled from the side stream on the j-th tray; j F represents the gas flow rate extracted from the side stream of the j-th tray; j Let be the feed flow rate on the j-th tray.

8. A simulation computing device for the low-temperature distillation separation of helium isotopes, characterized in that, include: A model unit is established to build a mathematical model of a helium isotope cryogenic distillation column. This mathematical model is based on the assumptions of theoretical plates and fully mixed plates: it is assumed that on each plate, the gas and liquid phases reach equilibrium rapidly after contact, meaning the gas mixture leaving the plate is in phase equilibrium with the liquid mixture; it is also assumed that the liquid on each plate and the gas between plates are completely mixed and have uniform pressure, temperature, and composition. The helium isotope cryogenic distillation column comprises N plates and M components, with each plate serving as an equilibrium stage in the mathematical model. The mathematical model includes a set of component material balance equations, a set of phase equilibrium equations, a set of mole fraction summation equations, and a set of heat balance equations for the N equilibrium stages. A parameter determination unit is used to determine initial parameters, wherein the initial parameters include initial values ​​of temperature, phase equilibrium constant, and gas phase flow rate; The initial values ​​of the phase equilibrium constants are calculated based on the ideal K-model equations, including: ； in, It is the saturated vapor pressure of component i. It is the total pressure; the components include helium-3 and helium-4. The liquid phase determination unit is used to solve the component material balance equations and phase equilibrium equations for each component based on the initial parameters using the tridiagonal matrix method, so as to obtain the liquid phase component concentration of each component on each tray. The simulation calculation unit is used to correct the temperature using the mole fraction summation equations and the gas flow rate using the heat balance equations, based on the liquid phase component concentration of each component on each tray, and finally simulate the concentration distribution, temperature distribution, and flow rate distribution of helium isotopes in the distillation column, as well as the heat load of the top condenser and bottom reboiler.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the simulation calculation method for separating helium isotopes by cryogenic distillation as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the simulation calculation method for the separation of helium isotopes by cryogenic distillation as described in any one of claims 1 to 7.

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