Method and system for predicting flux of pervaporation membrane module

Abstract

The present invention discloses a method and system for predicting the flux of a pervaporation membrane assembly, the method comprising: obtaining the membrane assembly parameters of a roll membrane; calculating the convective mass transfer coefficient according to the membrane assembly parameters; calculating the membrane surface solute concentration at the inlet of the membrane assembly according to the convective mass transfer coefficient and the concentration polarization relationship; taking the membrane surface solute concentration at the inlet of the membrane assembly as an initial value, inputting it into a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly for iteration, thereby outputting the membrane surface solute concentration of each step in the flow direction of the membrane assembly fluid as a prediction result of the local solute concentration in the length direction of the membrane assembly; calculating the solute flux of each step in the flow direction of the membrane assembly fluid according to the distribution coefficient of the separation membrane, the membrane surface solute concentration of each step and the mass transfer coefficient in the membrane, as a prediction result of the local solute flux in the length direction of the membrane assembly. The present invention is used to predict the separation performance of the membrane assembly under different structural parameters and operating parameters.

Description

Technical Field

[0001] The present invention relates to the field of membrane separation technology, and in particular to a method and system for predicting the flux of a pervaporation membrane module. Background Art

[0002] As an advanced separation technology, pervaporation membrane separation can be used for separation of organic matter in water, dehydration of organic matter, and separation of organic-organic mixed systems. For example, if the pervaporation membrane separation process is coupled with ethanol fermentation, the selectivity of the separation membrane for alcohol can be used to remove ethanol in situ, weaken its inhibitory effect on cell growth, and enhance the ethanol fermentation process. Reasonable design of the pervaporation membrane separation unit is a prerequisite for optimizing the operation of the pervaporation process. In order to reasonably design the membrane assembly, it is generally necessary to establish a suitable mass transfer model based on the consideration of various key influencing factors, realize the prediction of membrane assembly flux under different conditions, and then calculate the membrane area and design the membrane assembly structure.

[0003] In current research, the mass transfer models established for the pervaporation membrane separation process mostly regard the membrane assembly as a whole, study the effects of operating parameters such as flow rate, concentration, temperature, etc. on the mass transfer process, or establish mass transfer models for different separation systems. Taking the spiral membrane assembly as an example, under the same separation membrane conditions, there are obvious differences in the performance of the laboratory small-scale membrane assembly and the scaled-up industrial membrane assembly. The reason for this phenomenon is that when the membrane assembly after the size is enlarged, the continuous separation of ethanol along the flow direction (the length direction of the membrane assembly) will lead to a continuous decrease in the ethanol concentration in the feed liquid, that is, a decrease in the mass transfer driving force of the pervaporation separation process. The expansion of the membrane assembly size and the continued increase in the flow distance will further reduce the mass transfer driving force of the pervaporation separation, causing the membrane separation performance to continue to decline along the flow direction, and even the separation membrane near the membrane assembly outlet area loses its separation ability.

[0004] When the existing model is used to design the membrane module, the influence of the structural parameters of the membrane module on the separation performance of the entire membrane module is not taken into account. Therefore, the total membrane area, length and width of the membrane module designed may deviate from the actual requirements. When the deviation is serious, it may even cause the membrane module to fail to meet the expected separation effect, affecting the operation of the entire process. Summary of the invention

[0005] The main purpose of the present invention is to provide a method and system for predicting the flux of a pervaporation membrane module by establishing a mass transfer model that takes into account the influence of the membrane module structure on the pervaporation membrane separation process, aiming to solve the problem that the design results obtained when the existing membrane modules are scaled up are inconsistent with the actual needs.

[0006] To achieve the above object, the present invention provides a method for predicting the flux of a pervaporation membrane module, comprising the following steps:

[0007] Acquiring membrane module parameters of the spiral wound membrane, wherein the membrane module parameters include membrane module structural parameters and operation parameters during pervaporation;

[0008] Calculate the convective mass transfer coefficient based on the membrane module parameters;

[0009] According to the relationship between the convective mass transfer coefficient and the concentration polarization, the solute concentration on the membrane surface at the inlet of the membrane module is calculated;

[0010] The membrane surface solute concentration at the inlet of the membrane module is taken as the initial value, and input into the mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, so as to output the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module;

[0011] The solute flux of each step in the flow direction of the membrane module fluid is calculated based on the distribution coefficient of the separation membrane, the solute concentration on the membrane surface of each step, and the mass transfer coefficient inside the membrane, which is used as the prediction result of the local solute flux in the length direction of the membrane module.

[0012] Preferably, the mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is established in the following manner:

[0013] A micro-element segment is selected in the flow direction of the membrane module, and a material balance equation is established based on the fact that the mass change of the solute in the membrane module along the flow direction is equal to the mass of the solute permeating through the membrane in the micro-element segment;

[0014] Transform the material balance equation into a differential equation in the flow direction;

[0015] According to the definition of average concentration, determine the average concentration expression in the channel height direction of the membrane component;

[0016] According to the series resistance model, the relationship between the main solute concentration and the solute concentration on the membrane surface is determined, and the relationship between the main solute concentration and the solute concentration on the membrane surface is substituted into the average concentration expression, and then the average concentration expression after being substituted into one side of the differential equation in the flow direction, and the membrane surface adsorption equilibrium equation and the transmembrane mass transfer equation in the series resistance model are jointly substituted into the other side of the differential equation in the flow direction to obtain a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly.

[0017] Preferably, the material balance equation is:

[0018]

[0019] Among them, ρ l is the solution density, u is the membrane surface flow rate, A is the cross-sectional area of ​​the membrane module, ε is the cross-sectional porosity of the feed side, is the average solute concentration on the cross section, L is the length of the membrane module, ΔL is the microelement section on the membrane module, and J e is the solute flux, l1 and l2 are the arc length of the outer wall and the arc length of the inner wall of the microelement studied on the cross section of the membrane module respectively;

[0020] When ΔL→0, the material balance equation is transformed into a differential equation in the flow direction:

[0021]

[0022] The average concentration expression in the channel height direction of the membrane module is:

[0023]

[0024] h is the height of the screen on the feed side, x e is the main solute concentration, δ is the boundary layer thickness, the concentration change in the boundary layer is considered linear, x e,m is the solute concentration on the membrane surface, and the average concentration in the boundary layer is the main solute concentration x e and the solute concentration x on the membrane surface e,m 1 / 2 of the sum;

[0025] According to the series resistance model, the pervaporation mass transfer process is divided into the convective mass transfer equation in the boundary layer, the adsorption equilibrium equation on the membrane surface, and the transmembrane mass transfer equation:

[0026] The convective mass transfer equation in the boundary layer is:

[0027] J e =k l ρ l (x e -x e,m )

[0028] The adsorption equilibrium equation on the membrane surface is:

[0029] x e,mu =Kx e,m

[0030] The transmembrane mass transfer equation is:

[0031] J e =k m ρ l (x e,mu -x e,md )

[0032] Among them, k l is the convective mass transfer coefficient, K is the partition coefficient of the separation membrane, and x e,mu is the concentration of the solute after adsorption on the membrane surface, k m is the mass transfer coefficient within the membrane, x e,mdis the solute concentration downstream of the membrane. Since high vacuum is maintained downstream, x e,md is 0;

[0033] The mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is:

[0034]

[0035] Preferably, the convective mass transfer coefficient is calculated as follows:

[0036]

[0037]

[0038] Re=ρ l ud h / μ;

[0039] Sc=μ / (ρ l D e,l );

[0040] Where Re is the Reynolds number, Sc is the Schmidt number, and D e,l is the diffusion coefficient of the solute in the solution, d h is the equivalent diameter, a, b, c, k are coefficients to be determined;

[0041] The concentration polarization relationship is:

[0042]

[0043] Among them, D e0 is the limiting diffusion coefficient of the solute in the membrane, Z m is the film thickness, γ is the plasticization coefficient, φ u It is the total volume fraction of solute and solvent at the surface of the membrane phase.

[0044] Preferably, the step of taking the membrane surface solute concentration at the inlet of the membrane module as an initial value, inputting it into a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, thereby outputting the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module, comprises:

[0045] The solute concentration on the membrane surface at the inlet of the membrane module is taken as the initial value of the mathematical model calculation, and the length of the membrane module is taken as the solution interval. The differential equation is solved by using an iterative algorithm within each set calculation step length.

[0046] The mathematical model uses the membrane surface solute concentration output in each step as the initial value of the next step, and brings it into the mathematical model for solution to solve the membrane surface solute concentration of the next step, and iterates until the end.

[0047] Preferably, the iterative algorithm is a Runge-Kutta algorithm;

[0048] Among them, the Runge-Kutta algorithm is as follows:

[0049] k1=f(x i ,y i )

[0050] k2=f(x i +g / 2,y i +k1g / 2)

[0051] k3=f(x i +g / 2,y i +k2g / 2)

[0052] k4=f(x i +g,y i +k3g)

[0053]

[0054] In the above formula, g is the calculation step length, x i Represents the length of the membrane module at the i-th step in the mathematical model, y i represents the solute concentration on the membrane surface at the ith step in the mathematical model, and k1, k2, k3 and k4 are the coefficients in the Runge-Kutta algorithm.

[0055] Preferably, the partition coefficient of the separation membrane is calculated as follows:

[0056] According to thermodynamic equilibrium, the chemical activity was solved to obtain the volume fractions of solute, solvent and membrane at different membrane surface solute concentrations, and the relationship between the membrane surface solute concentration and the total volume fraction of the solvent in the membrane was obtained by fitting.

[0057] The calculated total volume fraction of the solvent in the membrane is converted into a mass fraction to obtain the solute concentration on the membrane surface after adsorption, and the distribution coefficient of the separation membrane is calculated based on the membrane surface adsorption equilibrium equation.

[0058] Preferably, the method is used to predict the local ethanol concentration of the ethanol-water solution along the length direction of the membrane module and the local ethanol flux along the length direction of the membrane module.

[0059] Preferably, the separation membrane is a PDMS composite membrane or a PVA composite membrane.

[0060] To achieve the above object, the present invention also proposes a prediction system, which applies the method for predicting the flux of a pervaporation membrane module; the prediction system includes a parameter acquisition module and a calculation module;

[0061] The parameter acquisition module is used for:

[0062] Acquiring membrane module parameters of the spiral wound membrane, wherein the membrane module parameters include membrane module structural parameters and operation parameters during pervaporation;

[0063] The calculation module is used for:

[0064] Calculate the convective mass transfer coefficient based on the membrane module parameters;

[0065] According to the relationship between the convective mass transfer coefficient and the concentration polarization, the solute concentration on the membrane surface at the inlet of the membrane module is calculated;

[0066] The membrane surface solute concentration at the inlet of the membrane module is taken as the initial value, and input into the mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, so as to output the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module;

[0067] The solute flux of each step in the flow direction of the membrane module fluid is calculated based on the distribution coefficient of the separation membrane, the solute concentration on the membrane surface of each step, and the mass transfer coefficient inside the membrane, which is used as the prediction result of the local solute flux in the length direction of the membrane module.

[0068] In the technical solution of the present invention, starting from the design of the membrane module, a mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is established, which takes into account the influence of the membrane module parameters on the membrane mass transfer process, and is used for the scale-up design of the membrane module. The mathematical model is based on the dissolution-diffusion theory, introduces the concentration-dependent mass transfer coefficient in the membrane, establishes the solute separation mass transfer differential equation in the flow direction of the fluid in the roll membrane module, and forms a mass transfer model. Through the mass transfer model, the solute concentration distribution in the membrane module is calculated, and the local solute flux in the membrane module is calculated, which is used to predict the separation performance of the membrane module under different structural parameters and operating parameters. Therefore, the method of the present invention has the following advantages:

[0069] First, the design basis of membrane modules is more accurate: the established model fully considers the influence of membrane module size parameters on membrane separation behavior, and can solve the true distribution law and average value of mass transfer coefficient and solute flux in the membrane under any parameters such as membrane module length, providing more accurate data for the scale-up design of membrane modules;

[0070] Second, it can optimize the operating conditions of the membrane module: This model can calculate the convective mass transfer coefficient at different flow rates by measuring the effect of the feed screen on the convective mass transfer, and realize the performance prediction of the membrane module at different feed flow rates. According to the calculation results, the operating conditions of the membrane module can be optimized to reduce the cost of trial and error in operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a schematic diagram of the structure of the membrane module in the present invention;

[0072] Figure 2 It is a microelement diagram of the membrane assembly in the present invention;

[0073] Figure 3 is a distribution diagram of ethanol concentration along the fluid flow direction in the present invention;

[0074] Figure 4 is a distribution diagram of ethanol flux along the fluid flow direction in the present invention;

[0075] Figure 5 The flowchart of the first embodiment of the method for predicting the flux of a pervaporation membrane module in the present invention.

[0076] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0077] It should be understood that the specific embodiments described herein are only used to explain the present invention, and are not used to limit the present invention.

[0078] In the following description, suffixes such as "unit", "component" or "unit" used to represent elements are only used to facilitate the description of the present invention, and have no specific meanings. Therefore, "unit", "component" or "unit" can be used in a mixed manner.

[0079] See also Figures 1 to 5 To achieve the above object, a method for predicting the flux of a pervaporation membrane module is provided in a first embodiment of the present invention, comprising the following steps:

[0080] Step S10, obtaining membrane assembly parameters of the spiral wound membrane, wherein the membrane assembly parameters include membrane assembly structural parameters and operation parameters during pervaporation;

[0081] Step S20, calculating the convective mass transfer coefficient according to the membrane module parameters;

[0082] Step S30, calculating the solute concentration on the membrane surface at the inlet of the membrane assembly according to the convective mass transfer coefficient and the concentration polarization relationship;

[0083] Step S40, taking the membrane surface solute concentration at the inlet of the membrane assembly as an initial value, inputting it into a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly for iteration, thereby outputting the membrane surface solute concentration of each step in the flow direction of the membrane assembly fluid as a prediction result of the local solute concentration in the length direction of the membrane assembly;

[0084] Step S50, calculating the solute flux of each step in the flow direction of the membrane module fluid according to the distribution coefficient of the separation membrane, the membrane surface solute concentration of each step and the mass transfer coefficient in the membrane as the local solute flux prediction result in the length direction of the membrane module.

[0085] In the technical solution of the present invention, starting from the design of the membrane module, a mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is established, which takes into account the influence of the membrane module parameters on the membrane mass transfer process, and is used for the scale-up design of the membrane module. The mathematical model is based on the dissolution-diffusion theory, introduces the concentration-dependent mass transfer coefficient in the membrane, establishes the solute separation mass transfer differential equation in the flow direction of the fluid in the roll membrane module, and forms a mass transfer model. Through the mass transfer model, the solute concentration distribution in the membrane module is calculated, and the local solute flux in the membrane module is calculated, which is used to predict the separation performance of the membrane module under different structural parameters and operating parameters. Therefore, the method of the present invention has the following advantages:

[0086] First, the design basis of membrane modules is more accurate: the established model fully considers the influence of membrane module size parameters on membrane separation behavior, and can solve the true distribution law and average value of mass transfer coefficient and solute flux in the membrane under any parameters such as membrane module length, providing more accurate data for the scale-up design of membrane modules;

[0087] Second, it can optimize the operating conditions of the membrane module: This model can calculate the convective mass transfer coefficient at different flow rates by measuring the effect of the feed screen on the convective mass transfer, and realize the performance prediction of the membrane module at different feed flow rates. According to the calculation results, the operating conditions of the membrane module can be optimized to reduce the cost of trial and error in operation.

[0088] The method of the present invention can be applied to the prediction of local solute concentration distribution and local flux of various materials (for example, methanol, ethanol, butanol, or other materials separated by pervaporation membrane modules) in the length direction of pervaporation membrane modules. In the present embodiment, the method is used to predict the local ethanol concentration of ethanol-water solution in the length direction of the membrane module and the local ethanol flux in the length direction of the membrane module.

[0089] Furthermore, the membrane assembly in the present invention may refer to a single membrane assembly or multiple membrane assemblies connected in series. When multiple membrane assemblies are used in series, the parameters of each membrane assembly may be the same or different. If the parameters of each membrane assembly connected in series are the same, the membrane assemblies connected in series can be regarded as different length positions (i.e., different step length positions) of the entire membrane assembly for prediction. If the parameters of each membrane assembly connected in series are different, each section of the membrane assembly needs to be predicted separately.

[0090] Specifically, the structural parameters of the membrane assembly include: feed side screen height h, feed side cross-sectional porosity ε, membrane assembly membrane total width l, membrane length L, feed channel area A, membrane thickness Z m , the interaction parameters between the separation membrane and ethanol are the limiting diffusion coefficient D e,0 , plasticization coefficient γ, distribution coefficient K;

[0091] The operating parameters include: membrane surface flow rate u, ethanol concentration x e , solution density ρ l , solution viscosity μ, and the diffusion coefficient D of the solute in the solution at the corresponding temperature e,l .

[0092] Figure 1 and Figure 2 In the equation, L is the fluid flow direction, r is the radial direction of the membrane assembly, and θ is the angle in the polar coordinate axis.

[0093] Based on the first embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, in the second embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, the mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is established by referring to the following method:

[0094] Step S41, selecting a micro-element segment in the flow direction of the membrane module, and establishing a material balance equation based on the mass change of the solute in the membrane module along the flow direction being equal to the mass of the solute permeating through the membrane in the micro-element segment;

[0095] Step S42, transforming the material balance equation into a differential equation in the flow direction;

[0096] Step S43, determining an expression for average concentration in the channel height direction of the membrane assembly according to the definition of average concentration;

[0097] Step S44, according to the series resistance model, determine the relationship between the main solute concentration and the solute concentration on the membrane surface, and substitute the relationship between the main solute concentration and the solute concentration on the membrane surface into the average concentration expression, and then substitute the average concentration expression into one side (left side) of the differential equation in the flow direction, and jointly substitute the membrane surface adsorption equilibrium equation and the transmembrane mass transfer equation in the series resistance model into the other side (right side) of the differential equation in the flow direction to obtain a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly.

[0098] Based on the second embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, in the third embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention:

[0099] The material balance equation is:

[0100]

[0101] Among them, ρ l is the solution density, u is the membrane surface flow rate, A is the cross-sectional area of ​​the membrane module, ε is the cross-sectional porosity of the feed side, is the average solute concentration on the cross section, L is the length of the membrane module, ΔL is the microelement section on the membrane module, and J e is the solute flux, l1 and l2 are the arc length of the outer wall and the arc length of the inner wall of the microelement studied on the cross section of the membrane module respectively;

[0102] When ΔL→0, the material balance equation is transformed into a differential equation in the flow direction:

[0103]

[0104] The average concentration expression in the channel height direction of the membrane module is:

[0105]

[0106] h is the height of the screen on the feed side, x e is the main solute concentration, δ is the boundary layer thickness, the concentration change in the boundary layer is considered linear, x e,m is the solute concentration on the membrane surface, and the average concentration in the boundary layer is the main solute concentration x e and the solute concentration x on the membrane surface e,m 1 / 2 of the sum;

[0107] The above model is based on the following assumptions: (1) the fluid is incompressible; (2) the material is in a fully developed steady-state flow in the spiral membrane module; (3) the temperature difference in the direction of fluid flow is negligible; and (4) the pressure drop in the permeate measurement is negligible compared to the feed measurement.

[0108] According to the series resistance model, the pervaporation mass transfer process is divided into the convective mass transfer equation in the boundary layer, the adsorption equilibrium equation on the membrane surface, and the transmembrane mass transfer equation:

[0109] The convective mass transfer equation in the boundary layer is:

[0110] J e =k l ρ l (x e -x e,m )

[0111] The adsorption equilibrium equation on the membrane surface is:

[0112] x e,mu =Kx e,m

[0113] The transmembrane mass transfer equation is:

[0114] J e =k m ρ l (x e,mu -x e,md )

[0115] Among them, k l is the convective mass transfer coefficient, K is the partition coefficient of the separation membrane, and x e,mu is the concentration of the solute after adsorption on the membrane surface, k m is the mass transfer coefficient within the membrane, x e,md is the solute concentration downstream of the membrane. Since high vacuum is maintained downstream, x e,md is 0;

[0116] The mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is:

[0117]

[0118] Based on the third embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, in the fourth embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention:

[0119] Convective mass transfer coefficient k l Calculate as follows:

[0120]

[0121] Re=ρ l ud h / μ;

[0122] Sc=μ / (ρ l D e,l );

[0123] Where Re is the Reynolds number, Sc is the Schmidt number, and D e,l is the diffusion coefficient of the solute in the solution, d h is the equivalent diameter, a, b, c, k are coefficients to be determined;

[0124] According to the calculated convective mass transfer coefficient k l The concentration polarization relationship is used to calculate the ethanol concentration x on the membrane surface at the inlet of the membrane module (i = 0). e,m(i＝0) .

[0125] The concentration polarization relationship is:

[0126]

[0127] Among them, D e0 is the limiting diffusion coefficient of the solute in the membrane, Z m is the film thickness, γ is the plasticization coefficient, φu is the total volume fraction of solute and solvent on the surface of the membrane phase, and e is a natural constant.

[0128] Convective mass transfer coefficient k l The determination method of the unknown coefficients a, b, c, and k is as follows:

[0129] Using a spiral membrane module (a small spiral membrane module can be used), at a fixed feed temperature and ethanol concentration, a pervaporation experiment was conducted at different feed flow rates to test the ethanol flux. m , distribution coefficient K and small spiral membrane module structural parameters (ie, the structural parameters described in S2), according to the ethanol flux at different feed flow rates, the convection mass transfer coefficient k l And the mathematical model is used for parameter regression to obtain k l The values ​​of each coefficient in the expression. The material type and structural parameters of the feed screen will affect the coefficients a, b, c, and k to be determined. The screen shape, channel height and other parameters can be designed independently, and the porosity on the feed side is measured by the drainage method.

[0130] Based on the first to fourth embodiments of the method for predicting the flux of a pervaporation membrane module of the present invention, in the fifth embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, the step S40 comprises:

[0131] The solute concentration on the membrane surface at the inlet of the membrane module is taken as the initial value of the mathematical model calculation, and the length of the membrane module is taken as the solution interval. The differential equation is solved by using an iterative algorithm within each set calculation step length.

[0132] The mathematical model uses the membrane surface solute concentration output in each step as the initial value of the next step, and brings it into the mathematical model for solution to solve the membrane surface solute concentration of the next step, and iterates until the end.

[0133] The iterative algorithm may adopt a variety of feasible algorithms, such as the Runge-Kutta algorithm, the gradient descent method, the steepest descent method, and the like.

[0134] Based on the fifth embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, in the sixth embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, the iterative algorithm is a Runge-Kutta algorithm;

[0135] Among them, the Runge-Kutta algorithm is as follows:

[0136] k1=f(x i ,y i )

[0137] k2=f(xi +g / 2,y i +k1g / 2)

[0138] k3=f(x i +g / 2,y i +k2g / 2)

[0139] k4=f(x i +g,y i +k3g)

[0140]

[0141] In the above formula, g is the calculation step length, x i Represents the length of the membrane module at the i-th step in the mathematical model, y i represents the solute concentration on the membrane surface at the i-th step in the mathematical model (i.e. x e,m(i) ), k1, k2, k3 and k4 are the coefficients in the Runge-Kutta algorithm.

[0142] Based on the fourth embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, in the seventh embodiment of the method for predicting the flux of a pervaporation membrane module of the present invention, the distribution coefficient of the separation membrane is calculated according to the following method:

[0143] Step S51, according to thermodynamic equilibrium, using chemical formula activity solution, obtain the volume fractions of solute, solvent and membrane at different membrane surface solute concentrations, and fit to obtain the relationship expression between membrane surface solute concentration and total volume fraction of solvent in the membrane:

[0144] Step S52, converting the calculated total volume fraction of the solvent in the membrane into a mass fraction to obtain the solute concentration on the membrane surface after adsorption, and calculating the distribution coefficient of the separation membrane according to the membrane surface adsorption equilibrium equation.

[0145] (1) Specifically, taking ethanol as the solute and water as the solute as the example, the partition coefficient K of the separation membrane is calculated as follows:

[0146] A rectangular membrane with fixed specifications was used to conduct swelling experiments with different ethanol concentrations at a fixed temperature. The concentration range set in the swelling experiment was consistent with the applicable ethanol concentration range of the established model. When the membrane reaches a thermodynamically stable state, the following relationship exists according to thermodynamic equilibrium:

[0147]

[0148] in is the activity of ethanol in the solution, is the activity of ethanol in the membrane phase, that is, the activity of ethanol in the solution is equal to the activity of ethanol at the membrane surface;

[0149] The activity of ethanol-water in solution, according to the Wilson equation:

[0150]

[0151] Wherein, a1 and a2 are the activity coefficients of the binary system ethanol and water, z1 and z2 are the component concentrations of ethanol and water, V1 and V2 are the component molar volumes of ethanol and water, respectively; Λ 12 ,Λ 21 are the parameters of the Wilson equation, g 11 , g 12 , g 21 , g 22 are Wilson model parameters, obtained by looking up the table; R is the molar gas constant, T is the solution temperature;

[0152] The activity of the ethanol-water-PDMS membrane ternary system is based on the Flory-Huggins equation:

[0153]

[0154] in, is the activity coefficient of water in the ethanol-water-membrane ternary system, is the activity coefficient of ethanol in the ethanol-water-membrane ternary system; φ e ,φ w ,φ m Respectively represent the volume fractions of ethanol, water and PDMS membrane at adsorption equilibrium; V e 、V w 、V m represent the molar volumes of ethanol, water and PDMS membrane respectively; χ em , χ wm and χ ew are the interaction parameters between ethanol / polymer, water / polymer and component ethanol / water, respectively; ew According to Flory-Huggins thermodynamics, χ em and χ wm Determined using the Flory-Rehner theory, χ em Take the calculation as an example:

[0155]

[0156] in is the volume fraction of the PDMS membrane obtained by performing a swelling experiment on pure ethanol and the PDMS membrane, and is calculated as follows:

[0157]

[0158] Where Dse is the mass fraction of pure ethanol in the swollen film, ρ e is the density of ethanol, ρ m is the density of the PDMS membrane. Similarly, the mass fraction of pure water in the swollen membrane D sw Calculate χ wm .

[0159] According to thermodynamic equilibrium, the volume fractions of ethanol, water, and membrane at different membrane surface ethanol concentrations can be obtained by using the chemical formula activity solution, and the membrane surface ethanol concentration x can be obtained by fitting. e,m The relationship expression with the total volume fraction of the solvent in the membrane is:

[0160] φ u =f(x e,m )

[0161] By converting the calculated total volume fraction of the solvent in the membrane into a mass fraction, the ethanol concentration x on the membrane surface after adsorption can be obtained. e,mu According to the membrane surface adsorption equilibrium equation (x e,mu =K x e,m ), and calculate the distribution coefficient K of the separation membrane.

[0162] (2) Intra-membrane mass transfer coefficient k m , plasticization coefficient γ and limiting diffusion coefficient D in the film e0 is determined as follows:

[0163] The pervaporation test of the separation membrane of the research object was carried out using an ordinary circular flat membrane. The convective mass transfer coefficient of the membrane assembly and the Reynolds number have the following relationship:

[0164] k l =0.3294×10 -6 ×Re 0.4903

[0165]

[0166] Where F is the liquid flow rate, ρ l is the solution density, f is the membrane module thickness, and μ is the solution viscosity.

[0167] At a fixed flow rate, pervaporation experiments with different feed ethanol concentrations were carried out. According to the measured ethanol flux and the corresponding convective mass transfer coefficient k at the flow rate, l , the ethanol concentration x on the membrane surface is calculated using the boundary layer convection mass transfer formula e,m Then, the mass transfer coefficient k in the membrane is calculated based on the distribution coefficient and the transmembrane mass transfer formula. m ;

[0168] According to the membrane mass transfer coefficient at different feed ethanol concentrations, the membrane mass transfer coefficient km The expression is fitted to obtain the plasticization coefficient γ and the limiting diffusion coefficient D in the membrane e0 , where the membrane thickness is obtained by scanning electron microscopy (SEM), and the expression of the mass transfer coefficient within the separation membrane with intrinsic parameters is obtained.

[0169] Convective mass transfer coefficient k of spiral membrane module l and the mass transfer coefficient k m After determination, according to the main solute concentration x e The relationship between the solute concentration on the membrane surface and x e,m , the ethanol concentration x on the membrane surface under the feed concentration condition can be obtained e,m , which is the initial value of the model calculation.

[0170] To achieve the above object, the present invention also proposes a prediction system, which applies the method for predicting the flux of a pervaporation membrane module; the prediction system includes a parameter acquisition module and a calculation module;

[0171] The parameter acquisition module is used for:

[0172] Acquiring membrane module parameters of the spiral wound membrane, wherein the membrane module parameters include membrane module structural parameters and operation parameters during pervaporation;

[0173] The calculation module is used for:

[0174] Calculate the convective mass transfer coefficient based on the membrane module parameters;

[0175] According to the relationship between the convective mass transfer coefficient and the concentration polarization, the solute concentration on the membrane surface at the inlet of the membrane module is calculated;

[0176] The membrane surface solute concentration at the inlet of the membrane module is taken as the initial value, and input into the mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, so as to output the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module;

[0177] The solute flux of each step in the flow direction of the membrane module fluid is calculated based on the distribution coefficient of the separation membrane, the solute concentration on the membrane surface of each step, and the mass transfer coefficient inside the membrane, which is used as the prediction result of the local solute flux in the length direction of the membrane module.

[0178] The separation membrane in the present invention can be specifically a PDMS composite membrane or a PVA composite membrane. Of course, other types of pervaporation membranes are also included in the protection scope of the present invention. Specifically, the PDMS composite membrane can be used to separate organic matter from water, and the PVA composite membrane can be used to dehydrate organic matter.

[0179] Among them, the PDMS composite membrane refers to a separation layer using PDMS, and the transition layer and the support layer can be adjusted as needed, for example, a PDMS / PVDF / PET composite membrane can be used. Of course, a two-layer composite membrane can also be used, for example, when there are only a separation layer and a support layer, a PDMS / PA composite membrane can be selected.

[0180] Preferably, when the separation membrane is a PDMS / PVDF / PET composite membrane, the separation layer thickness can be 15 μm; or when the separation membrane is a PDMS / PA membrane, the separation layer thickness of the separation membrane can be 2.6 μm. The method for predicting the flux of the pervaporation membrane module of the present invention can be applicable to solutions with various solute concentrations, for example, a solute concentration of 3 v / v% to 12 v / v%. For example, the concentration of the ethanol-water solution can be 3 v / v%, 5 v / v%, 6 v / v%, 9 v / v%, 12 v / v%.

[0181] Example 1

[0182] Performance prediction of PDMS / PVDF / PET spiral membrane assembly for separation of 6 v / v% ethanol-water solution at a membrane surface flow rate of 0.008 m / s.

[0183] In this embodiment, the membrane assembly uses a PDMS / PVDF / PET composite membrane, the membrane separation layer thickness is 15 μm, the feed screen is a corrugated type, the feed height h is 1.2 mm, there are two membrane sheets, each sheet width l is 1.5 m, and the membrane assembly length L is 1 m. After swelling experiments and flat membrane pervaporation experiments, the distribution coefficient K is 3.3, the plasticization coefficient γ is 7.3, and the ethanol limiting diffusion coefficient D is obtained. e,0 6.4×10 -12 m / s. The pervaporation experiment was carried out under different flow rate conditions to obtain k l The expression is k l =0.03Re 0.6 Sc 0.33 (d h / h) 0 D e,l / d h According to the ethanol flux prediction model, the ethanol concentration in the length direction of the membrane module decreases from 6v / v% at the inlet of the membrane module to 5.68v / v% at the outlet of the membrane module. The ethanol flux at the inlet of the membrane module is 89.25g / (m 2 ·h) to 83.65g / (m 2 h), the average ethanol flux of the membrane module was 86.41 g / (m 2 h).

[0184] Example 2

[0185] Performance prediction of PDMS / PA spiral membrane assembly for separation of 6 v / v% ethanol-water solution at a membrane surface flow rate of 0.008 m / s.

[0186] In this embodiment, the membrane assembly uses a PDMS / PA composite membrane with a separation layer thickness of 2.6 μm. After swelling experiments and flat membrane pervaporation experiments, the distribution coefficient K is 3.1, the plasticization coefficient γ is 4.8, and the ethanol limiting diffusion coefficient D is e,0 1.2×10 -11 m / s, the feed screen is corrugated, the feed height is 1.2mm, there are 2 membrane sheets, each sheet has a width of 1.5m, and the length of the membrane module is 1m. According to the model calculation, the ethanol concentration in the length direction of the membrane module decreases from 6v / v% at the inlet of the membrane module to 4.86v / v% at the outlet of the membrane module. The ethanol flux at the inlet of the membrane module is 257g / (m 2 ·h) to the membrane module outlet to reduce to 205g / (m 2 h), the average ethanol flux of the membrane module is 230g / (m 2 h).

[0187] Example 3

[0188] Performance prediction of PDMS / PA rolled membrane assembly for separating 6 v / v% ethanol aqueous solution at a membrane surface flow rate of 0.024 m / s.

[0189] In this embodiment, the membrane assembly uses a PDMS / PA composite membrane, the membrane separation layer thickness is 2.6 μm, the distribution coefficient K is 3.1, the plasticization coefficient γ is 4.8, and the ethanol limiting diffusion coefficient D is 0. e,0 1.2×10 -11 m / s, the feed screen is corrugated, the feed height h is 1.2mm, there are 2 membrane sheets, each sheet has a width l of 1.5m, and the length of the membrane module L is 1m. According to the model calculation, the ethanol concentration in the length direction of the membrane module decreases from 6v / v% at the inlet of the membrane module to 5.46v / v% at the outlet of the membrane module. The ethanol flux at the inlet of the membrane module is 432g / (m 2 ·h) to 390g / (m 2 h), the average ethanol flux of the membrane module is 411g / (m 2 h).

[0190] In the description of this specification, the description with reference to the terms "an embodiment", "another embodiment", "other embodiments", or "first embodiment to Xth embodiment" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, method steps or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0191] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or system. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or system including the element.

[0192] The serial numbers of the above embodiments of the present invention are only for description and do not represent the advantages or disadvantages of the embodiments.

[0193] The above are only preferred embodiments of the present invention, and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A method for predicting the flux of a pervaporation membrane module, characterized in that: The steps include: Acquiring membrane module parameters of the spiral wound membrane, wherein the membrane module parameters include membrane module structural parameters and operation parameters during pervaporation; Calculate the convective mass transfer coefficient based on the membrane module parameters; According to the relationship between the convective mass transfer coefficient and the concentration polarization, the solute concentration on the membrane surface at the inlet of the membrane module is calculated; The membrane surface solute concentration at the inlet of the membrane module is taken as the initial value, and input into the mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, so as to output the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module; The solute flux of each step in the flow direction of the membrane module fluid is calculated according to the distribution coefficient of the separation membrane, the solute concentration on the membrane surface of each step, and the mass transfer coefficient in the membrane, as the local solute flux prediction result in the length direction of the membrane module; Among them, the mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is: Where h is the height of the screen on the feed side; δ is the thickness of the boundary layer, and the concentration change in the boundary layer is considered linear; K is the distribution coefficient of the separation membrane, k m is the mass transfer coefficient within the membrane, k l is the convective mass transfer coefficient; x e,m is the solute concentration on the membrane surface, and the average concentration in the boundary layer is the main solute concentration x e and the solute concentration x on the membrane surface e,m 1 / 2 of the sum; L is the length of the membrane assembly, l1 and l2 are the arc length of the outer wall and the arc length of the inner wall of the micro-element segment studied on the cross-section of the membrane assembly respectively, u is the membrane surface flow velocity, A is the cross-sectional area of ​​the membrane assembly, and ε is the porosity of the feed side cross-sectional area.

2. The method for predicting the flux of a pervaporation membrane module according to claim 1, characterized in that: The mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is established in the following manner: A micro-element segment is selected in the flow direction of the membrane module, and a material balance equation is established based on the fact that the mass change of the solute in the membrane module along the flow direction is equal to the mass of the solute permeating through the membrane in the micro-element segment; Transform the material balance equation into a differential equation in the flow direction; According to the definition of average concentration, determine the average concentration expression in the channel height direction of the membrane component; According to the series resistance model, the relationship between the main solute concentration and the solute concentration on the membrane surface is determined, and the relationship between the main solute concentration and the solute concentration on the membrane surface is substituted into the average concentration expression, and then the average concentration expression after being substituted into one side of the differential equation in the flow direction, and the membrane surface adsorption equilibrium equation and the transmembrane mass transfer equation in the series resistance model are jointly substituted into the other side of the differential equation in the flow direction to obtain a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly.

3. The method for predicting the flux of a pervaporation membrane module according to claim 2, characterized in that: The material balance equation is: Among them, ρ l is the solution density, is the average solute concentration on the cross section, ΔL is the microelement section on the membrane module, and J e is the solute flux; When ΔL→0, the material balance equation is transformed into a differential equation in the flow direction: The average concentration expression in the channel height direction of the membrane module is: x e is the bulk solute concentration; According to the series resistance model, the pervaporation mass transfer process is divided into the convective mass transfer equation in the boundary layer, the adsorption equilibrium equation on the membrane surface, and the transmembrane mass transfer equation: The convective mass transfer equation in the boundary layer is: J e =k l ρ l (x e -x e,m ) The adsorption equilibrium equation on the membrane surface is: x e,mu =Kx e,m The transmembrane mass transfer equation is: J e =k m ρ l (x e,mu -x e,md ) Among them, x e,mu is the concentration of the solute after adsorption on the membrane surface, x e,md is the solute concentration downstream of the membrane. Since high vacuum is maintained downstream, x e,md is 0; The mathematical model for predicting the solute concentration on the membrane surface of the pervaporation membrane module is:

4. The method for predicting the flux of a pervaporation membrane module according to claim 3, characterized in that: The convective mass transfer coefficient is calculated as follows: Re=ρ l ud h / m; Sc=μ / (ρ l D e,l ); Among them, R e is the Reynolds number, Sc is the Schmidt number, D e,l is the diffusion coefficient of the solute in the solution, d h is the equivalent diameter, a, b, c, k are unknown coefficients, and μ is the solution viscosity; The concentration polarization relationship is: Among them, D e0 is the limiting diffusion coefficient of the solute in the membrane, Z m is the film thickness, γ is the plasticization coefficient, φ u It is the total volume fraction of solute and solvent at the surface of the membrane phase.

5. The method for predicting the flux of a pervaporation membrane module according to claim 1, characterized in that: The step of taking the membrane surface solute concentration at the inlet of the membrane assembly as an initial value, inputting it into a mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane assembly, and iterating, thereby outputting the membrane surface solute concentration of each step in the flow direction of the membrane assembly fluid as the local solute concentration prediction result in the length direction of the membrane assembly, comprises: The solute concentration on the membrane surface at the inlet of the membrane module is taken as the initial value of the mathematical model calculation, and the length of the membrane module is taken as the solution interval. The differential equation is solved by using an iterative algorithm within each set calculation step length. The mathematical model uses the membrane surface solute concentration output in each step as the initial value of the next step, and brings it into the mathematical model for solution to solve the membrane surface solute concentration of the next step, and iterates until the end.

6. The method for predicting the flux of a pervaporation membrane module according to claim 5, characterized in that: The iterative algorithm is the Runge-Kutta algorithm; Among them, the Runge-Kutta algorithm is as follows: k1=f(x i ,y i ) k2=f(x i +g / 2,y i +k1g / 2) k3=f(x i +g / 2,y i +k2g / 2) k4=f(x i +g,y i +k3g) In the above formula, g is the calculation step length, x i Represents the length of the membrane module at the i-th step in the mathematical model, y i represents the solute concentration on the membrane surface at the ith step in the mathematical model, and k1, k2, k3 and k4 are the coefficients in the Runge-Kutta algorithm.

7. The method for predicting the flux of a pervaporation membrane module according to claim 4, characterized in that: The partition coefficient of the separation membrane is calculated as follows: According to thermodynamic equilibrium, the chemical activity was solved to obtain the volume fractions of solute, solvent and membrane at different membrane surface solute concentrations, and the relationship between the membrane surface solute concentration and the total volume fraction of the solvent in the membrane was obtained by fitting. The calculated total volume fraction of the solvent in the membrane is converted into a mass fraction to obtain the solute concentration on the membrane surface after adsorption, and the distribution coefficient of the separation membrane is calculated based on the membrane surface adsorption equilibrium equation.

8. The method for predicting the flux of a pervaporation membrane module according to any one of claims 1 to 7, characterized in that: The method is used to predict the local ethanol concentration of an ethanol-water solution in the length direction of a membrane module and the local ethanol flux in the length direction of a membrane module.

9. The method for predicting the flux of a pervaporation membrane module according to any one of claims 1 to 7, characterized in that: The separation membrane is a PDMS composite membrane or a PVA composite membrane.

10. A prediction system, characterized in that: The method for predicting the flux of a pervaporation membrane module according to any one of claims 1 to 9 is used; the prediction system comprises a parameter acquisition module and a calculation module; The parameter acquisition module is used for: Acquiring membrane module parameters of the spiral wound membrane, wherein the membrane module parameters include membrane module structural parameters and operation parameters during pervaporation; The calculation module is used for: Calculate the convective mass transfer coefficient based on the membrane module parameters; According to the relationship between the convective mass transfer coefficient and the concentration polarization, the solute concentration on the membrane surface at the inlet of the membrane module is calculated; The membrane surface solute concentration at the inlet of the membrane module is taken as the initial value, and input into the mathematical model for predicting the membrane surface solute concentration of the pervaporation membrane module for iteration, so as to output the membrane surface solute concentration of each step in the flow direction of the membrane module fluid as the local solute concentration prediction result in the length direction of the membrane module; The solute flux of each step in the flow direction of the membrane module fluid is calculated based on the distribution coefficient of the separation membrane, the solute concentration on the membrane surface of each step, and the mass transfer coefficient inside the membrane, which is used as the prediction result of the local solute flux in the length direction of the membrane module.

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