Prediction method for gas separation process of hollow fiber membrane

Abstract

The invention relates to a hollow fiber membrane gas separation process prediction method, and belongs to the technical field of membrane separation. An improved two-dimensional (2-D) mathematical model with distribution parameters is established to describe the separation process of multi-component gas, wherein external resistance caused by concentration polarization (ECP) and lumen resistance (ELR) is clearly considered. Compared with a classical one-dimensional (1-D) model with lumped parameters, the average CO2 permeability predicted by the model has better consistency with experimental data under the same condition.

Description

Technical Field

[0001] The invention relates to a prediction method for a hollow fiber membrane gas separation process, belonging to the technical field of membrane separation. Background Art

[0002] Molecular sieve membranes have excellent thermal and chemical stability and a certain resistance to CO 2 DD3R (Deca-Dodecasil 3 Rhombohedral) is a pure silicon DDR type molecular sieve with two-dimensional octahedral (8-MR) channels, with an effective pore size of 0.36×0.44nm, which can be used for CO 2 There is limited discussion in the literature on the modeling of hollow fiber DD3R molecular sieve membranes (HF-DD3R), especially when considering the external resistance of the bulk gas phase. At the same time, most mathematical models that focus on the external resistance simplify the mass transfer process within the membrane phase, where the position-dependent permeability is usually assumed to be constant along the axial direction. Summary of the invention

[0003] The present invention establishes a mathematical model with distributed parameters, which explicitly considers the mass transfer process in the bulk phase and membrane pores. The model is used to describe the effect of HF-DD3R molecular sieve membrane on CO 2 / CH 4 The separation process was carried out and the distribution of transmembrane resistance was determined based on the relative pressure drop. Subsequently, the pressure drop along the CO 2 Separated external resistance distribution.

[0004] A method for predicting a hollow fiber membrane gas separation process, wherein the hollow fiber membrane comprises a support layer and a molecular sieve layer for screening, comprises the following steps:

[0005] Step 1, calculating the permeation flux of the gas components in the molecular sieve layer;

[0006] Step 2, calculating the permeation flux of the gas components in the support layer;

[0007] Step 3, divide the hollow fiber membrane into k micro-elements (segments) along the axial direction, and calculate the partial pressure drops of the shell side and the tube side by mass conservation between adjacent units.

[0008] In the gas separation process, a mixed gas of at least two components is separated, the gas to be separated enters the shell side, and the permeate gas enters the tube side.

[0009] In step 1, the gas component permeation flux is calculated by any one of the following formulas:

[0010]

[0011]

[0012] N z，α and N z，β are the permeation fluxes of gas components in the molecular sieve layer;

[0013] χ z is z / τ z , defined as the molecular sieve layer structure correction factor, ε z is the molecular sieve opening rate, τ z is the tortuosity factor;

[0014] Thermodynamic correction factors are calculated by the following formula:

[0015]

[0016] Among them, θ i is the adsorption rate of component i i is α or β; K i is the adsorption equilibrium constant, q i is the equilibrium adsorption capacity, p i is the partial pressure of component i; R g is the molar gas constant, T is the Kelvin temperature, μ is the chemical potential, ρ z is the molecular sieve density, n is the total number of components, and They correspond to the MS mutual diffusion coefficient and the MS corrected diffusion coefficient, respectively.

[0017] The permeation flux of the gas component in the support layer is calculated by the following formula:

[0018] N s，i =N Kn，i +N Vis，i ; N vis,i is the viscous flow flux of component i, N kn，i is the Knudsen diffusion flux.

[0019] The viscous flow flux is calculated as follows:

[0020] M i is the molar mass, d p is the average pore size, χ s is defined as the support porosity (ε s ) and the distortion factor (τ s ) ratio, d p It refers to the average pore size of the carrier;

[0021] The viscous flow flux is calculated by the following formula:

[0022]

[0023] η is the mixed gas viscosity, It refers to the average value of the total pressure of the mixed gas.

[0024] In step 3, the distribution of the pressure drop outside the shell is calculated by the following formula:

[0025] r b N b，i =r z N z，i =r s N s，i =r mem N mem,i

[0026] Among them, r b is the logarithmic mean radius of the boundary layer, N b,i is the permeation flux of component i in the boundary layer, r z is the logarithmic mean diameter of the molecular sieve layer, N z，i is the permeation flux of component i in the molecular sieve layer, r s is the logarithmic mean diameter of the support layer, N s，i is the permeation flux of component i in the support layer, r mem is the logarithmic mean diameter of the entire membrane, N mem，i is the average permeation flux through the entire membrane.

[0027] The radial mass transfer permeation flux is calculated by the following formula:

[0028]

[0029] k m represents the convective mass transfer coefficient, which is equal to D αβ / δ b , and δ b is the boundary layer thickness;

[0030] x α,up and x α,down Corresponding to the upstream and downstream CO 2 The mole fraction of

[0031] Sh=0.04Re 0.75 Sc 0.33 ;

[0032] L is the length of the infinitesimal element k; ρ is the density of the mixed gas.

[0033] The pressure drop in the tube is calculated by the following formula:

[0034]

[0035] H k is the gas molar flow rate through the microelement k, d e,HF is the equivalent diameter of the cavity.

[0036] Also included: calculation of gas permeability, obtained by the following formula:

[0037] Δp i It is the partial pressure drop.

[0038] Also includes: gas permeability K i The calculation is obtained by the following formula:

[0039] K i =δ zeo P i ; δ zeo is the thickness of DD3R molecular sieve layer.

[0040] The calculation of the separation factor for the two gases is also included.

[0041]

[0042] The beneficial effect of the present invention is: establish a HF-DD3R molecular sieve membrane to separate CO 2 / CH 4 An improved 2-D distributed parameter mathematical model is proposed. Compared with the classical 1-D model that only considers the radial mass transfer process, the gas permeability calculated by our model is more consistent with the experimental results under the same conditions, which is mainly due to its explicit consideration of the external resistance. Specifically, the external pressure drop loss of gas permeation is caused by the concentration polarization (ECP) of the shell side and the lumen resistance (ELR) of the tube side. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 : (a) Schematic diagram of two-dimensional mass transfer mode and (b) HF-DD3R molecular sieve membrane tube separation of CO 2 / CH 4 Schematic diagram of the finite element method.

[0044] Figure 2 : CO in HF-DD3R molecular sieve membrane module 2 / CH 4 Schematic diagram of the two-dimensional mass transfer principle of the separation.

[0045] Figure 3 : At a temperature of 293K and a feed pressure of 0.2-3.0MPa, equimolar CO 2 / CH 4Separation calculation results: (a) (b)

[0046] Figure 4 : Equimolar CO at 293K 2 / CH 4 Calculation results of separation: (a) Local pressure distribution in ordinary membrane at 0.2 MPa feed pressure; (b) CO2 in ordinary membrane and high permeability membrane when feed pressure is between 0.2 and 3.0 MPa 2 Relative pressure drop on the HF carrier. Figure 5 :Using ordinary membrane tube (tube length 0.40m) at 293K temperature and feed flow rate 400mL min -1 , equimolar CO under feed pressure of 0.2-3.0 MPa 2 / CH 4 Separation: (a)p CO2 ; (b) p CH4 ; (c) Shell side p CO2 Distribution; (d) pipe p CO2 distributed. DETAILED DESCRIPTION

[0047] High permeability hollow fiber DD3R (HF-DD3R) molecular sieve membrane exhibits excellent CO removal performance in natural gas reforming 2 In the following examples, an improved two-dimensional (2-D) mathematical model with distributed parameters was established to describe the CO removal performance. 2 / CH 4 The model predicts a higher average CO than the classical one-dimensional (1-D) model with lumped parameters under the same conditions. 2 The permeability is more consistent with the experimental data. The distribution of transmembrane resistance was investigated by relative pressure drop (RPD), where the external resistance produced a more significant pressure drop loss (up to 42%) in the high permeability membrane system with a membrane thickness of 0.5 μm, which was mainly attributed to the stronger radial main flow. 4 Purity (X CH4,retentate ) requirements, the external resistance significantly inhibited the CO 2 Separation efficiency. The calculation results show that when the feed pressure is 3.0 MPa and the flow rate is 200 mL min -1 When these resistances lead to CH 4 The loss rate increased by 6 times, and the gas processing capacity per unit membrane area decreased by about 66%. Finally, by adjusting the membrane packing density and the module diameter to reduce the shell-side flow area, it is also possible to promote shell-side convective mass transfer, thereby increasing CO 2The established 2-D mathematical model is used to clarify the separation efficiency of CO in high permeability HF-DD3R zeolite membrane. 2 / CH 4 The separation behavior of

[0048] The model of the present invention is constructed as follows Figure 1 As shown in (a), the gas mixture has a two-dimensional (2-D) countercurrent mass transfer mode, CO 2 and CH 4 The molecules penetrate the DD3R molecular sieve and the HF support layer in turn under the radial pressure gradient. The HF support is composed of a sponge-like layer with smaller pores and a finger-like layer with larger pores. At the same time, due to the selective separation, the radial pressure gradient of each component changes with the change of the axial position. Figure 1 As shown in (b), the entire HF-DD3R molecular sieve membrane assembly is divided into membrane tube units in series by the finite element method along the axial direction to describe the fluid parameter distribution of the shell side and the tube side, while considering the axial distribution of the external resistance. In order to simplify the mathematical modeling, the following assumptions are adopted.

[0049] 1) Steady-state operation.

[0050] 2) Actual gas behavior in the shell (medium and high pressure range).

[0051] 3) Ideal gas behavior in the tube (close to ambient pressure).

[0052] 4) The operating temperature and pressure on the shell side are constant.

[0053] 5) The mixed gas is an incompressible fluid.

[0054] 6) Ignore axial back diffusion in the shell.

[0055] 7) Ignore the concentration polarization on the tube side.

[0056] 8) Neglect the momentum loss caused by local frictional resistance.

[0057] 9) HF-DD3R molecular sieve membrane has a mutually independent multi-layer asymmetric structure.

[0058] 10) HF-DD3R molecular sieve membrane has a uniform and defect-free microscopic pore structure.

[0059] The mass transfer process within the DD3R molecular sieve layer is calculated in the following way:

[0060] The mass transfer process of gas in the molecular sieve channel is usually considered to be surface diffusion, which is the result of the combined action of adsorption and diffusion. These behaviors are mainly affected by the interaction of guest molecules between the molecular sieve frameworks, so the effects caused by the framework differences can be described by adjusting the adsorption and diffusion parameters. The required modeling parameters mainly involve gas adsorption and diffusion parameters, which can be determined by Grand Canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) simulations, respectively. The corresponding permeation process can be described by the generalized Maxwell-Stefan (GMS) equation:

[0061]

[0062] Where R g is the molar gas constant, T is the Kelvin temperature, μ is the chemical potential, ρ z is the molecular sieve density. The density of DD3R molecular sieve is 1740 kg m -3 , n is the total number of components, θ i is the adsorption rate of component i, q sat is the saturated adsorption capacity, and Corresponding to the MS mutual diffusion coefficient and MS corrected diffusion coefficient, q j and q i Refers to the equilibrium adsorption capacity of each component, N i and N j is the permeation flux of each component. The left term can be further converted into the thermodynamic correction factor Γ ij for:

[0063]

[0064] in

[0065]

[0066] Where p i is the partial pressure of component i. There is a common phenomenon of adsorption competition in multicomponent systems, where the respective θ i It can be obtained by the extended unit-point Langmuir equation:

[0067]

[0068] In the formula, K i is the adsorption equilibrium constant, which can be calculated by the Arrhenius equation, q i is the equilibrium adsorption capacity, p i is the partial pressure of component i.

[0069] Table 1 Gas adsorption parameters fitted by the single-site Langmuir model

[0070]

[0071]

[0072] The adsorption parameters in formula (4) can be obtained by static volume experimental measurement or Grand Canonical Monte Carlo (GCMC) algorithm simulation. The simulated diffusion results are fitted with a simple power function model as follows:

[0073]

[0074] In the formula, θ i is the adsorption rate, Ɖ i is the corrected diffusion coefficient, a pow 、b pow 、c pow are the power function correlation factors of the fitting, respectively. These related parameters are listed in Table 2 at 293K. In addition, the microstructure parameters of DD3R molecular sieve are listed in Table 3.

[0075] Table 2 Gas diffusion parameters fitted by power model

[0076]

[0077] Table 3 DD3R molecular sieve layer microstructure parameters

[0078]

[0079] CO 2 and CH 4 The permeation flux in the HF layer is obtained by the sum of Knudsen diffusion and viscous flow flux based on the dusty gas model (DGM). The modeling parameters mainly involve the microstructural parameters of the HF layer, as shown in Table 4.

[0080] Table 4 Microstructure parameters of hollow fiber layer

[0081]

[0082]

[0083] Therefore, CO 2 / CH 4 The thermodynamic correction factor for the binary system can be derived as

[0084]

[0085] Where α and β represent CO 2 and CH 4 .CO 2 / CH 4 CO in the mixture2 The permeation flux can be derived from formula (1-5) as follows:

[0086]

[0087] In the formula, χ z is z / τ z , defined as the molecular sieve layer structure correction factor, ε z is the molecular sieve opening factor, τ z is the tortuosity factor. In addition, D αβ is based on and The logarithmic mean algorithm is used to calculate .

[0088]

[0089] Similarly, it can be inferred that CO 2 / CH 4 CH in the mixture 4 The permeation flux N z,β .

[0090]

[0091] The gas permeation process in the HF support layer is calculated by the following formula:

[0092] The permeation of gases through a carrier is usually represented by a combination of Knudsen diffusion and viscous flow, as described by the Dust Gas model (DGM), which treats the pore walls as virtual components. The Knudsen diffusion flux of component i driven by the partial pressure gradient can be expressed as:

[0093]

[0094] Where M i is the molar mass, d p is the average pore size, χ s is defined as the support porosity (ε s ) and the distortion factor (τ s ) ratio, d p is the average pore size of the carrier. The viscous flow flux driven by the total pressure gradient is estimated by:

[0095]

[0096] Where η is the viscosity, It refers to the average value of the total pressure of the mixed gas. The permeation flux of component i through the HF carrier layer can be expressed as N Kn,i and N Vis,i The sum of is expressed as follows:

[0097] N s,i =N Kn,i +N Vis,i (11)

[0098] One-dimensional and two-dimensional mass transfer in membrane tubes

[0099] Combining Eq. (1-11), a classic one-dimensional (1-D) model can be established. Since only the mass transfer process perpendicular to the membrane surface itself (radial direction) is considered, the relationship between the permeation flux of component i through each layer follows the law of conservation of mass:

[0100] r z N z,i =r s N s,i =r mem N mem,i (12)

[0101] Where r is the logarithmic mean radius of each layer, subscript z represents the separation layer, s represents the support layer, and N mem,i is the average permeation flux through the entire membrane.

[0102] CO 2 Preferential permeation through the membrane results in CH 4 In the shell side, CO 2 In order to more clearly describe the gas distribution composition, the classical 1-D model can be extended to the classical two-dimensional (2-D) model, which includes the axial mass transfer process. Figure 1 The FEM shown in (b) is divided into k micro-elements along the tube direction. Compared with the adopted membrane tube length (0.01-3.0m), a membrane element length of 0.001m is adopted. The axial mass transfer in the k unit and its adjacent units follows the mass conservation equation:

[0103] G T,k+1 =G T,k -ΔA k N mem，k (13)

[0104] H T,k+1 =H T,k -ΔA k N mem，k (14)

[0105] Among them A k is the membrane area of ​​unit k, G T,k and H T,kare the gas molar flow rates through the microelement k in the shell side and tube side, respectively. In addition, the external non-ideal pressure drop caused by non-ideal effects (including concentration polarization and lumen resistance) can be further considered to derive a modified 2-D model. The following is its derivation process.

[0106] Shell-side pressure drop due to concentration polarization

[0107] In order to ensure sufficient processing capacity, higher feed pressure is widely used in actual natural gas reforming. Therefore, the van der Waals equation is used to describe the real gas state in the shell side as follows:

[0108]

[0109] Where n m and V correspond to the number of moles and gas volume, respectively, and a and b correspond to the correction terms for intermolecular forces and molecular volume, respectively.

[0110] In addition, the presence of concentration polarization (ECP) effect will cause the partial pressure change of the boundary layer near the membrane surface. 2 The preferential permeation of CO 2 The local depletion of CH 4 The gas mass transfer in this layer is determined by the interaction between molecular diffusion and bulk flow, so CO 2 (N b,α ) can be expressed as:

[0111]

[0112] where c m and x α denote the molar concentration of the mixed gas in the boundary layer and CO 2 Mole fraction, N b,α Represents CO in the boundary layer 2 Permeation flux, y is the radial length of the membrane tube. N b,β represents the CH in the boundary layer 4 The two terms on the right represent the diffusion term caused by the concentration gradient and the bulk flow term caused by the mixed gas permeation, respectively, while the binary diffusion coefficient D αβ It can be estimated by the Fuller-Schettler-Giddings equation. Therefore, Eq. (16) can be rearranged as:

[0113]

[0114] Among them, when i is α

[0115]

[0116] The Mickey correction factor derived from membrane theory, ζ c The distortion of the concentration curve at high mass transfer rates can be explained by:

[0117]

[0118] in

[0119]

[0120] Where x α,up and x α,down Corresponding to the upstream and downstream CO 2 Assume that D αβ Follow c m If it does not change, the following relationship can be established:

[0121]

[0122] Among them, k m represents the convective mass transfer coefficient, which is equal to D αβ / δ b , and δ b is the boundary layer thickness. The dimensionless fluid dynamics constant Sherwood number (Sh) can be used to relate k m as follows:

[0123]

[0124] Where, d e,S is the equivalent diameter of the shell channel. In laminar flow (Re<2100), the relationship between Sh and Reynolds number (Re) and Schmidt number (Sc) is:

[0125]

[0126] Where L is the characteristic length, i.e. the length of the membrane unit k. The values ​​of Re and Sc are obtained by the following formula:

[0127]

[0128] In the formula, ρ g is the density of the mixed gas, which can be calculated by the weighted average of each component, and η can be calculated by Wilke theory. Under turbulent conditions (Re>2100):

[0129] Sh=0.04Re 0.75 Sc 0.33 (26)

[0130] Substituting the ECP correction term directly into the radial mass transfer, similar to Eq. (12), we obtain:

[0131] rb N b,i =r z N z,i =r s N s,i =r mem N mem,i (27)

[0132] Therefore, the distribution of the pressure drop outside the shell can be determined by replacing Eq. (27) with Eq. (12).

[0133] Lumen resistance pressure drop

[0134] Due to the narrow lumen of the HF carrier, the gas velocity and CO 2 The purity is high enough so that the ECP of the tube side is negligible. However, such a geometry also poses challenges for timely evacuation of the pressure distribution along the length of the tube lumen. For example, an external pressure gradient must be accumulated to drive the permeating gas components, resulting in an external lumen resistance (ELR). The Hagen-Poiseuille equation is used to describe the steady-state flow at different locations in the tube side.

[0135]

[0136] The local pressure gradient is balanced with the lumen resistance, and the pressure gradient is in the opposite direction to the gas flow rate. Therefore, it can be determined that the local pressure at the dead end of the cavity is the largest. In order to simplify the mathematical modeling, the four-channel structure of the HF carrier is approximated as an equivalent diameter of d e,HF The ratio of the flow rate to the flow channel diameter in the original flow channel and the approximate flow channel is close, so the deviation caused by the equivalent process can be ignored. Combining the ideal gas state equation with equation (28), we get:

[0137]

[0138] In the formula, H k is the molar flow rate of the gas in the tube passing through the infinitesimal element k. This equation can be used to examine the local pressure at different positions in the tube.

[0139] Table 5 Import and export CO 2 / CH 4 Initial state parameters of the mixture

[0140]

[0141] Two-dimensional mass transfer in membrane units

[0142] In addition to a single membrane tube, similar FEM can also be applied to a membrane module consisting of multiple membrane tubes. Figure 2 Depicted effective area of ​​0.08m 2HF-DD3R molecular sieve membrane module, which shows an approximate 2-D mass transfer pattern. Based on the plug flow model, when the membrane module has a low packing density, the fluid properties including velocity and concentration are uniform in the radial direction, so the gas permeation process in each tube is the same and independent. In addition, the distributed flow parameters of the shell side are adjusted by the selective gas permeation of all membrane tubes, while the flow parameters of the tube side are independent of each other between membrane tubes. Therefore, A in Eq. (13) k represents the membrane area of ​​the module element. This is different from the case in equation (14), where A k Corresponds to the microelement area from a single membrane tube. G k and H k are the molar flow rates of the shell side and tube side, respectively. 2 / CH 4 The separation process can be described using the 2-D mass transfer model (classical and modified) established above. In the solution process, according to the established 2-D mass transfer model, under the given operating pressure and temperature conditions of the feed inlet and permeate outlet, the mass flow rate and partial pressure distribution of the shell and tube sides are determined through an iterative and orderly calculation procedure.

[0143] Gas permeation and separation indicators

[0144] By solving the established model, CO can be directly extracted 2 / CH 4 The permeation flux of each component in the mixture through the HF-DD3R molecular sieve membrane. From this, the ratio of the permeation flux to the partial pressure drop Δp i The gas permeability is calculated as follows:

[0145]

[0146] Permeability K i It can be further determined as:

[0147] K i =δ zeo P i (31)

[0148] Where δ zeo is the thickness of DD3R molecular sieve layer.

[0149] The separation selectivity can be calculated from the ratio of the permeances of the two gases:

[0150]

[0151] In addition, CH 4 Loss rate and It is also used to evaluate the CO 2 / CH 4The key parameters of separation effect are calculated by the following formulas:

[0152]

[0153] The mass transfer process described by the classical 1-D mass transfer model comes only from the molecular sieve membrane layer and the carrier layer, so the intrinsic separation performance of the membrane, such as permeability and selectivity, can be obtained without considering the external resistance of the gas phase. The influence of these resistances is fully elucidated by comparative analysis of the modeling results. Before using the established modified two-dimensional model, the classical one-dimensional model is used to describe the equimolar CO 2 / CH 4 Separation performance. Figure 3 HF-DD3R with different film thicknesses on P CO2 and α CO2 / CH4 As shown in the figure, as the film thickness decreases from 5.0 μm to 0.5 μm, P CO2 An enhancement of nearly one order of magnitude was obtained, which also highlights the application potential of ultrathin molecular sieve membranes. These two membranes were also selected as the calculation representatives of ordinary membranes and high-transmittance membranes, respectively.

[0154] The mass transfer resistance experienced by the permeating gas is balanced by the transmembrane pressure gradient. 2 and CH 4 The nonlinear local pressure distribution of the permeate. These pressure distributions can be directly determined using 1-D models, providing insights into CO 2 / CH 4 The separation process provides important theoretical insights. Figure 4 (a) describes the CO at a feed pressure of 0.2 MPa 2 and CH 4 The radial pressure distribution through the common membrane. As shown in the figure, the DD3R molecular sieve layer has a significant resistance to gas permeation, and the pressure drop is the largest among the three layers. 4 , this pressure drop is more significant. Considering the positive correlation between pressure drop and mass transfer resistance, CO is defined here 2 The radial relative pressure drop (RPD) was used to evaluate the distribution of transmembrane resistance. Figure 4 (b) describes the HF carrier (RPD) at different feed pressures HF ) 2 The relative pressure drop reveals a negative correlation between RPD and pressure increase. This can be explained by the shift in the dominant mass transfer mechanism in the HF carrier from Knudsen diffusion to viscous flow as pressure increases. Therefore, at 3.0 MPa, the RPD of the two membranes HF were all lower than 5.0%, indicating that HF ​​carrier has a significant effect on CO 2 / CH 4 On the contrary, at a low pressure of 0.2 MPa, the HF carrier has a significant effect on the CO permeation of the high permeability membrane, RPD HF Around 4%. Figure 3 This also further leads to the α CO2 / CH4 It is worth noting that these findings are derived only from a 1-D model that focuses on mass transfer inside the membrane, so significant deviations from experimental data are to be expected. In order to improve the calculation accuracy, the mass transfer model should fully consider the effect of external resistance.

[0155] Improved 2D mass transfer model

[0156] Gas mass transfer in the bulk phase, i.e., gas flow in the shell and tube, is the main factor affecting CO 2 / CH 4 The important components of separation. These regions have obvious non-ideal external resistances, including concentration polarization and cavity resistance causing non-ideal pressure drop. In order to explain these effects, an improved 2-D mass transfer model with distributed parameters is used to describe the gas mass transfer behavior in HF-DD3R molecular sieve membrane. Figure 5 (ab) describes the equimolar CO 2 / CH 4 Separation of P CO2 , P CH4 Comparison of experimental values ​​(bars) and calculated results (dashed lines) for a common HF-DD3R zeolite membrane. As expected, the 2-D model yields lower P values ​​than those obtained with the classical 1-D model. CO2 and higher P CH4 The observed differences are mainly attributed to the change in driving force along the membrane axis, which may generate additional transport resistance and hinder gas permeation. However, this effect is neglected in the classical 1-D model. Figure 5 (cd) Describe the modified 2-D model to obtain bulk CO 2 Partial pressure (p CO2 ) axial distribution. It can be seen that due to CO 2 The preferred permeation from the feed inlet to the retentate outlet is CO2 The value decreased significantly, resulting in P CO2 The value decreases, P CH4 At the same time, due to the countercurrent mode and the accumulation of permeate gas components, an opposite p CO2 Distribution. Considering P CO2 As the feed pressure increases, the net molar flow rate (H T,1 ) tends to be constant. Figure 5 As shown in (d), when the feed pressure exceeds 1.0 MPa, these pCO2 The curves almost overlap, indicating that there is a boundary effect with the increase in tube-side flow rate.

[0157] The average K calculated directly from the modified 2-D model CO2 and α CO2 / CH4 Comparison with experimental results reported in the literature. These experimental data also include the 3 O 2 The data obtained for the supported tubular DD3R zeolite membranes have a geometry similar to that of the HF-DD3R zeolite membranes. Again, our modified 2-D model successfully reproduces the K CO2 and α CO2 / CH4 The modeled values ​​are higher at lower feed pressures, although the difference can be attributed to the ideal microstructure assumption of HF-DD3R zeolite membranes, where most of the zeolite pores are considered to be open. The presence of non-ideal structural factors, such as heterogeneous crystals, pore blockage, slit pores, etc., will give CO 2 / CH 4 The additional resistance to separation leads to deviations between the model and experimental results. However, these limitations tend to weaken with increasing adsorption loading, resulting in improved consistency at high pressures. In summary, our mathematical model has been effectively validated and is able to describe the separation characteristics in HF-DD3R zeolite membranes under different operating conditions.

Claims

1. A method for predicting a hollow fiber membrane gas separation process, wherein the hollow fiber membrane comprises a support layer and a molecular sieve layer for screening, characterized in that: The steps include: Step 1, calculating the permeation flux of the gas components in the molecular sieve layer; Step 2, calculating the permeation flux of the gas components in the support layer; Step 3, divide the hollow fiber membrane into k micro-elements along the axial direction, and calculate the partial pressure drop of the shell side and the tube side by mass conservation between adjacent units.

2. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: In the gas separation process, a mixed gas of at least two components is separated, the gas to be separated enters the shell side, and the permeate gas enters the tube side.

3. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: In step 1, the gas component permeation flux is calculated by any one of the following formulas: N z,α and N z,β are the permeation flux of a gas component in the molecular sieve layer; z is z / τ z , defined as the structural correction factor of the molecular sieve, ε z is the molecular sieve opening factor, τ z is the tortuosity factor, q sat is the saturated adsorption capacity, α and β are the indexes of a gas component when used as subscripts, i refers to α or β; Thermodynamic correction factors are calculated by the following formula: Among them, θ i is the adsorption rate of component i, K i is the adsorption equilibrium constant, q i is the equilibrium adsorption capacity, p i is the partial pressure of component i; R g is the molar gas constant, T is the Kelvin temperature, μ is the chemical potential, ρ z is the molecular sieve density, n is the total number of components, D ij and D i They correspond to the MS mutual diffusion coefficient and the MS corrected diffusion coefficient, respectively.

4. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: The permeation flux of the gas component in the support layer is calculated by the following formula: N s,i =N Kn,i +N Vis,i ; N vis,i is the viscous flow flux of component i, N kn,i is the Knudsen diffusion flux.

5. The method for predicting a hollow fiber membrane gas separation process according to claim 4, characterized in that: The viscous flow flux is calculated by the following formula: M i is the molar mass, d p is the average pore size of the carrier, χ s is the correction factor defined as the ratio of the carrier porosity to the distortion factor, η is the mixed gas viscosity, It refers to the average value of the total pressure of the mixed gas, T is the temperature, and R is the ideal gas constant.

6. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: In step 3, the radial pressure drop distribution is calculated by the following formula: r b N b,i =r z N z,i =r s N s,i =r mem N mem,i ; r b is the logarithmic mean radius of the boundary layer, N b,i is the permeation flux of component i in the boundary layer, r z is the logarithmic mean diameter of the molecular sieve layer, N z,i is the permeation flux of component i in the molecular sieve layer, r s is the logarithmic mean diameter of the support layer, N s,i is the permeation flux of component i in the support layer, r mem is the logarithmic mean diameter of the entire membrane, N mem,i is the average permeation flux through the entire membrane.

7. The method for predicting a hollow fiber membrane gas separation process according to claim 6, characterized in that: The permeation flux of component i in the boundary layer is calculated by the following formula: k m represents the convective mass transfer coefficient, which is equal to D αβ / δ b , δ b is the boundary layer thickness; c m It represents the molar concentration of the mixed gas in the boundary layer; x α,up and x α,down They correspond to the mole fraction of CO2 in the upstream and downstream of the boundary layer, respectively; Sh=0.04Re 0.75 Sc 0.33 ; L is the length of the infinitesimal element k; ρ g is the density of the mixed gas.

8. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: The pressure drop in the tube is calculated by the following formula: H k is the molar flow rate of the gas passing through the tube of microelement k, d e,HF is the equivalent diameter of the cavity.

9. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: Also includes: The calculation of gas permeability is obtained by the following formula: Δp i It is the partial pressure drop.

10. The method for predicting a hollow fiber membrane gas separation process according to claim 1, characterized in that: Also includes: Permeability to gas K i The calculation of K is obtained by the following formula: i =δ zeo P i ; δ zeo is the thickness of DD3R molecular sieve layer.

Images