Numerical Simulation of a Mathematical Model for Dry/Wet-Spun Nascent Hollow Fiber Membrane

In an effort to find the effect of mass transfer, surface tension and drag forces on the velocity distribution, the mathematical model of the velocity profile of a nascent hollow fiber during membrane formation in the air gap region was numerically simulated by using the Runge-Kutta method (fourth-order method). The effect of mass transfer on velocity distribution based on the complicated function (G(Cs h)) was presented and the effects of a complicated function were studied in two cases: in the first case, G(Cs h) was constant; in the second, G(Cs h) was variable. The latter was done by varying with the concentration of solvent in a nascent hollow fiber through the air-gap region. One empirical equation was used to describe this change and the predicted values had a better agreement with the experimental values. To verify the model hypotheses, hollow fiber membranes were spun from 20∶80 polybenzimidazole/polyetherimide dopes with 25.6 wt% solid in N, N-dimethylacetamide (DMAc) using water as the external and internal coagulants. Based on the experimental results of dry-jet wet-spinning process for the fabrication of hollow fiber membranes, it is found that the model calculated values were in a good agreement with the experimental values.

Mathematic Model of Unsteady Penetration Mass Transfer in Randomly Packed Hollow Fiber Membrane Module

Based on the membrane-based absorption experiment of CO2 into water, shell-side flow distribution and mass transfer in a randomly packed hollow fiber module have been analyzed using subchannel model and unsteady penetration mass transfer theory. The cross section of module is subdivided into many small cells which contains only one hollow-fiber. The cross sectional area distribution of these cells is presented by the normal probability density distribution function. It has been obtained that there was a most serious non-ideal flow in shell side at moderate mean packing density, and the large amount of fluid flowed and transferred mass through a small number of large voids. Thus mass transfer process is dominated by the fluid through the larger void area. The mass transfer process in each cell is described by the unsteady penetration theory. The overall mass transfer coefficient equals to the probability addition of the mean mass transfer coefficient in each cell. The comparisons of the values calculated by the model established with the empirical correlations and the experimental data of this work have been done.The predicted overall mass transfer coefficients are in good agreement with experimental data.

MORPHOLOGIES AND GAS SEPARATION PROPERTIES OF MELT-SPUN ASYMMETRIC POLY(4-METHYL-1-PENTENE)HOLLOW FIBER MEMBRANES

Poly(4-methyl-1-pentene) (PMP) hollow fiber membranes were prepared by the melt-spun and cold-stretch(MSCS) method. Scanning electronic microscopy (SEM) was used to characterize the section and surface structures of themembranes with special asymmetric structure. The preliminary results of gas permeation measurements indicated that the resultant hollow fiber membranes have the potential ability for oxygen/nitrogen separation.

Enhanced gas separation performance of mixed matrix hollow fiber membranes containing post-functionalized S-MIL-53

Mixed matrix hollow fiber membranes（MMHFMs）filled with metal-organic frameworks（MOFs）have great potential for energy-efficient gas separation processes,but the major hurdle is polymer/MOFs interfacial defects and membrane plasticization.Herein,lab-synthesized MIL-53 was post-functionalized by aminosilane grafting and subsequently incorporated into Ultem-1000 polymer matrix to fabricate high performance MMHFMs.SEM,DLS,XRD and TGA were performed to characterize silane-modified MIL-53（S-MIL-53）and prepared MMHFMs.Moreover,the effect of MOFs loading was systematically investigated first;then gas separation performance of MMHFMs for pure and mixed gas was evaluated under different pressures.MMHFMs containing post-functionalized S-MIL-53 achieved remarkable gas permeation properties which was better than model predictions.Compared to pure HFMs,CO2permeance of MMHFM loaded with 15%S-MIL-53 increased by 157%accompanying with 40%increase for CO2/N2selectivity,which outperformed the MMHFM filled with naked MIL-53.The pure and mixed gas permeation measurements with elevated feed pressure indicated that incorporation of S-MIL-53 also increased the resistance against CO2plasticization.This work reveals that post-modified MOFs embedded in MMHFMs facilitate the improvement of gas separation performance and suppression of membrane plasticization.

A CONDENSED REVIEW ON THE FABRICATION OF HOLLOW FIBER MEMBRANES FOR GAS SEPARATION:HISTORICAL DEVELOPMENT AND TECHNOLOGY CHALLENGES AHEAD

A review on the polymeric hollow fibers membranes for gas separation has been conducted. In order to deyelop high performance membranes for gas separation, there are a few technology challenges awaiting the chemical engineers to overcome. There are four major challenges, namely: 1) material selection and synthesis; 2) fabrication of hollow fiber membranes with an ultra- thin dense selective layer; 3) materials against plasticization; and 4) aging. In each area, we summarize the scientific accomplishments and technical difficulties.

MATHEMATICAL AND EXPERIMENTAL ANALYSIS OF AIR SEPARATION BY HOLLOW FIBER MEMBRANES

Approximate solutions for gas separation by hollow fiber membranes have been developedby several investigators.However,there are few reports of experimental verification of the models forhigh stage cut separations.In this work,an approximate mathematical model was developed and wasexperimentally verified for high stage cut air separation.Both countercurrent and cocurrent now pat-terns were used.In addition,the applicability of feed-inside mode for low stage cut air separation byhollow fiber membrane was examined.It was found that feed-inside mods was more advantageousthan feed-outside mode when used for the generation of oxygen-enriched air.

Evaluation of a mathematical model using experimental data and artificial neural network for prediction of gas separation

In recent times, membranes have found wide applications in gas separation processes. As most of the industrial membrane separation units use hollow fiber modules, having a proper model for simulating this type of membrane module is very useful in achieving guidelines for design and characterization of membrane separation units. In this study, a model based on Coker, Freeman, and Fleming＇s study was used for estimating the required membrane area. This model could simulate a multicomponent gas mixture separation by solving the governing differential mass balance equations with numerical methods. Results of the model were validated using some binary and multicomponent experimental data from the literature. Also, the artificial neural network （ANN） technique was applied to predict membrane gas separation behavior and the results of the ANN simulation were compared with the simulation results of the model and the experimental data. Good consistency between these results shows that ANN method can be successfully used for prediction of the separation behavior after suitable training of the network

PREPARATION OF POLYVINYLIDENE FLUORIDE/POLYVINYL DIMETHYLSILOXANE COMPOSITE HOLLOW FIBER MEMBRANES AND THEIR SEPARATION PROPERTIES

Microporous polyvinylidene fluoride(PVDF)hollow fibre membranes were spun using the dry-wet phaseinversion method.By means of dip-coating technique,a uniform coating with thickness of around 5-12 μm of polyvinyldimethylsiloxane(PVDMS)was formed on the surface of porous PVDF hollow fibers.The structural parameters of PVDFsubstrate membrane were estimated by gas permeation test.Using N_2/O_2 as the medium,the separation properties ofPVDMS-PVDF composite hollow fiber membranes were also evaluated experimentally.The experimental data of bothpermeability and selectivity are in good agreement with the theoretical results predicted by the presented pore-distributionmodel.In order to obtain the compact composite membrane free of defects by the dip-coating technique,the thickness ofPVDMS skin must be higher than 5 μm.

Fabrication of ZIF-8 membranes on dual-layer ZnO-PES/PES organic hollow fibers by in-situ crystallization

Compared to inorganic supports, polymeric supports can offer additional benefits, e.g., easier processing and cheaper. However, the organic surface has weak adhesion to the zeolitic imidazolate frameworks(ZIFs) membrane layer, which usually requires complex surface modification or seeding. Herein, we demonstrate that a dual-layer asymmetric polymer support prepared by a simple spinning process is a good candidate for the preparation of ZIF-8 membrane. The inner layer of the support is an organic hollow fiber(PES) with finger-like pores, and the outer layer is a ZnO-PES composite layer with finger-like pores also. The ZnO-PES composite layer is expected to contain uniform ZnO crystals in the polymer matrix, i.e., the ZnO particles in the skin layer of the support are not easy to fall off. Under the induction of ZnO particles in the outer layers, continuous ZIF-8 membranes can be prepared by single in-situ crystallization, showing good adhesion to the supports. The obtained ZIF-8 membranes show a H_(2) permeance of 8.7 × 10^(-8)mol·m^(-2)·s^(-1)·Pa^(-1) with a H_(2)/N_(2) ideal separation selectivity of 18.0. The design and preparation of this dual-layer polymer support is expected to promote the large-scale application of MOF membranes on polymer supports.

A review on hollow fiber membrane module towards high separation efficiency:Process modeling in fouling perspective

Hollow fiber microfiltration(MF)and ultrafiltration(UF)membrane processes have been extensively used in water purification and biotechnology.However,complicated filtration hydrodynamics wield a negative influence on fouling mitigation and stability of hollow fiber MF/UF membrane processes.Thus,establishing a mathematical model to understand the membrane processes is essential to guide the optimization of module configurations and to alleviate membrane fouling.Here,we present a comprehensive overview of the hollow fiber MF/UF membrane filtration models developed from different theories.The existing models primarily focus on membrane fouling but rarely on the interactions between the membrane fouling and local filtration hydrodynamics.Therefore,more simplified conceptual models and integrated reduced models need to be built to represent the real filtration behaviors of hollow fiber membranes.Future analyses considering practical requirements including complicated local hydrodynamics and nonuniform membrane properties are suggested to meet the accurate prediction of membrane filtration performance in practical application.This review will inspire the development of high-efficiency hollow fiber membrane modules.

Removal of Aniline from Wastewater Using Hollow Fiber Renewal Liquid Membrane

Hollow fiber renewal liquid membrane(HFRLM) method was proposed based on the surface renewal theory for removal of aniline from waste water. The system of aniline + D2 EHPA in kerosene + HCl was used. Aqueous layer diffusion in the feed phase is the rate-control step, and the influence of lumen side flow rate on the mass transfer is more significant than that on the shell side. The resistance of overall mass transfer is greatly reduced because of the mass transfer intensification in the renewal of liquid membrane on the lumen side. The driving force of mass transfer can be considered as a function of distribution equilibrium, and the overall mass transfer coefficient increases with the increase of p H in the feed solution, HCl concentration and D2 EHPA concentration, and decreases with the increase of initial aniline concentration. A mass transfer model is developed for HFRLM based on the surface renewal theory. The calculated results agree well with experimental results. The HFRLM process is a promising method for aniline wastewater treatment.

Polyurethane-SAPO-34 mixed matrix membrane for CO_2/CH_4 and CO_2/N_2 separation

SAPO-34 nanocrystals(inorganic filler) were incorporated in polyurethane membranes and the permeation properties of CO_2, CH_4,and N_2 gases were explored. In this regard, the synthesized PU-SAPO-34 mixed matrix membranes(MMMs) were characterized via SEM, AFM, TGA, XRD and FTIR analyses. Gas permeation properties of PU-SAPO-34 MMMs with SAPO-34 contents of 5 wt%, 10 wt% and 20 wt% were investigated. The permeation results revealed that the presence of 20 wt% SAPO-34 resulted in 4.45%, 18.24% and 40.2% reductions in permeability of CO_2,CH_4,and N_2, respectively, as compared to the permeability of neat polyurethane membrane. Also,the findings showed that at the pressure of 1.2 MPa, the incorporation of 20 wt% SAPO-34 into the polyurethane membranes enhanced the selectivity of CO_2/CH_4 and CO_2/N_2, 14.43 and 37.46%, respectively. In this research, PU containing 20 wt% SAPO-34 showed the best separation performance. For the first time, polynomial regression(PR) as a simple yet accurate tool yielded a mathematical equation for the prediction of permeabilities with high accuracy(R^2>99%).

中空纤维膜气体分离器的数学模型

本文建立了中空纤维膜气体分离器的微分数学模型,对其数值解进行了实验验证,又将其简化的代数模型同文献上的模型进行了比较,指出了各种模型适宜的使用条件,并研究确定了气体膜分离过程中较适宜的丝内径、丝长度和操作压力的范围。

中空内压超滤膜丝的数学模型与运行特性

针对中空内压单支超滤膜的亲水短丝与疏水长丝,分别进行了丝壁透水系数与丝程阻力系数的压力及温度特性的测试分析;建立了膜丝运行的微分方程数学模型;分析了给水压力、给水温度、给水方式、膜丝长度、透水系数及阻力系数等内外因素变化时,各项膜丝沿程运行参数的变化分布规律,从而较为全面地揭示了中空内压超滤膜丝的运行规律。

界面聚合反应制备中空纤维纳滤膜的数学模型

采用界面聚合反应成膜机理制备中空纤维纳滤膜,建立在非稳态条件下化学反应-扩散控制的数学模型,并通过有针对性的简化,使该模型适用于扩散控制。以哌嗪-三乙胺水溶液作为水相,均苯三甲酰氯作为有机相单体,甲苯作为有机相溶剂进行界面聚合反应制备中空纤维膜,进而通过实验对数学模型进行验证。研究结果表明:通过模型计算,在反应达到10s时,复合膜的厚度约为0.9μm;从实验中甲苯体系反应10s后得到的扫描电镜照片可以看到,此时复合膜的厚度为1μm左右,说明界面聚合反应成膜原理能正确地指导建立数学模型;模型预测值与实验数据基本吻合;所建立的数学模型能够较好地揭示界面聚合反应成膜过程的实质。

交叉流聚丙烯中空纤维膜式氧合器的传质研究Ⅰ结构因子α、β的测定和氧合器传质效果评价

在膜式氧合器水气传递实验装置上分别对二种不同的交叉流微孔聚丙烯中空纤维膜式氧合器进行了水气传递实验，测得了氧合器的结构因子α、β，并用Ｍｏｃｋｒｏｓ和Ｌｅｏｎａｒｄ对Ｏ２传递建立的半经验数学模型拟合了血气传递实验中氧气在血中的传递速率。结果表明，理论计算与实验数据十分吻合，偏差小于１０％。讨论了α、β与膜式氧合器的传递效果的关系。

超滤过程中浸没式中空纤维膜组件的数学模拟优化研究

基于中空纤维膜轴向不均污染理论,运用响应曲面法建立了浸没式中空纤维超滤膜组件不同通量状态下,膜组件过滤过程中的膜阻力关于时间、空间的动态数学模型,对建立的模型进行了显著性分析及实验验证,并对中空纤维膜组件进行了数学优化.通过验证实验发现,发现实测数据与膜阻力动态数学模型计算值基本一致.通过对数学模型分析发现:在次临界通量状态下,膜丝长度及运行时间均存在最佳值;在临界和超临界状态下,膜阻力及运行时间与膜丝长度成正比.

水蒸气在中空纤维复合膜中渗透的微分阻力模型

建立了水蒸气在中空纤维复合膜中渗透的微分阻力模型,用实验验证了模型的可靠性。采用该模型估算出中空纤维膜的结构参数,研究了水蒸气在各层膜中的阻力,并以H2O/C2H2系统为例,考察了膜的结构参数对H2O/C2H2选择性的影响。

中空纤维膜低压超滤处理含油废水的数学模拟

提出一个不可忽略轴向压力降和膜渗透速率轴向变化的中空纤维膜低压超滤处理含油废水的传质模型 ,采用正交配点法并结合MATLAB软件进行模拟 ,解出速度分布和浓度分布 ,得到超滤速率的变化规律 ,与实验数据吻合很好 .用模拟结果讨论Peclet数对超滤的影响 ,并分析中空纤维丝内径向速度分布 ,为超滤膜及工艺条件的选择提供了重要依据 .

疏水性中空纤维膜组件操作过程模拟

采用疏水性中空纤维膜组件和去离子水分离混合气中CO2,研究了气液流速、混合气CO2浓度和操作温度以及膜形态等因素对总传质系数的影响。通过传质阻力层方程和质量微分方程的关联,建立了新型数学模型,模拟了各种条件下的传质过程。结果表明,流体力学状态的改变能够加强传质,但加强程度有限;提高气相CO2浓度能够提高总传质系数;具有高孔隙率的膜组件拥有高传质系数;提高操作温度能够促进扩散,提高传质系数,在较高温度下,存在膜孔湿润的现象。模型能够较好地模拟膜接触器—物理吸收过程,模型值能够较准确地反映疏水性中空纤维模组件传质过程。