Huiqi Xie,Yanying Wei*,Haihui Wang*

School of Chemistry and Chemical Engineering,South China University of Technology,Guangzhou 510640,China

1.Introduction

Mixed ionic-electronic conducting(MIEC)[1]oxides are one kind of materials which exhibit good oxygen permeability and selectivity when used as the oxygen separation membranes.The MIEC oxides are widely studied for application in catalytic membrane reactors for hydrocarbon conversion and solid oxide fuel cells(SOFCs)[2-8].At elevated temperatures,oxygen can be transported through dense MIEC membranes in the form of oxygen ions under an oxygen partial-pressure gradient across the membrane.Perovskite-type(normally in the form of ABO3)[9-13]MIEC membranes always present relatively higher oxygen permeation fluxes among various MIEC membranes due to their higher ambi-polarconductivity forionic and electronic.So far,MIEC membranes in different geometries such as disk,tubular and hollow- fiber[14-18]have been widely studied.Modeling has become a useful tool for oxygen permeation process simulation and theoretical analysis for perovskite oxides[19-21].Xu and Thomson[22]developed an explicit model for La0.6Sr0.4Co0.2Fe0.8O3-δdisk based on the permeation resistance analysis.They found that the controlling step of oxygen permeation is surface reaction at low temperatures(750°C)but is bulk diffusion at high temperatures(950°C)for their disk membrane.Wanget al.[23]used a mathematicalmodelto simulate the Ba0.5Sr0.5Co0.8Fe0.2O3-δmembrane tube under co-current or cross- flow patterns with purge or vacuum operation.They suggested a sufficiently high air flow rate on the sweep side to fully utilize the separation capacity of a tubular membrane.Tan and Li[24]investigated the oxygen permeation flux through a La0.6Sr0.4Co0.2Fe0.8O3-δlinearhollow- fiber module under various conditions with a mathematicalmodel.Theirresults revealed thatthe vacuum operation on the lumen side of the membrane is the most efficient operation module to achieve high oxygen productivity.However,there is no modeling study focused on the U-shaped hollow- fiber membrane in literatures.

In this study,a mathematical model is developed to simulate the oxygen separation from air with a Ba0.5Sr0.5Co0.8Fe0.2O3-δ(BSCF)U-shaped hollow- fiber membrane.BSCF is prepared by partially substituting SrCoO3-δwith Ba and Fe[25],and it is selected because of its high oxygen permeability and good chemical stability[25-30].The experimental data are compared with the ones calculated from the model in order to determine the diffusion coefficient and check the feasibility of the model.This work is aimed to develop a feasible model to predict the oxygen permeation ofBSCF membrane under vacuumoperation and provide a useful reference for industrial applications.

2.Model Development

The previous experimental study[30]has revealed that the oxygen permeation process ofU-shaped BSCFhollow- fiber membrane was controlled by both of the bulk diffusion and surface reaction at the temperatures range from 750 °C to 950 °C.

As is known,there are five steps(Fig.1)for oxygen permeation through a MIEC ceramic membrane.The permeation process includes:(1)diffusion of gaseous oxygen onto the membrane surface near the side ofrelatively high oxygen partial-pressure;(2)oxygen molecule decomposition and surface exchange between oxygen molecules and oxygen vacancies on high oxygen partial-pressure side;(3)bulk diffusion of oxygen vacancies through the ceramic membrane,while electrons move to the opposite direction forcharge compensation;(4)surface exchange between oxygen ions and electron-holes on low oxygen partialpressure side;and(5)mass transfer of oxygen to the gas stream on low oxygen partial-pressure side.

The resistances in steps 1 and 5 are negligible compared to that of steps 2,3 and 4,as discussed in the literatures[8,15,20,22].Therefore,only surface exchange between the oxygen molecules and oxygen vacancies and bulk diffusion are considered in this work.

Oxygen vacancies and electron holes are two of the charged species inside the perovskite membrane.The electronic conductivity of the BSCF perovskite is over 20 times of the ionic conductivity.An overwhelming electronic conductivity has negligible in fluence while the increase of ionic conductivity greatly increases the oxygen permeation flux[25,29].Therefore,the diffusion of oxygen vacancies is the ratelimiting step of oxygen permeation in the perovskite membrane[20,22].The oxygen permeation flux can be described by the flux of oxygen vacancies in Nernst-Planck equation as:

where σVis the conductivity of oxygen vacancy,?μVand ?φVare the gradients of chemical potential and the gradients of the electric field,respectively.

Since the electron-holes move too fast to establish a steady-state electric field,then inside the open-circuit membrane,

The chemical potential can be expressed by the concentration of oxygen vacancies in the formula

With Eqs.(2),(3)and(4),Eq.(1)can be transformed to the form offick's law:

DVandCVare the diffusion coefficient and concentration of oxygen vacancies,respectively.Based on the classical diffusion theories,DVcan be considered as constant under certain temperature.The oxygen permeation flux can be expressed byJVas

whereRoutandRinare the outerand innerradii of the U-shaped hollowfiber.C′VandCV″are the concentration of oxygen vacancies on the high and low oxygen pressure sides,respectively.They also can be governed by surface exchange kinetics for surface reactions in step 2 and step 4:

where OOxrepresents lattice oxygen in the perovskite crystalstructure,kfandkrare the forward and reverse reaction rate constants for the surface reactions,respectively.Because of the high electronic conductivity,the electron holes are essentially constant at both membrane surfaces,and thus the forward and reverse reaction rates of the surface reactions are pseudo zero-order at steady state under isothermal conditions.Therefore,these two reactions can be considered as elementary reactions and the law of mass action is applicable.The mole flow rate of oxygen can be expressed as:

Solve Eqs.(7),(8)and(9)simultaneously,the steady-state oxygen permeation flux can be correlated to the oxygen partial pressures on the two sides of the membrane:

In the mathematical model,purge operation and vacuum operation are simulated since they are widely used in industry.As shown in Fig.2,sweep gas is introduced into the shellside ofthe U-shaped hollow- fiber.

The following assumptions have been adopted:

1.The membrane reactor is under steady-state isothermal operation.

2.The charged species are diffused only in the radial direction of the hollow- fiber and negligible in axial direction.

3.Ideal gas law can be used to describe the gas behavior of singlecomponent and gas mixture.

4.The gas-phase mass-transfer resistances are negligible.Therefore,the oxygen partial pressures on the membrane surfaces are identical to the oxygen partialpressures in both shell and lumen,respectively.5.The feed gas mixed so rapidly in the reactor that the gas composition at the shell side remains the same.

Based on the assumptions above,the oxygen permeation equations for U-shaped hollow- fiber membrane can be derived as follows:

Overall mass balances:

wherebis the volume ratio of O2in the feed gas.

Pressure drop at the lumen side can be described by the Hagen-Poiseuille equation:

The equations derived above are a group of ordinary differential equations.They can be solved by the Runge-Kutta method.The oxygen partial pressure and oxygen permeation rate can be deduced based on the component of feed gas and operation conditions.

3.Results and Discussion

The parameters of the U-shaped BSCF hollow- fiber membrane and operation conditions are listed in Table 1.The calculated results were compared with experimental data from our previous work[30].The oxygen permeation fluxes under vacuum operating condition were predicted using the above mathematic model.

Table 1Parameters used in the simulation of the U-shaped hollow- fiber membrane

3.1.Effect of feed gas flow rate

Fig.3 shows the dependence of oxygen permeation flux through the BSCF membrane on the air flow rate at different temperatures.The helium flow rate was kept at 60 ml·min-1in both experiment and calculation.The trends of the simulation results are in good agreement with the experimental data.With the increasing air flow rate,the oxygen permeation flux increases rapidly with the air flow rates lower than 100 ml·min-1but nearly remains constant at the air flow rates higher than 150 ml·min-1.It means that when the air flow rate is higher than 150 ml·min-1,surface diffusion of oxygen on the membrane surface near the shell side is notthe rate-limiting step.The results indicate that air should be supplied sufficiently during the oxygen permeation operation.The simulation results are much lower than the experimental data at the air flow rate of 40 ml·min-1.The reason may be that the calculated resistant is larger than the real resistant during the oxygen permeation process.Although the U-shaped hollow- fiber is sintered to dense,there may be some pore structures inside the membrane wall and it helps in reducing the resistances of bulk diffusion.Therefore,the oxygen permeation flux in experiment is higher than simulation.

Fig.3.Dependence ofoxygen flux on the air flow rate under purge operation(helium flow rate:60 ml·min-1).

3.2.Effect of sweep gas flow rate

Fig.4 shows the simulation results and experimental data of the oxygen flux through the U-shaped BSCF hollow- fiber under different helium flow rates and temperatures.In this study,the air flow rate was kept at 150 ml·min-1in both experiment and simulation.The calculated results have shown the same trend as experimental data.At higher temperature,the helium flow rate increment has a greater impact on the oxygen permeation fluxes.A dramatic increase of the oxygen permeation flux is observed in the calculated results when the helium flow rate is increased from 20 ml·min-1to 100 ml·min-1.The oxygen permeation flux increases by 47%,64%,75%,97%and 115%at 750 °C,800 °C,850 °C,900 °C,and 950 °C,respectively.

Fig.4.Dependence of oxygen flux on the sweep helium flow rate with purge operation(air flow rate:150 ml·min-1).

Fig.5.Dependence of oxygen permeation flux on the oxygen partial pressure on the shell side(feed gas flow rate:300 ml·min-1,helium flow rate:100 ml·min-1,operating pressure:1.013×105 Pa).

3.3.Effect of oxygen partial-pressure on the shell side

The dependence of oxygen permeation flux on the oxygen partial pressure on the shell side has also been investigated.Fig.5 compares the experimental data with the calculated results based on the model.The feed gas consists of different ratios of N2and O2under corresponding oxygen partial pressure.The trend of the simulation results agrees well with the experimental data and the numerical value fits better at lower temperatures of 750 °C and 800 °C.As expected,the oxygen flux is increased dramatically with the increase of oxygen partial pressure on the shellside.Itcan be understood easily thatthe increase ofoxygen partial pressure enlarges the oxygen partial pressure gradient between the shell side and the lumen side,giving an increase driving force for oxygen permeation across the membrane.It can be seen in both Figs.4 and 5 that the gap between the simulation results and experimentaldata at950°C is wider than the lower temperatures.This behavior may be attributed to the reducing of surface reaction resistances at higher temperature in experiment.

3.4.Effect of vacuum pressure and temperature under vacuum operation

Calculated results for the effectofvacuum pressure and temperature based on the model are given in Fig.6.The operating pressure on the shell side is kept at 1.013×105Pa in the simulation.In Fig.6a,oxygen permeation flux is plotted against the vacuum pressure at the lumen side.As the vacuum level increased(the vacuum pressure dropt),the oxygen permeation flux is increased.But the vacuum pressure does not affect the oxygen permeation flux anymore when the vacuum level is higher than a certain value.It can be observed clearly in Fig.6b,the oxygen permeation flux is almost the same at the vacuum pressure of1.013×102Pa,5.066×102Pa and 1.013×103Pa.Therefore,1.013×103Pa can be expected as the effective vacuum pressure in this case.It also can be seen in Fig.6b that the increase of vacuum pressure has a relatively even effecton all temperatures.When the vacuum pressure drops from 1.013×104Pa to 1.013×103Pa(effective vacuum pressure),the oxygen permeation flux is increased by more than 44%.The vacuumoperation under 1.013×103Pa at all the five temperatures studied is much more advantageous than that of purge operation.

3.5.Effect of operating pressure on the shell side

Fig.7 plots the effect of operating pressure on the oxygen permeation flux when the lumen side pressure is kept at 1.013×105Pa but without any sweep gases.The elevation of the operating pressure at the shell side presents a positive effect on the oxygen permeation flux.Comparing the effectofoperating pressure on the shellside and the vacuum pressure on the lumen side,it can be seen thata high vacuum level on the lumen side is much bene ficial for oxygen permeation.When the vacuumpressure at the lumen side is reduced to 1.013×104Pa,the oxygen permeation flux is about3.5 ml·min-1·cm2at950 °C.Such an oxygen permeation flux could not be achieved by elevating the operating pressure to 3.040×106Pa atthe same temperature.Therefore,reducing the vacuumpressure atthe lumen side is preferable forgas separation in the U-shaped hollow- fiber membrane to get higher oxygen permeation flux.

Fig.6.Dependence of oxygen permeation flux on(a)the vacuum pressure and(b)temperature under vacuum operation(feed gas flow rate:300 ml·min-1,p=1.013 × 105 Pa).

Fig.7.Dependence of oxygen permeation flux on the operating pressure on the shell side(feed flow rate:300 ml·min-1,pv=1.013 × 105 Pa).

4.Conclusions

A mathematical model based on Nernst-Planck has been developed for a ceramic oxygen permeable membrane with U-shaped geometry under different operating conditions.The air separation process under purge and vacuum operation in a U-shaped BSCF hollow- fiber membrane has been simulated in this work.The trend of calculated results under purge operation is in good agreement with the experimental data.Parametric study under purge operation reveals that the air flow rate and helium flow rate have a great effect on oxygen permeation flux.Temperature is also another important factor in both purge and vacuum operation.It is found that the oxygen partial pressure gradient affects the driving force for oxygen permeation directly.Further study on the effect of oxygen partial pressure on the shell side proves that the U-shaped BSCF hollow- fiber membrane has a large capacity for oxygen separation.Vacuumoperation is more efficientto separate oxygen from air than purge operation.The calculated results based on the model indicate that 1.013×103Pa is the effective vacuum pressure on the lumen side under vacuum operation.Increase of the oxygen permeation flux can be achieved more easily by increasing vacuum levelon the lumen side than elevating operating pressure at the shell side.

Nomenclature

Ammembrane area,cm2

bthe volume ratio of O2in the feed gas

CVconcentration of oxygen vacancy,mol·cm-3

CV′ concentration ofoxygen vacancy on the high oxygen pressure side,mol·cm-3

CV″concentration of oxygen vacancy on the low oxygen pressure side,mol·cm-3

DVdiffusion coefficient of oxygen vacancy,cm2·s-1

JO2oxygen permeation flux across the membrane,mol·cm-2·s-1

JVoxygen vancancy across the membrane,mol·cm-2·s-1

kfforward reaction rate constant for the surface reactions,mol·cm-2·s-1

krreverse reaction rate constant for the surface reactions,cm·Pa-0.5·s-1

Llength of U-shaped hollow- fiber membrane,cm

llength variable ofU-shaped hollow- fibermembrane model,cm

Nffeed gas flow rate,mol·s-1

NRmolar flow rate of residual gas,mol·s-1

NR,outmolar flow rate of residual gas at the exit of the reactor,mol·s-1

NO2molar flow rate of oxygen on the lumen side of the hollowfiber,mol·s-1

NO2,outmolar flow rate of oxygen at the exit of the hollow- fiber,mol·s-1

poperating pressure on the shell side,Pa

pO2oxygen partial pressure on the shell side,Pa

p′O2oxygen partial pressure on the shell side,Pa

p″O2oxygen partial pressure on the lumen side,Pa

pvvacuum pressure on the lumen side,Pa

Rgas constant,Pa·cm3·mol-1·K-1

Rininner radius of U-shaped hollow- fiber,cm

Routouter radius of U-shaped hollow- fiber,cm

rradius variable of U-shaped hollow- fiber,cm

Toperating temperature,°C

xmembrane thickness variable,cm

μ oxygen viscosity,g·cm-1·s-1

σVconductivity of oxygen vacancy

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