Yonghou Xiao *,Shuang Qiu ,Qidong Zhao ,Yuhao Zhu ,Chirag B.Godiya ,Gaohong He3

1 Panjin Institute of Industrial Technology,Dalian University of Technology,Panjin 124221,China

2 State Key Laboratory of Fine Chemicals,School of Chemical Engineering,Dalian University of Technology,Panjin 124221,China

3 Supercomputing Center,Dalian University of Technology,Dalian 116000,China

Keywords:Carbon dioxide Adsorption Fixed bed Finite element analysis Distributions of concentration and temperature field

ABSTRACT Accurately predicting distributions of concentration and temperature field in fixed-bed column is essential for designing adsorption processes.In this study,a two-dimensional(2D),axisymmetric,nonisothermal,dynamic adsorption model was established by coupling equations of mass,momentum and energy balance,and solved by finite element analysis.The simulation breakthrough curves fit well with the low-concentration CO2 adsorption experimental data,indicating the reliability of the established model.The distributions of concentration and temperature field in the column for CO2 adsorption and separation from CO2/N2 were obtained.The sensitivity analysis of the adsorption conditions shows that the operation parameters such as feed flow rate,feed concentration,pellet size,and column height-to-diameter ratio produce a significant effect on the dynamic adsorption performance.The multi-physics coupled 2D axisymmetric model could provide a theoretical foundation and guidance for designing CO2 fixed-bed adsorption and separation processes,which could be extended to other mixed gases as well.

1.Introduction

Nowadays,global warming caused by CO2is becoming one of the most severe environmental problems.Capture and utilization of CO2have become an essential environmental concern that has been gradually recognized all over the world[1,2].Although the capture of CO2emitted from industrial exhaust gas and coal-fired power plants has been well solved[3,4],the removal of CO2from ambient air is still in the initial stage and has gained increasing attention recently.

Currently,the average concentration of CO2in the atmosphere is ca.400 ml·m?3[5].M.Oschatz and Antonietti [6] predicted that the concentration of CO2in the atmosphere would exceed 550 ml·m?3,twice that before industrialization in the 19th century,and more than 40%higher than that today.Small-scale pollution source involving automobiles,air conditioning,heating etc.directly contributes to the increase of CO2concentration in the atmosphere[5].Capturing low-concentration CO2directly from the air might be the most effective potential solution[7,8].Especially in closed space,such as submarines and space shuttles,it usually contains less than 5000 ml·m?3CO2[9,10].Therefore,highefficiency and low-cost removal or capture of low-concentration CO2is urgently desired[11].

The executable capture methods of CO2include absorption [12],cryogenic distillation[13],membrane separation[14],and adsorption[15–17].Compared with the other methods especially under lowconcentration CO2,adsorption is regarded as the most effective CO2separation technique due to its advantages of low energy penalty,high product purity,good selectivity,and easy regeneration[18].According to the different regeneration modes,the adsorption process can be classified into pressure swing adsorption(PSA)[19,20],thermal swing adsorption(TSA)[21]and vacuum pressure swing adsorption(VPSA)[22,23].

Theoretically,both the adsorbents and processes are crucial for high-efficiency separation of CO2by adsorption[18,24,25].Recent reports for low-concentration CO2adsorption and separation have mostly focused on the developing adsorbents and improving their efficiency[5–11,24].Process simulation can efficiently optimize the adsorption conditions,save time,and reduce experimental costs[18,26].

Some researchers investigated the adsorption process by constructing physical models[26–29].Due to the limited information of simulation results obtained from one-dimensional(1D)model,more researchers have focused on the development of two-dimensional (2D) and threedimensional (3D) models in recent reports [28–30].To improve the accuracy of the model and simultaneously save computational cost,Ben-Mansour et al.[30]found that the results of the 2D still had some deviation from that of the 3D in terms of CO2mass fraction change,especially when the adsorption approached equilibrium.At present,it is still a great challenge to obtain high accuracy and save computational cost for models describing dynamic adsorption process by numerical methods.

Generally,it is difficult to obtain the analytical solution for adsorption model composed of multiple complex partial differential equations(PDEs);therefore,it is crucial to choose a suitable numerical solution method for process simulation.Compared with the traditional finite difference and the orthogonal collocation methods [31],the finite element analysis method has attracted much attention because of its high accuracy and time-saving calculation[32,33].Shafeeyan et al.[34]established a model composed of Avrami and semi-empirical Toth equations,in which the PDEs were solved using finite element analysis method,and the simulation results were in good agreement with experimental data.Accurately predicting distributions of temperature and concentration field in fixed-bed column and simultaneously saving computational cost are essential for designing adsorption processes[29].To the best of our knowledge,the systematic investigation on process simulation for low-concentration CO2adsorption on molecular sieves is scarcely reported.The 2D axisymmetric model possesses advantages of high accuracy and cost-efficient calculation,which has gradually attracted much attention of researchers in recent years[33,35,36].For example,Xiao's team [33] employed this method in studying charge and discharge cycle of hydrogen storage.The simulated results are in good agreement with the experimental data.Additionally,Lehmann et al.[35]used the 2D axisymmetric model to simulate fixedbed dynamic adsorption for thermochemical energy storage.The results demonstrated that the developed adsorption equilibrium model could well predict the dynamic adsorption behavior of composites.It is expected that 2D axisymmetric model coupling equations of mass,momentum and energy balance should also be competent when employed in fixed-bed adsorption for separation or purification.

In this study,a 2D axisymmetric model for separation of CO2/N2in fixed-bed adsorption column was successfully established,based on mass conservation,basic equation of fluid dynamics,energy balance equation,mass transfer rate and adsorption equilibrium equation.The model was employed to accurately predict heat and mass transfer in time and space within a fixed-bed column.The model was established by extending a 2D plane model,and the output results were directly expressed in 3D form,which achieved the calculation accuracy of the 3D model and greatly saved the computational cost.And the PDEs in the model were solved by finite element analysis.Meanwhile,the dynamic adsorption experiments of CO2on a fixed-bed column of 5A molecular sieve were conducted to verify the rationality and accuracy of the model.The adsorption breakthrough behavior of fixed-bed column was accurately predicted,through the distributions of temperature and concentration field in the coupled adsorption process.Furthermore,the effects of operating parameters sensitivity on the adsorption process were established based on the 2D axisymmetric model.The multi-physics coupled 2D axisymmetric model is expected to provide a theoretical foundation and guidance for designing fixed-bed adsorption process.

2.Fixed-Bed Adsorption Experiments

In the dynamic adsorption experiments,5A molecular sieve(pellet size～2.0 mm)was employed as an adsorbent,which was provided by Langfang Pengcai fine chemical Co.,Ltd.The adsorbent was crushed,and the part with an average pellet diameter of～0.22 mm was sieved and placed in a dryer for preventing moisture adsorption after dehydration treatment.Physical characteristics of the adsorbent are listed in Table 1.To facilitate the experiments,binary mixtures of 500–2000 ml·m?3CO2balanced by nitrogen were used as the feed gases in the fixed-bed adsorption experiments[8].

Table1 Physical characteristics of 5A molecular sieve

The dynamic adsorption performance of CO2on 5A molecular sieve was evaluated by a laboratory-constructed device,and the schematic diagram of the evaluation system is shown in Fig.1.One experimental device was designed to perform in-situ pretreatment and evaluation of the adsorbents,which consists of the following components:two cylinders(CO2and N2),two mass flow controllers (MFC),a gas mixer,an open tube resistance furnace(heating jacket),thermocouple,an adsorption column,pressure gauge,polytetrafluoroethylene tubes with outside diameter of φ3 and φ6,some valves(two-way and three-way valves,shut-off valves,trimmer valves),a float flow meter,a gas chromatogram (GC),and a computer workstation.A stainless steel tube with an inner diameter of 8 mm and a length of 46 cm was used as the adsorption column.

Fig.1.Schematic diagram of fixed-bed dynamic adsorption evaluation system(MFC–mass flow controller,PG–pressure gauge,GC–gas chromatogram).

To avoid the influence of residual water on the performance of adsorbents,5A molecular sieve was dehydrated in situ under nitrogen atmosphere for 8 h prior to the evaluation experiments,and the breakthrough curve of CO2on the 5A molecular sieve was tested under the conditions of 298 K and 101.325 kPa.For each experiment,～10.1 g of 5A molecular sieve was filled in the middle of the adsorption column,and～7.3 g of glass beads were filled in the upper and lower parts of the column.Binary mixtures(500–2000 ml·m?3CO2balanced by nitrogen)were obtained by controlling flow rate of CO2and N2with MFC,respectively,mixed and then passed into a fixed-bed column for adsorption.

The CO2concentration at the outlet of the fixed-bed column was measured online using the GC7900 (Tianmei Scientific Instruments Co.,Ltd.).High purity nitrogen(99.999%)was employed as carrier gas.The working conditions of the GC7900 were set as:injection temperature=373.15 K,column oven temperature=333.15 K and flame ionization detector (FID) temperature=473.15 K.The single injection analysis time and the injection interval were set as 1.3 and 0.5 min,respectively.A multi-point calibration external standard curve was established by averaging the results obtained by multiple injections in sequence.

3.Numerical Modeling Methods

In an attempt to better understand CO2adsorption breakthrough behavior,design and optimize adsorption units,a 2D axisymmetric nonisothermal fixed-bed adsorption model coupling adsorption isotherms,mass,momentum,energy balance equation and mass transfer rate equation was established and numerically solved using a multiphysics coupled software COMSOL Multiphysics version 5.4.The 2D axisymmetric model has been developed using User Define Function based on COMSOL Multiphysics software.Mathematical discretization method,numerical research,theoretical analysis and computer simulation were conducted to simulate the dynamic adsorption process.

The model was built based on the following assumptions:

(1) The feed gas contains only CO2and N2,and it follows the ideal gas state equation.

(2) The initial temperature and pressure of the adsorption column are uniform.

(3) The porous media is homogenous,and the adsorption instantly reaches equilibrium.

(4) Physical properties of the adsorbents are constant.

(5) The mass transfer rate equation can be described by the linear driving force(LDF)model[37].

(6) The adsorption isotherms of CO2and N2coincide with the multisite Langmuir model[16,38].

3.1.Mass conservation equation

The total mass conservation equation of the mixture can be expressed as[29]:

where c is the gas concentration and D is the diffusion coefficient,M represents the molecular weight of gas,t represents the time of adsorption,represents the Darcy's velocity vector,or apparent velocity,ρbrepresents the bulk density of adsorbent in the bed,εbrepresents the bed porosity,and narepresents the adsorption amount of gas adsorbed by unit mass of 5A molecular sieve.

3.2.Momentum conservation equation

Darcy's law interface in COMSOL Multiphysics chemical engineering module was used to simulate the gas flow in the fixed bed adsorption column.The momentum transmission is solved by Darcy's Law[29,33],which can be expressed as:

where μ represents the viscosity of the gas phase,and κ represents the effective permeability.

Assuming that CO2and N2are ideal gases in the fixed-bed adsorption process,the pressure can be calculated according to the ideal gas state equation.Combining Darcy's law Eq.(2) with the mass conservation continuity equation can yield the following equation:

Eq.(3)describes the conservation of mass and energy in porous media,which is also one of expression forms of the governing equation in Darcy's law interface.The inertia resistance cannot be ignored,due to the high-speed fluid.Therefore,the Darcy law could be modified by using the Ergun equation and it can be expressed as:

where dprepresents the average particle diameter of 5A molecular sieve,||ν||represents the value of Darcy's velocity vector.Alternatively,1/κ represents the viscosity resistance coefficient,and βErepresents the inertia resistance coefficient.

To conform to the form of the momentum conservation equation in the model,Eq.(4)can be transformed into the representation form of Darcy's Law,which can be expressed as:

where κ′ represents the modified permeability,ρgrepresents the density of the gas,and ||?p|| represents the value of the pressure gradient vector.

3.3.Energy conservation equation

The total energy conservation equation involving the heat transfer of the column wall is expressed as[29,33]:

where keffrepresents the effective thermal conductivity,Cp,gand Cp,srepresent the specific heat capacity of the gas and solid phases.E represents the total energy.Q represents the energy source term.The expressions keffand Q are given by:

where kgdenotes thermal conductivity of gas,and kpdenotes thermal conductivity of the adsorbent in the column.Qadenotes the term of the heat source of adsorption,ΔH denotes the isosteric heat of adsorption,Qbdenotes the term of compression work,and β denotes the volume expansion coefficient;for ideal gas,βT=1.

For the column wall,the energy equation through the wall depends on the balance between the heat stored in the wall and the heat diffusing through the wall[30],as described by:

where ρw,Cp,w,kwand Twrepresent the density,specific heat capacity,the thermal conductivity and the local temperature of the column wall,respectively.

3.4.Mass transfer rate model

The adsorbate diffuses toward the surface of the solid adsorbent pellets due to the driving force generated by the difference in concentration.For the process of adsorbing CO2in molecular sieves in a fixed bed,the LDF model[37,39]can be used to accurately reflect the mass transfer rate between gas–solid two phases.As no complex pore diffusion model is employed herein,much calculation time could be saved.

LDF model can be expressed as:

where kf,i,Dp,iand Dc,irepresent the film mass transfer coefficient,macro-porous and micro-porous diffusion coefficients,respectively.rpand εpare the adsorbent particle radius and porosity,and rcis the adsorbent crystal radius.Q0,irepresents the concentrations of the solid phase.

3.5.Adsorption equilibrium model

The adsorption isotherm model can be employed to describe the relationship between pressure and adsorption capacity.The multisite Langmuir adsorption isotherm model [16,36] was used to describe the adsorption equilibrium of CO2on molecular sieves based on the accuracy of the fitted experimental data.The model assumed that an adsorbate molecule could occupy multiple adsorption sites at the same time,considering the interaction between adsorbate molecules,and the equation can be expressed as:

where q represents the amount of adsorption,qmrepresents the maximum amount of adsorption,a represents the number of adsorption sites that an adsorbate molecule can occupy,and K represents the adsorption constant.

K and adsorption temperature T are obtained by Van't Hoff equation[16]:

where K0represents the pre-factor,and R represents the universal gas constant.

3.6.General boundary conditions

This section is used to set up mass transport across boundaries where both convective inflow and outflow can occur.

(1) Boundary conditions at entry z=0

Mass and heat transfer at the inlet of the adsorption column could be expressed as the diffusion quantities in balance with the advection ones[30].

(2) Boundary conditions at exit z=H

Mass and heat fluxes at the axisymmetric axis and planes of symmetry are:

(3) Interfaces between column walls and adsorbent

The convective heat transfer between the bed and the column wall is estimated through the local heat transfer Eq.(21):

where hwrepresents the heat-transfer coefficient between the gas phase and the column wall.

3.7.Numerical solution

The numerical solution of the model was implemented in COMSOL Multiphysics version 5.4.The transport of diluted species module in Chemical Species Transport was used to describe the mass transfer process [28].Additionally,the modules of Heat Transfer in Fluids,Heat Transfer in Solids and Heat Transfer in Shells were selected to describe the heat transfer in the adsorption process.The PDEs for adsorption model were solved by adding Domain Ordinary Differential and Differential-algebraic equations module[40,41].Binary mixture gas of CO2/N2is selected as the feed,and the parameters of the adsorption process are listed in Table 2.

Table2 Parameters for adsorption process simulation

3.8.Grid division of fixed-bed model

A 2D axisymmetric fixed-bed adsorption model was established by coupling equations of mass,momentum and energy balance.After the model was constructed,the 2D axisymmetric model was meshed by free triangular mesh(case 2).

4.Results and Discussions

4.1.Grid independence verification

To explore the grid independence,the grid was divided by free triangular mesh.The 2D axisymmetric fixed-bed adsorption model(Fig.2)was meshed for five different cells number (more details are described in Table 3).The ordinate of z=0 and H was set as the inlet and outlet of the fixed-bed column,respectively.The verification of grid independency is carried out using 5A molecular sieve at inlet flow rate 20 ml·min?1,298 K and 101.325 kPa for the adsorbent bed,as shown in Fig.2.The effluent CO2concentration varied with changing the number of grids.As can be seen from Table 3,the concentration differences calculated in cases 1 and 2 are the same,lower than that in the other three cases.We selected mesh case 2 to solve our modeling,because it not only has small error but also saves computing time.At present,the computational running time of this model is much less than that of other 2D models built by other software.

Table3 Grid structure and its independence

4.2.Model rationality verification

To verify the rationality of the model,the CO2adsorption experiments were carried out in a fixed-bed column of 5A zeolite at different CO2feed concentrations and flow rates.The simulation results fit the experiments well as shown in Fig.3.The CO2breakthrough curve obtained by the simulation was slightly different from the experimental data at the inflection point before the adsorption attained equilibrium,but most of the data were well consistent,which was sufficient to demonstrate that the model was feasible to describe the CO2adsorption process in fixed-bed column.

4.3.Changes of 3D concentration field

To investigate the change of CO2concentration field in fixed-bed column of 5A molecular sieve at different time,the adsorption process was described by taking ten instants at 10,100,200,400,600,800,1000,1500,2000,and 2700 s,respectively.The simulation results of the variation of CO2concentration field in the fixed-bed column are demonstrated in Fig.4(a).

The CO2concentration wave moved ahead from the inlet to the outlet along the axial direction of the adsorption column,and the nearer to the entrance,the CO2adsorption approached equilibrium faster.The effluent CO2concentration reached equilibrium value at the outlet of the fixed-bed column after～1200 s under the feed flow of 50 ml·min?1and 1000 ml·m?3CO2.In addition,it can be clearly seen from the change of the 3D concentration gradient with the adsorption progressing that the adsorption amount of the“adsorption front”slightly increased,which demonstrated the unevenness of the concentration gradient throughout the adsorption process.

Fig.2.Schematic diagram of(a)2D axisymmetric model and(b)grid division of the fixed bed.

Fig.3.Comparison of simulation and experiments derived CO2 breakthrough curves.(a)Different flowrates(T=298 K,P=101.325 kPa,Cin=1000 ml·m?3,H/D=32.5),(b)different CO2 feed concentrations(T=298 K,P=101.325 kPa,Fin=50 ml·min?1,H/D=32.5).The symbols are experimental results while the solid lines represent numerical simulations.

It has been reported that strong wall effects exist in packed beds with small diameter-particle ratio(D/d)adsorption column because of the large void fraction near the wall[42].However,the wall effect can be ignored in the range of D/d>30[43],and the wall effect decreases with the increase of H/d.The D/d is about 36.4 and the fixed-bed column height to pellet diameter ratio(H/d)is 32.5 in the experiment and simulation process.As a result,the concentration on the column wall is slightly higher than the central concentration in the adsorption mass transfer zone,and the difference between the inner wall and the central concentration in the equilibrium zone is almost zero,indicating that the wall effect has little influence at this situation.

The changes of N2concentration field in the fixed bed at different times(0,10,50,100,200,400,600,800,1000,1500,2000,and 2700 s)are shown in Fig.4(b).The whole process of N2adsorption was similar to that of CO2,while the change of N2concentration was contrary to that of CO2.The concentration waves of N2moved ahead from the inlet to the outlet along the axial direction.By comparison,N2was adsorbed far less than CO2on 5A molecular sieve.This was due to the affinity of CO2molecules with larger permanent quadrupole moments than that of N2,which enabled it to interact more strongly with the cation-induced electric field of 5A molecular sieve [44].With the processing of CO2adsorption,the separation of CO2/N2was achieved.

4.4.Changes of 3D temperature field

Fig.4.Changes of concentration field at different time in fixed bed.(a)CO2 concentration field and(b)N2 concentration field(T=298 K,P=101.325 kPa,Fin=50 ml·min?1,H/D=32.5).

The simulation results of the 3D temperature field changes are shown in Fig.5.They were obtained by the 2D axisymmetric model highlighting some important in situ information that cannot be displayed by the 1D models.A non-adiabatic boundary condition at the column wall led to radial variations of the temperature inside the adsorption column.With the adsorption process proceeding,the temperature kept rising until the maximum value was reached due to the exothermic nature of adsorption.After adsorption approached equilibrium,the temperature of the whole column also tended to be constant.The change trend of the temperature field in the adsorption column was correlated with the concentration field of CO2,while the adsorption heat was transferred forward from the inlet to the outlet,and gradually propagated from the center to the wall surface of the column.

To further investigate the axial and radial temperature trends at the center and wall of the adsorption column,two points were selected at the positions of 5 and 15 cm from the center and wall of the adsorption column using the Cut Point 3D function,respectively,as shown in Fig.6.

The diagram of temperature change trend at the center and the wall of the adsorption column is shown in Fig.7,which was in one-to-one correspondence with the temperature field.The center temperature was the highest when the process of the adsorption reached equilibrium.Meanwhile,the heat exchanged with the outside of the column.In the radial direction of the adsorption column,the temperature from the center to the wall gradually decreased.The center temperature of the adsorption column was up to 311 K,while the wall temperature of the adsorption column was only ca.299.4 K.Judging by the changes in temperature and concentration field,the adsorption amount of the whole adsorption process was uneven.

4.5.Sensitivity analysis of operating parameters

To further evaluate the effect of operating parameters on the performance of CO2adsorption,the influences of feed flow rate on the adsorption column,CO2concentration in the gas stream,pellet size and height-to-diameter ratios (HDR) were investigated.Firstly,the breakthrough curves at the flow rates of 30,60,and 90 ml·min?1were simulated,and the results are shown in Fig.8(a).

As expected,with increasing the feed flow rate,the amount of feed treated per unit time increased,so that the adsorption process accelerated,and the breakthrough curve showed a greater slope,an earlier breakthrough point and a faster column equilibrium.This behavior is due to the increase in the interstitial velocity,which improves the external and overall mass transfer coefficient,thereby reducing the resistance of mass transfer.The results agree well that the H2S breakthrough curves exhibit a steeper slope as the interstitial velocity increases as reported by Aguilera and Ortiz[41].In this work,the increase in velocity leads to a decrease in residence time,which causes a reduction in the amount of CO2adsorption,resulting in a decrease in the efficiency of the adsorbent bed,and an earlier breakthrough time.When the gas feed flow rate was 90 ml·min?1,the breakthrough started at～100 s and approached adsorption equilibrium at～500 s,but the breakthrough started at～700 s and adsorption equilibrium attained at～2500 s when the gas feed flow rate was reduced to 30 ml·min?1.

Fig.5.Variation of temperature field in fixed-bed column at different time during CO2 adsorption(T=298 K,P=101.325 kPa,Fin=50 ml·min?1,H/D=32.5).

Fig.6.3D cut-off points at the center(a,b)and wall(c,d)of the adsorption column.

Fig.7.Temperature change trend at(a)the center and(b)the wall of the adsorption column at two different positions(T=298 K,P=101.325 kPa,Fin=50 ml·min?1,H/D=32.5).

Fig.8.Effects of operating parameters on CO2 adsorption in fixed bed.(a)Flow rate,(b)feed concentration,(c)pellet size,and(d)height-to-diameter ratios.

To investigate the effects of feed concentrations on CO2adsorption breakthrough curve in fixed bed,the dynamic adsorption experiments were carried out under CO2feed concentrations of 1000,2000,4000 and 8000 ml·m?3,respectively.And the results are shown in Fig.8(b).With increasing CO2concentration,the breakthrough points of the concentration profile appeared slightly earlier,while the mass transfer zone became steeper,and the adsorption equilibrium attained earlier,as shown in Fig.8(b).

With the aim to investigate the influences of pellet size of the adsorbents on the adsorption process,the dynamic adsorption simulations were performed,and the results were shown in Fig.8(c).The larger the pellet size is,the earlier the breakthrough point appears,and the faster the adsorption process approached equilibrium.Larger pellet size means larger gap between the adsorbent pellets,and the shorter the residence time of the feed gas on the surface of the adsorbent,resulting in the earlier appearance of the breakthrough point.The results demonstrated that the pellet size of the adsorbents had a significant influence on the adsorption process.

To investigate the effect of HDR of the column on the adsorption performance,the variation of the breakthrough curve versus HDR is plotted in Fig.8(d).The breakthrough process got slower and became more even as the HDR increased,under the same conditions.When HDR diminished,the resistance of the feed gas in the adsorption column decreased.As the residence time became shorter,the breakthrough points and the adsorption equilibrium approached earlier.In this case,the equilibrium of the bed was reached more quickly,resulting in less CO2being removed from the gas stream,which somewhat reduced the efficiency of the adsorption column.On the other hand,if HDR of fixed bed was too big,although the CO2was fully adsorbed,the amount of feed gas treated per unit time decreased,which also reduced the efficiency and performance of adsorbents.At the same time,the stability of mass transfer zone decreased obviously with increasing the height of column.Therefore,an optimum HDR of the adsorption column should be selected according to the specific adsorption process.

5.Conclusions

In this study,a multi-physics coupled 2D axisymmetric nonisothermal model for dynamic adsorption was established by coupling the source term of the mass,momentum and energy conservation equations.The numerical simulation of the model was carried out,and the adsorption breakthrough experimental verification was conducted by separating CO2from a binary mixture gas of CO2/N2on 5A molecular sieve fixed bed.The simulation results are in good agreement with the dynamic experimental data,indicating that the model can be employed to predict the CO2adsorption breakthrough curve.The distributions of temperature and concentration field for CO2adsorption process predicted by the 2D axisymmetric model are similar to those of the 3D model.The change of the temperature field in the fixed-bed column is correlated with the concentration field of CO2,and the position of maximum temperature moves forward from the inlet to the outlet and spreads from the center to the wall surface.

The sensitivity of the operating parameters was analyzed,and the effects of process parameters such as feed gas flow rate,HDR,pellet size and feed concentration on the adsorption breakthrough process were further evaluated.The results demonstrate that the effects of the feed gas flow rate on the breakthrough curves are more significant than that of the HDR in the fixed bed.It results in an earlier breakthrough when the feed gas flow rate increases.Reducing the height of column and increasing the CO2feed concentration led to a steeper mass transfer zone.Furthermore,the pellet size of the adsorbents influences the breakthrough curves remarkably.As the pellet size decreases,the diffusion resistance is reduced and eventually the breakthrough time is prolonged.These findings provide a theoretical basis for the designing of low-concentration CO2dynamic adsorption processes and the model could be extended to other mixed gases as well.

Nomenclature

ainumber of neighboring sites occupied by a molecule of component i

Cp,gspecific heat capacity of gas,J·kg?1·K?1

Cp,sspecific heat capacity of adsorbent,J·kg?1·K?1

Cp,wspecific heat capacity of wall,J·kg?1·K?1

c gas concentration,mol·m?3

D diffusion coefficient,m?2·s

Dp,imacro-porous diffusion coefficient,m?2·s

Dc,imicro-porous diffusion coefficient,m?2·s

dpaverage particle diameter,m

E total energy,J·m?3

ΔH heat of adsorption,J·mol?1

hwheat-transfer coefficient between the gas phase and the wall,W·m?2·K?1

K isotherm adsorption constant

K0pre-exponential factor

keffeffective thermal conductivity,W·m?1·K?1

kgthermal conductivity of gas,W·m?1·K?1

ki(linear driving force)lumped coefficient,s?1

kpthermal conductivity of adsorbent,W·m?1·K?1

kwthermal conductivity of wall,W·m?1·K?1

M molar mass,g·mol?1

nanumber of moles per mass adsorbent,mol

p pressure,Pa

qiadsorption amount,mol·kg?1

qi* equilibrium adsorption amount,mol·kg?1

qmmaximum adsorption amount,mol·kg?1

R universal gas constant

rcadsorbent crystal radius,m

rpadsorbent particle radius,m

T temperature of adsorption bed,K

Twwall temperature,K

t time,s

ν Darcy's velocity vector,m·s?1

Yimolar fraction of component i

z axial position in the bed,m

β volume expansion coefficient

βEinertia resistance coefficient,m?1

εbbed porosity

εpadsorbent particle porosity

μ viscosity of the gas phase,Pa·s?1

κ permeability

κ′ modified permeability

ρ density,kg·m?3

Subscripts

0inlet

b bed

i gas composition

g gas

p particle

w wall

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the National Natural Science Foundation of China(21776028),Key Research and Development Projects of Liaoning Province(2017308004).