Feng Xue,Fugang Wang,Shuai Chen,Sheng Wang,Shengui Ju*,Weihong Xing

College of Chemical Engineering,Nanjing Tech University,Nanjing 210009,China

Keywords:Cefoselis hydrochloride Breakthrough curve Orthogonal collocation Macroporous resin Fixed bed Simulation

A B S T R A C T Adsorption operation is of great importance for separation and purification of semi-synthetic cephalosporin compounds in pharmaceutical industry.The adsorption dynamics of Cefoselis hydrochloride(CFH)on XR 920C adsorbent in fixed bed was predicted by the model of modified film-pore diffusion(MFPD).The intraparticle diffusion equation and mass balance equation in fixed bed are discretized into two ordinary differential equations(ODEs)using the method of orthogonal collocation which largely improves the calculation accuracy.The MFPD model parameters including the pore diffusion coefficient(Dp),external mass-transfer coefficient(kf),and the axial dispersion(DL)were estimated.The kfvalue was calculated by the Carberry equation,in which the effective diffusion coefficient Dewas fitted based on Crank Model through experimental data.Moreover,three key operating parameters(i.e.,initial adsorbate concentration; flow rate of import feed,and bed height of adsorbent)and the corresponded breakthrough curves were systematically studied and optimized.Therefore,this research not only provides valuable experimental data,but also a successfully mathematical model for designing the continuous chromatographic adsorption process of CFH.

1.Introduction

Cefoselis sulfate (CFS) is a new parenteral cephalosporin which has a broad use for killing both Gram positive and Gram negative bacteria,particularly for Pseudomonas aeruginosa[1,2].Cefoselis hydrochloride(CFH)is the key intermediate to synthesize CFS in pharmaceutical industry[3].The purity of CFH plays an extremely important role in guaranteeing the purity,efficacy and safety performance of CFS[4].Adsorption by macroporous resin has the advantages including high adsorption of targeted components, low operating temperature and feasibility to desorption for further separation and purification[5].Hence,using macroporous resin as adsorbent has been considered as one of the most effective purification methods for CFH product,and understanding the column dynamic adsorption breakthrough curve of CFH on macroporous resin is an essential work to design, operate and control of the adsorption process.

In the field of dynamic adsorption process research,mathematical modeling is to deal with varying equations in the absorbent phase including adsorption isotherm equation,mass balance equations and mass transfer rate equation.In 2000,McKay's group[6]reported that they successfully developed a membrane pore diffusion model for the adsorption of cadmium and copper ions at low concentration on the basis of the assumption of using linear isotherm as adsorption isotherm equation that the theory was firstly proposed by other researchers in the 1980s[7].Some kinds of hole diffusion methods for nonlinear isotherm were also proposed in the 1990s [7,8].Mass transfer rate equation was commonly simplified into a linear driving force(LDF)equation to describe adsorption process by many researchers[9–13],but the main error of the mathematical model is stemmed from the assumption of driving force as linear.Vermeulen[14]confirmed that the driving force(?q/?t)between adsorbents and liquid film is nonlinear and adsorption process of the adsorbate in liquid phase on the porous adsorbent is very complicated in practical applications.

Recently there have been otherdynamic adsorption models reported based on the film mass transfer domination theory,surface diffusion domination theory, film-pore diffusion domination theory,axis diffusion domination theory or the various combinations of these adsorption theories[15].Biot number(Bi),which describes the ratio of membrane mass transfer rate and the intra-particle diffusion(kf/Dm),is usually used to illustrate the behavior of dynamic adsorption model.Gu et al.[16,17]used a general rate model(GRM)to imitate the adsorption dynamics in a multiple components system in which the Biot number is within 10–100 and the competitive adsorption behavior is dominated by surface diffusion.However,Pérez-Foguet et al.[18]classified Biot number into three regions and indicated the corresponded dynamic adsorption models separately.From mathematical equations of driving force and adsorption phase equilibrium perspective, adsorption behavior is obvious dominated by the synergetic effect of film and pore.Thus,we modified the film-pore diffusion model with non-liner driving force equation and non-liner adsorption phase equilibrium equation and propose a modified film-pore diffusion(MFPD)model in the present research to investigate our practical system.

To solve the numerical model,partial differential equations are discretized into a set of ordinary differential equations(ODEs)using numerical solver.In recent years,several approaches have been proposed and most of them are based on finite difference scheme[19,20]or combined schemes(e.g. finite difference and orthogonal collocation schemes[20];orthogonal collocation on finite elements scheme[21,22];Orthogonal collocation and Laplace transformation schemes[23,24]).Qian et al.[23]reported that they successfully simulated a general rate model(GRM)with an ODE solver(integrator)in Matlab by orthogonal collocation on finite element scheme which took 0.06–0.5 h.Solsvik et al.[24]made a comparison of several numerical algorithms with orthogonal collocation for the solutions of a population balance(PB)model and found that the orthogonal collocation scheme offers the simplest algebra with high accuracy and efficiency.

In the past of our studies,a series of adsorption processes were investigated.In 2000[25],our group successfully imitated the adsorption of CO on activated carbon loaded with Cu2+by MFPD model.Subsequently,we used MFPD model to predict the adsorption behavior of active aluminum oxide containing fluorine ion in 2002[26]and the dehydration of trace water from tetrahydrofuran by 4A molecular sieve was investigated in 2007[27],respectively.All these work provides essential fundamentals for the design of adsorption model and its practical application.

In our research,we aim to simulate the adsorption dynamic behavior of CFH on the porous resin by using the MFPD model,which is vitally important for separation and purification of this semi-synthesis antibiotic compound with continuous bed chromatography technique.The modeling parameters including the external mass transfer coefficients kf,the axial diffusion coefficient DL,and pore diffusion coefficients Dpwere estimated using a series of Series empirical equations.Some of coefficients were obtained based on our experimental results.Besides,the type of rate controlling for our adsorption process was identified and the model was evaluated by the absolute average deviation(AAD)determined by empirical correlations[28].The adsorption operating parameters including the velocity of import feed,initial CFH concentration,and bed height of adsorbent and their corresponded breakthrough curves were systematically investigated.

2.Mathematical Model Development

2.1.Modified film-pore diffusion(MFPD)model

The development of MFPD model for the fixed bed adsorption process for CFH purification on a macroporous resin is based on the following hypotheses:

i.The fixed bed column is isothermal throughout the adsorption process.

ii.The mass transfer coefficient is regarded as a constant in the differential unit.

iii.The pressure drop of the liquid through the fixed bed is negligible.

iv.The isotherm equilibrium is based on Langmuir equation.

v.The mobile phase model is considered as plug- flow model in fixed bed column,where the type of mass transfer flow is axial diffusion transfer[29].

vi.The velocity of flow in column of fixed bed remains constant.

vii.The internal mass transfer is governed by pore diffusion(Dp),which showed the distribution in the adsorbents was along the radial direction[16,17].

2.1.1.The particle phase continuity equation in spherical coordinates

For the model of CFH diffusion through pore fluid,the internal particle mass transfer equation is shown below[26,27]:

where εprepresents the particle porosity,Cpis the liquid phase concentration in the pore of the resin particle,t is the time,q is the equilibrium adsorption capacity,r represents the radial distance within the adsorbent particle,Dpis the pore diffusion coefficient in the resin particle.

Under the low concentration and the single molecular adsorption(Langmuir model)condition,the change in the concentration of liquid in the adsorbent hole is far lower than the change of the adsorption amount of the adsorbent,i.e.Thus,the change of the liquid phase concentration in the hole of adsorbent can be ignored and the formula(1)can be simplified as follow:

2.1.2.Mass balance in fixed bed column

Mass balance in the liquid phase of the adsorption fixed bed column includes accumulation within the liquid,convection,axial dispersion,and external mass transfer through the liquid film outside the resin particles[27]:

where DLrepresents the axial dispersion coefficient of liquid phase component in fixed bed,C represents the concentration in solution,Cprepresents the concentration in pore,z represents the bed direction distance coordinate,ufrepresents the fluid flow speed,εBrepresents the bed porosity,Rprepresents the radius of particle,kfrepresents the external film mass transfer coefficient.

2.1.3.Initial conditions and boundary conditions

The initial conditions,the boundary conditions for the particles and the fixed bed column are shown below[26]:

where L is the height of the absorbent fixed-bed column,Rpis the particle radius.

2.1.4.Langmuir adsorption equilibrium equation

The diffusion rate is much smaller than the adsorption rate and each differential unit reaches adsorption equilibrium,which can be expressed by the Langmuir adsorption isotherm[26]:

where qmis the Langmuir isotherm constant at maximum adsorption capacity(mg·g-1),b is the Langmuir isotherm constant(L·mg-1).

2.2.Numerical solver

Orthogonal collocation has proved to be a useful numerical method for solving differential equations.The detailed orthogonal collocation solving method and parameters could be found in supporting information.Briefly,several dimensionless variables are given below:

where Q is the adsorption capacity of dimensionless;qeis the maximum adsorption capacity based on the theoretical calculation;X is the inlet concentration of dimensionless,T and Xprepresent the time and outlet concentrations(dimensionless),respectively;C0is the initial adsorbate concentration;Φ is the dimensionless resin particle radial distance;θ is the dimensionless fixed bed direction axial distance;Np,αbare the dimensionless parameters;ρpis the density of the surface of the resin;Rpis the particle radius;Pe,Stand Birepresent the Peclet number,Stanton number and Biot number,respectively.

The following dimensionless equations could be deduced by substitution of above-mentioned dimensionless parameters into Eqs.(2)–(10):

The dimensionless fixed bed equation is given along axial coordinate θ and can be expressed as[26]:

The dimensionless intra-particle diffusion equation is given along radial coordinate Ф and can be expressed as:

The dimensionless Langmuir equation is given(θ,Ф coordinates)as follows:

The corresponded dimensionless initial conditions and boundary conditions can be express as follows:

where Csis the liquid phase concentration in the appearance of the resin particle.

The orthogonal collocation method of the intraparticle diffusion equation and mass balance equation(Eqs.(12)–(13))are discretized into two ordinary differential equations(ODEs)can be confer in supporting information.

2.3.Determination of the model parameters

2.3.1.The pore diffusion coefficient Dp

The Mackie–Meares equation can be used to estimate the pore diffusion coefficient Dp[16,17]:

where Dmis the molecular diffusion coefficient of CFH.

Generally,considering low concentration of CFH solution as an ideal infinite dilution single salt system,thus,the molecular diffusion coefficient(Dm)could be estimated by the Wilke-Chang equation[30].

where Tkis the absolute temperature,αsvis the association coefficient,Msvis the molecular weight,ηsvis the viscosity,and Vbis the molar volume at the regular boiling point.The subscripts sv is solvents and a is solutes.

2.3.2.The external film mass transfer coefficient(kf)

The external film mass transfer coefficient(kf)can be calculated according to the following related relationships developed by Carberry[31]:

where Schmidt number(Sc)and Reynolds number(Re)were obtained from the following equations:

where dprepresents particle diameter;ρ represents density of the CFH solution(g·ml-1);u represents empty column flow rate(cm·s-1);μ represents the fluid viscosity(g·cm-1·s-1).The efficient film coefficient(De)was obtained by fitting static dynamic experimental data[29].

2.3.3.Axial dispersion coefficients(DL)

Axial dispersion coefficients(DL)is calculated by using Eq.(25):

2.3.4.Absolute average deviation(AAD)

To evaluate the model prediction,absolute average deviation(AAD)equation is commonly used.Generally,an AAD value ranging from 0.05 and 0.1 indicates the developed model is in a general agreement with the experimental data.AAD value below the range means that the model is almost perfectly fitting to the experimental values,while an AAD value above 0.1 indicates the model may not correlate with the experimental data[28].

where Nais the number of test points,Ci,exp|X=1is the experimental dimensionless concentration at the outlet of bed,Ci,pre|X=1is the dimensionless concentration of the bed outlet of the model prediction.

3.Experimental Section

3.1.Reagents,materials and apparatus

CFH is home-made with a purity of 97.5%followed by a procedure that could be found elsewhere[3].HPLC-grade methanol for the preparation of mobile phase was purchased from Sigma-Aldrich.Na2HPO4.10H2O,KH2PO4and methanol in analytical grade were purchased from Sinopharm Chemical Reagent Co.,Ltd.XR 920C resin was obtained from Xuner Chemical Co.,Ltd.(Shanghai China).The physical and chemical properties of XR 920C resin are summarized in Table 1.The resin was pretreated to remove the monomer and porogen that were trapped in the pores with 1 mol·L-1HCl and NaOH solution using a reported method[31,32].Then it was immersed in methanol at least 24 h and washed by deionized water prior to the adsorption experiments.

Table 1Parameters of the XR 920C resin and fixed bed columns

3.2.Analytical procedures

High performance liquid chromatography (HPLC)was used to determine the chemical component of samples on a Wufeng liquid chromatographic system equipped with an ODS-3 C18 column(GL Science Co.Ltd.,180 × 4.6 mm i.d.,5.0 μm)[33].The temperature of column oven was set at 295 K.The mobile phase consists of methanol and deionized water(20:80,v/v)which was flowed through the column in 15 min at a rate of 1.0 ml·min-1.Photodiode array detection was performed to identify CFH at the wavelength of 254 nm.

3.3.Static adsorption equilibrium experiments

To determine static adsorption isotherms,a fixed concentration of CFH and fixed weight of resin were filled into flasks and then the flasks were placed on a shaker and continuously agitated for 8 h at room temperature to reach equilibrium.The concentration of CFH in the liquid phase was determined by spectrophotometry.The adsorbed amount was obtained by the following relationship:

where qeis the adsorption quantity at equilibrium(mg·g-1);C0is the initial concentration(mg·ml-1);Ceis the equilibrium concentration(mg·ml-1);V is the volume of the solution(ml);w is the mass of the wet resin(g).

The Langmuir isotherm was used to fit the equilibrium experimental data to describe the interaction between solute and resin:

where qmis the maximum adsorption capacity of theoretical calculation[mg·(g resin)-1];b is the adsorption equilibrium constant(L·mg-1).

3.4.Adsorption kinetics tests

The adsorption kinetics of the XR 920C macroporous resin was investigated via contacting 100ml CFH and 5 g hydrated resins in a shaker solution.The composition of the aqueous solution was determined by HPLC at different time till adsorption equilibration was achieved.

The Crank's single-hole diffusion model is used to fit the data of static dynamic experimental data and the efficient film coefficient(De)was obtained by Eq.(13)[5,34].

where Mtrepresents the adsorption capacity of t at the moment(mg·g-1);M∞r(nóng)epresents the adsorption capacity at the end of time(mg·g-1).

3.5.Column dynamic adsorption tests

The column dynamics experiment of the bed was used to evaluate the separation properties of CFH with XR 920C resin at 298 K±1 K.The constant flow micro syringe pump(WZ50-C6,Smiths medical,Hangzhou,China)was used to control the velocity of the fluid.Air bubbles were removed prior to experiments with deionized water.The detailed experimental conditions are given in Table 2.Briefly,the experiments were executed at four following conditions:(i)Under different initial concentrations of 200 mg·L-1and 100 mg·ml-1with the same bed height of 20.5 cm and the same injection speed of 35 ml·h-1;(ii)Under different bed heights of 16.5 cm and 20.5 cm with the same initial concentration of 0.2 mg·ml-1and thesame injection speed of 35 ml·h-1;(iii)Under different residence time of 10 min and 17.5 min with the same initial concentration of 0.2 mg·ml-1and the same bed height of 20.5 cm.The sample was collected under predetermined time interval at the column outlet and the CFH concentration was analyzed regularly through HPLC.All experiments in this study were repeated at least three times and the reported values are the mean of three data sets.

Table 2Experimental conditions for the column runs and parameters for prediction of the breakthrough curves of CFH

3.6.Determining the model parameters

3.6.1.Adsorption isotherms

Fig.1.Langmuir isotherms of adsorption CFH on XR 920C resin at 298 K.

Fig. 1 describes the Langmuir isotherm model of CFH on XR 920 resin at 298 K and the corresponding Langmuir model parameters were obtained through Langmuir curve fittings in Origin 8.6.The curve of Ce/qeand Ceproduces a line that has a slope of 1/qmand intercepts 1/(b×qm).The parameter values of the Langmuir model qmand b were calculated as 25.56 mg·g-1and 9.88 L·mg-1,respectively.The model fit well with the experimental data under the investigated test condition and the variances(R2)of the modeling for the experiment is 0.9993.This result suggested that the adsorption process was mostly a monomolecular layer adsorption.

3.6.2.The diffusion coefficient(De)

The Crank model[32]was applied to predict the adsorption rate of CFH on the XR 920C resin at 298 K(Fig.2).The simulation results fit the experimental data fairly well.The diffusion coefficients(De)were calculated by Eq.(29)as 8.39×10-9cm2·s-1at 298 K.The correlation coefficients(R2)are obtained as 0.8617.

Fig.2.Fitting results of adsorption data by Crank model with the CFH on XR 920C resin by static dynamic test.

3.6.3.The external film mass transfer coefficient(kf)

The kfvalues estimated by the flow velocity of the empty bed can simplify the calculation in data processing and supply useful data for the design of the fixed bed.As Eq.(23)described,kfwas related to the bed parameters,Reynolds number and Schmidt number.Table 2 lists the fixed bed and operation parameters for the empty bed.Reynolds and Schmidt numbers were accordingly calculated by Eq.(24).Therefore,the kfvalue was estimated by Eq.(23)as 1.535×10-3and 1.98×10-3cm·s-1at the flow velocity of the empty bed of 20 ml·h-1and 35 ml·h-1,respectively.

3.6.4.Computing time of simulation

After the data configuration,the developed program was executed meanwhile the data processing time from the beginning to the end was recorded by a chronoscope.

3.7.MFPD model for adsorption dynamic behaviors of CFH on XR 920C resin

Breakthrough curve is of great importance in the adsorption operating process,which reflects the adsorption equilibrium relationship between mobile phase and the fixed phase.The experimental and predicted breakthrough curves of CFH at various experimental conditions with respect to the initial concentrations of adsorbate,inlet flow rate,and adsorbent bed height were systematically investigated.MFPD model was used as mathematical model to predict the adsorption dynamics influences of CFH on XR 920C resin.Eq.(18)was used to calculate Bi,and the results were shown in Table 2. It can be seen from Table 2 that the values of Biat different operating condition are all in the range from 1 to 100,implying that the diffusion of film-pore is dominated for the rate controlling in the adsorption experiment of CFH on XR 920C resin.

One of important parameter,pore diffusion coefficient in the resin particle Dp,was used to model the breakthrough curves at the feed rate,the initial adsorbate concentration, and the height of the adsorbent bed. Ponnusami et al. [35] have reported an internal diffusion coefficient independent of concentration,which was used to attach methylene blue to plant leaf powder.The individual particle diffusion coefficient values have been successfully applied by Quek and Al-Duri[36]to predict the concentration distribution of lead ions to coir under different experimental conditions.However,the Dpvalues for CFH were different from each other.For each adsorption system,the Dpvalue was specific.When using the same adsorbent,the physical and chemical properties of the solute,including the size,polarity and solubility,may influence the pore diffusion[37].

Pore diffusion,external film mass transfer and axial dispersion coefficients were determined by Eqs.(21),(23),and(25),respectively.As can be seen from Table 2,we found that the kfvalues varied with different velocities but remain stable in different initial adsorbate concentrations.This result is consistent with the conclusion by Guiochon et al.[38]that kfincreases with the decrease of film mass transfer resistance.The membrane mass transfer resistance was relevant to the thickness of the external liquid film of the resin particles. At a higher flow rate, film mass transfer decreases as liquid film outside the resin particles becomes thinner caused by the increasing turbulence.Therefore,the external mass transfer coefficient kfincreases with increasing flow rates.The kfdepends primarily on the flow rate of the specific system of adsorbate adsorbent.The velocity of the fluid in all concentration ranges was constant in our experiments.Thus,if the initial feed concentration is different,the value of kfremains constant.

There are four runs presented in this research.The modeling and practical operating data were summarized in Table 2.The experimental CFH breakthrough curves and the corresponded MFPD model prediction were presented in the following figures.

The variation of the initial CFH feed concentration has an important influence on the breakthrough curve as shown in Fig.3.The adsorption rate of the adsorbent in the column increases along with the increase of initial concentration,which reduces the breakthrough time.Therefore,the larger initial concentration leads to a faster breakthrough.Other scholars have found similar findings[6,39].These studies indicate that the rate and capacity of adsorption can be affected by the change of concentration gradient,the diffusion process is concentration-dependent.This problem was better explained by the theory that the driving force was controlled by the concentration gradient of the solute and can producea greater concentration difference by using a higher initial concentration[21,40].

Fig.3.Experimental and predicted breakthrough curves of CFH on XR 920C resin compared the initial concentration of 200 mg·ml-1with 100 mg·L-1,at the same bed height of 20.5 cm and injection speed of 20 ml·h-1.

Fig.4 shows the time evolution of Ci/C0ratio when the bed heights are 16.5 and 20.5 cm,respectively.The adsorption rate for a longer bed(20.5 cm)was slightly slower than that of a shorter bed(16.5cm).The reason was that a larger bed height corresponds to a larger amount of adsorbent in the column,and more active sites are available for sorption of the adsorbate with the increase of adsorbent bed height,which enhanced the utilization of the adsorbent.Under this experimental condition,the value of Biincreased from 28.2 to35 when the bed height enhanced from 16.5 to 20.5 cm.(see Table 2).However,the height of the bed increases with the increase of pressure drop, so the appropriate height of the bed was 20.5 cm.

Fig.4.Experimental and predicted breakthrough curves of CFH on XR 920C resin compared the bed height of 20.5 cm with 16.5 cm under the same initial concentration of 200 mg·ml-1,and injection speed of 20 ml·h-1.

Fig.5.Experimental and predicted breakthrough curves of CFH on XR 920C resin compared the resident time 17.5 min(20 ml·h-1)with 10 min(35 ml·h-1)under the same initial concentration of 200 mg·ml-1,bed height of 20.5 cm.

Fig.5 shows the breakthrough curves of CFH on XR 920C resin by experimentation and prediction with the resident time of 10 min and 17.5 min,where the corresponded flow rates are 35 ml·h-1and 20 ml·h-1,respectively.The same initial concentration of 200mg·ml-1and bed height of 20.5 cm were controlled. The simulated data good consistency with the experimental data, indicating that as the flow becomes higher,the penetration time becomes faster.It is found that the residence time in the bed was reduced as the flow rate increased,which resulted in lower bed utilization.Thus,the breakthrough time and the bed capacity will decrease with the increasing flow rate.The change of velocity will affect the membrane mass transfer coefficient kf(see Table 2,1.53×10-3cm·s-1at the resident time 17.5 min,1.98× 10-3cm·s-1at the resident time 10 min correspondingly),while the intraparticle diffusion Dpremains constant.The low flow rate will require longer operating time for separation.

4.Conclusions

The MFPD model has been very mature to simulate and predict CFH adsorption kinetics of XR 920C resin under different working parameters in fixed bed column under high calculation accuracy level(10-6).The experimental-based and MFPD model simulated breakthrough curves of CFH were obtained under the optimized operating conditions.The Langmuir isotherm constants(qeand b)and axial dispersion DL,external mass transfer coefficient kf,and pore diffusion coefficient Dpobtained from the CFH adsorption experiment could be used in the practical prediction directly. The ADD value obtained from the empirical correlations under the most optimized condition(Run 1)is 0.017(below 0.05),indicating the model we used is almost perfectly fitting to the experimental data.The Bibetween1and100at the four operating conditions indicates that the mass transfer rate of CFH during the adsorption of XR 920C resin is dependent on film-pore diffusion.The proposed experimental data and mathematical models are valuable which offers effective fundamentals for designing the process of continuous chromatographic separation of CFH product.

Nomenclature

A,B (M+1,M-1)dimensional configuration coefficient matrix of symmetric sphere

Aa,Ba(N+2,N+2)dimensional configuration coefficient matrix of symmetric cylinder

Bi Biot number

b Langmuir isotherm constant,L·mg-1

C liquid concentration,mg·L-1

Ci,pdimensionless concentration in the pores

Cpconcentration of liquid in the pores of the resin particles,mg·L-1

Csconcentration of liquid in the surface of the resin particles,mg·L-1

C0initial adsorbate concentration,mg·L-1

DLaxial dispersion coefficient of liquid phase component in fixed bed,cm2·s-1

Dppore diffusion coefficient in the resin particle,cm2·s-1

kfexternal film mass transfer coefficient,m·s-1

L height of the fixed-bed column,m

M configuration points along axial in the fixed bed

N configuration points along radial in the adsorbent particle

Npdimensionless number

Pe Peclet number

Pi-1(θ) (i-1)-th power orthogonal polynomials for θ

Pi-1(Ф2)j-th power orthogonal polynomials for Ф2

Q dimensionless adsorption capacity

qmLangmuir isotherm constant of maximum adsorption capacity,ml·g-1

q,qrequilibrium adsorption capacity,mg·g-1

Rpparticle radius,cm

r radial distance within the adsorbent particle,cm

St Stanton number

T dimensionless time

Tkabsolute temperature

t time,s

uffluid flow speed,cm·s-1

X dimensionless concentration in fixed bed

Xpdimensionless concentration in resin particle

z bed direction distance coordinate,cm

Φ dimensionless resin particle radial distance

αb, dimensionless number

εpParticle porosity

εBbed porosity

θ dimensionless fixed bed direction axial distance

ρpapparent density of the resin,g·ml-1

Acknowledgements

Special thanks have to go to Xuner Chemical Co.Ltd.for the free XR 920C resins supplied.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2017.12.001.