A more precise method to evaluate kinetic leakage of anion exchange resin used in condensate polishing of power plant

Tianping Wang,Xuxiang Jia,Chunsong Ye

Department of Water Quality Engineering,School of Power &Mechanical Engineering,Wuhan University,Wuhan 430072,China

Keywords:Sulfate mass transfer coefficient (MTC)Anion exchange resin Kinetic leakage Condensate polishing Power plant

ABSTRACT Sulfate mass transfer coefficient (MTC) is a sensitive parameter to evaluate the kinetic leakage of anion exchange resin used in condensate polishing system of thermal and nuclear power plant.However,a sufficiently precise determination method has not been well established.In this paper,the final expression of sulfate MTC derived based on plug flow reactor model is the same as Harries’ model,which is widely acknowledged in this field.In the determining system we constructed,in-situ calibration of the concentration of sulfate and its cation conductivity was conducted and sulfate MTCs of four typical strongly basic anion exchange resin samples were determined.The systematic error is 8.26% and the calibrated curve used for quantifying sulfate is obtained.The repeatability and reproducibility standard deviation are 0.05×10-4 m·s-1 and 0.07×10-4 m·s-1 respectively,which are lower than previous works.By controlling test condition accurately,this study has developed a more precise sulfate MTC determining method.This method provides a basis for further research.

1.Introduction

Condensate polishing system is widely used in thermal and nuclear power plant.The system can remove trace amounts of ions or other contamination before such impurity become concentrated enough to cause damage to devices such as boiler,steam generator,pipeline and turbine.In condensate polishing management,kinetic performance of ion exchange resin is of primary concern.The worse kinetic performance,the earlier breakthrough would occur,resulting in more frequent regeneration and longer washing period.Moreover,boiler water quality is becoming more and more stringent nowadays [1].In general,kinetic performance of ion exchange resin plays an important role in guaranteeing the quality of boiler water and the economic operation of mixed-bed ion exchange reactor.This is especially true for anion exchange resin for which it is more vulnerable to heating,oxidation and fouling than cation exchange resin [2-4].Thus,kinetic performance of anion exchange resin has attracted more attention in condensate polishing.

Once kinetic performance of anion exchange resin deteriorates,kinetic leakage would occur.In this field,it is necessary here to clarify exactly what is meant by kinetic leakage.Mixed-bed ion exchange reactor in condensate polishing power plant (CPP)operates at a high flow rate (100 m·h-1-120 m·h-1) through a shallow bed (0.9 m-1.2 m).Within rarely short contact time,some ions in the condensate water may not be completely exchanged and will furtherly leak into the water-steam system.Kinetic leakage is used to describe such phenomenon,which would happen even if resin is just regenerated or new.Kinetic leakage fundamentally differs from equilibrium leakage [5,6].Equilibrium leakage of resin has much to do with its basic property such as exchange capacity and ionic selectivity coefficient.Nevertheless,both the basic property of resin and the hydraulic characteristic of the system jointly account for kinetic leakage.In this specific context,some classic methods such as shallow-bed test,single-particle test and mass transfer correlation are of inapplicability to evaluate kinetic leakage of anion exchange resin used in condensate polishing [7,8].

Sulfate mass transfer coefficient(MTC)is a sensitive parameter to evaluate the kinetic leakage of anion exchange resin.Sulfate is broadly acknowledged as the test anion.Comparing with other common anions,chloride for example,with larger hydrated ionic radius and twice smaller diffusion coefficient,sulfate moves slower than chloride.With respect to the valence of anion,sulfate has two negative charges which needs two exactly neighboring exchange sites [5,9].If kinetic impairment occurs,the exchange ability of anion exchange resin with sulfate would decreases more obviously.Comparing with other resin parameters such as exchange capacity or moisture,a large sulfate MTC drop may have a slightly change in those parameters [10].Actually,sulfate MTC represents the effective migration rate of counter ions from bulk solution to the ion exchange site since the real condensate water also contains other anions.

The theoretical basis for sulfate MTC determination is Harries’model [9,11,12].Based on widely accepted Harries’ model,several institutions had designed their own determining system and had developed their own determining method[12-15].In brief,sulfate MTC is determined by a simple column test.The test solution with known sulfate concentration flows through resin sample at a sufficiently high flow rate.The concentration of sulfate () in the effluent originating from kinetic leakage is detected.Finally,sulfate MTC is calculated by Harries’ model.However,a unified sulfate MTC determining system and method have not been well established up to now.Moreover,a more precise sulfate MTC determining method is urgently needed for further study on anion exchange resin such as kinetic impairment mechanism and recovery strategy.There is a current paucity of studies investigating how to improve method precision by determining system design and test condition control.

The overall aim of this paper was to propose a more precise method for sulfate MTC determination.Specifically,the purpose of this study was to (a) derivate sulfate MTC of anion exchange resin in mixed-bed based on plug flow reactor model,(b) in-situ calibrateand its solution cation conductivity (κH) on our determining system and(c)determine sulfate MTCs of four typical resin samples and comment the method precision by comparing with previous studies.

2.Experimental

2.1.System construction

The schematic diagram of MTC determination system for anion exchange resin is shown in Fig.1.The system mainly consists of three parts:mainstream circuit (1-2-3-5-6-7-8-9-10-1),injection bypass(4) and thermostatic circuit(1-2-8-1).The detailed specification of each item can refer to Table S1 or our previous work[16].

Fig.1. MTC determination system.1-thermostatic water tank;2-magnetic pump P1;3-mixed-bed polishing column;4-injection pump Pi;5-magnetic pump P2;6-mixing chamber;7-float flow meter;8-determining column;9-cation column;10-conductivity meter.

The mixed-bed polishing column was designed to guarantee pure water context and the recycling use of water.As for the cation column,it was used to exchange all cations in the effluent into hydrogen ion and thus the κHcan be obtained.This method is widely used to characterize anionic contamination of high purity water[17].The distinct advantage of determining κHhere was that it can extend the lower detection limit ofsince the conductivity of hydrogen ion is the largest of all cations.

In order to determine sulfate MTC in a unified condition,the standard cation exchange resin and standard anion exchange resin should be settled.In this study,two types of brand-new Dowex resins,650C-H and 550A-OH,were chosen as the standard cation exchange resin and anion exchange resin,respectively.The mixed-bed polishing column (3 in Fig.1) was filled with the mixture of 550A-OH and 650C-H.Prior to filling the mixed-bed polishing column,550A-OH and 650C-H,the volume ratio of which was 2:1,were mixed using a glass rod until there was no obvious resin clumping.The mixed-bed polishing column was then filled to the bed depth of 350 mm.As for the cation column (9 in Fig.1),it was filled with 650C-H to a depth of 300 mm.Following column filling,the tightness of the determining system was checked.In the end of this part,the determining system was purified until a stable effluent conductivity was reached.

2.2.In-situ calibration

To offset the systematic error,it was necessary to conduct insitu calibration on our determination system.Sodium sulfate was guarantee reagent (GR) in this experiment.Prior to test solution preparation,sodium sulfate was dried at 100 °C for 1 h and was stored in a desiccator.Sulfate standard solutions were then prepared by dissolving sodium sulfate in water,theof which were 1 mg·L-1,2 mg·L-1,5 mg·L-1,10 mg·L-1,20 mg·L-1,40 mg·L-1,60 mg·L-1,80 mg·L-1and 100 mg·L-1,respectively.During solution preparation,CO2in the air would dissolve in the solution.However,it is difficult to guarantee the dissolved amount of CO2to be the same every time.In order to avoid such error,the water for preparing solutions was equilibrated with the CO2,the conductivity of which was(1.0±0.1)μS·cm-1(25°C).Then,injection pump was calibrated to the flow rate of 0.5 ml·min-1.With determining column empty,in-situ calibration of the determining system was carried out.The determining system was purified at 1 L·min-1until a stable effluent conductivity was reached.The water for preparing solutions was then injected at 0.5 ml·min-1into the mainstream and the stable effluent conductivity was collected as the blank conductivity(κ0).In the same way,sulfate standard solution was injected at the same flow rate in the order of low concentration to high concentration.The stable effluent conductivity was collected as κS.Once sulfate standard solution changed,the determining system was purified again.The experiment was conducted at(25.0±0.2)°C.The determined κHof each sulfate standard solution was calculated according to Eq.(1).In this equation,0.055 was the conductivity of pure water at 25 °C.The relationship betweenand its κHwas linearly fitted.Finally,the calibrated curve ofand its κHcan be obtained.

2.3.Sulfate MTC determination

Four types of strongly basic anion exchange resin samples (A1,A2,A3and A4) were selected for sulfate MTC determination.A1and A2were typically used in thermal power plant while A3and A4for nuclear power plant.Both of them were in the form of ROH.Prior to test,anion exchange resin sample was backwashed to remove resin leachables and broken resin particles.The harmonic mean diameter of resin sample was measured using a laser diffraction particle size analyzer [18].The determining column (8 in Fig.1)was filled with the mixture of anion exchange resin sample and 650C-H.75 ml anion exchange resin sample and 150 ml 650C-H were then mixed until there was no obvious resin clumping.On completion of resin mixing,the process of transfer was carried out.The well-mixed resin was carefully transferred into the determining column using a glass funnel.During the transfer,only about 5 mm of free water was kept above the resin to prevent resins from separating out.The depth of the mixed-bed was measured using a measuring ruler.

0.9 g·L-1Na2SO4was prepared by dissolving the dried sodium sulfate in water.Injection pump was calibrated to the flow rate of 0.5 ml·min-1.The determining system was then purified at 1 L·min-1to a stable conductivity.Following system purification,the stable conductivity was measured while injecting the water for preparing solutions or test solution.The water for preparing solutions was injected at 0.5 ml·min-1and the stable conductivity was collected as the blank conductivity.In the same way,0.9 g·L-1Na2SO4was injected at the same flow rate and κHof the effluent was measured.All the determination was carried out at(25.0 ± 0.2) °C.was quantified according to the calibrated curve ofand its κH.Finally,sulfate MTC was calculated according to Harries’ model [9,11,12],as shown in Eq.(2).

In order to investigate the effect of ammonia on sulfate MTC determination,an ammonia control experiment was carried out.The only difference from the above experiment was the composition of test solution.The control test solution that composed of 0.9 g·L-1Na2SO4and 1.5 mg·L-1ammonia was prepared with Na2-SO4solution and ammonium hydroxide (GR).

2.4.Statistical analysis

Three representative samples were taken from each type of resin.For every determination,four times of repetitive tests were required.Statistical analysis of the result followed GB/T 6379.2[19].In brief,the outlier check was carried out using Cochran and Grubbs tests.Standard deviation was calculated based on all the valid datum.

3.Mathematical Modeling

Mixed-bed ion exchange units used in CPP are typical packedbed.Plug flow reactor model is widely acknowledged to describe the performance of pack-bed[20].The specific model assumptions are:(1) The experiment is conducted at the initial stage of the anion exchange resin and the concentration of test ion is at the trace level.Thus,the rate determining step of ion exchange reaction is the ion diffusion across Nernst film[21].(2)The mixed resin bed is regarded as a plug flow reactor.(3) The resin is regarded as pseudo-homogeneous without swelling and shrinkage.(4) The effects of electric potential gradient,the difference between concentration and activity,and mutual interference of ions can be ignored.On the basis of the plug flow reactor model,the mass balance of the differential volume (Fig.2) is given by Eq.(3).

Inflow=Outflow+Generation+Accumulation

In the case of steady state operation,there is no accumulation of sulfate in the bulk solution.Thus,Eq.(3) can be simplified into

Fig.2. Mass balance of the differential volume.

The exchange process here is controlled by Nernst film diffusion.The linear driven force model[22]is used to describe the concentration profiles of sulfate within Nernst film,which is

In this case,is assumed to be zero [5,8,10,14].

Combining Eq.(4) and Eq.(5)

Integrating along the bed depth using the following boundary conditions

Then we get

Resin particle is supposed to be spherical,thus

Sulfate MTC is

Eq.(10)is the same as Harries’model[9,11,12],which is widely accepted in this field.The unit of Sulfate MTC is m·s-1,which is the same as velocity.It can be interpreted that sulfate MTC is the diffusion rate of sulfate across Nernst film [14].

To our best of known,sulfate MTC of anion exchange resin used in condensate polishing system was first derived based on the conventional plug flow reactor model.The derivation is more concise than previous works [5,8] and can be furtherly extended in radial flow mixed resin bed.As presented in Eq.(3),the mass balance is widely acknowledged in plug flow reactor model.It is also easy to be understood in this specific context.Moreover,the mass balance equation can be furtherly extended to radial flow mixed resin bed.It has been demonstrated that MTC of radial flow mixed-bed is essentially the same as that of axial flow mixed-bed [10].In that work,the fluid velocity was introduced in the mass balance equation.Nevertheless,the fluid velocity varied along radial distance in radial flow,which required a more equation to describe it.It would be more convenient to useFrather than fluid velocity becauseFis constant in every differential volume.In summary,plug flow reactor model can concisely describe the mass balance of sulfate in the mixed resin bed and the final expression falls in line with previous reports [5,8,10,14].

4.Results and Discussion

4.1.In-situ calibration

The theoretical κHofsolution is calculated based on the following assumptions:(1)CO2in the mainstream(1 L·min-1)is 0.(2) CO2in the air reaches the dissolved equilibrium with the test solution(0.5 ml·min-1).(3)The effect of pH change on the dissociation of cation exchange resin and the existence of impurities can be ignored.The dissociation equilibriums of carbonates and sulfates can be described as

At 25 °C,Km=1.58 × 10-3,K1=4.47 × 10-7mol·L-1,K2=4.6 8 × 10-11mol·L-1,K=1.10 × 10-2mol·L-1.By Henry’s law,the total carbonates concentrationCT0=1.23 × 10-5mol·L-1when CO2in the air reaches the dissolved equilibrium with pure water.After mixed with the mainstream,CT0in the test solution is diluted to 6.15 × 10-9mol·L-1(CT).Thus,

Combining Eq.(17) and Eq.(18),the concentration of H+,OH-,in differentsolution can be calculated.Referring to the molar conductivity of ions in the infinitely diluted solution,the theoretical κHof 0.5 μg·L-1-50 μg·L-1sulfate solution can be calculated based on the additivity of conductivity.

The theoretical κHand the determined κHof differentsolution are shown in Fig.3.The mean error between them is 8.26% (Table S2).It is inferred that the flow rate and the ionic impurity mainly account for this positive error.The flow rate should be limited to kinetic leakage rather than equilibrium leakage[10].In this study,the flow rate is 122 m·h-1,which is consistent with the field condition.Besides,the ionic impurity in the test solution and the determining system may also introduce error into conductivity determination.The error can be offset by in-situ calibration since the error is systematic rather than random.With the determining column empty,the curve ofand its κHhad been calibrated.By this in-situ way,the influence of the flow rate and the ionic impurity can be offset well.

Fig.3. The theoretical and determined κH of different [SO42-] solution.

4.2.Effect of ammonia on sulfate MTC

The test solution that composed of 0.9 g·L-1Na2SO4and 1.5 mg·L-1ammonia would give a better simulation of field operation.However,whether ammonia is added to the test solution remains to be controversial.To figure out the impact of ammonia on sulfate MTC determination,an ammonia control experiment was designed in this study.Fig.4 compares the determined sulfate MTCs in the presence and absence of ammonia.Comparing the two results,it can be seen that sulfate MTC of control experiment is about 10%lower on average,which indicates smaller mass transfer force of.The result is consistent with previous study and can be attributed to the difference of solution pH [11].The whole ion exchange reaction mainly includes two parts:ion exchange betweenand OH-and then OH--H+neutralization.The solution pH plays a significant role in maintaining H+concentration gradient around anion exchange resin.In the absence of ammonia,OH-exchanged fromwould react immediately with H+in this acid solution.Whereas the solution pH is higher with ammonia,the effective mass transfer force ofis smaller in nature.

Fig.4. Sulfate MTCs in the presence and absence of ammonia in the influent.

Though previous study confirmed the effect of ammonia on the determined sulfate MTC,they failed to investigate the effect of ammonia on method precision.As shown in Fig.4,another important finding is that the relative standard deviation (RSD) of the results is higher in the case of ammonia.This result can be explained by the fact that alkalescent test solution would absorb CO2in the air and produce anionic impurity.This unwanted reaction makes it really hard to ensure the consistency of test solution in every determination.Moreover,ammonia is generally assumed to play a role in sulfate equilibrium leakage [15].With respect to the experimental operability,it is also inconvenient to conduct the experiment in the case of ammonia because of the awful smell of ammonia.Furtherly,this finding broadly supports that it is possible to improve the precision of sulfate MTC determination by controlling test condition.In general,we advise to choose Na2SO4as the test solution.

4.3.Sulfate MTC comparison

Sulfate MTC indicates the kinetic performance of anion exchange resin and can also be used to guide the design of the mixed-bed ion exchange reactor.As can be seen from Fig.4 and Fig.5,the sulfate MTC of A1,A2,A3 and A4 is 1.72 × 10-4m·s-1,1.91 × 10-4m·s-1,2.53 × 10-4m·s-1and 2.60 × 10-4m·s-1,respectively.The raw datum and sulfate MTC calculation of these anion exchange resin samples can be referred to Tables S3.1-S3.4(see Supplementary Material).Among which,A1 and A2 are used in coal-fired power plant.Whereas,A3 and A4 are used in nuclear power plant.Generally speaking,the requirement on MTC of anion exchange resin used in condensate polishing for nuclear power plant is stricter than that for thermal power plant,as we proposed in DL/T 771 [23].The impact of sulfate MTC on the sulfate profiles in the effluent with bed depth is displayed in Fig.5.Sulfate MTC intuitively displays the kinetic performance of anion exchange resin.It clearly shows that the lower sulfate MTC,the worse mixed-bed performance.Among these curves,A3 and A4 are almost in the same trend.This is because their sulfate MTCs are approximately the same.Sulfate MTC can be used to guide the design of ion exchange resin reactor,including the choice of reactor diameter,the type of anion exchange resin and the depth of mixedbed.The concentration of the kinetic leakage ion can be predicted for different MTC if the bed depth of ion exchange resin reactor is known.Once the maximum leakage concentration of the target ion is required,the corresponding bed depth can be calculated for different MTC.What’s more,Fig.5 also reveals that there has been a markeddecrease at the first 0-30 cm,while the decrease rate becomes slighter with increasing bed depth.For economic operation,comprehensive consideration should be taken to choose an appropriate bed depth if kinetic leakage exists.

Fig.5. Sulfate profiles in the effluent with bed depth.

Sulfate MTC can be used to indicate the fouling degree of anion exchange resin since resin fouling is one of the main reason for MTC impairment.Once resin severely fouled,kinetic leakage would happen because of the exchange capacity loss,physical barrier formation and the electrostatic repulsion between counter ion and contaminant [3,14].There are several possible reasons that can result in resin fouling.As compared in Fig.4 and Fig.5,the sulfate MTC sequence of resin samples is A4＞A3＞A2＞A1in this study.Though resin samples are new,synthesis process and storage condition would make a difference.Commercial resin usually contains different content of oligomers,solvents and other soluble impurities.The type and amount of these byproducts are different since the resin synthesis method varies from manufacturer to manufacturer [24].What’s more,the polymer matrix and functional group of anion exchange resin degrade naturally at a certain rate during storage.The degradation product that remains in the resin pore or on the resin surface would impair the kinetic performance of anion exchange resin.This has been supported by the earlier observations that MTC of anion exchange resin decreases linearly with the storage age [14].Besides synthesis process and natural degradation,anion exchange resin may also be contaminated by organic matters during condensate polishing,such as natural organic matters(NOM),corrosion inhibitor and leachables of cation resin.The boiler feed water contains a small amount of NOM like humic and fulvic acid [25].Anion exchange resin is in positive charge and it thus can easily absorb NOM in negative charge [26].Although the concentration of NOM is usually low in the boiler feed water,the contamination would accumulate in the long term.In some cases,lubricants,corrosion preventative coating may get access to the resin unit and foul the resin [12,14].For example,octadecylamine (ODA),one of the film forming amines for corrosion inhibition,could irreversibly impair the kinetic performance of anion exchange resin.It has been confirmed that anion exchange resin exposed to ODA has 18% kinetic capacity loss and only 2%recovery even after regeneration [14].Mixed-bed ion exchange reactor is typically used in condensate polishing system.In mixed-bed,cation exchange resin releases organic leachables because of resin degradation.As a result of heat or oxidation in the operating environment,cation exchange resin would be degraded at a quicker rate and would release more organic leachables than nature degradation [27].Because the opposite charges attract,anion exchange resin would spontaneously absorb the organic leachables.This is an inevitable problem in mixed-bed operation.Moreover,the organic leachables can be decomposed into,which is one of typical corrosive anion[28].Once anionexchange resin fouled,may not be exchanged completely and will leak into the water-steam system.However,this study has not been able to establish the relationship between sulfate MTC decrease and resin fouling degree.Further studies are needed to shed light on anion exchange resin fouling mechanism and sulfate MTC recovery using sulfate MTC as the indicating parameter.

Table 1 Standard deviation of sulfate MTC determination

4.4.Method comparison

The summary statistics for the determined sulfate MTCs are presented in Table 1.Cochran and Grubbs tests found no statistically significant outlier in all the determined sulfate MTCs [19].Thus,standard deviation was calculated based on all the datum.The repeatability standard deviation (Sr) and the reproducibility standard deviation (SR) of each resin sample was calculated(Table 1).Since the standard deviation has no obvious correlation with the MTC,the mean standard deviation of the method is calculated by averaging the standard deviation of each resin.Hence,Srand SRof the determining method are 0.05 × 10-4m·s-1and 0.07 × 10-4m·s-1,respectively (Table 1).

In this paper,the standard deviation is lower than previous works,which indicates that a more precise method for determining sulfate MTC has been established.SrandSRhere are 0.05 × 10-4m·s-1and 0.07 × 10-4m·s-1,respectively.Taking MTC as the benchmark,RSDrand RSDRare 2.3% and 3.2%,respectively.One of the first and seminal study in this area reported that the standard deviation was 0.33×10-4m·s-1for different brand of new anion exchange resin[12].To our best of known,the standard proposed by American Society of Testing Materials (ASTM) probably offered the newest analysis of the precision of MTC determination.In ASTM D6302,the typical reproducibility error (RSDR) had been found to be (2%-8%) [13].Compared with previous works,it can be concluded that our determining method is more precise owing to lower standard deviation.As a determining method,high precision is of great significance.The higher precision is,the more reliable the method is,and the more detailed information can be obtained.

The test condition here is accurately controlled to which we attribute the high precision.The main strength of our method is that the negative impact of CO2and temperature on precision has been minimized.In this study,the test solution without ammonia was chosen.As confirmed in section 4.2 of this paper,the contamination of CO2in the air on the test solution can be eliminated in this way.Besides,the test solution injection bypass(Fig.1) was used here.The test solution was prepared separately and then was injected into the mainstreamviathe injection pump.After mixed by the mixing chamber,the influent of the determining column can be obtained.By separating the mainstream and the injection bypass,the test solution preparation would be more convenient and the negative influence of CO2in the air can be minimized as much as possible.Temperature has great effect on ion exchange reaction and conductivity determination.Thus,it is necessary to control the experimental temperature to be constant.As shown in Fig.1,the determined column made of glass is jacketed.The backflow of circulating pump flows through the jacketed determining column and then returns to the thermostatic water tank.In this way,the temperature of the determining system can be kept at (25.0 ± 0.2) °C,which avoids the influence of temperature change on ion exchange reaction and conductivity determination.Surprisingly,previous studies seemed do not pay enough attention to accurately control this significant factor [12,13,15].

A possible main source of experimental error might be that the determining column was filled as mixed-bed in this study.To simulate the actual condition,the volume ratio of anion resin sample to the standard cation resin was 1:2,which is commonly used in the hydrogen type mixed-bed [29].For mixed-bed,the mixing state of resin cannot be guaranteed to be exactly the same in every determination.There is still a small amount of resin clumping even if the mixing time is long enough.However,those problems also exist in industrial application.In conclusion,our method is more precise than previous reports.

5.Conclusions

Sulfate MTC of anion exchange resin can be used in trouble shooting and operation optimization for mixed-bed ion exchange reactor in condensate polishing system.This study set out with the aim of developing a more precise sulfate MTC determining method.In this paper,sulfate MTC of anion exchange resin in mixed-bed was derived based on plug flow reactor model.The final expression is consistent with the widely accepted Harries’ model.Sulfate MTC determining system was constructed and the precision of sulfate MTC determination was tested.This study demonstrates that it is feasible to improve sulfate MTC determining precision by designing determining system properly and controlling test condition accurately.In general,the present study has developed a more precise sulfate MTC determining method,which will serve as a basis for future research.Further study designing an integrated and portable sulfate MTC determining device would be worthwhile.More broadly,researches are also needed to investigate the mechanism and recovery of kinetic impairment.

Nomenclature

Ainner cross sectional area of determining column,m2

asspecific surface area of resin sample,m2·m-3

fluid phase concentration of sulfate,mol·L-1

bulk fluid phase concentration of sulfate,mol·L-1

liquid-solid interfacial concentration of sulfate,mol·L-1

fluid phase concentration of sulfate in the influent,mol·L-1

fluid phase concentration of sulfate in the effluent,mol·L-1

dpharmonic mean size of resin sample,m

Fvolumetric flow rate,m3·s-1

FRvolumetric fraction of resin sample in mixed-bed,m3·m-3

Hbed depth,m

kf,SO42-mass transfer coefficient of sulfate across Nernst film,m·s-1

qSO42-resin phase concentration of sulfate,mol·L-1

Rradius of resin sample,m

ttime,s

ε bed porosity,m3·m-3

κ0the effluent conductivity while injecting water for preparing solutions,μS·cm-1

κ1the effluent conductivity while injecting test solution,μS·cm-1

κSthe effluent conductivity while injecting sulfate standard solution,μS·cm-1

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.

Appendix A.Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.03.035.