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Design of adsorption column for reclamation ofmethyldiethanolamine using homogeneous surface

diffusion modelPravin Kannan Priyabrata Pal Fawzi Banat

To cite this versionPravin Kannan Priyabrata Pal Fawzi Banat Design of adsorption column for reclamation ofmethyldiethanolamine using homogeneous surface diffusion model Oil amp Gas Science and Technology -Revue drsquoIFP Energies nouvelles Institut Franccedilais du Peacutetrole 2020 75 pp82 102516ogst2020073hal-03018065

Design of adsorption column for reclamation ofmethyldiethanolamine using homogeneous surface diffusion modelPravin Kannan Priyabrata Pal and Fawzi Banat

Department of Chemical Engineering Khalifa University PO Box 127788 Abu Dhabi United Arab Emirates

Received 7 April 2020 Accepted 14 September 2020

Abstract A predictive simulation model was applied to design a fixed-bed adsorber for studying the removalof Total Organic Acid (TOA) anions from lean Methyldiethanolamine (MDEA) solution using CalciumAlginate Bentonite (CAB) clay hybrid composite adsorbent Unlike other conventional techniques typicallyused for packed bed design the predictive Homogeneous Surface Diffusion Model (HSDM) does not requireany test column breakthrough curves a priori Mass transfer coefficients and isotherm model parameters areprovided as input data to HSDM for simulating column breakthrough curves Various isotherm models werefitted to batch equilibrium data for TOA adsorption on CAB composite adsorbent Based on Akaike Informa-tion Criterion (AIC) Freundlich isotherm was selected and the model parameters were obtained by non-linearregression Film transfer coefficients and surface diffusivities were determined using appropriate empirical cor-relations available in the literature HSDM predictions were first validated using lab-scale column adsorptiondata generated at lower residence times The effects of dimensionless numbers (Biot and Stanton) on break-through times were investigated using the dimensionless HSDM system and a suitable scale-up regime(Bi ~ 1 and St gt 10) was established wherein the sensitivity of mass transfer parameters would be minimalUsing similitude rules on key design parameters a pilot-scale adsorption column was designed and break-through curves were generated using the validated HSDM The appropriateness of the design technique wasverified by comparing the estimated breakthrough data and column design parameters with conventionalscale-up and kinetic approaches

1 Introduction

Almost all natural gas has H2S CO2 or both that needs tobe removed before the gas is pumped through transmissionpipelines The sweetening process is carried out using aque-ous Methyldiethanolamine (MDEA 45ndash50 wt) in aregeneration column where heat is applied to strip the acidgas components and recover leanaqueous MDEA solution(Keewan et al 2018 Mehassouel et al 2018 Younas andBanat 2014) However contamination of industrial leanMDEA from heat stable salts such as total organic acids(produced by the reaction between aerial oxygen andCO2H2S) and heavy metal ions like chromium lead etc(produced from the makeup water or due to the metal cor-rosion or erosion caused during the continuous running ofthe plant) always remain a challenge to the gas industry(Cummings et al 2007 Pal et al 2015)

The acidic heat stable salts play a vital role in the regen-eration column acting as enhancers for the strippingprocess On the other hand the presence of HSS (Heat

Stable Salts) in a lean amine solution is detrimental tothe absorption process intended for amine enrichment(Verma and Verma 2009 Weiland 2008) Hence partialremoval of Total Organic Acid (TOA) anions from aqueousamines is crucial for avoiding some operational issuesencountered during natural gas sweetening process Differ-ent methods have been used for the removal of Heat StableSalts (HSS) from amine solvents in natural gas sweeteningunits Currently vacuum distillation electrodialysis ionexchange and adsorption are used for the removal of HSSfrom lean MDEA solutions Adsorption is widely usedamong others and has been in practice for several yearsThe technique is efficient easy to operate and requireslow maintenance cost (Edathil et al 2020) The removalhas mainly been facilitated through the development ofnovel adsorbents including Calcium Alginate Bentonite(CAB) clay composites that serve to remove TOA andmetal ions from lean amine solvents (Pal et al 2013)The oxidative degradation of MDEA produces high concen-trations of organic acid anions that remain as contaminantsin the solvent MDEA contains both amine and hydroxylgroups that adhere strongly to these contaminants therebymaking separation by any available technique largely

Corresponding authors pravinkannankuacaefawzibanatkuacae

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (httpscreativecommonsorglicensesby40)which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) Available online atP Kannan et al published by IFP Energies nouvelles 2020 ogstifpenergiesnouvellesfr

httpsdoiorg102516ogst2020073

REGULAR ARTICLEREGULAR ARTICLE

challenging Calcium alginate biopolymer contains twofunctional groups namely carboxyl and hydroxyl groupsthat serve as adsorption sites and aid in the removal oforganic acid anions from a lean MDEA solution Furtherreinforcing bentonite into the alginate matrix increasesthe mechanical properties density and adsorptiveefficiency (Edathil et al 2018 Pal et al 2019)

However testing the efficiency of the adsorbent in abroad range of process conditions is sometimes not feasibledue to the sensitive nature of MDEA that would otherwisealter the physical properties For instance it is a challengingtask to generate adsorption equilibrium data as any dilutionto lean amine solution would result in significant changes inpH viscosity and other molecular properties that would sig-nificantly affect the stripping tendency of the solventDue to these limitations in adsorbent performance testingreliable simulation capable of accurately modeling thebreakthrough behavior under real plant conditions is imper-ative Such models could be beneficial for scale-up studiesby identifying critical design parameters interpreting lab-scale test results and designing full-scale adsorber

For the design of fixed bed adsorber manymethods havebeen developed that could be categorized into short-cut orscoping methods and rigorous methods (Crittenden andThomas 1998 Patel 2019) Design of fixed-bed adsorptioncolumn by short-cut methods including Mass Transfer ZoneLength (MTZL) model Length of Unused Bed (LUB)Empty Bed Contact Time (EBCT) method Bed DepthService Time (BDST) method Transfer Unit Approach(NTU and HTU) and breakpoint capacity methods requireslab-scale pilot-scale or plant-scale experimentally deter-mined BreakthroughCurve (BTC) data On the other handrigorous methods are based on complex solutions of the con-servation transport and equilibrium relationships Undercertain assumptions a simplified analytical solution (equi-librium and reaction rate models) could be obtained forBTC prediction that is however limited for specific cases

Predictive models on the other hand consider all thesub-processes of film transfer intraparticle diffusion andadsorption kinetics to generate the complete sinusoidalshaped BTC This is achieved by the development ofadvanced numerical techniques that aid in solving the com-plex set of partial differential equations used to describe thecolumn behavior A brief review of literature indicates thatpredictive models have been developed and employed forion exchange and fixed-bed adsorption operations inwastewaterwater treatment (Chowdhury et al 2015Crittenden et al 1986a Hand et al 1984 1989 Hudayaand Rachmat 2019 Srivastava et al 2008) The most com-monly used general rate models are usually considered ascomplete models since they predict the entire breakthroughcurves of the adsorption process (Xu et al 2013) Amongthese the Homogeneous Surface Diffusion Model (HSDM)has been successfully proved and thus is widely used forpredicting the fixed bed adsorber dynamics of many adsor-bateadsorbent systems Generally a complete BTC modelwould constitute the material balance equation the equilib-rium relationship and a set of equations that describe theexternal and internal mass transfer processes Sincedispersion is negligible in typical adsorption process flow

conditions mass balance equation based on plug flow typewas considered The superficial velocity was assumed to beconstant along the bed as removal of trace TOA compo-nents from bulk MDEA solution will pose a negligible effecton material balance It was also assumed that surface diffu-sion is the predominant intraparticle mass transfer mecha-nism and is not a function of local liquid concentrationMany complete BTC models that encompass all three masstransfer processes (film pore and surface diffusion) havebeen reported in the literature (Crittenden et al 1987)These models differ in the assumptions about the flow pro-cesses and mass transfer mechanisms used to describe thecolumn behavior Homogeneous Surface Diffusion Model(HSDM) has been successfully employed to predict thefixed-bed dynamics for many adsorbate-adsorbent systemsreported earlier (Hand et al 1984) Many simulation pack-ages [FAST AdDesignSTM] that have been developedutilize HSDM (dimension and dimensionless forms) alongwith a powerful numerical solver for simultaneously solvingthe complex transport-reaction equations and non-linearadsorption isotherms to predict the breakthrough behaviorof the column satisfactorily Like other predictive modelsHSDM requires minimal equilibrium data on isothermsand mass transfer characteristics that could be sourced fromliterature or through lab-scale experiments

For the mass-transfer controlled process column designcould be solely based on techniques that employ similitudesin mass transfer characteristics A frequently employedmethod for full-scale performance prediction is the RapidSmall-Scale Column Test (RSSCT) that employs scalingrelationships of the design and operational parametersbetween the small-scale and large-scale adsorber By main-taining perfect similarity and using a relatively smalleradsorbent particle the RSSCT would exhibit identicalbreakthrough profiles as the full-scale unit (Crittendenet al 1991) Few other researchers also accomplished simi-larity between scales by maintaining the dimensionalparameters namely solute distribution parameter (Dg)the surface diffusion modulus (Ed = StBi) Stanton num-ber (St) and Reynolds number (Re) (Crittenden et al1986b Hand et al 1983) Equating the dimensionlessparameters of the small-scale and full-scale column mathe-matical equations describing the relationships between thecritical design parameters were established However thederived relationships required varying adsorbent particlediameters between the scales to maintain similitudes Pre-dictive models are more advantageous when constant parti-cle size needs to be maintained between the scales tominimize any operational and hydraulic problems in full-scale unit This is particularly true for some adsorbentmaterials where it is practically impossible to engineer uni-form particle size during synthesis Hence in the scale-up offixed-bed adsorption columns typically particle size andhydraulic loading rate or superficial velocity remainunchanged between the scales However it is not feasibleto keep the velocity fixed during scale-up due to geometricaldesign limitations in LD ratio of the lab-scale column(Inglezakis and Poulopoulos 2006) In fact when highervelocities were used at larger scales it offered increasedadvantages in terms of driving the system to diffusion

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)2

control rather than film control In other words it resultedin higher breakthrough times as film resistances are mini-mized and uniform flow distribution inside the columnAny issues associated with higher velocities like attritionand fluidization could be easily resolved by switching todownflow operation in large-scale unit

Inglezakis and Poulopoulos (2006) have summarized thecritical design parameters and the influence it may have onthe performance of fixed-bed operations As it can be seenfrom Table 1 apart from particle size contact time isanother critical parameter that has a significant effect onbreakthrough times By maintaining similar particle sizeand contact times results from lab-scale studies could bedirectly transferred to plant-scale making the scale-up pro-cedure more simple and precise However contact timesand the resulting breakthrough times encountered in lab-scale are too small and impractical to be employed inplant-scale operations where higher breakthrough timesare desired Therefore apart from other similitude rulesmentioned in Table 1 particle size and superficial velocityare typically maintained constant in the conventionalscale-up techniques

As it can be seen the optimum scale and design dependson several key variables associated with the adsorbent char-acteristics and process variables It can be challenging todetermine the appropriate pilot-scale residence time andloading rates with an experimental method that is basedonly on column breakthrough studies Numerous experi-ments may be required to conclude on the design valuesincluding flow characteristics making the approach costlyand time-consuming Hence an efficient predictive modelin conjunction with dimensionless number(s) that definethe mass transfer behavior would be necessary to ensuresimilitudes during the design process For example columnadsorption process has been successfully modeled by HSDMand characterized using Bi number by several researchers(Hand et al 1983 Lee et al 1983 Smith 1997 Traegnerand Suidan 1989 Wolborska 1999) However in an appli-cation towards adsorption of arsenate and other contami-nants using granular ferric hydroxide filters Sperlich et al(2008) concluded that characterization based on Bi numberalone was not sufficient to completely characterize theHSDM model It was suggested to complement Bi with Stnumber in order to predict the BTC satisfactorily and nodimensionless similarities were required In the currentwork a similar approach has been demonstrated to designa pilot-scale fixed-bed adsorption column for TOA adsorp-tion using CAB particles

Simulation and column design of TOA adsorption fromlean MDEA solutions has never been reported in literaturetill date The objective of the present work is to utilizeHSDM for designing a fixed bed adsorber removing TOApresent in lean MDEA solution A series of lab-scale break-through experiments would be conducted at differenthydraulic loading rates using different sized columns packedwith CAB adsorbent These experiments would serve tovalidate the HSDM results and assess the qualitative fea-tures of the model in terms of breakthrough curves Theoptimum design range would be established based onsensitivity analysis of Bi and St in conjunction with certain

critical design parameter guidelines available in literatureFinally the appropriateness of the design technique wouldbe verified by comparing the scale-independent HSDM pre-dictions with conventional scale-up and kinetic approachesFigure 1 illustrates the overall design methodologyemployed in this work

2 Method description

21 Selection of isotherm model

Equilibrium experiments were performed using a batch sys-tem to generate TOA-CAB adsorbent isotherm data andthe results have been published in the literature (Edathilet al 2020) In this study the batch experimental datawere evaluated with the isotherm models of LangmuirFreundlich Jovanovic Two-step Langmuir Langmuir-Freundlich Fritz-Schlunder and Li and the constants wereobtained by non-linear regression A standard procedure inchoosing an appropriate model equation is based on thevalue of regression coefficient (R2) However regressioncoefficients and other error functions are prone to errorwhen comparing equations with different degrees of free-dom (Daacutevila-Jimeacutenez et al 2014) To overcome this prob-lem Akaike Information Criterion (AIC) was used to rankthe isotherm models since it is more sensitive to model devi-ations and takes into consideration the number of parame-ters in an equilibrium isotherm model unlike other errorfunctions The AIC values for all the models mentionedabove were calculated using the following expression

AIC frac14 N lnSSEN

thorn 2N p thorn 2N pethN p thorn 1THORN

N N p 1 eth1THORN

where N is the number of isotherm data points SSE is thesum of squared residuals and Np is the number of fittedparameters As can be seen AIC takes both accuracyand model complexity into account while regression coef-ficients consider only accuracy as the determining factorFor a given experimental dependent variable response

Table 1 Critical design parameters reproduced fromInglezakis and Poulopoulos (2006)

Parameter Comments

LUs CriticalLdp Minimal effect if it is higher than 150LD Minimal effect if it is greater than 5Ddp Minimal effect if it is higher than 30

and geometrical similarity can be ignoredRep Minimal effect if Ldp gt 150dp CriticalΕ Minimal effect if dpD lt 01Us Minimal effect if solid diffusion is rate-

controlling and if the unit operation is inup-flow mode

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 3

(equilibrium solid concentration) on the independent vari-able (influent concentration) the above-mentioned mod-els with a different number of parameters could be ratedbased on the values of model AICrsquos The particular iso-therm model that exhibits the lowest AIC value wouldbest describe the equilibrium between the adsorbent andadsorbate under consideration

22 Lab-scale column experiments

Adsorbent material properties of CAB adsorbent includingporosity and density were reported in previous works(Edathil et al 2018) Figure 2 presents a schematic ofthe fixed-bed adsorption setup used in this work for theremoval of TOA from lean MDEA solution The adsorptionsystem was designed to treat industrial lean MDEA solu-tion and provide clean MDEA (without TOA) at the outletof the column The system was designed in such a way thatthe same column could be utilized for both adsorption andregeneration Adsorption studies were conducted using dif-ferent borosilicate glass columns (BUCHI Switzerland) ofvarying dimensions (d (cm) h (cm) 15 10 26 1026 23 and 46 23) The column was filled with a knownquantity of 2 CAB adsorbent and then lean MDEA solu-tion of known TOA concentration was pumped through thecolumn using a peristaltic pump at the desired flow rate inan up-flow mode Treated MDEA effluent samples were col-lected from the outlet of the column at definite time inter-vals and the concentration of TOA ions in the effluent wasmeasured using a UV-vis spectrophotometer The operationof the column was stopped once the concentration of TOAions in effluent samples reached the influent concentrationAll adsorption experiments were performed at room tem-perature and an influent pH ~ 105 For the column dimen-sions and flow rates considered in this study the EmptyBed Contact Time (EBCT) varied from 235 min to382 min

23 BTC predictive model

In this work a complete Breakthrough Curve (BTC) modelconsidering both adsorption equilibrium and kinetics wasused to model the real S-shaped BTCs for TOA adsorptionon CAB adsorbents HSDM is simultaneously repre-sented by two partial differential equations that describethe macroscale liquid phase fluid movement over a bed ofadsorbent particles (Eq (2)) and the unsteady state surfacediffusion into the spherical adsorbent particle (Eq (3))

Fig 1 HSDM based fixed-bed adsorber design technique employed in this study

Fig 2 Schematic diagram representing the fixed-bed columnadsorption setup

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)4

epoCot

thorn vfoCot

thorn 3 1 epeth THORN kLrp

C C eth THORN frac14 0 eth2THORN

oqot

frac14 Dso2qor2

thorn 2roqor

eth3THORN

It would be shown later in this study from the AIC criterionanalysis Freundlich isotherm would be the most suitablemodel to describe the isothermal equilibrium between thediluted fluid mass and adsorbed mass in solid phase Thenon-linear temperature-independent Freundlich isothermequation couples the two partial differential equationsthrough the adsorption term of the transport equationWith the non-linear adsorption isotherm embedded itbecomes highly challenging to find an analytical solutionSolutions to the set of PDEs along with the boundaryand initial conditions were obtained using finite differencesmethod as published in literature (Sperlich et al 2008) Allcalculations were performed using the software FAST 20Beta (Fixed-bed Adsorption Simulation Tool) that wasdeveloped originally for water treatment applications

24 Calculation of mass transfer coefficients

In order to estimate the dimensionless numbers severalmodel parameters need to be determined either throughexperiments or through empirical correlations The columnand adsorbent geometric parameters such as particle sizeparticle density (qa) particle porosity (ep) superficial veloc-ity empty bed contact time bed porosity (e) influent ini-tial concentration (C0) were directly measured Filmdiffusion coefficients kL and surface diffusion coefficientsDs were estimated using the Gnielinski correlation whichis a function of Reynolds and Schmidt numbers andSontheimer correlation respectively (Sperlich et al 2008)

kL frac14 1thorn 15 1 eeth THORNfrac12 DdP

2thorn 0644Re1=2Sc1=3

eth4THORN

Ds frac14 DepC 0

spqaq0 SPDFR eth5THORN

In the above equations D represents molecular diffusivityand is calculated as

D frac14 1326 1005

g114 V b0589 eth6THORN

where g is kinematic viscosity Vb is normal molar vol-ume sp is tortuosity (set to 1) q0 is equilibrium loadingand SPDFR is the surface to pore diffusion flux ratio

25 HSDM model validation

HSDM can be satisfactorily used to predict breakthroughcurves for different adsorption column sizes and flow condi-tions without any experimental data a priori However inorder to establish reliability and confidence over the chosenisotherm model and mass transfer correlations HSDM pre-dictions were first compared to lab-scale experimental datagenerated using different sized adsorption columns and flowrates with CAB adsorbent of 1 mm particle size Five differ-ent adsorption column experiments were designed repre-senting varying residence times The bed porosity wasmaintained between 035 and 05 by adjusting the mass ofadsorbent loaded into the column Experiments were runusing lean MDEA with an initial concentration of 3250ndash3500 ppm and breakthrough data were recorded as a func-tion of residence time The corresponding Biot and Stantonnumbers have also been shown in Table 2 along with otherprocess conditions The same feed and process conditionswere provided as input to the HSDMmodel and simulations

Table 2 Column parameters used in HSDM validation study

Parameter Test 1 Test 2 Test 3 Test 4 Test 5

Height L (cm) 10 10 23 23 23Bed diameter D (cm) 15 26 46 26 46Intraparticle porosity e 085 085 085 085 085Bed porosity eb 048 046 035 045 036Particle diameter dp (mm) 1 1 1 1 1Particle density qp (gcc) 104 104 104 104 104Equivalent bed mass M (g) 9 29 255 70 255MDEA flow rate Q (mLmin) 075 075 43 075 1Empty bed contact time (min) 235 71 89 163 382Superficial velocity Us (cmmin) 042 014 026 014 006Residence time T (min) 845 254 34 58 137Freundlich coefficient KF ((mgg)(Lmg)n) 00015 00015 00015 00015 00015Freundlich exponent n 08 08 08 08 08Film mass transfer coefficient kL (cms) 69E-05 48E-05 53E-05 48E-05 51E-05Surface diffusion coefficient Ds (cm

2s) 24E-06 24E-06 24E-06 24E-06 24E-06Stanton number St 11 24 37 56 105Biot number Bi 107 076 097 076 061

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 5

were performed to predict the complete breakthroughcurves Instead of comparing CCo at certain points HSDMsimulation provides a way to compare the entire BTCwhich is significant in establishing similarities in flowpattern between scales

26 Sensitivity analysis

To investigate the effect of these dimensionless numbers onbreakthrough curves Peacuterez-Foguet et al developed adimensionless analysis of HSDM (Peacuterez-Foguet et al2013) The macroscale liquid phase mass transport equationand the intraparticle diffusion equation were transformedinto a dimensionless form using dimensionless variablesfor the liquid and solid phase concentration axial positionand contact time The derivation of the dimensionlessmodel equations and the corresponding boundary andinitial conditions could be found elsewhere (Sperlich et al2008) The two characteristic partial differential equationsof the HSDM were transformed into a system of two ordi-nary differential equations coupled with the macroscaletransport-reaction PDE Discretization was accomplishedusing a discontinuous Galerkin scheme and the overall sys-tem evolution was integrated with a time-marching schemebased on the forward Euler method The overall system wassuccessfully used to simulate the adsorption of differentadsorbates on granular ferric hydroxide

The detailed dimensionless analysis of HSDM presentedby Peacuterez-Foguet et al (2013) facilitates establishing limitbehavior of the model to determine the values of Bi andSt number (Peacuterez-Foguet et al 2013) The influence ofdimensionless numbers including Bi St Ed Dg and n onthe breakthrough curves was thoroughly assessed usingthe dimensionless HSDM Excerpts from this work havebeen presented in Section 33 and the results have beendirectly applied to determine the working range of Bi andSt numbers

Design parameters from this technique were comparedwith direct scale-up and kinetic approaches Details of thesetwo conventional techniques including key equations havebeen summarized in the Supplementary Section

3 Results and discussion

31 Equilibrium studies

Different isotherm models were fitted to batch equilibriumdata and the model parameters were determined by non-lin-ear regression Equilibrium isotherms for TOA adsorptionon CAB adsorbents have been presented in the Supplemen-tary Section see Figure S1 Figure 3 shows the comparisonof simulated data from various models with batch equilib-rium data obtained by varying adsorbent mass at 23 Cand Table 3 shows the regressed model parameters andthe corresponding AIC values for different isotherm modelsIt can be noticed that the Freundlich model exhibited theleast AIC value indicating the best fit with experimentaldata Hence Freundlich model was incorporated into theHSDM model to describe the equilibrium behavior betweenthe solute present in the liquid and solid phases

32 HSDM model validation

Figure 4 shows a comparison plot of normalized concentra-tion against adsorption time between lab-scale experimen-tal data and HSDM predictions for different residencetimes An inset has been provided in order to better visual-ize the dynamics at early adsorption times As shown inFigure 4 HSDM is able to capture the overall processdynamics described by the ldquoSrdquo shaped curve for all theHRTrsquos considered Also the general trend in BTC time-shift with varying HRTs was predicted reasonably well bythe HSDM On comparison of simulated BTCs with exper-imental data in Figure 4 some discrepancies are evidentespecially for the case of HRT = 137 min Many differentfactors influence the shape of the BTCs primarily the val-ues of mass transfer coefficients employed in the HSDMThe sensitivity of these coefficients has been analyzed viatwo dimensionless parameters namely Bi and St numbersAs outlined in Section 33 and in the range of Bi values con-sidered St remains a significant parameter in determiningBTC dynamics However in order to minimize the discrep-ancies between experimental data and simulation the coef-ficients should be determined accurately from controlledbatch experiments rather than from empirical correlationsOther known possible factors that influence BTC dynamicsinclude HSDM assumptions concerning negligible pore dif-fusion and unaccounted experimental factors like backpres-sure and influent pumping issues encountered duringcolumn experiments Nevertheless as shown in this studyHSDM could be employed for the rapid design of theadsorption column where the application of othertechniques is severely challenged by the inherent depen-dency on experimental data

33 Sensitivity analysis

Sensitivity analysis on the dimensionless numbers providesknowledge on the variation of column breakthrough behav-ior in different scales Breakthrough curves were predictedfor ranges of St and Bi numbers to understand the masstransfer behavior at different process conditions The

Fig 3 Comparison of batch equilibrium data with variousisotherm models (legend details Exp ndash experimental JC ndash

Jovononic FR ndash Freundlich L-F ndash Langmuir-Freundlich 2sL ndash

2 step-Langmuir F-S ndash Fritz-Schlunder Lang ndash Langmuir)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)6

control rather than film control In other words it resultedin higher breakthrough times as film resistances are mini-mized and uniform flow distribution inside the columnAny issues associated with higher velocities like attritionand fluidization could be easily resolved by switching todownflow operation in large-scale unit

Inglezakis and Poulopoulos (2006) have summarized thecritical design parameters and the influence it may have onthe performance of fixed-bed operations As it can be seenfrom Table 1 apart from particle size contact time isanother critical parameter that has a significant effect onbreakthrough times By maintaining similar particle sizeand contact times results from lab-scale studies could bedirectly transferred to plant-scale making the scale-up pro-cedure more simple and precise However contact timesand the resulting breakthrough times encountered in lab-scale are too small and impractical to be employed inplant-scale operations where higher breakthrough timesare desired Therefore apart from other similitude rulesmentioned in Table 1 particle size and superficial velocityare typically maintained constant in the conventionalscale-up techniques

As it can be seen the optimum scale and design dependson several key variables associated with the adsorbent char-acteristics and process variables It can be challenging todetermine the appropriate pilot-scale residence time andloading rates with an experimental method that is basedonly on column breakthrough studies Numerous experi-ments may be required to conclude on the design valuesincluding flow characteristics making the approach costlyand time-consuming Hence an efficient predictive modelin conjunction with dimensionless number(s) that definethe mass transfer behavior would be necessary to ensuresimilitudes during the design process For example columnadsorption process has been successfully modeled by HSDMand characterized using Bi number by several researchers(Hand et al 1983 Lee et al 1983 Smith 1997 Traegnerand Suidan 1989 Wolborska 1999) However in an appli-cation towards adsorption of arsenate and other contami-nants using granular ferric hydroxide filters Sperlich et al(2008) concluded that characterization based on Bi numberalone was not sufficient to completely characterize theHSDM model It was suggested to complement Bi with Stnumber in order to predict the BTC satisfactorily and nodimensionless similarities were required In the currentwork a similar approach has been demonstrated to designa pilot-scale fixed-bed adsorption column for TOA adsorp-tion using CAB particles

Simulation and column design of TOA adsorption fromlean MDEA solutions has never been reported in literaturetill date The objective of the present work is to utilizeHSDM for designing a fixed bed adsorber removing TOApresent in lean MDEA solution A series of lab-scale break-through experiments would be conducted at differenthydraulic loading rates using different sized columns packedwith CAB adsorbent These experiments would serve tovalidate the HSDM results and assess the qualitative fea-tures of the model in terms of breakthrough curves Theoptimum design range would be established based onsensitivity analysis of Bi and St in conjunction with certain

critical design parameter guidelines available in literatureFinally the appropriateness of the design technique wouldbe verified by comparing the scale-independent HSDM pre-dictions with conventional scale-up and kinetic approachesFigure 1 illustrates the overall design methodologyemployed in this work

2 Method description

21 Selection of isotherm model

Equilibrium experiments were performed using a batch sys-tem to generate TOA-CAB adsorbent isotherm data andthe results have been published in the literature (Edathilet al 2020) In this study the batch experimental datawere evaluated with the isotherm models of LangmuirFreundlich Jovanovic Two-step Langmuir Langmuir-Freundlich Fritz-Schlunder and Li and the constants wereobtained by non-linear regression A standard procedure inchoosing an appropriate model equation is based on thevalue of regression coefficient (R2) However regressioncoefficients and other error functions are prone to errorwhen comparing equations with different degrees of free-dom (Daacutevila-Jimeacutenez et al 2014) To overcome this prob-lem Akaike Information Criterion (AIC) was used to rankthe isotherm models since it is more sensitive to model devi-ations and takes into consideration the number of parame-ters in an equilibrium isotherm model unlike other errorfunctions The AIC values for all the models mentionedabove were calculated using the following expression

AIC frac14 N lnSSEN

thorn 2N p thorn 2N pethN p thorn 1THORN

N N p 1 eth1THORN

where N is the number of isotherm data points SSE is thesum of squared residuals and Np is the number of fittedparameters As can be seen AIC takes both accuracyand model complexity into account while regression coef-ficients consider only accuracy as the determining factorFor a given experimental dependent variable response

Table 1 Critical design parameters reproduced fromInglezakis and Poulopoulos (2006)

Parameter Comments

LUs CriticalLdp Minimal effect if it is higher than 150LD Minimal effect if it is greater than 5Ddp Minimal effect if it is higher than 30

and geometrical similarity can be ignoredRep Minimal effect if Ldp gt 150dp CriticalΕ Minimal effect if dpD lt 01Us Minimal effect if solid diffusion is rate-

controlling and if the unit operation is inup-flow mode

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 3

(equilibrium solid concentration) on the independent vari-able (influent concentration) the above-mentioned mod-els with a different number of parameters could be ratedbased on the values of model AICrsquos The particular iso-therm model that exhibits the lowest AIC value wouldbest describe the equilibrium between the adsorbent andadsorbate under consideration

22 Lab-scale column experiments

Adsorbent material properties of CAB adsorbent includingporosity and density were reported in previous works(Edathil et al 2018) Figure 2 presents a schematic ofthe fixed-bed adsorption setup used in this work for theremoval of TOA from lean MDEA solution The adsorptionsystem was designed to treat industrial lean MDEA solu-tion and provide clean MDEA (without TOA) at the outletof the column The system was designed in such a way thatthe same column could be utilized for both adsorption andregeneration Adsorption studies were conducted using dif-ferent borosilicate glass columns (BUCHI Switzerland) ofvarying dimensions (d (cm) h (cm) 15 10 26 1026 23 and 46 23) The column was filled with a knownquantity of 2 CAB adsorbent and then lean MDEA solu-tion of known TOA concentration was pumped through thecolumn using a peristaltic pump at the desired flow rate inan up-flow mode Treated MDEA effluent samples were col-lected from the outlet of the column at definite time inter-vals and the concentration of TOA ions in the effluent wasmeasured using a UV-vis spectrophotometer The operationof the column was stopped once the concentration of TOAions in effluent samples reached the influent concentrationAll adsorption experiments were performed at room tem-perature and an influent pH ~ 105 For the column dimen-sions and flow rates considered in this study the EmptyBed Contact Time (EBCT) varied from 235 min to382 min

23 BTC predictive model

In this work a complete Breakthrough Curve (BTC) modelconsidering both adsorption equilibrium and kinetics wasused to model the real S-shaped BTCs for TOA adsorptionon CAB adsorbents HSDM is simultaneously repre-sented by two partial differential equations that describethe macroscale liquid phase fluid movement over a bed ofadsorbent particles (Eq (2)) and the unsteady state surfacediffusion into the spherical adsorbent particle (Eq (3))

Fig 1 HSDM based fixed-bed adsorber design technique employed in this study

Fig 2 Schematic diagram representing the fixed-bed columnadsorption setup

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)4

epoCot

thorn vfoCot

thorn 3 1 epeth THORN kLrp

C C eth THORN frac14 0 eth2THORN

oqot

frac14 Dso2qor2

thorn 2roqor

eth3THORN

It would be shown later in this study from the AIC criterionanalysis Freundlich isotherm would be the most suitablemodel to describe the isothermal equilibrium between thediluted fluid mass and adsorbed mass in solid phase Thenon-linear temperature-independent Freundlich isothermequation couples the two partial differential equationsthrough the adsorption term of the transport equationWith the non-linear adsorption isotherm embedded itbecomes highly challenging to find an analytical solutionSolutions to the set of PDEs along with the boundaryand initial conditions were obtained using finite differencesmethod as published in literature (Sperlich et al 2008) Allcalculations were performed using the software FAST 20Beta (Fixed-bed Adsorption Simulation Tool) that wasdeveloped originally for water treatment applications

24 Calculation of mass transfer coefficients

In order to estimate the dimensionless numbers severalmodel parameters need to be determined either throughexperiments or through empirical correlations The columnand adsorbent geometric parameters such as particle sizeparticle density (qa) particle porosity (ep) superficial veloc-ity empty bed contact time bed porosity (e) influent ini-tial concentration (C0) were directly measured Filmdiffusion coefficients kL and surface diffusion coefficientsDs were estimated using the Gnielinski correlation whichis a function of Reynolds and Schmidt numbers andSontheimer correlation respectively (Sperlich et al 2008)

kL frac14 1thorn 15 1 eeth THORNfrac12 DdP

2thorn 0644Re1=2Sc1=3

eth4THORN

Ds frac14 DepC 0

spqaq0 SPDFR eth5THORN

In the above equations D represents molecular diffusivityand is calculated as

D frac14 1326 1005

g114 V b0589 eth6THORN

where g is kinematic viscosity Vb is normal molar vol-ume sp is tortuosity (set to 1) q0 is equilibrium loadingand SPDFR is the surface to pore diffusion flux ratio

25 HSDM model validation

HSDM can be satisfactorily used to predict breakthroughcurves for different adsorption column sizes and flow condi-tions without any experimental data a priori However inorder to establish reliability and confidence over the chosenisotherm model and mass transfer correlations HSDM pre-dictions were first compared to lab-scale experimental datagenerated using different sized adsorption columns and flowrates with CAB adsorbent of 1 mm particle size Five differ-ent adsorption column experiments were designed repre-senting varying residence times The bed porosity wasmaintained between 035 and 05 by adjusting the mass ofadsorbent loaded into the column Experiments were runusing lean MDEA with an initial concentration of 3250ndash3500 ppm and breakthrough data were recorded as a func-tion of residence time The corresponding Biot and Stantonnumbers have also been shown in Table 2 along with otherprocess conditions The same feed and process conditionswere provided as input to the HSDMmodel and simulations

Table 2 Column parameters used in HSDM validation study

Parameter Test 1 Test 2 Test 3 Test 4 Test 5

Height L (cm) 10 10 23 23 23Bed diameter D (cm) 15 26 46 26 46Intraparticle porosity e 085 085 085 085 085Bed porosity eb 048 046 035 045 036Particle diameter dp (mm) 1 1 1 1 1Particle density qp (gcc) 104 104 104 104 104Equivalent bed mass M (g) 9 29 255 70 255MDEA flow rate Q (mLmin) 075 075 43 075 1Empty bed contact time (min) 235 71 89 163 382Superficial velocity Us (cmmin) 042 014 026 014 006Residence time T (min) 845 254 34 58 137Freundlich coefficient KF ((mgg)(Lmg)n) 00015 00015 00015 00015 00015Freundlich exponent n 08 08 08 08 08Film mass transfer coefficient kL (cms) 69E-05 48E-05 53E-05 48E-05 51E-05Surface diffusion coefficient Ds (cm

2s) 24E-06 24E-06 24E-06 24E-06 24E-06Stanton number St 11 24 37 56 105Biot number Bi 107 076 097 076 061

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 5

were performed to predict the complete breakthroughcurves Instead of comparing CCo at certain points HSDMsimulation provides a way to compare the entire BTCwhich is significant in establishing similarities in flowpattern between scales

26 Sensitivity analysis

To investigate the effect of these dimensionless numbers onbreakthrough curves Peacuterez-Foguet et al developed adimensionless analysis of HSDM (Peacuterez-Foguet et al2013) The macroscale liquid phase mass transport equationand the intraparticle diffusion equation were transformedinto a dimensionless form using dimensionless variablesfor the liquid and solid phase concentration axial positionand contact time The derivation of the dimensionlessmodel equations and the corresponding boundary andinitial conditions could be found elsewhere (Sperlich et al2008) The two characteristic partial differential equationsof the HSDM were transformed into a system of two ordi-nary differential equations coupled with the macroscaletransport-reaction PDE Discretization was accomplishedusing a discontinuous Galerkin scheme and the overall sys-tem evolution was integrated with a time-marching schemebased on the forward Euler method The overall system wassuccessfully used to simulate the adsorption of differentadsorbates on granular ferric hydroxide

The detailed dimensionless analysis of HSDM presentedby Peacuterez-Foguet et al (2013) facilitates establishing limitbehavior of the model to determine the values of Bi andSt number (Peacuterez-Foguet et al 2013) The influence ofdimensionless numbers including Bi St Ed Dg and n onthe breakthrough curves was thoroughly assessed usingthe dimensionless HSDM Excerpts from this work havebeen presented in Section 33 and the results have beendirectly applied to determine the working range of Bi andSt numbers

Design parameters from this technique were comparedwith direct scale-up and kinetic approaches Details of thesetwo conventional techniques including key equations havebeen summarized in the Supplementary Section

3 Results and discussion

31 Equilibrium studies

Different isotherm models were fitted to batch equilibriumdata and the model parameters were determined by non-lin-ear regression Equilibrium isotherms for TOA adsorptionon CAB adsorbents have been presented in the Supplemen-tary Section see Figure S1 Figure 3 shows the comparisonof simulated data from various models with batch equilib-rium data obtained by varying adsorbent mass at 23 Cand Table 3 shows the regressed model parameters andthe corresponding AIC values for different isotherm modelsIt can be noticed that the Freundlich model exhibited theleast AIC value indicating the best fit with experimentaldata Hence Freundlich model was incorporated into theHSDM model to describe the equilibrium behavior betweenthe solute present in the liquid and solid phases

32 HSDM model validation

Figure 4 shows a comparison plot of normalized concentra-tion against adsorption time between lab-scale experimen-tal data and HSDM predictions for different residencetimes An inset has been provided in order to better visual-ize the dynamics at early adsorption times As shown inFigure 4 HSDM is able to capture the overall processdynamics described by the ldquoSrdquo shaped curve for all theHRTrsquos considered Also the general trend in BTC time-shift with varying HRTs was predicted reasonably well bythe HSDM On comparison of simulated BTCs with exper-imental data in Figure 4 some discrepancies are evidentespecially for the case of HRT = 137 min Many differentfactors influence the shape of the BTCs primarily the val-ues of mass transfer coefficients employed in the HSDMThe sensitivity of these coefficients has been analyzed viatwo dimensionless parameters namely Bi and St numbersAs outlined in Section 33 and in the range of Bi values con-sidered St remains a significant parameter in determiningBTC dynamics However in order to minimize the discrep-ancies between experimental data and simulation the coef-ficients should be determined accurately from controlledbatch experiments rather than from empirical correlationsOther known possible factors that influence BTC dynamicsinclude HSDM assumptions concerning negligible pore dif-fusion and unaccounted experimental factors like backpres-sure and influent pumping issues encountered duringcolumn experiments Nevertheless as shown in this studyHSDM could be employed for the rapid design of theadsorption column where the application of othertechniques is severely challenged by the inherent depen-dency on experimental data

33 Sensitivity analysis

Sensitivity analysis on the dimensionless numbers providesknowledge on the variation of column breakthrough behav-ior in different scales Breakthrough curves were predictedfor ranges of St and Bi numbers to understand the masstransfer behavior at different process conditions The

Fig 3 Comparison of batch equilibrium data with variousisotherm models (legend details Exp ndash experimental JC ndash

Jovononic FR ndash Freundlich L-F ndash Langmuir-Freundlich 2sL ndash

2 step-Langmuir F-S ndash Fritz-Schlunder Lang ndash Langmuir)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)6

(equilibrium solid concentration) on the independent vari-able (influent concentration) the above-mentioned mod-els with a different number of parameters could be ratedbased on the values of model AICrsquos The particular iso-therm model that exhibits the lowest AIC value wouldbest describe the equilibrium between the adsorbent andadsorbate under consideration

22 Lab-scale column experiments

Adsorbent material properties of CAB adsorbent includingporosity and density were reported in previous works(Edathil et al 2018) Figure 2 presents a schematic ofthe fixed-bed adsorption setup used in this work for theremoval of TOA from lean MDEA solution The adsorptionsystem was designed to treat industrial lean MDEA solu-tion and provide clean MDEA (without TOA) at the outletof the column The system was designed in such a way thatthe same column could be utilized for both adsorption andregeneration Adsorption studies were conducted using dif-ferent borosilicate glass columns (BUCHI Switzerland) ofvarying dimensions (d (cm) h (cm) 15 10 26 1026 23 and 46 23) The column was filled with a knownquantity of 2 CAB adsorbent and then lean MDEA solu-tion of known TOA concentration was pumped through thecolumn using a peristaltic pump at the desired flow rate inan up-flow mode Treated MDEA effluent samples were col-lected from the outlet of the column at definite time inter-vals and the concentration of TOA ions in the effluent wasmeasured using a UV-vis spectrophotometer The operationof the column was stopped once the concentration of TOAions in effluent samples reached the influent concentrationAll adsorption experiments were performed at room tem-perature and an influent pH ~ 105 For the column dimen-sions and flow rates considered in this study the EmptyBed Contact Time (EBCT) varied from 235 min to382 min

23 BTC predictive model

In this work a complete Breakthrough Curve (BTC) modelconsidering both adsorption equilibrium and kinetics wasused to model the real S-shaped BTCs for TOA adsorptionon CAB adsorbents HSDM is simultaneously repre-sented by two partial differential equations that describethe macroscale liquid phase fluid movement over a bed ofadsorbent particles (Eq (2)) and the unsteady state surfacediffusion into the spherical adsorbent particle (Eq (3))

Fig 1 HSDM based fixed-bed adsorber design technique employed in this study

Fig 2 Schematic diagram representing the fixed-bed columnadsorption setup

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)4

epoCot

thorn vfoCot

thorn 3 1 epeth THORN kLrp

C C eth THORN frac14 0 eth2THORN

oqot

frac14 Dso2qor2

thorn 2roqor

eth3THORN

It would be shown later in this study from the AIC criterionanalysis Freundlich isotherm would be the most suitablemodel to describe the isothermal equilibrium between thediluted fluid mass and adsorbed mass in solid phase Thenon-linear temperature-independent Freundlich isothermequation couples the two partial differential equationsthrough the adsorption term of the transport equationWith the non-linear adsorption isotherm embedded itbecomes highly challenging to find an analytical solutionSolutions to the set of PDEs along with the boundaryand initial conditions were obtained using finite differencesmethod as published in literature (Sperlich et al 2008) Allcalculations were performed using the software FAST 20Beta (Fixed-bed Adsorption Simulation Tool) that wasdeveloped originally for water treatment applications

24 Calculation of mass transfer coefficients

In order to estimate the dimensionless numbers severalmodel parameters need to be determined either throughexperiments or through empirical correlations The columnand adsorbent geometric parameters such as particle sizeparticle density (qa) particle porosity (ep) superficial veloc-ity empty bed contact time bed porosity (e) influent ini-tial concentration (C0) were directly measured Filmdiffusion coefficients kL and surface diffusion coefficientsDs were estimated using the Gnielinski correlation whichis a function of Reynolds and Schmidt numbers andSontheimer correlation respectively (Sperlich et al 2008)

kL frac14 1thorn 15 1 eeth THORNfrac12 DdP

2thorn 0644Re1=2Sc1=3

eth4THORN

Ds frac14 DepC 0

spqaq0 SPDFR eth5THORN

In the above equations D represents molecular diffusivityand is calculated as

D frac14 1326 1005

g114 V b0589 eth6THORN

where g is kinematic viscosity Vb is normal molar vol-ume sp is tortuosity (set to 1) q0 is equilibrium loadingand SPDFR is the surface to pore diffusion flux ratio

25 HSDM model validation

HSDM can be satisfactorily used to predict breakthroughcurves for different adsorption column sizes and flow condi-tions without any experimental data a priori However inorder to establish reliability and confidence over the chosenisotherm model and mass transfer correlations HSDM pre-dictions were first compared to lab-scale experimental datagenerated using different sized adsorption columns and flowrates with CAB adsorbent of 1 mm particle size Five differ-ent adsorption column experiments were designed repre-senting varying residence times The bed porosity wasmaintained between 035 and 05 by adjusting the mass ofadsorbent loaded into the column Experiments were runusing lean MDEA with an initial concentration of 3250ndash3500 ppm and breakthrough data were recorded as a func-tion of residence time The corresponding Biot and Stantonnumbers have also been shown in Table 2 along with otherprocess conditions The same feed and process conditionswere provided as input to the HSDMmodel and simulations

Table 2 Column parameters used in HSDM validation study

Parameter Test 1 Test 2 Test 3 Test 4 Test 5

Height L (cm) 10 10 23 23 23Bed diameter D (cm) 15 26 46 26 46Intraparticle porosity e 085 085 085 085 085Bed porosity eb 048 046 035 045 036Particle diameter dp (mm) 1 1 1 1 1Particle density qp (gcc) 104 104 104 104 104Equivalent bed mass M (g) 9 29 255 70 255MDEA flow rate Q (mLmin) 075 075 43 075 1Empty bed contact time (min) 235 71 89 163 382Superficial velocity Us (cmmin) 042 014 026 014 006Residence time T (min) 845 254 34 58 137Freundlich coefficient KF ((mgg)(Lmg)n) 00015 00015 00015 00015 00015Freundlich exponent n 08 08 08 08 08Film mass transfer coefficient kL (cms) 69E-05 48E-05 53E-05 48E-05 51E-05Surface diffusion coefficient Ds (cm

2s) 24E-06 24E-06 24E-06 24E-06 24E-06Stanton number St 11 24 37 56 105Biot number Bi 107 076 097 076 061

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 5

were performed to predict the complete breakthroughcurves Instead of comparing CCo at certain points HSDMsimulation provides a way to compare the entire BTCwhich is significant in establishing similarities in flowpattern between scales

26 Sensitivity analysis

To investigate the effect of these dimensionless numbers onbreakthrough curves Peacuterez-Foguet et al developed adimensionless analysis of HSDM (Peacuterez-Foguet et al2013) The macroscale liquid phase mass transport equationand the intraparticle diffusion equation were transformedinto a dimensionless form using dimensionless variablesfor the liquid and solid phase concentration axial positionand contact time The derivation of the dimensionlessmodel equations and the corresponding boundary andinitial conditions could be found elsewhere (Sperlich et al2008) The two characteristic partial differential equationsof the HSDM were transformed into a system of two ordi-nary differential equations coupled with the macroscaletransport-reaction PDE Discretization was accomplishedusing a discontinuous Galerkin scheme and the overall sys-tem evolution was integrated with a time-marching schemebased on the forward Euler method The overall system wassuccessfully used to simulate the adsorption of differentadsorbates on granular ferric hydroxide

The detailed dimensionless analysis of HSDM presentedby Peacuterez-Foguet et al (2013) facilitates establishing limitbehavior of the model to determine the values of Bi andSt number (Peacuterez-Foguet et al 2013) The influence ofdimensionless numbers including Bi St Ed Dg and n onthe breakthrough curves was thoroughly assessed usingthe dimensionless HSDM Excerpts from this work havebeen presented in Section 33 and the results have beendirectly applied to determine the working range of Bi andSt numbers

Design parameters from this technique were comparedwith direct scale-up and kinetic approaches Details of thesetwo conventional techniques including key equations havebeen summarized in the Supplementary Section

3 Results and discussion

31 Equilibrium studies

Different isotherm models were fitted to batch equilibriumdata and the model parameters were determined by non-lin-ear regression Equilibrium isotherms for TOA adsorptionon CAB adsorbents have been presented in the Supplemen-tary Section see Figure S1 Figure 3 shows the comparisonof simulated data from various models with batch equilib-rium data obtained by varying adsorbent mass at 23 Cand Table 3 shows the regressed model parameters andthe corresponding AIC values for different isotherm modelsIt can be noticed that the Freundlich model exhibited theleast AIC value indicating the best fit with experimentaldata Hence Freundlich model was incorporated into theHSDM model to describe the equilibrium behavior betweenthe solute present in the liquid and solid phases

32 HSDM model validation

Figure 4 shows a comparison plot of normalized concentra-tion against adsorption time between lab-scale experimen-tal data and HSDM predictions for different residencetimes An inset has been provided in order to better visual-ize the dynamics at early adsorption times As shown inFigure 4 HSDM is able to capture the overall processdynamics described by the ldquoSrdquo shaped curve for all theHRTrsquos considered Also the general trend in BTC time-shift with varying HRTs was predicted reasonably well bythe HSDM On comparison of simulated BTCs with exper-imental data in Figure 4 some discrepancies are evidentespecially for the case of HRT = 137 min Many differentfactors influence the shape of the BTCs primarily the val-ues of mass transfer coefficients employed in the HSDMThe sensitivity of these coefficients has been analyzed viatwo dimensionless parameters namely Bi and St numbersAs outlined in Section 33 and in the range of Bi values con-sidered St remains a significant parameter in determiningBTC dynamics However in order to minimize the discrep-ancies between experimental data and simulation the coef-ficients should be determined accurately from controlledbatch experiments rather than from empirical correlationsOther known possible factors that influence BTC dynamicsinclude HSDM assumptions concerning negligible pore dif-fusion and unaccounted experimental factors like backpres-sure and influent pumping issues encountered duringcolumn experiments Nevertheless as shown in this studyHSDM could be employed for the rapid design of theadsorption column where the application of othertechniques is severely challenged by the inherent depen-dency on experimental data

33 Sensitivity analysis

Sensitivity analysis on the dimensionless numbers providesknowledge on the variation of column breakthrough behav-ior in different scales Breakthrough curves were predictedfor ranges of St and Bi numbers to understand the masstransfer behavior at different process conditions The

Fig 3 Comparison of batch equilibrium data with variousisotherm models (legend details Exp ndash experimental JC ndash

Jovononic FR ndash Freundlich L-F ndash Langmuir-Freundlich 2sL ndash

2 step-Langmuir F-S ndash Fritz-Schlunder Lang ndash Langmuir)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)6

epoCot

thorn vfoCot

thorn 3 1 epeth THORN kLrp

C C eth THORN frac14 0 eth2THORN

oqot

frac14 Dso2qor2

thorn 2roqor

eth3THORN

It would be shown later in this study from the AIC criterionanalysis Freundlich isotherm would be the most suitablemodel to describe the isothermal equilibrium between thediluted fluid mass and adsorbed mass in solid phase Thenon-linear temperature-independent Freundlich isothermequation couples the two partial differential equationsthrough the adsorption term of the transport equationWith the non-linear adsorption isotherm embedded itbecomes highly challenging to find an analytical solutionSolutions to the set of PDEs along with the boundaryand initial conditions were obtained using finite differencesmethod as published in literature (Sperlich et al 2008) Allcalculations were performed using the software FAST 20Beta (Fixed-bed Adsorption Simulation Tool) that wasdeveloped originally for water treatment applications

24 Calculation of mass transfer coefficients

In order to estimate the dimensionless numbers severalmodel parameters need to be determined either throughexperiments or through empirical correlations The columnand adsorbent geometric parameters such as particle sizeparticle density (qa) particle porosity (ep) superficial veloc-ity empty bed contact time bed porosity (e) influent ini-tial concentration (C0) were directly measured Filmdiffusion coefficients kL and surface diffusion coefficientsDs were estimated using the Gnielinski correlation whichis a function of Reynolds and Schmidt numbers andSontheimer correlation respectively (Sperlich et al 2008)

kL frac14 1thorn 15 1 eeth THORNfrac12 DdP

2thorn 0644Re1=2Sc1=3

eth4THORN

Ds frac14 DepC 0

spqaq0 SPDFR eth5THORN

In the above equations D represents molecular diffusivityand is calculated as

D frac14 1326 1005

g114 V b0589 eth6THORN

where g is kinematic viscosity Vb is normal molar vol-ume sp is tortuosity (set to 1) q0 is equilibrium loadingand SPDFR is the surface to pore diffusion flux ratio

25 HSDM model validation

HSDM can be satisfactorily used to predict breakthroughcurves for different adsorption column sizes and flow condi-tions without any experimental data a priori However inorder to establish reliability and confidence over the chosenisotherm model and mass transfer correlations HSDM pre-dictions were first compared to lab-scale experimental datagenerated using different sized adsorption columns and flowrates with CAB adsorbent of 1 mm particle size Five differ-ent adsorption column experiments were designed repre-senting varying residence times The bed porosity wasmaintained between 035 and 05 by adjusting the mass ofadsorbent loaded into the column Experiments were runusing lean MDEA with an initial concentration of 3250ndash3500 ppm and breakthrough data were recorded as a func-tion of residence time The corresponding Biot and Stantonnumbers have also been shown in Table 2 along with otherprocess conditions The same feed and process conditionswere provided as input to the HSDMmodel and simulations

Table 2 Column parameters used in HSDM validation study

Parameter Test 1 Test 2 Test 3 Test 4 Test 5

Height L (cm) 10 10 23 23 23Bed diameter D (cm) 15 26 46 26 46Intraparticle porosity e 085 085 085 085 085Bed porosity eb 048 046 035 045 036Particle diameter dp (mm) 1 1 1 1 1Particle density qp (gcc) 104 104 104 104 104Equivalent bed mass M (g) 9 29 255 70 255MDEA flow rate Q (mLmin) 075 075 43 075 1Empty bed contact time (min) 235 71 89 163 382Superficial velocity Us (cmmin) 042 014 026 014 006Residence time T (min) 845 254 34 58 137Freundlich coefficient KF ((mgg)(Lmg)n) 00015 00015 00015 00015 00015Freundlich exponent n 08 08 08 08 08Film mass transfer coefficient kL (cms) 69E-05 48E-05 53E-05 48E-05 51E-05Surface diffusion coefficient Ds (cm

2s) 24E-06 24E-06 24E-06 24E-06 24E-06Stanton number St 11 24 37 56 105Biot number Bi 107 076 097 076 061

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 5

were performed to predict the complete breakthroughcurves Instead of comparing CCo at certain points HSDMsimulation provides a way to compare the entire BTCwhich is significant in establishing similarities in flowpattern between scales

26 Sensitivity analysis

To investigate the effect of these dimensionless numbers onbreakthrough curves Peacuterez-Foguet et al developed adimensionless analysis of HSDM (Peacuterez-Foguet et al2013) The macroscale liquid phase mass transport equationand the intraparticle diffusion equation were transformedinto a dimensionless form using dimensionless variablesfor the liquid and solid phase concentration axial positionand contact time The derivation of the dimensionlessmodel equations and the corresponding boundary andinitial conditions could be found elsewhere (Sperlich et al2008) The two characteristic partial differential equationsof the HSDM were transformed into a system of two ordi-nary differential equations coupled with the macroscaletransport-reaction PDE Discretization was accomplishedusing a discontinuous Galerkin scheme and the overall sys-tem evolution was integrated with a time-marching schemebased on the forward Euler method The overall system wassuccessfully used to simulate the adsorption of differentadsorbates on granular ferric hydroxide

The detailed dimensionless analysis of HSDM presentedby Peacuterez-Foguet et al (2013) facilitates establishing limitbehavior of the model to determine the values of Bi andSt number (Peacuterez-Foguet et al 2013) The influence ofdimensionless numbers including Bi St Ed Dg and n onthe breakthrough curves was thoroughly assessed usingthe dimensionless HSDM Excerpts from this work havebeen presented in Section 33 and the results have beendirectly applied to determine the working range of Bi andSt numbers

Design parameters from this technique were comparedwith direct scale-up and kinetic approaches Details of thesetwo conventional techniques including key equations havebeen summarized in the Supplementary Section

3 Results and discussion

31 Equilibrium studies

Different isotherm models were fitted to batch equilibriumdata and the model parameters were determined by non-lin-ear regression Equilibrium isotherms for TOA adsorptionon CAB adsorbents have been presented in the Supplemen-tary Section see Figure S1 Figure 3 shows the comparisonof simulated data from various models with batch equilib-rium data obtained by varying adsorbent mass at 23 Cand Table 3 shows the regressed model parameters andthe corresponding AIC values for different isotherm modelsIt can be noticed that the Freundlich model exhibited theleast AIC value indicating the best fit with experimentaldata Hence Freundlich model was incorporated into theHSDM model to describe the equilibrium behavior betweenthe solute present in the liquid and solid phases

32 HSDM model validation

Figure 4 shows a comparison plot of normalized concentra-tion against adsorption time between lab-scale experimen-tal data and HSDM predictions for different residencetimes An inset has been provided in order to better visual-ize the dynamics at early adsorption times As shown inFigure 4 HSDM is able to capture the overall processdynamics described by the ldquoSrdquo shaped curve for all theHRTrsquos considered Also the general trend in BTC time-shift with varying HRTs was predicted reasonably well bythe HSDM On comparison of simulated BTCs with exper-imental data in Figure 4 some discrepancies are evidentespecially for the case of HRT = 137 min Many differentfactors influence the shape of the BTCs primarily the val-ues of mass transfer coefficients employed in the HSDMThe sensitivity of these coefficients has been analyzed viatwo dimensionless parameters namely Bi and St numbersAs outlined in Section 33 and in the range of Bi values con-sidered St remains a significant parameter in determiningBTC dynamics However in order to minimize the discrep-ancies between experimental data and simulation the coef-ficients should be determined accurately from controlledbatch experiments rather than from empirical correlationsOther known possible factors that influence BTC dynamicsinclude HSDM assumptions concerning negligible pore dif-fusion and unaccounted experimental factors like backpres-sure and influent pumping issues encountered duringcolumn experiments Nevertheless as shown in this studyHSDM could be employed for the rapid design of theadsorption column where the application of othertechniques is severely challenged by the inherent depen-dency on experimental data

33 Sensitivity analysis

Sensitivity analysis on the dimensionless numbers providesknowledge on the variation of column breakthrough behav-ior in different scales Breakthrough curves were predictedfor ranges of St and Bi numbers to understand the masstransfer behavior at different process conditions The

Fig 3 Comparison of batch equilibrium data with variousisotherm models (legend details Exp ndash experimental JC ndash

Jovononic FR ndash Freundlich L-F ndash Langmuir-Freundlich 2sL ndash

2 step-Langmuir F-S ndash Fritz-Schlunder Lang ndash Langmuir)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)6

were performed to predict the complete breakthroughcurves Instead of comparing CCo at certain points HSDMsimulation provides a way to compare the entire BTCwhich is significant in establishing similarities in flowpattern between scales

26 Sensitivity analysis

To investigate the effect of these dimensionless numbers onbreakthrough curves Peacuterez-Foguet et al developed adimensionless analysis of HSDM (Peacuterez-Foguet et al2013) The macroscale liquid phase mass transport equationand the intraparticle diffusion equation were transformedinto a dimensionless form using dimensionless variablesfor the liquid and solid phase concentration axial positionand contact time The derivation of the dimensionlessmodel equations and the corresponding boundary andinitial conditions could be found elsewhere (Sperlich et al2008) The two characteristic partial differential equationsof the HSDM were transformed into a system of two ordi-nary differential equations coupled with the macroscaletransport-reaction PDE Discretization was accomplishedusing a discontinuous Galerkin scheme and the overall sys-tem evolution was integrated with a time-marching schemebased on the forward Euler method The overall system wassuccessfully used to simulate the adsorption of differentadsorbates on granular ferric hydroxide

The detailed dimensionless analysis of HSDM presentedby Peacuterez-Foguet et al (2013) facilitates establishing limitbehavior of the model to determine the values of Bi andSt number (Peacuterez-Foguet et al 2013) The influence ofdimensionless numbers including Bi St Ed Dg and n onthe breakthrough curves was thoroughly assessed usingthe dimensionless HSDM Excerpts from this work havebeen presented in Section 33 and the results have beendirectly applied to determine the working range of Bi andSt numbers

Design parameters from this technique were comparedwith direct scale-up and kinetic approaches Details of thesetwo conventional techniques including key equations havebeen summarized in the Supplementary Section

3 Results and discussion

31 Equilibrium studies

Different isotherm models were fitted to batch equilibriumdata and the model parameters were determined by non-lin-ear regression Equilibrium isotherms for TOA adsorptionon CAB adsorbents have been presented in the Supplemen-tary Section see Figure S1 Figure 3 shows the comparisonof simulated data from various models with batch equilib-rium data obtained by varying adsorbent mass at 23 Cand Table 3 shows the regressed model parameters andthe corresponding AIC values for different isotherm modelsIt can be noticed that the Freundlich model exhibited theleast AIC value indicating the best fit with experimentaldata Hence Freundlich model was incorporated into theHSDM model to describe the equilibrium behavior betweenthe solute present in the liquid and solid phases

32 HSDM model validation

Figure 4 shows a comparison plot of normalized concentra-tion against adsorption time between lab-scale experimen-tal data and HSDM predictions for different residencetimes An inset has been provided in order to better visual-ize the dynamics at early adsorption times As shown inFigure 4 HSDM is able to capture the overall processdynamics described by the ldquoSrdquo shaped curve for all theHRTrsquos considered Also the general trend in BTC time-shift with varying HRTs was predicted reasonably well bythe HSDM On comparison of simulated BTCs with exper-imental data in Figure 4 some discrepancies are evidentespecially for the case of HRT = 137 min Many differentfactors influence the shape of the BTCs primarily the val-ues of mass transfer coefficients employed in the HSDMThe sensitivity of these coefficients has been analyzed viatwo dimensionless parameters namely Bi and St numbersAs outlined in Section 33 and in the range of Bi values con-sidered St remains a significant parameter in determiningBTC dynamics However in order to minimize the discrep-ancies between experimental data and simulation the coef-ficients should be determined accurately from controlledbatch experiments rather than from empirical correlationsOther known possible factors that influence BTC dynamicsinclude HSDM assumptions concerning negligible pore dif-fusion and unaccounted experimental factors like backpres-sure and influent pumping issues encountered duringcolumn experiments Nevertheless as shown in this studyHSDM could be employed for the rapid design of theadsorption column where the application of othertechniques is severely challenged by the inherent depen-dency on experimental data

33 Sensitivity analysis

Sensitivity analysis on the dimensionless numbers providesknowledge on the variation of column breakthrough behav-ior in different scales Breakthrough curves were predictedfor ranges of St and Bi numbers to understand the masstransfer behavior at different process conditions The

Fig 3 Comparison of batch equilibrium data with variousisotherm models (legend details Exp ndash experimental JC ndash

Jovononic FR ndash Freundlich L-F ndash Langmuir-Freundlich 2sL ndash

2 step-Langmuir F-S ndash Fritz-Schlunder Lang ndash Langmuir)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)6

analysis is based on a comparison of normalized concentra-tion CC0 versus dimensionless time T defined as the ratioof operation time to ideal (stoichiometric) breakthrough time

The values of dimensionless parameters of the lab-scaleexperiment used for HSDM validation study are presentedin Table 2 Since solute distribution parameter (Dg) andFreundlich exponent (n) were determined from batchexperiments in this study they were treated as constantsand not included in the sensitivity analysis Further sinceEd = StBi the influence of Ed is dependent on the individ-ual values of Bi and St numbers Detailed results on thedimensionless analysis could be found elsewhere (Peacuterez-Foguet et al 2013) and only key findings have been dis-cussed in this section It was shown by Peacuterez-Foguet et al that BTC shapes and limit behaviors for bothlinear and nonlinear cases (n 1) are similar with minordifferences in the sharpness of the wave-front This was alsoverified in this study by performing a dimensionless analysison ldquonrdquo varying from 025 to 1 (equivalent to an initial con-centration of 75ndash3250 mgL) while keeping Bi and St con-stant at 09 and 10 respectively As it could be seen from

Figure 5 the effect of n is not so significant on the BTCdynamics and thus extrapolation of Freundlich isothermtowards zero adsorbate concentration may be assumed toimpart negligible discrepancies in the HSDM predictionsHence for all subsequent sensitivity and scale-up studiesthe value of n was held constant at the regressed value of08

A representative plot illustrating the effect of St at lowand high Bi numbers see Figures 6a and 6b was repro-duced and assessed using the dimensionless HSDM systemVariation of St at fixed Bi would be attained by varying theflow velocity of the solvent flowing through the packed bedcolumn Breakthrough curves shown in both the plots weregenerated by varying Stanton numbers between 0 and 104

for fixed Bi values of 09 and 100 while other dimensionlessparameters Dg and n were held constant At low Bi num-ber film diffusion dominates and thus acts as the control-ling mechanism Since differences between the resultsobtained at smaller pairs of Bi number were negligible(Peacuterez-Foguet et al 2013) only Bi = 09 and Bi = 100 wereconsidered for the analysis Also since limit behavior was

Table 3 Summary of isotherm model equations and parameters

Isothermmodel

Equation Modelfitting

parameters

Values AIC

Langmuir q frac14 qmbC1thornbC

qm bqm = 378 mgg 552b = 0027 Lg

Langmuir-Freundlich q frac14 qmbC

n

1thornbCnqmb n

qm = 837 mgg 379b = 106E-11 (Lmg)n

n = 277

Jovanovic q frac14 qm 1 exp ajC

exp bjC

qm aj bjqm = 825 mgg 386aj= 76E-06 Lmgbj = 00009 Lmg

Fritz-Schlunder

q frac14 a1Cb1

1thorna2Cb2a1 a2 b1 b2

a1 = 2E-07 (mg(1 b1) Lb1)g 488a2 = 436255 (Lmg)b2

b1 = 371b2 = 00001

Freundlich q = kF Cn kf n kf = 00015 ((mgg)(Lmg)n) 287

n = 08

Liq frac14 KL ln 1thorn b0Ceth THORN1M

h iKL b0 M 0 bL

kL = 6513 (mmolg) 771b0 = 0014

1M

frac14 1thorn ln 1 1 bLCeth THORNfrac12 M 0

M0 = 0332bL = 0015 (Lmmol)

Two-stepLangmuir q frac14 a1b1C

1thorn b1Cthorn a2b2 C c2eth THORN thorn abs C c2eth THORNfrac12 2thorn b2 C c2eth THORN thorn abs C c2eth THORNfrac12

a1 b1 a2 b2 c2

a1 = 4356 1005b1 = 61E-06a2 = 286E+04 (meqg)b2 = 504E-07 (Lmeq)c2 = 6675 (meqL)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 7

found at these values for Bi the predicted breakthroughcurves are strongly dependent on St number as evidencedin Figure 6 At Bi number close to 1 and St gt 10 referFigure 6a Mass Transfer Zone (MTZ) pattern is fullyestablished as indicated by the sinusoidal BTC shapedcurves This regime (St gt 10) could be thought ofinstantaneous adsorption regime where film transfer domi-nates advection However at St lt 10 the MTZ is stilldeveloping and shows a varying trend indicating relativelyslower adsorption and at St = 0 the condition changes tono adsorption Also since Bi number is small and close to1 the BTCs are purely dependent on St number withinthe range from 0 to 10 However at higher Bi numberand thus higher Ed see Figure 6b when intraparticle diffu-sion is rate controlling BTC shows a varying trend till thevalue of St is around 1000 The sensitiveness of break-through curves at low Stanton number (St lt 10) was evi-dent in the lab-scale column experiments reported in

previous sections As a comparison Test 2 and Test 4 wererun at varying Stanton numbers (Test 2 St = 24 Test 4St = 56) and at constant Biot number of 076 It can benoticed from Figure 4 that the dynamics of the two break-through curves are different with significant difference inbreakthrough times

Thus columns of different sizes would exhibit similarmass transfer behavior or similar controlling mechanism ifBi was chosen close to 1 and St 10 This analysis provideda working range of influent flow rates and loading rates orsuperficial velocity that could serve as a guideline whiledesigning adsorption columns of larger scales

HSDM assumes that solid phase mass transfer occursonly by surface diffusion and hence tortuosity and SPDFRare not considered significant The sensitivity of intraparti-cle diffusion coefficient (Ds) was tested on the BTC charac-teristics in a wide range from 1011 to 109 m2s seeFigure 7 The effect of Ds on the BTC dynamics could bebetter understood through analysis of the dimensionlessBiot number Since Bi and Ds are inversely proportionalincreasing Ds by two orders of magnitude from 1011 to109 would proportionally decrease Bi that would eventu-ally lead to faster adsorption characterized by sharp wave-front Figure 8 illustrates the dimensionless BTC fordifferent Biot numbers and a fixed St of 10 This impliesa case of constant film transfer rate and flow velocity butvarying surface diffusion efficient As it can be noticed formsharpness of the wavefront adsorption rate increases withdecreasing Bi or increasing Ds However the effect of Bion BTC shape beyond Bi = 01 (or 101) is not significantand practically remains unchanged thereby setting thelimits for surface diffusion coefficient

By performing a sensitivity analysis on the Freundlichexponent the impact of extrapolation of model parame-ters could be analyzed BTC shapes and limit behaviorsfor both linear and nonlinear cases (n 1) are similarwith minor differences in the sharpness of the wave-front

Fig 5 Effect of Freundlich exponent on breakthrough curvedynamics

Fig 4 Validation of HSDM with lab-scale BTC data (lines represent simulation and marker represents lab data inset depicts thegoodness of fit at lower times)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)8

(Peacuterez-Foguet et al 2013) This was also verified in thisstudy by performing a dimensionless analysis on ldquonrdquo varyingfrom 025 to 1 (equivalent to an initial concentration of 75to 3250 mgL) while keeping Bi and St constant at 08 and10 respectively As it could be seen from Figure 9 the effectof Freundlich exponent is not so significant on the BTCdynamics and thus extrapolation of Freundlich isothermtowards zero adsorbate concentration can be assumed tohave negligible influence on the HSDM predictions Hence

for all sensitivity and scale-up studies the value of n washeld constant at the regressed value of 08

34 Design scale assessment

From sensitivity analysis the range of Bi and St numbersthat would exhibit similar mass transfer phenomena forTOA adsorption were determined Based on these resultsa pilot-scale adsorption column was designed using thecritical design parameter rules recommended by Inglezakisand Poulopoulos as shown in Table 1 For all subsequentanalysis lab-scale test column Case 3 shown in Tables 2and 4 was chosen as the representative lab-scale designand compared with the pilot-scale design parameters

Figure 10 illustrates the complete breakthrough curvespredicted for different scales using the validated HSDMThe scales from the lab to pilot differ in residence timehowever the critical design parameters remain the sameFor a lab-scale column with a residence time of 34 minthe estimated breakthrough time was ca 26 min that isin good agreement with the experimentally determinedvalue of 285 min Similarly pilot-scale unit with a residencetime of 205 min resulted in relatively higher breakthroughtimes of ca 330 min

As expected breakthrough time to attain a normalizedeffluent concentration of 01 increases with increasing resi-dence time It should be noted that mass transfer coeffi-cients were calculated by empirical correlations from theliterature because they are not scalable from batch-scalestudies to pilot-scale studies due to differences in flow pat-tern in the reactor The accuracy of HSDM predictionsdepends strongly on the appropriateness of these correla-tions and the estimated equilibrium parameters from batchstudies

Additionally the column design was carried out usingthe conventional packed-bed scale-up procedure and simpli-fied kinetic models (detailed in the Supplementary Section)and compared with the HSDM design parameters It isworth noting that both the scale-up and the kineticapproach depends entirely on the breakthrough data gener-ated using test column either laboratory or pilot plant Inthe scale-up approach using the Length of Unused Bed(LUB) model the loading rate and the unused bed length

Fig 7 Effect of surface diffusion coefficient on BTC dynamics

Fig 8 Effect of Biot number on Dimensionless BTC dynamics

(a)

(b)

Fig 6 Effect of Stanton number on the breakthrough curves at(a) Bi = 09 (b) Bi = 100

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 9

found at these values for Bi the predicted breakthroughcurves are strongly dependent on St number as evidencedin Figure 6 At Bi number close to 1 and St gt 10 referFigure 6a Mass Transfer Zone (MTZ) pattern is fullyestablished as indicated by the sinusoidal BTC shapedcurves This regime (St gt 10) could be thought ofinstantaneous adsorption regime where film transfer domi-nates advection However at St lt 10 the MTZ is stilldeveloping and shows a varying trend indicating relativelyslower adsorption and at St = 0 the condition changes tono adsorption Also since Bi number is small and close to1 the BTCs are purely dependent on St number withinthe range from 0 to 10 However at higher Bi numberand thus higher Ed see Figure 6b when intraparticle diffu-sion is rate controlling BTC shows a varying trend till thevalue of St is around 1000 The sensitiveness of break-through curves at low Stanton number (St lt 10) was evi-dent in the lab-scale column experiments reported in

previous sections As a comparison Test 2 and Test 4 wererun at varying Stanton numbers (Test 2 St = 24 Test 4St = 56) and at constant Biot number of 076 It can benoticed from Figure 4 that the dynamics of the two break-through curves are different with significant difference inbreakthrough times

Thus columns of different sizes would exhibit similarmass transfer behavior or similar controlling mechanism ifBi was chosen close to 1 and St 10 This analysis provideda working range of influent flow rates and loading rates orsuperficial velocity that could serve as a guideline whiledesigning adsorption columns of larger scales

HSDM assumes that solid phase mass transfer occursonly by surface diffusion and hence tortuosity and SPDFRare not considered significant The sensitivity of intraparti-cle diffusion coefficient (Ds) was tested on the BTC charac-teristics in a wide range from 1011 to 109 m2s seeFigure 7 The effect of Ds on the BTC dynamics could bebetter understood through analysis of the dimensionlessBiot number Since Bi and Ds are inversely proportionalincreasing Ds by two orders of magnitude from 1011 to109 would proportionally decrease Bi that would eventu-ally lead to faster adsorption characterized by sharp wave-front Figure 8 illustrates the dimensionless BTC fordifferent Biot numbers and a fixed St of 10 This impliesa case of constant film transfer rate and flow velocity butvarying surface diffusion efficient As it can be noticed formsharpness of the wavefront adsorption rate increases withdecreasing Bi or increasing Ds However the effect of Bion BTC shape beyond Bi = 01 (or 101) is not significantand practically remains unchanged thereby setting thelimits for surface diffusion coefficient

By performing a sensitivity analysis on the Freundlichexponent the impact of extrapolation of model parame-ters could be analyzed BTC shapes and limit behaviorsfor both linear and nonlinear cases (n 1) are similarwith minor differences in the sharpness of the wave-front

Fig 5 Effect of Freundlich exponent on breakthrough curvedynamics

Fig 4 Validation of HSDM with lab-scale BTC data (lines represent simulation and marker represents lab data inset depicts thegoodness of fit at lower times)

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)8

(Peacuterez-Foguet et al 2013) This was also verified in thisstudy by performing a dimensionless analysis on ldquonrdquo varyingfrom 025 to 1 (equivalent to an initial concentration of 75to 3250 mgL) while keeping Bi and St constant at 08 and10 respectively As it could be seen from Figure 9 the effectof Freundlich exponent is not so significant on the BTCdynamics and thus extrapolation of Freundlich isothermtowards zero adsorbate concentration can be assumed tohave negligible influence on the HSDM predictions Hence

for all sensitivity and scale-up studies the value of n washeld constant at the regressed value of 08

34 Design scale assessment

From sensitivity analysis the range of Bi and St numbersthat would exhibit similar mass transfer phenomena forTOA adsorption were determined Based on these resultsa pilot-scale adsorption column was designed using thecritical design parameter rules recommended by Inglezakisand Poulopoulos as shown in Table 1 For all subsequentanalysis lab-scale test column Case 3 shown in Tables 2and 4 was chosen as the representative lab-scale designand compared with the pilot-scale design parameters

Figure 10 illustrates the complete breakthrough curvespredicted for different scales using the validated HSDMThe scales from the lab to pilot differ in residence timehowever the critical design parameters remain the sameFor a lab-scale column with a residence time of 34 minthe estimated breakthrough time was ca 26 min that isin good agreement with the experimentally determinedvalue of 285 min Similarly pilot-scale unit with a residencetime of 205 min resulted in relatively higher breakthroughtimes of ca 330 min

As expected breakthrough time to attain a normalizedeffluent concentration of 01 increases with increasing resi-dence time It should be noted that mass transfer coeffi-cients were calculated by empirical correlations from theliterature because they are not scalable from batch-scalestudies to pilot-scale studies due to differences in flow pat-tern in the reactor The accuracy of HSDM predictionsdepends strongly on the appropriateness of these correla-tions and the estimated equilibrium parameters from batchstudies

Additionally the column design was carried out usingthe conventional packed-bed scale-up procedure and simpli-fied kinetic models (detailed in the Supplementary Section)and compared with the HSDM design parameters It isworth noting that both the scale-up and the kineticapproach depends entirely on the breakthrough data gener-ated using test column either laboratory or pilot plant Inthe scale-up approach using the Length of Unused Bed(LUB) model the loading rate and the unused bed length

Fig 7 Effect of surface diffusion coefficient on BTC dynamics

Fig 8 Effect of Biot number on Dimensionless BTC dynamics

(a)

(b)

Fig 6 Effect of Stanton number on the breakthrough curves at(a) Bi = 09 (b) Bi = 100

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 9

(Peacuterez-Foguet et al 2013) This was also verified in thisstudy by performing a dimensionless analysis on ldquonrdquo varyingfrom 025 to 1 (equivalent to an initial concentration of 75to 3250 mgL) while keeping Bi and St constant at 08 and10 respectively As it could be seen from Figure 9 the effectof Freundlich exponent is not so significant on the BTCdynamics and thus extrapolation of Freundlich isothermtowards zero adsorbate concentration can be assumed tohave negligible influence on the HSDM predictions Hence

for all sensitivity and scale-up studies the value of n washeld constant at the regressed value of 08

34 Design scale assessment

From sensitivity analysis the range of Bi and St numbersthat would exhibit similar mass transfer phenomena forTOA adsorption were determined Based on these resultsa pilot-scale adsorption column was designed using thecritical design parameter rules recommended by Inglezakisand Poulopoulos as shown in Table 1 For all subsequentanalysis lab-scale test column Case 3 shown in Tables 2and 4 was chosen as the representative lab-scale designand compared with the pilot-scale design parameters

Figure 10 illustrates the complete breakthrough curvespredicted for different scales using the validated HSDMThe scales from the lab to pilot differ in residence timehowever the critical design parameters remain the sameFor a lab-scale column with a residence time of 34 minthe estimated breakthrough time was ca 26 min that isin good agreement with the experimentally determinedvalue of 285 min Similarly pilot-scale unit with a residencetime of 205 min resulted in relatively higher breakthroughtimes of ca 330 min

As expected breakthrough time to attain a normalizedeffluent concentration of 01 increases with increasing resi-dence time It should be noted that mass transfer coeffi-cients were calculated by empirical correlations from theliterature because they are not scalable from batch-scalestudies to pilot-scale studies due to differences in flow pat-tern in the reactor The accuracy of HSDM predictionsdepends strongly on the appropriateness of these correla-tions and the estimated equilibrium parameters from batchstudies

Additionally the column design was carried out usingthe conventional packed-bed scale-up procedure and simpli-fied kinetic models (detailed in the Supplementary Section)and compared with the HSDM design parameters It isworth noting that both the scale-up and the kineticapproach depends entirely on the breakthrough data gener-ated using test column either laboratory or pilot plant Inthe scale-up approach using the Length of Unused Bed(LUB) model the loading rate and the unused bed length

Fig 7 Effect of surface diffusion coefficient on BTC dynamics

Fig 8 Effect of Biot number on Dimensionless BTC dynamics

(a)

(b)

Fig 6 Effect of Stanton number on the breakthrough curves at(a) Bi = 09 (b) Bi = 100

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 9

for both the lab-scale and pilot-scale units had to be main-tained constant to obtain similar mass transfer characteris-tics In this study the lab-scale test column of 43 cmdiameter and 23 cm height was used with a filtration orloading rate of 0256 cm3min cm2 and an EBCT of96 min The length of unused bed corresponding to the frac-tion of bed unused was calculated as 131 cm As per theLUB model this length should remain the same in scale-up and thus the length of unused bed in pilot-plant designwas taken as 131 cm and the corresponding breakthroughtime was estimated as 345 min

The kinetic approach was based on the simplifiedBohart and Adams model that employed a kinetic rate

equation to determine the reaction constant and maximumsolid phase loading However this approach necessitates abreakthrough volume or time to be specified in the designequation A breakthrough time of 335 min (taken fromHSDM) was used to calculate other design parametersincluding the mass of adsorbent required and breakthroughvolume Table 5 shows a comparison of various designparameters calculated from different techniques It can benoted that all three techniques yield similar results for thedesign of a pilot-scale adsorber however with different com-plexities HSDM could be used to design adsorption columnof various scales with minimal input about equilibrium dataand mass transfer coefficients However the other two tech-niques scale-up and kinetic approaches are dependent onthe accuracy of the supplied breakthrough data

4 Conclusion

The objective of the present work was to utilize the predic-tive homogeneous surface diffusion model for designing afixed-bed adsorber to remove TOA present in lean MDEAsolution using CAB adsorbent As part of the design tech-nique various isotherm models were fitted to batch equilib-

Fig 10 Comparison of BTC curves between different scales aspredicted by HSDM

Fig 9 Effect of Freundlich exponent on breakthrough curvedynamics

Table 4 Summary of lab-scale and pilot-scale adsorptioncolumn design parameters

Parameter Lab testcolumn

Pilotcolumn

Scale-upfactor

Adsorber bed heightL (cm)

23 150 65

Bed diameter D (cm) 46 30 65Adsorbent particlediameter dp (mm)

1 1 ndash

LD 5 5 ndash

Ldp 230 1500 ndash

Ddp 46 300 ndash

Equivalent bed mass (kg) 026 70 270MDEA flow rate(mLmin)

43 185 43

Empty bed contact time(min)

89 573 65

Residence time (min) 34 205 65Superficial velocity(cmmin)

026 026 1

Stanton number St 37 24 ndash

Biot number Bi 097 091 ndash

Table 5 Comparison of pilot-scale design parametersbetween various techniques

Design parameter HSDM Scale-up

Kinetic

Column diameter (cm) 30 30 30Bed height (cm) 150 160 1602Flow rate (ccmin) 185 185 185Adsorbent mass (kg) 706 707 797Breakthrough time (min) 330 370 330Maximum solid phase loading (mgg)

385 NA 28

Breakthrough volume (L) 615 685 615

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)10

rium data and based on Akaike Information Criterion(AIC) it was found that the equilibrium isotherms werebest described by the Freundlich equation SubsequentlyFreundlich isotherm parameters and appropriate masstransfer correlations for film and surface diffusivities wereincorporated into the HSDM equation matrix Numericalsolution to the simultaneous transport-reaction equationsand non-linear Freundlich equation was executed throughcommercial software Simulation results were comparedwith lab-scale experimental data collected at lower resi-dence times (lt140 min) and it was evident that HSDMcould predict breakthrough curves with reasonable accu-racy Dimensionless HSDM equations were employed todescribe the limit behavior of the model based on dimen-sionless numbers Bi and St Sensitivity analysis on thetwo parameters established the operating range for thedesign units as Bi ~ 1 and St gt 10 Further in order to pre-serve the flow pattern during scale-up process key columnparameters and similitude rules from literature werereviewed and integrated into the column design Based onthe design guidelines 30 cm by 150 cm fixed-bed adsorberwith a continuous throughput of 111 Lh was consideredsuitable HSDM predicted a 330 min column operating timewith an equivalent lean amine treatment capacity of 60 Lbased on a 10 breakthrough limit for the designed columnAccuracy of the HSDM based design technique was evalu-ated by comparing with conventional scale-up and kineticapproaches and was found to be in good agreement Resultsdemonstrated the rapid ease-of-use and accuracy of theHSDM technique for the design of fixed-bed adsorption col-umns for complex systems

Supplementary materials

The supplementary material of this article is available athttpsogstifpenergiesnouvellesfr102516ogst2020073olmDetails of these two conventional techniques (scale-upapproach kinetic approach) including key equations havebeen summarized in the supplementary section

Fig S1 Plot of ln ((C0C t) 1) vs timeTable S1 Kinetic parameters obtained by linear regressionFig S2 Adsorption equilibrium curve qe vs Ce for theadsorptive removal of TOA using CAB compositesSupplementary References

Acknowledgments The authors would like to acknowledge thesupport provided by the Gas Research Center (GRC) at KhalifaUniversity under research grant GRC11006

References

Chowdhury ZZ Hamid SB Zain SM (2015) Evaluatingdesign parameters for breakthrough curve analysis andkinetics of fixed bed columns for Cu(II) cations usinglignocellulosic wastes BioResources 10 1 732ndash749

Crittenden B Thomas WJ (1998) Adsorption technology anddesign Butterworth-Heinemann Woburn MA USA

Crittenden JC Berrigan JK Hand DW (1986a) Design ofrapid small-scale adsorption tests for a constant diffusivity JWater Pollut Control Fed 58 4 312ndash319

Crittenden JC Hand DW Arora H Lykins BW (1987)Design considerations for GAC treatment of organic chemi-cals J Am Water Works Ass 79 1 74ndash82

Crittenden JC Hutzler NJ Geyer DG Oravitz JLFriedman G (1986b) Transport of organic compounds withsaturated groundwater flow Model development and param-eter sensitivity Water Resour Res 22 3 271ndash284

Crittenden JC Reddy PS Arora H Trynoski J (1991)Predicting GAC performance with Rapid Small-Scale ColumnTests J Am Water Works Ass 83 1 77ndash87

Cummings AL Smith GD Nelson DK (2007) Advances inamine reclaiming Why there is no excuse for operating a dirtyamine system in Laurance Reid Gas Conditioning Confer-ence Dickinson TX USA pp 227ndash244

Daacutevila-Jimeacutenez MM Elizalde-Gonzaacutelez MP Garciacutea-Diacuteaz EGonzaacutelez-Perea M Guevara-Villa MRG (2014) Usingakaike information criterion to select the optimal isothermequation for adsorption from solution Adsorpt Sci Technol32 7 605ndash622

Edathil AA Pal P Banat F (2018) Alginate clay hybridcomposite adsorbents for the reclamation of industrial leanmethyldiethanolamine solutions Appl Clay Sci 156 213ndash223

Edathil AA Pal P Kannan P Banat F (2020) Total organicacid adsorption using alginateclay hybrid composite for indus-trial lean amine reclamation using fixed-bed Parametric studycoupled with foaming Int J Greenh Gas Con 94 102907

Hand DW Crittenden JC Arora H Miller JM Lykins BW(1989) Designing fixed-bed adsorbers to remove mixtures oforganics J Am Water Works Ass 81 1 67ndash77

Hand DW Crittenden JC Thacker WE (1983) User-oriented batch reactor solutions to the homogeneous surfacediffusion model J Environ Eng 109 1 82ndash101

Hand DW Crittenden JC Thacker WE (1984) Simplifiedmodels for design of fixed-bed adsorption systems J EnvironEng 110 2 440ndash456

Hudaya T Rachmat V (2019) Activated carbon fixed-bedadsorber design for treating chromium hexavalent wastewa-ter Makara J Technol 22 3 135ndash141

Inglezakis VJ Poulopoulos SG (2006) Adsorption Ion Exchangeand Catalysis Elsevier Amsterdam The Netherlands

Keewan M Banat F Pal P Zain J Alhseinat E (2018)Foaming of industrial lean methyldiethanolamine solution inthe presence of hydrocarbon and fatty acid based corrosioninhibitors Oil Gas Sci Technol - Rev IFP Energies nouvelles73 76 1ndash7

Lee MC Crittenden JC Snoeyink VL Ari M (1983) Designof carbon beds to remove humic substances J Environ Eng109 3 631ndash645

Mehassouel A Derriche R Bouallou C (2018) Kinetics studyand simulation of CO2 absorption into mixed aqueoussolutions of methyldiethanolamine and hexylamine Oil GasSci Technol - Rev IFP Energies nouvelles 73 19 1ndash10

Pal P AbuKashabeh A Al-Asheh S Banat F (2015) Role ofaqueous methyldiethanolamine (MDEA) as solvent in naturalgas sweetening unit and process contaminants with probablereaction pathway J Nat Gas Sci Eng 24 124ndash131

Pal P Banat F AlShoaibi A (2013) Adsorptive removal ofheat stable salt anions from industrial lean amine solventusing anion exchange resins from gas sweetening unit J NatGas Sci Eng 15 14ndash21

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 11

rium data and based on Akaike Information Criterion(AIC) it was found that the equilibrium isotherms werebest described by the Freundlich equation SubsequentlyFreundlich isotherm parameters and appropriate masstransfer correlations for film and surface diffusivities wereincorporated into the HSDM equation matrix Numericalsolution to the simultaneous transport-reaction equationsand non-linear Freundlich equation was executed throughcommercial software Simulation results were comparedwith lab-scale experimental data collected at lower resi-dence times (lt140 min) and it was evident that HSDMcould predict breakthrough curves with reasonable accu-racy Dimensionless HSDM equations were employed todescribe the limit behavior of the model based on dimen-sionless numbers Bi and St Sensitivity analysis on thetwo parameters established the operating range for thedesign units as Bi ~ 1 and St gt 10 Further in order to pre-serve the flow pattern during scale-up process key columnparameters and similitude rules from literature werereviewed and integrated into the column design Based onthe design guidelines 30 cm by 150 cm fixed-bed adsorberwith a continuous throughput of 111 Lh was consideredsuitable HSDM predicted a 330 min column operating timewith an equivalent lean amine treatment capacity of 60 Lbased on a 10 breakthrough limit for the designed columnAccuracy of the HSDM based design technique was evalu-ated by comparing with conventional scale-up and kineticapproaches and was found to be in good agreement Resultsdemonstrated the rapid ease-of-use and accuracy of theHSDM technique for the design of fixed-bed adsorption col-umns for complex systems

Supplementary materials

The supplementary material of this article is available athttpsogstifpenergiesnouvellesfr102516ogst2020073olmDetails of these two conventional techniques (scale-upapproach kinetic approach) including key equations havebeen summarized in the supplementary section

Fig S1 Plot of ln ((C0C t) 1) vs timeTable S1 Kinetic parameters obtained by linear regressionFig S2 Adsorption equilibrium curve qe vs Ce for theadsorptive removal of TOA using CAB compositesSupplementary References

Acknowledgments The authors would like to acknowledge thesupport provided by the Gas Research Center (GRC) at KhalifaUniversity under research grant GRC11006

References

Chowdhury ZZ Hamid SB Zain SM (2015) Evaluatingdesign parameters for breakthrough curve analysis andkinetics of fixed bed columns for Cu(II) cations usinglignocellulosic wastes BioResources 10 1 732ndash749

Crittenden B Thomas WJ (1998) Adsorption technology anddesign Butterworth-Heinemann Woburn MA USA

Crittenden JC Berrigan JK Hand DW (1986a) Design ofrapid small-scale adsorption tests for a constant diffusivity JWater Pollut Control Fed 58 4 312ndash319

Crittenden JC Hand DW Arora H Lykins BW (1987)Design considerations for GAC treatment of organic chemi-cals J Am Water Works Ass 79 1 74ndash82

Crittenden JC Hutzler NJ Geyer DG Oravitz JLFriedman G (1986b) Transport of organic compounds withsaturated groundwater flow Model development and param-eter sensitivity Water Resour Res 22 3 271ndash284

Crittenden JC Reddy PS Arora H Trynoski J (1991)Predicting GAC performance with Rapid Small-Scale ColumnTests J Am Water Works Ass 83 1 77ndash87

Cummings AL Smith GD Nelson DK (2007) Advances inamine reclaiming Why there is no excuse for operating a dirtyamine system in Laurance Reid Gas Conditioning Confer-ence Dickinson TX USA pp 227ndash244

Daacutevila-Jimeacutenez MM Elizalde-Gonzaacutelez MP Garciacutea-Diacuteaz EGonzaacutelez-Perea M Guevara-Villa MRG (2014) Usingakaike information criterion to select the optimal isothermequation for adsorption from solution Adsorpt Sci Technol32 7 605ndash622

Edathil AA Pal P Banat F (2018) Alginate clay hybridcomposite adsorbents for the reclamation of industrial leanmethyldiethanolamine solutions Appl Clay Sci 156 213ndash223

Edathil AA Pal P Kannan P Banat F (2020) Total organicacid adsorption using alginateclay hybrid composite for indus-trial lean amine reclamation using fixed-bed Parametric studycoupled with foaming Int J Greenh Gas Con 94 102907

Hand DW Crittenden JC Arora H Miller JM Lykins BW(1989) Designing fixed-bed adsorbers to remove mixtures oforganics J Am Water Works Ass 81 1 67ndash77

Hand DW Crittenden JC Thacker WE (1983) User-oriented batch reactor solutions to the homogeneous surfacediffusion model J Environ Eng 109 1 82ndash101

Hand DW Crittenden JC Thacker WE (1984) Simplifiedmodels for design of fixed-bed adsorption systems J EnvironEng 110 2 440ndash456

Hudaya T Rachmat V (2019) Activated carbon fixed-bedadsorber design for treating chromium hexavalent wastewa-ter Makara J Technol 22 3 135ndash141

Inglezakis VJ Poulopoulos SG (2006) Adsorption Ion Exchangeand Catalysis Elsevier Amsterdam The Netherlands

Keewan M Banat F Pal P Zain J Alhseinat E (2018)Foaming of industrial lean methyldiethanolamine solution inthe presence of hydrocarbon and fatty acid based corrosioninhibitors Oil Gas Sci Technol - Rev IFP Energies nouvelles73 76 1ndash7

Lee MC Crittenden JC Snoeyink VL Ari M (1983) Designof carbon beds to remove humic substances J Environ Eng109 3 631ndash645

Mehassouel A Derriche R Bouallou C (2018) Kinetics studyand simulation of CO2 absorption into mixed aqueoussolutions of methyldiethanolamine and hexylamine Oil GasSci Technol - Rev IFP Energies nouvelles 73 19 1ndash10

Pal P AbuKashabeh A Al-Asheh S Banat F (2015) Role ofaqueous methyldiethanolamine (MDEA) as solvent in naturalgas sweetening unit and process contaminants with probablereaction pathway J Nat Gas Sci Eng 24 124ndash131

Pal P Banat F AlShoaibi A (2013) Adsorptive removal ofheat stable salt anions from industrial lean amine solventusing anion exchange resins from gas sweetening unit J NatGas Sci Eng 15 14ndash21

P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020) 11

Pal P Edathil AA Banat F (2019) Calcium alginate gel andhard beads for the removal of total organic acid anions andheavy metal ions from industrial lean methyldiethanolaminesolvent Polym Bull 76 1 103ndash118

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Peacuterez-Foguet A Casoni E Huerta A (2013) Dimensionlessanalysis of HSDM and application to simulation of break-through curves of highly adsorbent porous media J EnvironEng 139 5 667ndash676

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Srivastava VC Prasad B Mishra IM Mall ID Swamy MM (2008) Prediction of breakthrough curves for sorptive

removal of phenol by bagasse fly ash packed bed Ind EngChem Res 47 5 1603ndash1613

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P Kannan et al Oil amp Gas Science and Technology ndash Rev IFP Energies nouvelles 75 82 (2020)12

• Introduction
• Method description
• • Selection of isotherm model
  • Lab-scale column experiments
  • BTC predictive model
  • Calculation of mass transfer coefficients
  • HSDM model validation
  • Sensitivity analysis
  • • Results and discussion
    • • Equilibrium studies
      • HSDM model validation
      • Sensitivity analysis
      • Design scale assessment
      • • Conclusion
        • Supplementary materials
        • Acknowledgements
        • References