Model Optimization for the Dynamic Simulation of Reactive Absorption Processes

ReviewModel Optimization for the Dynamic Simulation of ReactiveAbsorption Processes

By Ralf Schneider and Andrzej Górak*

The optimal design of reactive separations is impossible without reliable process models. Especially for the dynamic simulationand the model-based control of complex reactive absorption processes the model development leads to a contradiction betweenthe required model accuracy to reflect the process complexity and the feasibility of process simulations regarding thecomputation time. In this respect, we have developed a new rigorous dynamic two-phase model based on the two-film theory as afirst step, which takes into account the influence of chemical reactions and additional driving forces in electrolyte systems onmass transfer considering thermodynamic nonidealities as well as the impact of column internals on the process hydrodynamics.For a model optimization, we have performed an analysis of different model approaches for complicated industrial absorptionprocesses and determined an appropriate model complexity. Based on results of sensitivity studies, we have accomplisheddifferent model modifications leading to a stabilization of the numerical solution without affecting the good agreement betweensimulation results and the experimental data. This time-optimized model can be considered superior as compared to previousapproaches and facilitates for the first time a rigorous dynamic simulation of entire reactive absorption columns and theapplication within an on-line process control system.

1 Introduction

Modeling and design of reactiveabsorption processes comprising thecomplex mass transfer in two-phasesystems combined with chemical reac-tion are based on the theoreticaldescription of the reaction and masstransport in multicomponent systemsconsidering the superposition of manydriving forces, like multicomponentdiffusion, chemical interactions, con-vective flows, multicomponent ther-modynamic interplay, etc. [1,2]. Rig-orous steady-state and dynamicdescriptions of industrial reactive ab-sorption processes often lead to veryextended systems of equations which can hardly be solvedreliably and quickly enough. Therefore, for the design andmodel-based control of industrial reactive absorption pro-cesses the question of the required and useful modeling deptharises to achieve a sufficient model accuracy at a feasiblecomputation time (Fig. 1).

In general, the model accuracy increases with risingcomplexity. But for very detailed and accurate models a hugeextension of the complexity has to be accepted for a little gainin accuracy. Especially for the investigation of the dynamic

process behavior and the application within a model-basedprocess control, the model complexity has to be limited. Onthe other hand, the desired objective is to build a predictivemodel valid for a variety of processes without adaptation ofcertain specific parameters. Therefore, in this paper wepresent different general guidelines for the dynamic simula-tion of complicated reactive absorption processes togetherwith their experimental validation.

2 Model Approaches

Reactive absorption columns can be regarded as a cascadeof segments (called stages) which are connected by mass andenergy balance equations [2]. In Fig. 2, different model

Chem. Eng. Technol. 24 (2001) 10, Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 0930-7516/01/1010-0979 $ 17.50+.50/0 979

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[*] Dr.-Ing. R. Schneider, Univ-Prof. Dr.-Ing. A. Górak, University ofDortmund, Chemical Engineering Department, D-44221 Dortmund,Germany; e-mail: [email protected]

0930-7516/01/1010-0979 $ 17.50+.50/0

Figure 1. Model complexity as a function of the accuracy with regard to the description of mass transfer,chemical reaction and process dynamics.

approaches representing different complexities concerningthe description of mass transfer and chemical reaction on eachstage are presented.

While the easiest models assume thermodynamic equilib-rium of both phases and infinitely fast mass transport andchemical reactions within a single stage, one can moverightwards, increasing the model accuracy and predictivitygradually by considering the bulk phase reaction kinetics orboth the bulk and film reaction kinetics. Moving upwards,mass transfer resistances are taken into account in the so-called rate-based approach [3]. One of the importantadvantages of kinetic models (in the top row of the diagram)is that the process hydrodynamics can be directly involved viacorrelations for the holdup, pressure drop, mass transfercoefficients, etc. [4].

Traditional equilibrium stage models and efficiency ap-proaches are mostly inadequate for the description ofchemisorption processes, since in practice mass and heattransfer are actually rate processes that are driven by gradientsof chemical potential and temperature. An importantpeculiarity of reactive absorption processes is that reactionvelocities range widely. Therefore, the chemical reaction caneither be considered as instantaneous (chemical equilibrium isattained) or kinetically controlled. Although the latter variant isinconsistent with the assumption of thermodynamic equilib-rium, this model has often been applied in literature [5±7].

3 Rigorous Rate-Based Approach

For the determination of the required model complexity forreactive absorption processes, a very detailed model has to beavailable which can be used as a reference model forsensitivity studies and be compared to more simple, reducedmodels, whereas significant and insignificant influences arerecognized.

In rigorous and predictive models the influence of chemicalreactions on mass transfer cannot be neglected, if bothphenomena occur with similar velocities. Therefore, we have

developed a new rigorous rate-based approach based on thetwo-film theory [8] which is suitable for the description of anycomplex reactive separation process [9,10] (Fig. 3).

Figure 3. Differential two-film model and schematic film concentration profilefor the rate-based approach.

This model takes into account diffusional interactions,thermodynamic nonidealities and the direct influence ofchemical reactions on mass transfer and considers thehydrodynamics of particular column internals.

3.1 Dynamic Differential Balance Equations

Dynamic differential mass and energy balances withsimultaneous calculation of accumulation terms like liquidholdups on each column segment reflect the continuous anddynamic character of the process. In the dynamic componentmaterial balances for the liquid bulk phase, changes of both, thespecific molar component and the total molar holdup, areconsidered which thus represent partial differential equations1):

( ) ( ) ; 1,...,lb lb lb lb

i i i i liq cU Lx n a R A i mt z

∂ ∂f

∂ ∂= − + + = (1)

The dynamic changes of both, the total molar hold-up andliquid-phase composition, are considered based on thefollowing hold-up relation:

Ulbi� xlb

iUlb

t; i � 1; :::;m (2)

An obvious summation relation connects the liquid bulkmole fractions of all components:Pmi�1

xlbi� 1 (3)

The volumetric liquid holdup uliq depends on the gas andliquid flow rates and is calculated from empirical packing

980 Ó WILEY-VCH Verlag GmbH, D-69469 Weinheim, 2001 0930-7516/01/0808-0980 $ 17.50+.50/0 Chem. Eng. Technol. 24 (2001) 10

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1) List of symbols at the end of the paper.

Figure 2. Reference frame for the model complexity regarding the considera-tion of mass transfer and chemical reaction.

Review

correlations [11]. The gas holdup can be neglected due to thelow gas phase density at atmospheric operating pressure whichleads to the following balance equation for each component ofthe gas phase:

( )0 ; 1,...,gb gb

i i c

dGy n aA i m

dz= − = (4)

The summation relation similar to Eq. (3) is also valid forthe gas phase:Pmi�1

ygbi� 1 (5)

For the determination of axial temperature profiles,differential dynamic energy balances are formulated includ-ing the conductive and convective heat fluxes as well as theproduct of the liquid molar holdup and the specific molarenthalpy:

( )

( )1

0 ;

gf m

gb gf gb

gf i gb gf gf

c V

i igfi

dGh q aA q

q T T n h

dz

l

d =

= − −

= − − +∑(6)

( )

( )1

;

lb

lf m

lb lf lb

lf lb i lf lf

tc V

i ilfi

ELh q aA q

q T T n h

t z

l

d =

∂ ∂= − + −

= − − +

∂ ∂

∑(7)

The heat balance for the liquid phase includes the energyholdup as an accumulation term. The energy fluxes across theinterface are linked by the continuity equation:

0gf lfq q= − (8)

The thermodynamic equilibrium at the gas-liquid interfaceis described as follows:

yii� Ki x

ii

; i � 1; :::;m (9)

where the distribution coefficient Ki comprises fugacities inboth phases and activity coefficients in the liquid phase.

For the determination of the film thicknesses, empiricalmass transfer coefficient correlations are used, which allow forthe influence of column internals and hydraulics (see e.g. [12]).These correlations have to be incorporated into the wholesystem of model equations. In addition, pressure drop alongthe column is considered via specific correlations (seee.g. [13]).

3.2 Film Reaction

The component fluxes ni incorporated in Eqs. (1) and (4)result from the mass transfer mechanism assumed in the film

region. The key assumption of the classical film model is theone-dimensional mass transport normal to the interface. Incontrast to this, we have taken into account the chemicalreaction kinetics and mass action laws in differential equationsdescribing the liquid film region:

1�lf

dnlfi

d�ÿ Rlf

i� 0 ; i � 1; :::;m (10)

Due to the chemical conversion in the film, the values of themolar fluxes at the interface and at the boundary between thefilm and the bulk phase differ and changing mass transfer ratesalong the film co-ordinate have to be considered. Thedifferential mass balance for the film region (10) leads tononlinear concentration profiles [10,14].

3.3 Constitutive Relations

In multicomponent systems, such unusual phenomena asreverse mass transfer (transport of the component in thedirection opposite to its own driving force), osmotic masstransfer (transport of the component when its driving force isequal to zero), and mass transfer barrier (no transport of thecomponent in the presence of its own driving force) can occur[2,15]. Therefore, a suitable mass transfer model should takeinto account the molecular interactions of the componentsinvolved. Multicomponent diffusional mass transport can befairly well described with the Maxwell-Stefan equationsderived from the kinetic theory of gases:

di �Pmj�1

xlfi

nlfjÿxlf

jnlf

i

clft Dÿij

; i � 1; :::;m (11)

Similar equations can be also written for the gas phase. To beable to describe the presence of electrolytes in the system, theelectrical driving force needs to be additionally taken intoaccount. Therefore, the gradient of the electrical potential isintroduced into the generalized driving force di [2,16]:

di �xlf

iRT

1�lf

d�id�� xlf

izi

FRT

1�lf

d'd�

; i � 1; :::;m (12)

The consideration of the electrical potential requires anadditional condition of the electroneutrality which has to besatisfied everywhere in the liquid phase:Pmi�1

xi zi � 0 (13)

4 Model Reductions

The system of equations described above can be very large,especially in the case of complex chemical systems. This oftenresults in significant numerical troubles, unstable convergenceand, eventually, unreliable simulation results. Therefore, theevaluation of reasonable model reductions is very important.


Review

In absorption systems with comparable temperatures of thegas and liquid feed streams and limited reaction rates theassumption of isothermal stages is justified [17,18]. Never-theless, for the calculation of axial temperature profilesenergy balance equations considering heat losses are requiredand have been implemented into our model.

In addition, in dilute electrolyte systems the diffusionalinteractions can usually be neglected and the generalizedMaxwell-Stefan equations (12) are reduced to the Nernst-Planck equation [10]:

nlfi� ÿ

clft Dlf

i;eff

�lf

dxlfi

d�� xlf

izi

FRT

d'd�

!� xlf

inlf

m; i � 1; :::;m

(14)

On the other hand, the influence of the chemical reactionwithin the film region on the mass transfer rates should not beneglected beforehand as the majority of reactions in electro-lyte systems can be regarded as instantaneous or at least veryfast classified by the corresponding Ha-number (see e.g. [19]).For simple reactions of first or pseudo-first order the masstransfer acceleration can be expressed by enhancement factorsderived from analytical solutions of Eq. (10) defined as theratio of interfacial fluxes with and without chemical reaction:

i

ichem

A i

iphys

nE

n= (15)

Although in recent publications different approaches ofenhancement factors for reversible and multistep reactionsare presented, a general analytical expression could not beobtained and numerical techniques are required as well assimplifications, such as irreversibility of reaction steps, equaldiffusivities or limited reaction orders [20,21]. To avoidunpredictive correction terms based on inappropriate modelassumptions, the differential mass balances for the liquid filmregion should be considered in the system of equationsreflecting the changing mass transfer rates along the filmco-ordinate. A significant reduction of the number of modelequations results from the linearization of the film concentra-tion profiles (Fig. 4). In this case, the differential balances aresubstituted by material balances across the entire film. Thecomponent mass transfer rates calculated at the bulkconditions are enhanced by the amount of generation withinthe film region.

Figure 4. Schematic film concentration profiles with and without linearization.

The relevant film reaction rates are evaluated by usingaverage values of the interfacial and bulk conditions [9].

( )

; 1,...,

,

lb i lf lf

i i i

lf lf lf

i i

n n R i m

R f c T

d= + =

=

(16)

The following further model reductions especially for thedynamic simulation of absorption columns have been takeninto account:± the assumption of steady-state behavior of certain process

elements, such as the liquid holdup of the distributors,± the dynamic changes of the total liquid holdup Ulb

t may benegligible if the column is operated without significantperturbations of the gas or liquid load,

± due to the low density of the gas phase and the smalldimension of the film region, accumulation of mass andenergy is less important in these areas and a quasi-stationaryformulation of the relevant equations seems to be sufficient.On the other hand, the holdup of the periphery often

exceeds the amount of material in the column itself andelements, like pipelines or tanks, can determine the dynamicbehavior of the whole process. In this case, the model has to beextended by considering all relevant parts of the plant.

5 Industrial Application

As an example of industrial applications, we have simulatedthe reactive absorption of sour gases with the selectiveremoval of H2S, NH3 and HCN by suppressing competingreactions of the major impurity CO2 in an air purificationprocess with packed columns (Fig. 5). 14 molecular and ioniccomponents and 8 parallel and consecutive reactions have tobe considered:

Instantaneous reversible reactions

NH3 + H2O $ NH4+ + OH±

H2S + H2O $ HS± + H3O+

HCN + H2O $ CN± + H3O+

HCO3± + H2O $ CO3

2± + H3O+

H3O+ + OH± $ 2 H2O

Kinetically controlled reversible reactions

CO2 + OH± $ HCO3±

CO2 + 2 H2O $ HCO3± + H3O+

CO2 + NH3 + H2O $ H2NCOO± + H3O+

The reactions including CO2 obey first and second orderkinetics, whereas the other reversible reactions are based onsimple proton transfers and are therefore regarded as


Review

instantaneous by the corresponding mass action law equa-tions. The formation of bicarbonate ions (HCO3

±) takes placevia two different mechanisms, the reaction with OH± ions orwater. The rate of the direct reaction between carbon dioxideand hydroxyl ions (the most important step) is given by

r1 � k1 T� � cOHÿ cCO2ÿ ceq

CO2

� �(17)

where ceqCO2

represents the molar concentration at chemicalequilibrium [22]. Usually, the reaction between CO2 and wateris very slow and hardly contributes to the total rate of reactionof carbon dioxide. Nevertheless, in this work it has beenconsidered to be of the first order with respect to the CO2,since the reaction kinetics depends on the carbonation ratio.

The absorption rate of carbon dioxide increases in thepresence of amines or ammonia. Therefore, the reactionkinetics of NH3 and CO2 has been considered in the modelequations as well:

r3 � k3 T� � cCO2cNH3

ÿ 1Keq

3

cH2 NCOOÿ cH3 O�

!(18)

The rate constant as a function of the temperature has beendetermined according to Danckwerts and Sharma [23]. Thecoefficients for the calculation of the chemical equilibriumconstants in this system of volatile weak electrolytes are takenfrom Maurer [24].

The CO2 absorption is hindered by a slow chemical reactionin which the dissolved carbon dioxide molecules are convertedinto the more reactive ionic species. Therefore, when gasescontaining H2S, NH3 and CO2 are contacted with water, theH2S and ammonia are absorbed much more rapidly than CO2

and this selectivity can be accentuated by optimizing the

operating conditions [25]. Neverthe-less, all chemical reactions arecoupled by hydronium ions and addi-tional CO2 absorption leads to thedesorption of hydrogen sulfide anddecreases the scrubber efficiency.

Our model has been used forseveral steady-state and dynamic sim-ulations which have been validated byexperiments performed in a pilotplant absorber at the Berlin Univer-sity of Technology with a diameter of100 mm [26]. In this case, the impu-rities have been removed by a coun-tercurrent flow of recovered solventusing the NH3 included in the cokeoven gas and, optional, a concentratedammonia solution entering the col-umn as a side stream.

6 Numerical Solution

In contrast to recent publications (e.g. [16]), we havedeveloped a detailed dynamic model and applied it to thesimulation of a whole absorber instead of a single stage. Forthis process, the complex rate-based approach led to a DAEsystem of more than 30,000 equations for a single columnwhich had to be solved numerically after a discretization inaxial and film direction.

The numerical solution of the model equations requires adiscretization with regard to the axial (column height) andnormal (film thickness) co-ordinates. As the dynamic formula-tion of the problem, including the consideration of theaccumulation capacity of the column, leads to a system ofdifferential and algebraic equations (DAE), its solution requiresinitial values for the differential variables. A careful analysis ofthe whole system of equations with the choice of suitable initialconditions has been performed in order to prevent high indexproblems. The resulting DAE system has been implementedinto the numerical solver SpeedUp which converts the DAEsystem into ordinary differential equations (ODE) bydifferentiating all algebraic expressions. The necessarynumber of differentiations to get a set of differential equationsdefines the index of this DAE system. To prevent a high indexproblem, no algebraic variable should appear exclusively indifferential equations [27]. For instance, the gas and liquidflows are part of the differential mass and energy balances andare not used in any algebraic equation if the column hydraulicsare neglected. Therefore, correlations for the column hydrau-lics as a function of the gas and liquid flow have been included.

The simulation results for the H2S scrubber show a goodagreement with the steady-state experiments. The investiga-tion of the dynamic column behavior requires some modelreductions to limit the calculation time which allows to use themodel within an on-line process control system.


Figure 5. Ammonia Hydrogen Sulfide Circulation Scrubbing process for the coke oven gas purification and H2Sabsorber.

Review

7 Sensitivity Analysis and Feasible ModelReduction

Much of the important information on the process behaviorcan be obtained from the analysis of a single stage, includingboth the numerical parameters and physicochemical effects.Within an extensive sensitivity analysis for the steady state, thesignificance of both, numerical and physical parameters hasbeen investigated in order to discover potential mathematicalmodel reductions for the dynamic simulations without asignificant decrease of the accuracy.

7.1 Numerical Parameters

For the investigation of the impact of the numericalparameters on the simulation results, the discretization ofthe packing section and the grid points in the liquid film regionhave been varied and the corresponding profiles and totalcolumn absorption rates have been compared.

Figure 6. Liquid film concentration profiles for the key components at differentgrid point distributions.

In Fig. 6, the calculated liquid film concentration profiles forsome key components depending on the number and distribu-tion of the grid points are shown. A limited number of segmentsseems to be justified since the gradients and the boundary valuesdiffer only slightly in all cases. The influence of the filmdiscretization on the mass transfer rates appears as mostlysignificant for the components involved in kinetically controlledreactions (CO2 and carbamate). The detailed analysis of theliquid film region provides additional information about thedirect impact of the chemical reactions on the mass transferwhich can be clearly recognized via the curvature of the profiles(see also [14]). The largest concentration gradients appear forthe ionic components near the interface, which corresponds tothe very fast transfer of protons and causes a significantenhancement of the H2S and NH3 transport. Nevertheless, alogarithmic distribution of the grid points does not cause anysignificant change of the profiles [10]. A similar investigation hasbeen performed for the axial packing co-ordinate leading to therequired number of axial and film segments and decreasing thetotal number of equations by half.

7.2 Physical Parameters

This knowledge has been further applied for the simulationand design of the whole absorber. All relevant physicalparameters have been varied within a range that covers themajority of the published correlations, and the changes of thecolumn absorption rates have been observed.

Figure 7. Relative changes [%] of the total column absorption rates for the keycomponents after a 200 % increase of each physical parameter.

Fig. 7 demonstrates the effect on the total columnabsorption rates for the H2S absorber after increasing thekinetic constants for the reactions of CO2 with OH± (k1), H2O(k2) and NH3 (k3), the gas and liquid phase mass transfercoefficients (kg and kl), the interfacial area and the liquidholdup by 200 %. The most significant parameters are thereaction kinetics of the carbamate reaction and the interfacialarea, as both determine the selectivity of the absorptionprocess. As a consequence, some extremely nonlinearempirical correlations for the other parameters have beenapproximated by suitable linearizations.

The film reaction belongs to the most important phenomenaof reactive absorption processes and reflects the directinteraction of diffusional mass transfer and chemical reaction.

Fig. 8 indicates the essential function of the film reaction, asboth simplifications, the neglection of the conversion withinthe liquid film region (dotted lines) and the equilibrium stagemodel (thin lines) lead to significant deviations from theexperimental results.


Figure 8. Liquid phase axial concentration profiles for the key components inthe H2S absorber, calculated by different model approaches.

Review

A comparison of the corresponding interfacial mass transferand liquid film reaction rates demonstrates the importance ofthe film reaction in this process as both terms are of the sameorder of magnitude (Fig. 9).

Figure 9. Axial profiles of the interfacial mass transfer and film reaction rates forthe H2S absorber.

Figure 10. Calculated column absorption rates for different model assumptionsconcerning the film reaction.

However, some model reductionsrelated to the film reaction are justi-fied. Fig. 10 represents the columnabsorption rates of the key compo-nents for different considerations ofthe film reaction. In the referencemodel, all relevant kinetics are takeninto account within the liquid film andbulk region. The assumption of chem-ical equilibrium in the liquid bulkphase does not change the absorptionrates significantly whereas the ne-glection of the reaction kinetics withinthe film results in completely differentorders of magnitude for the calculatedremovals. As a consequence, thereactions of carbon dioxide may notbe regarded as instantaneous al-

though the corresponding Ha number is about 7 whichcharacterizes the reaction as very fast [19]. As already pointedout by the axial concentration profiles (Fig. 8), neglecting thefilm reaction unrealistically reduces the absorption rates.

The only feasible simplification is the linearization of thefilm profiles including the implementation of average reactionkinetics in the liquid film region (Eq. (16)). In this case, thedifferential balances are substituted by the material balancesacross the entire film thus significantly reducing the number ofmodel equations.

As a result, we can state that the film reaction is a decisiveparameter and has to be considered in the model.

In aqueous solutions of strong electrolytes differentdiffusivities of the charged ions cause immeasurably smallminute charge imbalances that influence the mass transferrates, since even small electrical potential differences can giverise to enormous driving forces [28]. In this process, thepresence of electrical potential gradients, taken into accountvia the Nernst-Planck equation (14), supports the selectiveabsorption of H2S and HCN as representatives of strongelectrolytes (Tab. 1).

The resulting model has been validated by steady-stateexperiments in a column of pilot-plant scale [26]. Figs. 11 and12 underline a good agreement between the experimentaldata and the simulation results for the rate-based approach,whereas the equilibrium model overestimates the absorptionrates of CO2. In this case, the complex process configuration of


Figure 11. Liquid phase axial concentration profiles for the H2S scrubber; comparison between experimentaland simulation results based on different model approaches.

Table 1. Total column absorption rates [%] of the main components andcomparison of Fick's law and Nernst-Planck equation.

Component Fick Nernst-Planck Deviation

CO2 0.778 0.746 ±4.1 %

H2S 11.379 17.742 55.9 %

HCN 7.780 9.127 17.3 %

NH3 ±29.832 ±29.589 ±0.8 %

Review

the H2S scrubber with two separate liquid feed streams hasbeen investigated.

The rate-based approach serves as a basis for the investiga-tion of the dynamic process behavior.

8 Dynamic Simulations

The steady-state modeling is not sufficient if one facesvarious disturbances in reactive absorption operations (e.g., afeed variation), or for control issues, process safety and for theon-line process optimization. In this case, some knowledgeabout the dynamic process behavior is necessary.

In the reactive absorption process described above, theprocess dynamics are determined by the column hydraulics.Due to the different residence times of gas and liquid, thesystem is controlled by the liquid flow. Therefore, the liquidholdup, the liquid distributors and the bottom of the columnare included in the system of model equations to represent thecorrect dynamic behavior.

Figure 13. Dynamic change of the liquid holdup at different positions after asudden change of the gas and liquid load.

Fig. 13 shows the delayed holdupdecrease at four positions of thecolumn as a response to a suddenchange of the gas and liquid flow.

Fig. 14 presents the correspondingsolvent composition at the bottom ofthe column. Both figures indicate asmall time lag for the column until anew steady state has been achieved.For the dynamic simulation of thepilot plant it is necessary to considerthose elements of the column periph-ery leading to larger time lags than thecolumn itself. Therefore, a stirred tankas mixing vessel, pipelines and a heatexchanger for the liquid feed areimplemented into the dynamic pro-cess model.

Although the real dynamic behav-ior of the column periphery is rather

complex, the elements for the liquid phase mentioned abovehave been implemented as consecutive time lag elements offirst order (PT1) and dead-time elements (Tt). The timeconstants of the transfer functions have been determinedexperimentally and adapted after the theoretical values basedon the geometric dimensions of the periphery had led tosimulation results which deviated significantly from theexperimental data (Fig. 15).

This proves the nonideal fluid dynamic behavior andunderlines that the assumption of plug flow for the pipelinesand ideal mixing for the vessel is inaccurate. Fig. 15 alsounderlines the necessity for the model implementation of thecolumn periphery because its time constants are similar tothose of the column itself.

With this extended model we have analyzed and investi-gated the dynamic behavior by observing local perturbationsof the gas load and its composition. Fig. 16 shows the responseto a sudden increase of the gas flow by 20 % and its H2S load by100 %. As expected, the H2S load increases along the column


Figure 12. Gas phase axial concentration profiles for the H2S scrubber; comparison between experimental andsimulation results based on different model approaches.

Figure 14. Dynamic change of the solvent composition at the bottom of the H2Sabsorber.

Review

height in the gas phase whereas in the lower part of theabsorber the change is more significant than at the top. Thenew steady state has been achieved after 30 minutes.

Figure 16. Dynamic change of the H2S gas phase concentration along thecolumn after a sudden increase of the gas flow and its H2S load.

As pointed out by Schneider et al. [9], a higher concentrationof H2S in the coke oven gas causes an additional absorption ofhydrogen sulfide, but the parallel reactions of CO2 lead to anincreasing amount of carbon dioxide in the purified gas. Thecorresponding solvent composition proves the CO2 formationdue to the decreasing mole fractions of the carbonate (CO3

2±)and carbamate (H2NCOO±) ions.

On the other hand, after the ammonia concentration in thesolvent feed has been increased, the purified gas contains lessH2S. However, the competitive reactions of CO2 with theadditional OH± ions generate a higher amount of carbondioxide and products of its reaction in the solvent. Much moreCO2 is absorbed and leaves the column as carbonate andbicarbonate (HCO3

±) and carbamate ions. This means that theincreasing solvent concentration reduces the selectivity of theprocess and much of the ammonia gets lost by the CO2

consumption.

9 Conclusions

Reactive absorption processes represent a complex combi-nation of mass transfer and chemical reaction. Due to the veryfast process dynamics its on-line simulation and model-basedcontrol is rather complicated and requires an accuratemathematical description with an adequate model complexity.

In this paper, we have developed a detailed rate-basedapproach for reactive absorption processes. The model isbased on the two-film theory and takes into account the directinfluence of electrical forces and reaction-diffusion interac-tion on mass transfer via differential balances of the filmregion. Depending on the relation of the transport andreaction rates, the species can react either in the bulk phases,or in the bulk and interfacial regions, or purely in theinterfacial layers.

Optimal reactive absorption models have to be bothrigorous enough in order to reflect the process complexityand simple enough in order to ensure feasibility of dynamicprocess simulations and the application within on on-lineprocess control system. In order to reduce the necessarycomputation time, we have performed several simulationsstarting with a single stage and ending with the dynamicsimulation of a whole column in order to demonstrate theinfluence of numerical and physicochemical parameters onthe calculated absorption rates. Different grid point distribu-tions for the film and packing section, several mass transferand hydrodynamic correlations, and different driving forcesand diffusion models have been thoroughly tested leading tofeasible model reductions which caused no significant devia-tions from the simulation results of the complex referencemodel but reduced the total number of equations by half andstabilized the numerical solution. Although the considerationof the film reaction was observed to be essential for achievingrealistic absorption rates, linearizations of the film concentra-tion profiles represented a possible model simplification forthe dynamic simulation of fast absorption processes.

The resulting model can be considered superior as comparedto previous approaches and has been successfully applied to anindustrial gas absorption process for the purification of cokeplant gases. For this process, the most sensitive parameters arerelated to the components involved in kinetically controlledreactions and the interfacial area. Furthermore, the influenceof the electrical potential gradient on the axial concentrationprofiles has been investigated which is found to be significantfor ionic components. The results underline that the process isdominated by the chemical reaction and its influence on thediffusional mass transfer whereas an implementation of theMaxwell-Stefan approach is not required. In addition, for thedynamic simulation the influence of the column internals andthe periphery has been analyzed and validated by experi-mental data. It should be noted that the simulations of thescrubber based on the equilibrium stage model extended bythe chemical reaction kinetics yielded results completelyinconsistent with the experimental studies as the selectivity ofthe absorption could not be reflected.


Figure 15. Dynamic change of the ammonia concentration in the solvententering the H2S absorber simulated with theoretical and experimentalparameters for the periphery models.

Review

Acknowledgment

Financial support for this project by Volkswagen Founda-tion is gratefully acknowledged.

Received: September 28, 2000 [CET 2715]

Symbols used

Ac [m2] column cross sectiona [m2/m3] specific gas-liquid interfacial areac [mol/m3] molar concentrationd [1/m] generalized driving forceD [m2/s] Maxwell-Stefan diffusion

coefficientDeff [m2/s] effective diffusion coefficientE [J/m] specific energy holdupEA [±] enhancement factorF [9.65 ´ 104 C/mol] Faraday's constantG [mol/s] gas molar flow rateh [J/mol] molar enthalpyki [m3/mol s] second order reaction rate constantKeq

i [±] equilibrium constant of reaction iK [±] phase distribution coefficientL [mol/s] liquid molar flow ratem [±] number of components of mixture,

solvent indexn [mol/m2s] molar fluxq [W/m2] heat fluxqV [W/m] specific heat lossr [mol/m3s] reaction rateRi [mol/m3s] total component reaction rateR [8.3144 J/mol K] gas constantt [s] timeT [K] temperatureU [mol/m] specific molar holdupx [mol/mol] liquid mole fractiony [mol/mol] gas mole fractionz [m] axial co-ordinatezi [±] ionic charge of component i

Greek symbols

d [m] film thicknessu [m3/m3] volumetric holdupg [±] dimensionless film co-ordinate' [V] electrical potentialk [W/m K] molecular thermal conductivityl [J/mol] chemical potential

Subscripts

gas gas phaseliq liquid phase

i,j component/ reaction indicesm solvent indext total

Superscripts

eq equilibriumgb gas bulk phasegf gas filmi phase interfacelb liquid bulk phaself liquid film

References

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Review

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Model Optimization for the Dynamic Simulation of Reactive Absorption Processes