Modeling a continuous multistage liquid phase cyclohexane oxidation reactor network

Chemical Engineering and Processing 44 (2005) 567–579

Modeling a continuous multistage liquid phase cyclohexaneoxidation reactor network

Arijit Bhattacharya∗

Chemical Engineering and Process Development Division, National Chemical Laboratory, Pune 411008, India

Received 22 January 2004; received in revised form 28 July 2004; accepted 28 July 2004Available online 14 October 2004

Abstract

A model is presented for a continuous multistage liquid phase cyclohexane oxidation reactors-in-series network, which uses, unlike previousefforts, a closed form rate model derived on the basis of the well-known free-radical kinetic mechanism of the oxidation reaction leading to amore generalized representation of the oxygen dependence of the rate.

The model calculates the required transport and hydrodynamic parameters by one of the best available set of correlations shown earlier tob such as airr ompared veryw validatingt

rms of ay , it can aidi n laboratoryo©

K

1

dobmpotsco

stry

le-oge-

uble). The–Aield

e arete cy-ata-

yclo-thanngeinic

.

0d

e successfully used in cyclohexane oxidation in a well-designed laboratory reactor. Process sensitivities with regard to variablesate, residence time, head pressure, inlet air composition and sparger configuration have been predicted. Some of these trends cell with the limited published experimental data in a three (35 l) agitated and sparged tank-in-series reactor system, thus partially

he model.The model has highlighted a fairly generalized way of correlating performance data from a given reactor, namely in te

ield–conversion characteristic which can change depending on the mass transfer efficiency and the effective kinetics. Hencen plant monitoring and optimization. It has also been shown how to use the same as an aid in preliminary scale-up studies based or pilot plant reactor performance data.2004 Elsevier B.V. All rights reserved.

eywords:Liquid phase oxidation; Cyclohexane; Continuous multistage reactor

. Introduction

Many high volume monomeric organic chemical interme-iates containing only the elements carbon, hydrogen andxygen are commercially manufactured in very large scaley direct oxidation of a hydrocarbon substrate. Some of theost important examples of the liquid phase oxidation (LPO)rocesses are oxidation ofp-xylene to terephthalic acid, thatf cumene to hydroperoxide (and thence to phenol and ace-

one), that of butane to acetic acid and related products, ando on. Air oxidation of cyclohexane to cyclohexanol and cy-lohexanone is an important and typical example of this classf processes. This forms the first of the two-step process of

∗ Tel.: +91 020 25893041; fax: +91 020 25893041.E-mail address:[email protected].

production of adipic acid, currently practised in the induworld wide.

The oxidation of cyclohexane is carried out at evated temperature and pressure and is usually homneously catalysed under mild conditions by using solcatalysts (such as cobalt octoate/oleate/naphthenateconversion is limited to 4–15% in order to promote K(ketone:cyclohexanone–alcohol:cyclohexanol) product y(85–90%). Large quantities of unconverted cyclohexanrecycled. This is necessitated as the primary intermediaclohexyl hydroperoxide is decomposed (aided by the clyst) to the desired products such as cyclohexanol and chexanone, which are actually more readily oxidizablecyclohexane. Even with a limited conversion, a whole raof further oxidation products such as adipic, glutaric, succand oxalic acids and their cyclohexyl esters are formed

255-2701/$ – see front matter © 2004 Elsevier B.V. All rights reserved.oi:10.1016/j.cep.2004.07.002

568 A. Bhattacharya / Chemical Engineering and Processing 44 (2005) 567–579

Cyclohexane oxidation is a two-phase process carried outin a gas–liquid reaction system with the absorption of oxy-gen gas followed by the complex steps of oxidation reactionin the liquid phase. The course of the reaction, in general,may, therefore, be affected as much by the kinetic factors asby the hydrodynamic and transport factors. Since one of thereactants, oxygen, has to be transported from the gas to theliquid phase, its concentration in the liquid phase, therefore,depends on its rate of supply across the gas–liquid interfaceand its consumption by various reaction steps in the liquidphase.

Industrially, the reaction is carried out, commonly, in hor-izontal multistaged (three to five partitioned stages) reac-tors wherein liquid cyclohexane and a catalyst solution arecharged at one end and the “olone” product mixture (or the“K–A oil”) is withdrawn at the other. Partially reacted liquidfrom a previous stage overflows into and out of each stage ina serial sequence. Oxygen-containing gas (air/diluted air) issparged through some sparging device (grids/frits) into eachof the reactor stages in a cross-flow manner. There is an in-stance mentioned in the literature[1] wherein the multistageoxidation has been carried out in a pilot plant comprising ofa series of continuous stirred tanks with air sparged into eachof them.

It is of considerable practical interest to develop a suffi-c cy-c r sys-t someo ely

( er-

( in ak) inystem

( tory

ntedi paste odelo

2

ech-a wass Rus-s ra-t mper-a on thep and( ar[ de-r echa-

Scheme 1.

nisms and validating these under industrially relevant processand operating conditions.

However, chemical engineers showed early interest in elu-cidating the influence of the reactor type (extent of backmix-ing) on the conversion–selectivity relationship on the basis ofsome simple but representative reaction networks for the cy-clohexane oxidation. In terms of a five-component networkinvolving a series of simultaneous and consecutive reactions(seeScheme 1), Spielman[7] had found that at any conversionlevel, selectivity (or the K–A product yield) was higher in abatch or a plug flow reactor than in a continuous flow stirredtank reactor. Also for any type of reactor, the K–A yield or theproduction “efficiency” decreased with an increase in conver-sion. This analysis, however, assumed a simplified first-orderrate dependence on the hydrocarbon concentration and didnot account for any mass transfer limitations and a uniformdissolved oxygen concentration was assumed.

Saunby and Kiff[8] had posed an optimization problem inthe design of the staging of the oxidation reactor. In view ofthe inverse relationship between the conversion and the yield,improved product quality means restricting the conversion,which would entail larger cost of separation and recycling ofunreacted cyclohexane to the reactor feed tank. Increasing thenumber of stages can somewhat offset this effect. A trade offbetween the degree of conversion and the number of reactors ctionnb pri-m tionsa d thata actorc

id-p nsid-e dies ofc (1.5 l

iently general model for a typical continuous, multistagelohexane oxidation reactor (or a tanks-in-series reactoem) that can form the basis for adequately addressingf the following concerns of the process engineers, nam

a) monitoring, troubleshooting and optimization of the pformance of an operating reactor network system;

b) estimation of the relevant kinetic parameters (withgeneral and representative kinetic model frameworthe case of a newly developed process or a catalyst sin the bench/pilot plant scale;

c) aiding preliminary scale-up studies based on laboraor pilot plant reactor performance data.

In course of a review of the pertinent literature presen the next section, one finds that despite some notablefforts, there does seem to be a lack of availability of a mf such general applicability in the public domain.

. Previous work

There have been numerous studies on the reaction mnisms of cyclohexane oxidation. The basic knowledgeummarised in a couple of well-regarded treatises by theian scientists[2,3]. There is also a voluminous patent liteure on the effect of various process variables such as teture, pressure, catalysts and the contacting conditionsroduct distribution. Very few publications, on the other he.g., Potter and coworkers[4,5], Bhattacharya and Mungik6], Pohorecki et al.[13]), have addressed the question ofiving consistent kinetic expressions based on these m

tages was found possible. Using a six-component reaetwork (seeScheme 2; the difference with theScheme 1eing the inclusion of cyclohexyl hydroperoxide as theary intermediate species), pseudo-first-order rate equand no mass transfer limitations, these authors showeseries of three CSTR’s with equal conversion per re

onducting the oxidation would be an optimal choice.Alagy et al.[9] as part of the development of a boric ac

romoted liquid phase cyclohexane oxidation process cored various aspects of the reactor design. Based on stuyclododecane oxidation in a laboratory scale reactor

Scheme 2.

A. Bhattacharya / Chemical Engineering and Processing 44 (2005) 567–579 569

Scheme 3.

turbine stirrer agitated) as well as studies on a 150 l pilot plantscale cyclohexane oxidation reactor (a cylindrical one withstirring generated by gas injection at the column bottom andrecirculation of a part of the outgoing liquid from the columnbottom), the authors conceptually examined the possible in-fluence of mass transfer on the reaction selectivity. Using asimplified reaction scheme (Scheme 3) and a power law type(1–1 order) kinetics, they developed a reactor model that cor-related the data on the selectivity–conversion characteristicsobtained from their pilot plant reactor. Unfortunately, boththe scheme and the rate model were specifically valid for thecase of boric acid-promoted processes, therefore, of limitedgeneralizability.

Krzysztoforski et al.[10] brought in another authentic in-dustrial contribution to the reaction engineering of the cyclo-hexane oxidation. Their work referred to the CYCLOPOLprocess (Industrial Chemistry Research Institute in Warsawand Nitrogen Works in Tarnow) which represented, accord-ing to the authors, the “classical” process (still prevalent dueto its simplicity and lower capital cost) involving almost thesame scheme as that of Alagy et al. minus the boric acid path-way and including the initial formation of the hydroperoxidespecies (Scheme 4).

The point of departure of their work was the explicit con-sideration of the film transport (interphase transport of oxy-g re-

actor model. Also unlike Alagy et al. who used specific val-ues for the mass transfer parameters (which may not have ageneral validity), Krzysztoforski et al. used the correlationsgiven by Akita and Yoshida[11] for estimating these pa-rameters. However, the interphase transport of oxygen wasanalyzed in terms of a pseudo-first-order rate dependencewith respect to oxygen in the film. Considering that eventu-ally the authors found on analyzing data from commercialreactors that the film reaction, if any, was marginal (and thatthe bulk liquid phase oxygen concentration of oxygen wassubstantial), the abundance of oxygen should have been con-sistent with zero-order dependence of the rate on the oxygenconcentration rather than the first order that was assumed[4].

Later, Pohorecki et al. have postulated a somewhat ex-tended reaction network[12,13]of a rather eclectic admixtureof some elementary free-radical steps and some molecularlumped reactions assumed to produce byproduct(s). Repre-senting the interphase transport of oxygen in the same man-ner as Krzysztoforski et al.[10], a model for a five-chamber,sparged, CYCLOPOL reactor was claimed to have been de-veloped. Computed results of product selectivity versus themean residence time compared[12] well with limited pro-prietary industrial scale reactor data from a paper (in Polish)cited by the authors. However, surprisingly, both the modelp oweda encet ser-v

3

del-i ingp

1 e ance-tantn int al.

2 andtionodel

ork,ble,

3 er-arlys ofratetentrate

en through the liquid film at the g–l interface) in their

Scheme 4.

redictions and the plant data presented in the paper shn increase of the selectivity with the increase in resid

ime which is at variance with the available empirical obations (e.g.,[7,9]).

. Present work

From the above review of the previous work on the mong of liquid phase cyclohexane oxidation reactors, followoints emerge:

. While the interphase transport of oxygen does havimportant role to play in the model, chemical enhanment of the rate (film reaction) does not seem imporin the light of data on dissolved oxygen concentratioa commercial oxidator, as quoted by Krzysztoforski e[10].

. While ideally it would be preferable to use a detailedvalidated free-radical-based model for the LP oxidakinetics, for the purpose of integrating into a reactor mintended to be used in practical design and scale-up wa reliable set of closed form rate equations, if availashould suffice.

. Almost all previous reactor modeling effort used ovsimplified pseudo-first-order rate equations (or similarbitrary 1–1 order power law) to describe the kineticthe individual reaction steps. Even if a closed formequation is to be used, it should be in a form consiswith the known complex dependence of the oxidationon the dissolved oxygen concentration[4], showing in-


dependence vis-a-vis dissolved oxygen for large oxygenconcentrations and a first-order dependence with respectto the same as it depletes significantly under some condi-tions.

The paper presents at the outset a model of a realistic re-actor configuration representative of a single stage in a mul-tistage oxidation reactor system (or a serial network) thatallows variation of the concerned transport and hydrody-namic parameters automatically as a result of variations inthe process, design and the operating variables like temper-ature, pressure, residence time, air feed rate and its compo-sition, sparger design, etc. The model also uses a representa-tive and new form of the kinetic model taking into accountthe lacunae highlighted in the point 3 above. The completereactor model comprising of several such reactor stages inseries is then put together. The model predicts characteristicperformance indicators such as conversion of cyclohexaneand K–A product yield (based on the cyclohexane conver-sion) as functions of various process, design and operatingparameters.

The model is then validated against a limited set of pub-lished experimental data obtained in a three (35 l) tanks-in-series pilot plant reactor system.

Finally, the utility of the model in performance monitor-ing, design and scale-up of such a reactor is demonstrated bys

4

del:

• inrged

• r inthe

• e uprod-senteam

• ) en-nsed

• allyough/gridse-

may

• ctoren to

• Auto thermal (non-boiling liquid) operation is assumed fora specified temperature, superincumbent pressure and inletair composition.

• Gas side transport resistance is considered negligible.• It is assumed that there exists a sub-model correlating the

inlet air flow rate and composition, reactor dimensions,sparging (and agitation, if present) device specificationsto the desired hydrodynamic and mass transfer-related pa-rameters (e.g., volume hold-up of the dispersed phase, in-terfacial area and the liquid-side mass transfer coefficient)that are assumed to be spatially invariant in a given reactorstage.

• It is further assumed that interphase mass transfer rate isnot chemically enhanced.

• Ideal gas law, Raoult’s law and Henry’s law are assumedto be valid in the respective contexts.

A reaction network is assumed involving usual compo-nents such as oxygen (A), cyclohexane (B), cyclohexanol(P1), cyclohexanone (P2), and a side product (P3) representedmainly by adipic acid (in practice, it is a mixture of severalorganic acids). The network can be written in terms of a seriesof competitive–consecutive reactions of definite stoichiome-try shown below:

B + 12A → P1

B

P

P

I tionsi ghlyr ady-s hat isc tions,t rablec

rt anola -formr m thet statec oth-e

R

R

R

R

howing some examples of its applications.

. Mathematical model framework

Following assumptions were made in deriving the mo

Liquid phase oxidation of cyclohexane to K–A mixturea serially connected sequence of three to five air spacontinuous flow tank reactors is being considered.Cyclohexane is fed continuously into the first reactothe train and overflows (constant density) along withproducts formed out of one to flow into the next.The feed cyclohexane normally consists of fresh makand the recycled one (after separation from the K–A puct mixture at the end of the train). However, for the prework, our focus being on the reactor train, recycle strcontaining separated cyclohexane is ignored.Cyclohexane evaporated from each reactor (stagetrained with the exit gas is assumed to be fully condeand the condensate returned to the same stage.Total airflow into the reactor system is distributed equover each reactor with the air sparged into the same thrsome gas-dispersing device such as perforated pipesor frits kept near the bottom of the reactor. Additional mchanical agitation device of appropriate configurationbe used.Complete backmixing of the liquid phase within a reastage. The dispersed phase backmixing was also takbe complete.

+ A → P2 + H2O

1 + 12A → P2 + H2O

2 + (n − 1)A → P3

t is understood that each of these stoichiometric reacs the result of a series of elementary steps involving hieactive free radicals that quickly reach very low but stetate concentrations in a time scale much less than tharacteristic of the process. The postulated rate equaherefore, will not have these free radicals but the measuomponents as above.

Recently, Bhattacharya and Mungikar[6] have shown fohe liquid phase oxidation of cyclohexane to cyclohexnd cyclohexanone as the main products that closedate equations such as shown below can be derived froypical free-radical mechanism using the usual steady-oncentration of the free-radicals and the long chain hypsis:

eaction 1 :R1 = k1cAcB

k11cA + k12cB

eaction 2 :R2 = k2cAcB

k21cA + k22cB

eaction 3 :R3 = k3cAcP1

k31cA + k32cP1

eaction 4 :R4 = k4cAcP2


Similar rate expressions have also been postulated in the lit-erature (Suresh et al.[4]) for the same reaction system. More-over, it was shown by Bhattacaharya and Mungikar (2003)that these models provide a fairly close approximation of thelocal rates predicted by a more complete model using a de-tailed reaction network of elementary reaction steps (namelyinitiation, propagation, chain branching and termination) in-volving various free radicals. The advantage in using such ageneralized rate expression (than the simple power law rateforms used earlier) is that these can be used to reflect in aconsistent manner the appropriate rate dependence on thedissolved oxygen concentration from the saturation level tonear zero level (if and when this occurs) and one does nothave to make arbitrary assumption about the form of the rateequations.

The last reaction (further oxidative degradation of cyclo-hexanone to undesired side products like dibasic acids) isactually a lumped representation of a large number of ele-mentary reaction steps. Ideally, a rate equation of the sameform asR1,R2 andR3 can be proposed forR4 with referenceto other identifiable intermediate and side products. However,for the present work, we propose to use a 1–1 order rate equa-tion (R4) for this lumped reaction step. The treatment can beextended if required.

Since only two rate constants for each of the rate equationsR thers1 rated

5o

5

5F

F

y

5L

L

L

L

L

5

c

pB = p0B(T )xl

B (10)

5.1.4. Rate sub-modelrA = −

(12R1 + R2 + 1

2R3 + (n − 1)R4

)(11)

rB = −(R1 + R2) (12)

rP1 = R1 − R3 (13)

rP2 = R2 + R3 − R4 (14)

rP3 = R4 (15)

Above equations [(1)–(15)] along with subsidiary expres-sions/correlations for the calculation of the hydrodynamicand mass transfer parameters represent the complete modelfor the simplest situation prevailing in a typical stage of acyclohexane oxidation reactor.

5.2. Mass transfer sub-model

In order to complete the model computation, one wouldneed to provide, for the specified sparging and agitation de-vice configuration, values for the gas hold-up, interfacial areaand the liquid phase mass transfer coefficients. The literatureis replete with a large number of correlations to estimate theseq erts[ so . De-s idea me-t hicht cana nade[ et ofc imep in al tions[ niesaw s nott tionso ela-ta orre-l enceh rans-f el tod n thisp

5

in-d y un-kc feed

1, R2 andR3 need to be given, we propose here a furimplification of the rate forms by way of settingki1 = 1 (i =, 2, 3) without prejudice to the above generality of theependence on the dissolved oxygen concentration.

. Mathematical model of a liquid phase cyclohexanexidator stage

.1. Reactor model

.1.1. Gas phaseing yin

N = FgyN (1)

ing yin

A − FgyA − kla′Vd(ci

A − clA) = 0 (2)

A + yN + yB = 1 (3)

.1.2. Liquid phasecin

A + kla′Vd(ci

A − clA) − Lcl

A + rAVd(1 − εg) = 0 (4)

cinB − Lcl

B + rBVd(1 − εg) = 0 (5)

cinP1

− LclP1

+ rP1Vd(1 − εg) = 0 (6)

cinP2

− LclP2

+ rP2Vd(1 − εg) = 0 (7)

cinP3

− LclP3

+ rP3Vd(1 − εg) = 0 (8)

.1.3. Gas–liquid equilibriaiA = pA

HA(9)

uantities. One can cite authoritative reviews by Danckw14], van Landeghem[15], Charpentier[16], etc. The perilf using empirical correlations cannot be exaggeratedpite their well-known infirmities, however, these provquick and practical method of estimating these para

ers and allow primary reaction engineering analysis, when can form the basis for more detailed (and if onefford a CFD-based) reactor engineering analysis (Ra

17]). Of course, one has to use discretion to select a sorrelations that best approximate the flow-mixing regrevailing in a given reactor. In this paper, as shown

atter section, we have used Sridhar and Potter correla18] for a situation where mechanical agitation accompair sparging, whereas the Miller methodology[19] was usedhere only air sparging was considered. Our usage i

o be construed as a recommendation of these correlaver others. For example, the Akita and Yoshida corrions [11] have been used by Krzysztoforoski et al.[10] forir-sparged contactors and we found that this latter c

ation, though it gave rather low mean bubble sizes (higher interfacial area) and also overpredicts the mass t

er coefficient values, could have been used in the modemonstrate some of the issues to be highlighted later iaper.

.3. Solution procedure

Eqs.(1)–(10)can be combined to give a set of eightependent, non-linear, algebraic equations in as mannowns, namelyFg, yA, yB, c1

A, c1B, c1

P1, c1

P2andc1

P3. These

an be solved easily, once the gas and the liquid stream


flow rates and compositions are specified, in an iterative man-ner by any standard equation-solving method (software pack-age), starting from some initial guess values for these vari-ables. In this work, we have used the IMSL routine calledNEQNJ.

It is to be noted that these equations involve further setsof equations for evaluating the rates of consumption or for-mation of each of the dissolved components, namelyrA, rB,rP1, rP2 and rP3. This is done by using the rate sub-model[Eqs. (11)–(15)] as a module, which, given the above statevariables, would return values for the rate terms.

Similarly, for evaluating the hydrodynamic and the masstransfer parameters,εg,a′ andkl , the mass transfer sub-modelwas used as a module in much the same way as the rate sub-model.

Once the liquid phase component concentrations at theexit of a stage have been calculated, these become the inletquantities for the next stage and the calculations progress tillthe last stage is reached. At the exit of the last stage, over-all cyclohexane conversion, K–A yield are reported. A sim-ple computer program implemented the procedure outlinedabove with built-in calls to equation solver at each stage.

6. Results and discussion

6

uredd ob-t ex-a thera was

e Oxida

good enough for providing a template for at least partiallyvalidating the present model.

Following on some preliminary oxidation runs in a one-stage mixing reactor to select a window of process and operat-ing conditions, Steeman et al.[1] then conducted experimentson multistage oxidation on a pilot plant scale.

The reactor configuration (as shown schematically in asomewhat simplified manner inFig. 1) involved oxidationcarried out in three jacketed autoclaves each with 35 l ef-fective volume. Each autoclave was provided with a stirrer(magnetic stirrers of Hoffer type, turbo stirrers and propellersof several types were tried out in various runs) and a gas-dispersion element (grids with fine nozzles through whichair was introduced). Partially oxidized cyclohexane issuingfrom each reactor was fed to the next one in series and theoxidate at the exit of the last reactor was sent to a stripperin which unreacted cyclohexane was recovered and recycledback to the feed tank. The off-gases containing evaporatedcyclohexane coming out of each reactor are fed to a coolerwhere cyclohexane was condensed out and the condensaterecycled and mixed with fresh make up cyclohexane beingfed to the reactors.

The temperature range was chosen to be between 155 and160◦C in order to optimize the production efficiency. Pres-sure was chosen (8–9 atm) to ensure auto thermal operation int feedrc ala

stant,S e cy-c K–Ap re-

.1. Comparison with experimental data

For proprietary reasons, there are hardly any measata in open literature on the conversion and K–A yield

ained under commercially relevant conditions of cyclohne oxidation with perhaps the sole exception of a rancient but a classic piece of work which we thought

Fig. 1. Schematic of Cyclohexan
tion Pilot Plant (Steeman et al. 1961).
he temperature range concerned. Air and cyclohexaneates were varied within wide limits (air, 7–17 m3 NTP h−1;yclohexane 50–125 l h−1). All the autoclaves received equmounts of air.

The temperature and pressure having been kept conteeman et al.’s results showed primarily the effect of thlohexane and air feed rate on the conversion and theroduct yield (seetheir Table 1). They attempted to cor


late empirically the observed data on conversion as well asproduct yield as unique functions of a composite parameter,namely air/cyclohexane feed rate ratio (A/L). While this cor-relation was apparently observed for conversion, in the caseof product yield, no such unique correlation in terms of A/Lalone was feasible (additional correlating parameter beingresidence time and the dispersion method). More commonly,however, in the published literature, the K–A product yieldhas been plotted against the cyclohexane conversion.

The model presented here is of general applicability inrespect of a multistaged (or multireactor-in-series) cyclohex-ane oxidation reactor system under industrially significantprocess and operating conditions. It was not our primary in-tention to reproduce accurately the results of a specific set ofexperiments as in a vintage and classic work such as that ofSteeman et al., an effort which, in any case, is fraught withsome difficulties. Due to the incomplete specification of thesparging and agitation, there is uncertainty as to the prevail-ing flow and mixing conditions in the reactor and hence aboutthe values of the appropriate hydrodynamic and mass trans-fer parameters. Also in the experiments, they used condensaterecycle to the feed of the first reactor in series leading to aslight variability in residence times over the reactor stages,unlike a constant value assumed in developing the model.Despite these handicaps, consistent with the objectives of thep fart ancec onesc

asst l-e rgedsd

series exane.

Table 1Rate constant ratios used in the model

k2/k1 = 0.75 k2/k1 = 21k3/k1 = 143 k22/k12 = 1.0k4/k3 = 2000 k32/k22 = 333k1/kla′ = 1.68× 10−3 − 2.55× 10−3

mated by Calderbank and Moo-Young’s correlation[21], εganda′, estimated by Sridhar and Potter correlation[18]. Inthe same work, it was also shown that the kinetic data on theoxidation reaction obtained in the same reactor could be wellpredicted by a model that used kinetic equations based onan extended free-radical mechanism apart from employingthese estimated transport and hydrodynamic parameters. Itwas, therefore, thought adequate to use the same correlationsin the present context with an appropriate assumption of thestirrer speed so as to maintain roughly the same tip speed forthe liquid hold-up in the case of Steeman et al.’s data as it wasfor the experimental data of Suresh et al.[4]. This gavekla′values in the range that was a little less than those found bythe latter authors[20] consistent with the increase in the scale.The oxygen solubility was calculated using the Henry’s lawconstant as reported by the same authors. Physical properties(density, viscosity and surface tension) of the liquid mixturecomprising of mainly cyclohexane and also cyclohexanol,cyclohexanone and adipic acid (at about 7–17% conversioncovered in the experiments) and oxygen diffusivity were cal-culated using standard property estimation methods (Reid etal. [22]).

In Figs. 2 and 3, we present comparison with the exper-imental data, of the model-predicted variation of the con-version and the product yield with the air–cyclohexane feedr ratec of

resent paper, it was thought worthwhile to examine howhe model could be tuned so that the calculated performharacteristics approach the experimentally observedlosely.

Suresh et al.[20] had presented measured volumetric mransfer coefficient (kla′) data under typical conditions revant for cyclohexane oxidation in an agitated air-spaemi-batch reactor. It was shown by us recently[6] that theseata could be reproduced reasonably well by usingkl , esti-

Fig. 2. Effect of air-to-cyclohexane feed ratio on conversion for a
(three number) of CSTRs conducting liquid phase oxidation of cycloh
atio (A/L), respectively. In doing these calculations, theonstants had to be assumed.Table 1summarises ratios


Fig. 3. Effect of air-to-cyclohexane feed ratio on product yield for a series (3 no.) of CSTRs conducting liquid phase oxidation of cyclohexane.

these constants that were chosen (and kept the same for alldata sets) in order to get the predicted results fairly closeto the experimental data. The estimation of these parameterswas numerically very tricky what with problems of slow con-vergence, significant sensitivity with the constraints, etc. Wehave adapted a non-linear constrained optimization routinefrom the IMSL package based on quadratic programmingby including additional operational feasibility constraints ateach reactor stage (as the routine often gets into infeasibleregions). The application of this numerical technique to therelated estimation problems will be presented elsewhere.

Increasing air rate at a fixed liquid rate or decreasing theliquid rate at a given air rate tends to increase conversion,by way of increased mass transfer in the first instance andbecause of increased residence time in the second. Sincethe rates of the first two reactions in the sequence, namelyR1 andR2 (which reflect cyclohexane consumption), in gen-eral depend on the dissolved oxygen concentration, increasedoxygen availability should increase cyclohexane conversion.This is also an indication of the importance, under experi-mental conditions, of both the mass transfer and the oxygendependence of the reaction kinetics. For the chosen set of ki-netic parameters, the calculated conversion seems to be verywell correlated (seeFig. 2) with A/L. This is quite in confor-mity with the observations made by Steeman et al.

ireda th for-m in-c of ther ee ex-c hatt an be

seen in the comparison shown inFig. 3. Although the scat-ter in Fig. 3 is more than that inFig. 2, the correlation doesseem to exist within the space of the limited data in theseexperiments. However, that this may not be always so will beshown later in the paper.

6.2. Process sensitivity

Having shown that the multistage reactor model seemscapable of approaching quite closely a specific set of reac-tor performance characteristics observed under experimentalconditions, it would perhaps be logical to explore, via numer-ical experiments using this model and the same parameters asused above, the sensitivity of the reactor performance undervarious process and operating conditions of practical inter-est. In what follows, we systematically evaluate the effect ofeach of the following variables while keeping others constant.Table 2summarises the conditions for all these numerical ex-periments.

6.2.1. Liquid rateFor a fixed value of the reactor hold-up, variation of the liq-

uid rate entails the same in the residence time and, therefore,an increase in the liquid rate decreases cyclohexane conver-sion with an attendant increase in the yield.

6ocity

t volu-m olvedo ctions con-c h thec

In view of the degradation of cyclohexanone to undescids, as a consequence of increased conversion, boation of the K–A products and their degradation would

rease. Furthermore, due to the oxygen dependenceates of these reactionsR2, R3 andR4, in general, it is to bxpected that the yield will also be correlated with A/L,ept that the yield would decrease with increase in A/L. This was indeed true in the case of Steeman et al.’s data c

.2.2. Air rateIncreasing air rate increases superficial gas vel

hrough the reactor stages bringing about increase in theetric mass transfer coefficients and hence greater dissxygen concentration. Since each of the constituent reateps in the oxidation process depends on the oxygenentration as well, an increase in conversion results witonsequent loss in yield.


Table 2Process and operating conditions for the process sensitivity calculation

Air rate(m3 NTP h−1)

Liquid rate(m3 h−1 × 103)

Pressure(MPa)

Oxygen molefraction in air

6.6 75 0.86 0.219.9 75 0.86 0.21

13.3 75 0.86 0.2116.2 75 0.86 0.219.9 50 0.86 0.219.9 100 0.86 0.219.9 125 0.86 0.21

16.645 125 0.86 0.2113.3 100 0.86 0.219.9 75 0.91 0.219.9 75 0.96 0.219.9 75 0.86 0.159.9 75 0.86 0.19.9 75 0.86 0.21

6.2.3. PressureIncrease in pressure (within the limits of auto thermal op-

eration) mainly causes increase in the interfacial concentra-tion of oxygen (hence the driving force for mass transfer)and therefore leads to an increase in conversion (and a lossof yield).

6.2.4. Inlet air compositionThe effect on conversion (and yield) is just the same as

with the pressure but in this case, a greater range of variationbeing possible can cause larger changes in the driving forceleading to a more pronounced effect on the conversion andthe yield. In view of the safety-related limits on the oxygenconcentration in the vent, the use of oxygen–lean feed gasmay be seriously considered balancing it against the increasedrecycle cost and the model may help finding a compromise.

F of the K R-in-so

6.2.5. Data correlationIn a bid to summarise the above results, we tried at first cor-

relating conversion and yield with the feed flow ratio (A/L).In Fig. 4is shown a gross plot of the yield against A/L for allthe four groups of variation, each group being identified by aseparate legend. This immediately brings out the deficiencyof the correlating parameter A/L. Firstly, for cases like vari-ation of pressure or inlet air composition where A/L is allbut constant, the yield would still change drastically due tochanges in the mass transfer rate without having to changethe air rate. Secondly, for the variation of air rate (with con-stant liquid rate) and vice versa, even if the yield is correlatedwith A/L quite well separately in each case, the trend linesare distinctly apart.

Finally, for cases in which an increase in the residencetime takes place simultaneously with a decrease in the airrate, keeping, however, the ratio A/L constant, the yield is notinvariant, though the extent of change is much smaller thanfound when either air or the liquid flow rates were changedalone. Interestingly, in the experimental data of Steeman et al.[1], shown inFig. 3, similar variation of yield even at almostidentical A/L can be observed.

When we plotted, on the other hand, the above processsensitivity data as K–A yield versus cyclohexane conversion,all the data could be collapsed, remarkably, into a single cor-r tafr arlyp n asw d (atc ncet leastp ferd eansa

ig. 4. Effect of process and operating parameters on the variationxidation reactor network.

–A product yield with air-to-cyclohexane feed ratio for a three-CSTeries

elating trend line (seeFig. 5) running smoothly through darom all the five groups of variation discussed above (R2 cor-elation coefficient = 0.998). On this gross plot, we can clelace the relatively small change in yield with conversioould occur when both air and liquid rates are reduceonstant A/L) in perspective. The effect of higher resideime to bring about higher conversion seems to be atartially nullified by the effect of lower oxygen mass transue to lower air rate. A smaller increase in conversion msmaller loss of yield.


Fig. 5. Effect of process and operating parameters on the variation of the K–A product yield with cyclohexane conversion for a three-CSTR-in-series oxidationreactor network.

The significance of the unique yield–conversion plot inthe present context should not be lost sight of. For a givenreactor configuration such as used by Steeman et al. underconditions as above, both mass transfer and the kinetics in-fluence the rates of the individual steps in a complex manner.Process and operating conditions that increase or decreasethe mass transfer rate will lead to greater or less dissolvedoxygen concentration. This in turn will affect the rates ofindividual reaction steps to different extents depending ontheir ‘variable’ oxygen dependence causing a specific ex-tent of conversion of cyclohexane, formation of cyclohex-anol and cyclohexanone and their degradation to acids. Theoperating point corresponding to the dissolved oxygen con-centration and the residence time in each stage then becomesfairly unique giving rise to a fixed conversion–yield pair. Theapparent correlation between the yield and the conversionin Fig. 5 represents the locus of all such feasible operatingpoints in the space of the process and operating variables.This generalization suggested based on the process sensitiv-ity analyses presented above seems to be borne out by thelimited experimental observations made by Steeman et al.

Spielman[7] and later Alagy et al.[9] presented suchplots of inverse relationship for cyclohexane oxidationreactors (batch and CSTR). Bhattacharya and Mungikar[6] have shown similar performance characteristics for ab ical-b util-i d outb

6

ants( rentc me-w ts

showing higher yields at lower conversion. The aim of thissub-section is to generate conceptually, using the model, newoperating situationsnot reportedin the data obtained by Stee-man et al.[1] and to show that a different yield–conversioncorrelation could be consistent withmodified estimates forthe kla′ and the kinetic parameter values.

For the purpose of this demonstration, we consider thesame three-stage reactor system as above, but this time withair-sparging only. That being the only means of gas disper-sion, we propose to use superficial velocities much higherthan that used above. The sparging device is assumed to bea single perforated ring placed at a specified depth under theliquid. Miller [19] had conducted experiments with just sucha sparged tank configuration and using air–water model sys-tem and summarised a concise procedure for calculating themean bubble size, gas hold-up and the interfacial area. Inaddition, they had also provided a correlation for the masstransfer coefficient. The correlations within this methodol-ogy to calculate the average hydrodynamic and mass transferparameters have been verified by us extensively testing themagainst published literature data onεg andkla′ at least forair–water systems at various scales (up to∼70 cm diametervessels).

Applicability of the Miller methodology to air–organicliquid systems may be debatable as it may overpredict them nder-p em-i r, weh tivelyc et-r quidr ns ofa cep-t therc lanto

atch reactor model using a more detailed free-radased kinetics. However, the unique data correlation

ty of these plots does not seem to have been pointeefore.

.3. Model adaptation

The yield–conversion characteristics in modern plwith varying sparging configurations and/or using a diffeatalyst or its concentration) are, in general, likely to be sohat different from that inFig. 5, with, say, operating poin

ean bubble size and the mass transfer coefficient and uredict the interfacial area. Using appropriate physicoch

cal properties for the air–cyclohexane system, howeveave had at least a base procedure that gives qualitaorrect trends in values for the hold-up and the volumic mass transfer coefficients as functions of air and liates, pressure and inlet air composition under conditioir-sparging alone. For the purpose of the present con

ual demonstration, this was considered sufficient. Any oorrelation/methodology, more appropriate to a given pperation, should do equally well.


Fig. 6. Effect of process and operating parameters on the variation of the K–A product yield with cyclohexane conversion for a three-sparged tank-in-seriesoxidation reactor network.

Fig. 6 shows primarily the mean yield–conversion char-acteristic corresponding to this new process and/or reactorconfiguration, showing the range of variation of each of theparameters. The direction of these variations is similar to thatin Fig. 5, though the characteristic line running through thedata is steeper and laterally shifted towards lower conver-sions. Thus, for a small change in the conversion, there is amore significant change in the yield. Thekla′ values used arelower in this case (in the range 0.08–0.14 s−1) and the rateconstants have been appropriately modified (which could cor-respond to, say, a different catalyst system or concentration)to provide a different yield–conversion relationship than oneshown inFig. 5. Finally, corresponding yield–conversion datafrom Steeman et al.[1] have been superimposed on this plotto show both the qualitatively similar nature of the character-istics, at the same time distinguishing, by the slope and thelocation of the curves, clearly different processing conditions.The model seems adaptable to both the scenarios.

6.4. Scale effects

There is yet another useful way the model can be utilized.As an example, with a reactor stage volume of, say 0.0252 m3,

TS

R r config )

No

0 8 200 5 250 5 250 9 400 9 40

N

as a base case, as the volume is increased corresponding toa higher liquid rate (consistent with an increased produc-tion rate) so that one maintains identical residence times ata higher scale (say, 0.252 m3) as in the base case, there is aquestion about choosing the right air rate at the higher scale.Let us consider the same cylindrical air-sparged tank as thereactor configuration fitted with a simple ring sparger as inthe preceding sub-section. The number of sparger holes inthe small-scale tank could be chosen to keep the lateral mal-distribution to within∼10%. The number of holes for thelarger tank size, on the other hand, as per a common scale-uppractice, can be chosen to keep about the same hole spacingfor the corresponding hole size. On this basis, the spargerhole size, number of holes and the spacing between the holeswere chosen for the larger size reactor (Miller[19]).

With reference toTable 3, the model calculations showthat maintaining the same superficial air velocity as in thebase case is unlikely to reproduce the base case operatingpoint. Rather, a little higher superficial velocity (ug) wouldbe called for, which the model can be systematically usedto find. As expected, for the same superficial velocity, thevolumetric mass transfer coefficient (kla′) is reduced as onegoes to higher scale. This is compensated by increasingug

able 3cale effect on the multistage oxidation reactor performance

eactor hold-up (m3) L × 106 (m3 s−1) ug × 102 (m s−1) Sparge

Do (m)

.0252 27.44 6 0.0031

.252 274.4 6 0.0063

.252 274.4 6.75 0.0063

.00252 2.744 6 0.0015

.00252 2.744 5.26 0.0015

ote: Head pressure = 0.86 MPa; inlet oxygen mole fraction = 0.21.

uration εg × 101 kla′ (s−1) Conversion (%) K–A yield (%

X (m)

0.0279 1.964 0.0935 7.77 80.360.0518 1.793 0.0876 7.52 81.750.0518 1.963 0.0961 7.72 80.610.00698 2.168 0.1 7.91 79.330.00698 1.963 0.0908 7.75 80.41


and an almost identical operating point as in the lower scaleis reached with about the same dissolved oxygen concentra-tion. In the last row of the table are presented model calcu-lations for the corresponding scale-down scenario (reactorvolume of 0.00252 m3) and the appropriateug to use in thatcase.

This is perhaps a somewhat idealized but a safe scale-upprocedure. In the above calculations, identical head pressureand inlet air composition were used in both the scales. How-ever, even if one were to choose a different operating pressureor use a more dilute or enriched air (from other considera-tions) than in the base case, the model can still be used tochoose the appropriateug in the higher scale (within the lim-its of applicability of the correlation in terms of theug range).It is safe because the model helps one to easily find the A/Lratio that would be required in another scale to maintain afeasible operating point. This then can be refined further byaltering the value ofug as shown above. The results of thesemodel calculations are expected to be of interest to those in-volved with process development efforts (say, with a newlydeveloped catalyst or modified process conditions) in pilotplant studies on LP oxidation processes such as consideredhere.

The reactor sizes considered in demonstrating the scaleeffect are indeed much smaller than the commercial reac-t cor-r monc ntalv t too eemt vinga andm thers ita-t id inp dela del, ifa ctuad

7

tinu-o r (orm hichu sub-m bet-t wnf Thisr encet e re-a

mat-i micp tions

shown earlier to be successfully used in cyclohexane ox-idation in a well-designed laboratory reactor. This has al-lowed the model to predict process sensitivities with regardto variables such as air rate, residence time, head pressureand inlet air composition. Some of these predicted varia-tions appear to be fairly close in comparison with limitedpublished experimental data, thus partially validating themodel.

In the context of a newly developed process or a catalystsystem in the bench/pilot plant scale, the model can be usedin the estimation of the relevant kinetic parameters. It hasalso been shown how to use the same as an aid in preliminaryreactor scale-up studies based on the laboratory or pilot plantreactor performance data.

There is no reason why the mass transfer sub-models usedhere as examples cannot be replaced with a more appropriateone should this be warranted. This along with the possibil-ity of tuning (or reestimating) the rate constants makes themodel quite adaptable to typical operating plant behaviour.The model has highlighted a fairly generalized way of corre-lating performance data from a given reactor, namely in termsof a yield–conversion plot and, hence, can aid in plant moni-toring and providing technical services. Together with a unitmodule for the downstream cyclohexane separation system,the model provides a way to simulate the entire oxidations

A

AacDFHkkkLn to

Npp

r ent

R ps

TuVxXy

ors and were limited by conditions under which theelations used were derived and tested. For the comommercial reactor configurations of partitioned horizoessels with overflowing liquids from one compartmenther and with cross-flow air-sparging, there does not s

o be any published set of correlations (especially involir–organic systems) for calculating the hydrodynamicass transfer parameters. Miller methodology or any o

imilar set of empirical correlations can only give qualive indications of the trends and may be used as an areliminary designs. Ideally, coupled with a kinetic mos presented here, a rigorous CFD-based reactor mond when developed, should serve the requirements of aesign.

. Concluding remarks

In this paper, we have presented a model for the conus multistage liquid phase cyclohexane oxidation reactoultiple stirred and/or air-sparged reactors-in-series) wses, unlike in the previously published efforts, a kineticodel comprising of closed-form rate equations that has

er justification being derived on the basis of the well-knoree-radical kinetic mechanism of the oxidation reaction.ate model allows complex oxygen concentration dependo be included in an intrinsic manner and therefore morlistic representation of the reaction kinetics.

The model also uses another sub-model that autocally calculates the required transport and hydrodynaarameters by one of the best available set of correla

l

ection and optimize the same.

ppendix A. Nomenclature

inlet air volumetric flow rate (m3 NTP s−1)′ interfacial area per unit dispersion volume (m2 m−3)

concentration (kmol m3)o sparger hole diameter (m)g molar flow rate of gas (kmol s)A Henry’s law coefficient (Pa kmol−1 m3)

l liquid side mass transfer coefficient (ms−1)1, k2, k3, k4 reaction rate constants (m3 kmol−1 s−1)ij , i = 1, 3,j = 1, 2 additional rate parameters (m3 kmol−1)

liquid overflow rate (m3 s−1)kmol oxygen per kmol cyclohexane convertedbyproducts

o number of sparger holesA partial pressure of oxygen (Pa)0B vapour pressure of cyclohexane (Pa)

rate of consumption/production of a compon(kmol m−3 s−1)

1, R2, R3, R4 rates of individual reaction ste(kmol m−3 s−1)reactor temperature (K)

g superficial air velocity (ms−1)d dispersion volume (m3)B mole fraction of cyclohexane in liquid

sparger hole spacing (m)component mole fractions in gas


Greek lettersεg fractional gas hold-up

Superscriptsi gas–liquid interfacein reactor inletl liquid phase

SubscriptsA oxygenB cyclohexaneN nitrogenP1 cyclohexanolP2 cyclohexanoneP3 adipic acid

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