rni236

amcteSMinstedr eer r000ctoy at

as beeineericlude tmicalreactass traing onperties

ner surface (smooth and rough) of an annular duct by the electro-chemical technique under developing ow conditions. Table 1provides a list of some of the correlations available in the litera-ture. Even though the design of annular reactors has relied formany years on the use of such correlations, they present the disad-vantage of being applicable only to a specic reactor congurationoperated under a certain range of hydrodynamic conditions. Be-

Practical annular reactors, however, often do not have an en-trance length to assure a fully developed ow. In fact, in mostof the cases, developing ow is desirable since it gives rise to en-hanced mass transfer. In this sense, inlet and outlet port congu-rations, so as internal accessories (e.g., internal bafes) usuallyplay an important role in improving mass transfer performanceof the reactor.

Mass transfer modeling under developing ow condition is acomplex task. However, the application of computational uiddynamics (CFD) has demonstrated to be a very effective approach

* Corresponding author. Tel.: +1 604 822 0047; fax: +1 604 822 6003.

International Journal of Heat and Mass Transfer 52 (2009) 53905401

Contents lists availab

H

.eE-mail address: mmohseni@chbe.ubc.ca (M. Mohseni).when modeling these reactors, an accurate prediction of uid owand thus, local mass transfer is needed.

Most of the previous studies on mass transfer in annular reac-tors reported in the open literature have concentrated on obtainingcorrelations of dimensionless numbers for different congurationsand operating conditions. Rai et al. [8] compiled several correla-tions for both developed and developing boundary layers underlaminar and turbulent ow conditions. More recently, Mobaraket al. [9] measured the rates of solidliquid mass transfer at the in-

which a rst order heterogeneous reaction was taking place atthe wall. The simulation results were in excellent agreement withthose yielded by the experiments and the investigation revealedthat annular reactors exhibit a mass transfer efciency which isnoticeably higher than that of empty tubes. Other researchershave proposed and evaluated several mathematical models whichincluded mass transfer in annular reactors used for differentapplications, but their systems were limited either to laminar,or to fully developed turbulent ow conditions [10,11,1521].1. Introduction

The annular reactor geometry hmany applications in chemical engthe most common congurations inmembrane reactors [3], electroche[5], and immobilized photocatalyticpotential success and applications, mbe an issue in these reactors dependconditions, and the geometrical pro0017-9310/$ - see front matter 2009 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2009.07.004n increasingly ndingng processes. Some ofube wall reactors [1,2],reactors [4], dialyzersors [6,7]. Despite theirnsfer limitations couldthe kinetics, operatingof the system. Hence,

sides, this type of design correlations does not take into account lo-cal effects. Moreover, the non-idealities introduced by scaling up ofthe lab or pilot-scale equipment are difcult, if not impossible, topredict empirically [13].

A better approach to estimate mass transfer in annular reac-tors is nding suitable models that allow predicting the concen-tration elds inside the reactor. Several researchers have takenthis approach; for instance, Houzelot and Villermaux [14] per-formed a numerical simulation of radial diffusional mass transferin a uid owing in fully developed laminar ow in a reactor inLow Reynolds number ke model reactors. 2009 Elsevier Ltd. All rights reserved.CFD modeling of mass transfer in annula

J. Esteban Duran, Fariborz Taghipour, Madjid MohseDepartment of Chemical and Biological Engineering, The University of British Columbia,

a r t i c l e i n f o

Article history:Received 16 January 2009Received in revised form 10 July 2009Available online 14 August 2009

Keywords:CFDModelingMass transferAnnular reactorTurbulence model

a b s t r a c t

A computational uid dynannular reactors was conduable ke, Reynolds stress (Rmodel) were evaluated agaThe laminar model predict(Re < 1500). Among the fouof the average mass transfconditions (3000 < Re < 11entrance region of the reaAKN and RSM models ver

International Journal of

journal homepage: wwwll rights reserved.reactors*

0 East Mall, Vancouver, BC, Canada V6T 1Z3

ics (CFD) investigation of single-phase ow mass transfer prediction ind. Different hydrodynamic models including laminar, standard ke, realiz-), and the Abe-Kondoh-Nagano (AKN) (a low Reynolds number turbulenceexperimental data in terms of their mass transfer predication capabilities.successfully the average mass transfer in the ows under laminar regimevaluated turbulence models, the AKN model provided a better predictionates in the systems when operated both under transitional and turbulent). The RSM performed very similarly to the AKN model, except for thers where it predicted lower mass transfer rates. These results make thetractive to be integrated in CFD-based simulations of turbulent annular

le at ScienceDirect

eat and Mass Transfer

l sevier .com/locate / i jhmt

V total volume of liquid (m3)X non-dimensional axial position, 4x(1a)/(Re d2)x axial position (m)y+ non-dimensional distance from the wall (dimension-

less)

Greek symbolslt turbulent viscosity (m2 s1)q density (kg m3)s viscous stress tensor (N m2)u function dened as [(1a)/a] [1/2(a2/(1a2)) ln(1/a)] /

[((1 + a2)/(1a2)) ln(1/a)1]

Subscripts0 initial condition (t = 0)1 inner annular cylinder2 outer annular cylindera adjacent to the wallb bulk value

Heat and Mass Transfer 52 (2009) 53905401 5391for tackle this challenge. Taghipour and Mohseni [6] and Mohseniand Taghipour [22] applied computational uid dynamics (CFD)

Nomenclature

A area of mass transfer (m2)a annulus diameter ratio, d1/d2 (dimensionless)C concentration of benzoic acid (mol m3)Dm molecular diffusivity of species k in the mixture

(m2 s1)Dt eddy (or turbulent) diffusivity for species concentration

(m2 s1)d diameter (m)hm average mass transfer coefcient (m s1)h local mass transfer coefcient (m s1)Jk diffusive ux of species k (kg s1 m2)L mass transfer section length (m)mk mass fraction of species k (dimensionless)m0k uctuating mass fraction of species k (dimensionless)P pressure (Pa)Q ow rate (m3 s1)Re Reynolds number (dimensionless)Rey wall-distance-based turbulent Reynolds number

(dimensionless)Sct turbulent Schmidt number (dimensionless)Shav Sherwood number based on the average mass transfer

coefcient (dimensionless)t elapsed time (s)U velocity (m s1)u uctuating ow velocity (m s1)

J. E. Duran et al. / International Journal ofand simulated laminar ow annular photocatalytic reactors treat-ing chlorinated VOCs. The CFD-models were capable of predictingthe reactor performance and provided insight into the concentra-tion gradients of the species in the reactor. For the case of annularreactors operating under developing turbulent ow regime, littlemodeling work has been done. Sozzi and Taghipour [23] performeda detailed CFD simulation of the hydrodynamics of two annularphotoreactor congurations (concentric and normal inlets), andevaluated the results with the velocity proles from particle imag-ine velocimetry (PIV). Under the evaluated operational conditions,the realizable ke and the Reynolds stress model (RSM) turbulencemodels displayed the best overall match to the experimental PIVmeasurements. Even though this investigation brought an impor-tant outcome in terms of recommending appropriate turbulencemodels for computing the uid velocity eld inside annular reac-tors, further investigation is needed to assess their applicabilityto mass transfer modeling. Since the wall-liquid mass transfer phe-nomenon takes place almost completely within the near-wall re-gion, near-wall modeling signicantly impacts the validity ofnumerical solutions and requires experimental evaluation. To theauthors knowledge, no research has been performed on modelingand experimentally evaluating mass transfer of transient and tur-bulent ow with simultaneous development of velocity and con-centration boundary layers in commonly used annular reactorcongurations.

This research has focused on applying CFD for modeling single-phase liquid uid ow and mass transfer phenomena in commer-cial-type annular reactors. CFD allows for an in-depth analysis ofthe uid mechanics, local mass transfer, and other physicochemi-cal processes occurring in chemical reactors, thereby offering thepossibility of achieving an improved performance, a better reliabil-ity, and a more condent scale-up of the equipment. The aim ofthis work was to carry out a comprehensive CFD study in whichsimulation results obtained using different hydrodynamic modelswere evaluated with experimental measurements of external mass

e equivalent or hydraulici inlet conditiono outlet conditionsat saturation conditionx along the axial positiontransfer in annular reactors. The case of mass transfer from the in-ner surface of the outer tube (at constant concentration) was ana-lyzed. The experimental determination of the mass transfer rateswas achieved by coating the inner wall with benzoic acid (as amodel chemical) and then measuring the dissolution of the slightlysoluble acid into the ow stream. Two commonly used annularreactor congurations were studied: with the inlet normal (U-shape) and parallel (L-shape) to the main reactor body. Commer-cial CFD code Fluent 6.3.26 was used to perform the simulations.

Table 1Some correlations reported in the literature for mass transfer in annuli.

Hydrodynamiccondition

Source Correlation Condition Eq.no.

Laminar owFully developed [10] Shav = 1.614(ReScude/L)1/3 (1)Developing [9] Shav = 1.029Sc1/3Re0.55(de/

L)0.472(2)

[11] Shav = 0.66Sc1/3(Reude/L)0.52 X 6 42 104 (3)Shav = 1.56Sc1/3(Reude/L)0.34 XP 42 104 (4)

[12] Shav = 2.703(ReScude/L)1/3 (5)

Turbulent owFully developed [10] Shav = 0.276Sc1/3Re0.58(de/L)1/3 L/de < 2 (6)

Shav = 0.023Sc1/3Re0.8 L/de > 2 (7)[8] Shav = 0.027Sc1/3Re0.8(d2/

d1)0.53(8)

[4] Shav = 0.145Sc1/3Re2/3(de/L)0.25

L/de < 7.5 (9)

Developing [9] Shav = 0.095Sc0.33Re0.85(de/L)0.472

6.8 < L/de < 34.4

(10)

[12] Shav = 0.305Sc1/3Re2/3(ude/L)1/3

(11)

[8] Shav = 0.032Sc1/3Re0.8(1 + (de/L)2/3)(d2/d1)0.53

L/de < 7 (12)

eat2. CFD modeling

2.1. Governing equations

In the present study, it is assumed that the uid (water) is New-tonian, incompressible, isothermal, non-reactive, with constantphysical properties and under turbulent steady state ow. Underthese assumptions and following the Reynolds averaged NavierStokes (RANS) turbulence modeling approach [24], the CFD modelinvolves solving the continuity equation (13), Reynolds averageNavierStokes equation (14) and time-average conservation ofspecies equation (15) which are expressed as

r U 0 13r qUU quu rP r s 14r qUmk qum0k r Jk 15where the overbar indicates a time-averaged value, q is density, U isvelocity, P is pressure, s is viscous stress tensor, mk is mass fractionof species k, Jk is diffusive ux of species k, and u and mk are uc-tuating ow velocity and mass fraction of species k, respectively.Time averaging of the basic governing equations of ow processesleads to the appearance of apparent stress gradients (quu) and masstransfer uxes qum0k associated with turbulent motion. The mainchallenge in modeling turbulent ow lies in the specication ofthese turbulent stresses and mass uxes in terms of the time-aver-aged variables. Generally, for most engineering ow modelingapplications, this so-called closure problem is solved by introducinga turbulence model. Several turbulence models have been proposedin the open literature [25,26], but unfortunately, there is none thatcan be used universally. Proper turbulence models need to be se-lected according to the problem under consideration.

This investigation intended to evaluate CFD modeling of masstransfer in annular reactors over a broad range of hydrodynamicconditions. The Reynolds number (Re) range analyzed was be-tween 500 and 11,000, in which laminar, transitional and turbulentow regimes were present. For the simulations having 500 < Re 0.999 and standard errors for the mass transfer coef-cients

Fig. 4. Schematic of the recirculated batch annular reactor system used for determining the average mass transfer coefcients.

larbta

5396 J. E. Duran et al. / International Journal of Heat and Mass Transfer 52 (2009) 53905401Fig. 5. Average mass transfer coefcients obtained for the U-shape and L-shape annusections coated with benzoic acid. The error bars represent the standard deviation oexpected, mass transfer coefcients increased monotonically withow rates. For both reactor congurations the average mass trans-fer coefcients in section A were much higher than those in sec-tions B, and those in section B were in turn slightly higher thanthe ones in section C. Mass transfer coefcient in section A wasnearly twice that of sections B and C indicating that more than halfof the total mass transfer in the reactor happened in the rst thirdof its volume. This result was the same for all the hydrodynamicconditions investigated (500 < Re < 11,000). An important resultis that the values of the average mass transfer coefcients obtainedat each of the different sections were very similar for both reactortypes. This nding indicates that in terms of average mass transferefciency, both annular reactor congurations perform similarly

Fig. 6. Comparison of the average mass transfer coefcients obtained in the experimentsand C indicate the sections coated with benzoic acid. The error bars represent the standreactors operating under different hydrodynamic conditions. A, B and C indicate theined with triplicate runs.and therefore, there is no particular advantage of one over theother.

Themass transfer data obtained in thiswork showed good agree-ment with those from other reported investigations where similarannular congurationswere used. Fig. 6 compares the averagemasstransfer coefcients obtained for transitional and turbulent ows(3000 < Re < 11,000) with the values predicted by the correlationstabulated in Table 1. The averagemass transfer coefcients obtainedin section A coincided well with the results calculated with the cor-relations corresponding to developing ow, in particular with Eqs.(22) and (23). The experimental data from sections B and C were inclose agreement with the predictions of the correlations proposedfor completely developedow. These results suggest that the abrupt

with the ones estimated using different correlations reported in the literature. A, Bard deviation obtained with triplicate runs.

expansion and change of direction that the uid experiences at theinlet zone of both reactor geometries generate high turbulence, aswell as a large near-surface concentration gradient, which resultsin high mass transfer in section A. The turbulence created in this re-gion is then transported by convection and mass transfer decreasesas the ow redevelops downstreamof the entrance in sections B andC. Althoughnot presented here, similar resultswere obtained for thelaminar-ow data when compared with Eqs. (1)(5).

4.2. CFD hydrodynamic simulations

CFD simulations of the annular reactors (U-shape and L-shape)operating at the same ow rates and conditions of the experimentswere performed. From the perspective of hydrodynamic modeling,the inlet region of both annular reactors is the more challengingzone. The inlet ow impinges on the inner tube, from the top inthe case of the U-shape reactor and from the front for the L-shape

J. E. Duran et al. / International Journal of Heat and Mass Transfer 52 (2009) 53905401 5397Fig. 7. Velocity vectors (m/s) on the longitudinal center plane at the inlet region of theresults correspond to a ow rate of 24.6 L/min (Re = 11,000).L-shape (left) and U-shape (right) reactors using different turbulence models. The

conguration, causing the split of the ow and the creation of owseparation, recirculation, and reattachment zones. Fig. 7 shows thevelocity vector eld at the inlet regions of both reactors whichwere obtained from the simulations performed at a ow rate cor-responding to Re = 11,000. The results correspond to the longitudi-nal center plane of the reactors. Similar velocity vector patternswere obtained in the simulations at the other ow rates. As itcan be seen, the core velocity elds computed using the differentturbulence models look somewhat similar. For example, all thesimulations predicted the same recirculation zones, which inthe case of the L-shape reactor were located at the entrance ofthe annular region (between the inner tube rounded end and theouter wall) and behind the holder prongs. The generation and loca-tion of such recirculation zones in similar reactor geometries wereobserved experimentally by Sozzi and Taghipour [23] using PIVtechniques.

Fig. 8 shows the velocity magnitude contours along the U-shape and L-shape reactor volumes computed using the R k-e tur-bulence model and for Re = 11000. The same ow patterns werealso found when using the other turbulence models as well asfor the other ow rates. As seen in Fig. 8, the velocity magnitudedistribution along the annular space for the L-shape reactor is

more uniform than that for the U-shape reactor. The U-shapereactor shows higher velocities in the section opposite the inletand outlet ports (bottom of the reactor) and a low velocity regionat the top. Such dissimilar velocity elds will produce very differ-ent local mass transfer at the walls of both reactor congurations(this topic is discussed further in Section 4.3). The veracity ofthese particular velocity distributions predicted by the CFD simu-lations was veried by letting the water ow in the reactors for along time, so that the benzoic acid coatings were eroded by thestream at the regions of high velocity. The analysis of erosion pat-terns observed in both reactor congurations agreed with the CFDsimulation predictions.

The previously analyzed results indicate that all the turbulencemodels under evaluation (S ke, R ke, RSM and AKN), indistinctlyof the near-wall region model they utilized, were capable of some-how predicting the main characteristics of the core ow hydrody-namics within both annular reactors. However, accurate masstransfer prediction depends largely on the near-wall region owmodeling; consequently, the fact that a turbulence model can de-scribe appropriately the core ow eld does not guarantee its cor-rect prediction of the surface mass transfer phenomenon. Thissubject matter will be analyzed in the following section.

Fig. 8. Contours of velocity magnitude (m/s) in the U-shape (left) and L-shape (right) annular reactors calculated using the R ke model. The gure shows the longitudinalcenter plane and transversal planes at the middle of sections A, B and C. The results correspond to a ow rate of 24.6 L/min (Re = 11,000).

5398 J. E. Duran et al. / International Journal of Heat and Mass Transfer 52 (2009) 53905401Fig. 9. Comparison of the average mass transfer coefcients obtained in the CFD simulatioobtained using different hydrodynamic models and at sections A, B and C of the reactorns with the experimental values for the U-shape reactor. The results presented were. The error bars represent the standard deviation obtained with triplicate runs.

4.3. Comparison of CFD mass transfer predictions with experimentaldata

Having the CFD simulation results obtained for different owrates and hydrodynamic models, the corresponding average masstransfer coefcients in the reactors were calculated using:

hm QA lnCsat CiCsat C0

22

where Q is the ow rate, Ci and Co are the concentrations of benzoicacid at the inlet and outlet of the reactor, respectively. Eq. (22) is ob-tained by performing a mass balance over the system, assumingthat the concentration of benzoic acid at the wall is constant andcorresponds to the saturation concentration of the acid in water.Fig. 9 presents the average mass transfer coefcients calculatedusing the CFD simulation results for the U-shape conguration.Also, the experimental results are presented for comparison withthe CFD simulations. The results obtained for the L-shape annularconguration were very similar to those of the U-shape and there-fore not shown here.

Fig. 9(a) shows the results corresponding to the case wheremass transfer was taking place at all the sections (A + B + C). Itcan be seen that the results for laminar ow regimes showed excel-lent agreement with the predictions by the laminar model. How-ever, all the evaluated turbulence models to some extentunderestimated the global mass transfer rates associated with allthe ow rates. The AKN predictions were the ones having the clos-est agreement with the experimental data (around 10% error), fol-lowed by those of the RSM. More insight on the capabilities of the

transfer in section A, but the agreement between the results in sec-tions B and C were quite close over the whole evaluation range(3000 < Re < 11,000). This result demonstrates that the disagree-ment found in the case corresponding to sections (A + B + C) isdue to the underprediction computed by the turbulence modelsat section A. One possible reason for this discrepancy is that theturbulence models were not able to capture all the small eddiesgenerated at the inlet, due to the sudden expansion of the ow.However, once the ow redeveloped through sections B and C, tur-bulence decreased and the models performed better.

Further investigation on the liquid-to-wall mass transfer pre-dicting capabilities of the hydrodynamic and near-wall modelswas carried out by analyzing their ability to predict local masstransfer coefcients. A user dened function (UDF) for calculatingthe local mass transfer coefcient (h) at the wall of the reactorswas programmed and integrated into the CFD model using the fol-lowing equation:

h DmCsat CadCsat Cb 23

where is Ca and Cb are the benzoic acid concentrations in the wall-adjacent cell and in the bulk of the uid, respectively, and d is thedistance from the wall-adjacent-cell center to the wall. The three-dimensionality of the ow in the analyzed annular reactors, gener-ated mainly by the specic inlet congurations, creates a two-dimensional local mass transfer distribution at the reactor wall.Fig. 10 shows the maps of local mass transfer coefcients in sectionA for both reactor congurations as computed utilizing the AKNmodel (Re = 11,000). In the case of the L-shape conguration, local

mpu

J. E. Duran et al. / International Journal of Heat and Mass Transfer 52 (2009) 53905401 5399turbulence models to predict mass transfer is obtained via theanalysis of the results acquired for the individual sections (seeFig. 9(b)(d)). All the turbulence models underestimated the mass

Fig. 10. Local mass transfer coefcient (m/s) distributions at entrance section A as coand (b) L-shape reactor conguration.Fig. 11. CFD predictions of the local mass transfer coefcient along the reactor axis comshape conguration.mass transfer at the wall is more uniform; however, three regionsof low mass transfer are evident behind each of the lamp holderprongs. The local mass transfer distribution in the U-shape reactor

ted using the AKNmodel and for a ow rate of 24.6 L/min (Re = 11,000): (a) U-shape,pare with values calculated from correlations: (a) Re = 530 and (b) Re = 11,000, L-

in section A obtained with either a parallel or perpendicular inlet

L-shape reactor which provides a more uniform near-wall velocitygradient might be a better option.

The turbulence models under evaluation (S ke, R ke, RSM andAKN) predicted comparable core ow hydrodynamics which werein agreement with previous PIV investigations of similar systems.The mass transfer measurements demonstrated that the laminarmodel was able to predict successfully the mass transport in lam-inar ows. On the other hand, the AKN and the RSM models per-formed well and predicted turbulent mass transfer in bothannular reactors, except for a moderate underestimation at the en-trance region where high turbulence and mass transfer rates werefound. For the case where the entire reactor was analyzed, the rel-ative error of the estimations for the AKN and RSM models were

eatpresents high values at the bottom and low values at the top of sec-tion A. These results are in accordance with the velocity eld resultsobtained in Section 4.2, since higher mass transfer rates are ex-pected in areas with higher uid velocity gradients near the wall.

The most desirable way to evaluate these CFD simulationswould be to compare the predictions with experimental measure-ments of local mass transfer throughout the walls. Unfortunately,such measurements were not within the scope of this work, northere were any found in the open literature for the studied cong-urations. As a result, an alternative evaluation was performed uti-lizing the one-dimensional correlations reported in Table 1. Fromthese correlations, a local mass transfer coefcient was calculatedthrough differentiation according to:

hx dhmxdx 24

where x is the axial position. These data were compared with theaverage values at axial position x, calculated from the CFD-com-puted local mass transfer coefcients. The averaging was donearound the circumference of the wall at each axial position (x).Fig. 11 presents the results obtained for both reactor congurationsoperating at Re = 530, and for the L-shape conguration operatingat Re = 11,000. The results for the U-shape conguration and forother turbulent ow rates were similar and therefore not shownhere.

As it can be seen in Fig. 11 (a), laminar CFD-computed localmass transfer coefcients were consistent with those calculatedfrom the correlations, especially with the data of Ould-Rouiset al. [11]. Even though the different types of reactor inlets pro-duced different local mass transfer distributions on the reactorwall (as shown in Fig. 10), the average values at an axial positionx were not much different from one another. These results demon-strate the advantage of applying CFD modeling as it brings moreinsight into the analyzed system by providing the local mass trans-fer coefcient at each point; information which cannot be obtainedfrom the correlations. For the predictions of the turbulence models,the results presented in Fig. 11 (b) show a better performance forthe AKN model, followed by the RSM. AKN was able to predicthigher local mass transfer coefcients in the entrance region andas a consequence, provided values closer to the data obtained fromcorrelations (22) and (23). It should be noted that Eq. (22) had theclosest agreement with the average mass transfer coefcientsexperimentally obtained in this work. For values of x/de > 2(x > 0.024 m), the agreement with Eqs. (22) and (23) was excellent,but for values of x/de < 2 (x < 0.024 m) some underprediction withrespect to Eq. (22) was found. Other investigations reported thatthe AKN model could successfully predict separating and reattach-ing ows downstream of a backward-facing step [30], so as liquid-to-wall mass transfer in pipes [32]. The analyzed L-shape annularreactor involves most of the essential physics of these two systems.Fig. 11 (b) also evidences that the difference in the predictions ofthe turbulence models happens in the entrance region. Afterx/de > 5 (x > 0.06 m) the predictions of all of the turbulence modelsare basically the same.

Overall, AKN model provided better mass transfer predictions,particularly in section A. Based on the hydrodynamic simulationsand the experimental evidences obtained in this investigation, itwas not possible to nd any signicant difference between theow elds computed using any of the ke-based turbulence mod-els. Consequently, the better performance of the AKN model mightbe explained in terms of the large impact that near-wall regionmodeling has on surface mass transfer predictions. In this sense,

5400 J. E. Duran et al. / International Journal of Hit appears that for the systems under investigation, the LRN ap-proach simulates better the near-wall region than the two-layerapproach employed in the enhanced wall treatment.port is twice the value obtained without these ports. Interestingly,in the case of laminar ow, the mass transfer coefcient is lowerwhen an inlet section is present. These results demonstrate the sig-nicant impact of the inlet section on the reactor overall masstransfer performance, so as the importance of considering the in-let/outlet ports when modeling commercial-type annular reactors.

5. Conclusions

In this study, experiments and CFD simulations were carried outin order to evaluate the accuracy of different hydrodynamic mod-els for the prediction of surface mass transfer in annular reactors.Two common reactor congurations (U-shape and L-shape) weretested within a range of ow rates corresponding to 500 < Re