Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chemical Engineering Science 54 (1999) 5633}5645 Gas}liquid interfacial mass transfer in trickle-bed reactors: state-of-the-art correlations Ion Iliuta , FamK c7 al Larachi *, Bernard P. A. Grandjean , Gabriel Wild Department of Chemical Engineering and CERPIC, Laval University, Que& bec, Canada G1K 7P4 Laboratoire des Sciences du Ge& nie Chimique, CNRS-ENSIC, 1 Rue Grandville, BP 451, 54001 Nancy, France Received 3 August 1998; received in revised form 12 February 1999; accepted 12 February 1999 Abstract The state-of-the-art of the gas}liquid mass transfer characteristics in trickle-bed reactors was summarized and its quanti"cation methods were reevaluated based on a wide-ranging data base of some 3200 measurements. A set of three uni"ed whole#ow-regime dimensionless correlations for volumetric liquid- and gas-side mass transfer coe$cients, and gas}liquid interfacial area, each of which spanned four-order-of-magnitude intervals, were derived. The correlations involved combination of arti"cial neural networks and dimensional analysis. The dimensionless interfacial area, Sh and Sh were expressed as a function of the * % most pertinent dimensionless groups: Re , Re , =e , =e , Sc , Sc , St , X , Mo , Fr , Eo , S . 1999 Elsevier Science Ltd. * % * % * % * % * * K @ All rights reserved. Keywords: Trickle-bed reactor; Arti"cial neural networks; Dimensional analysis; Gas}liquid mass transfer; Correlations 1. Introduction Trickle-bed reactors (TBRs) are randomly packed "xed-bed tubular reactors in which gas and liquid streams are processed in downward cocurrent two-phase #ow. TBR technology is prevalent in diverse industrial areas and spans a wide spectrum of applications including the manufacture of petroleum derivatives and fuels (Chen and Tsai, 1997; Landau et al., 1998), the production of commodity and specialty chemicals (Westerterp and Wammes, 1992; Chou et al., 1997), pharmaceuticals, pesticides and herbicides (Khadilkar et al., 1998; Jiang et al., 1998), pollution abatement and bio-scrubbing, etc. (Cheng and Chuang, 1992; Pintar et al., 1997; Ravindra et al., 1997; WuK bker et al., 1997). The permanent market demands at meeting high-quality products while ful"lling both environmental and economical requirements, drives the researchers and developers to improve constantly On leave from Department of Chemical Engineering, Faculty of Industrial Chemistry, University Politehnica of Bucharest, Polizu 1, 78126 Bucharest, Romania. * Corresponding author. Tel.: #1-418-656-3566; fax: #1-418-6565993. E-mail address: #[email protected] (F. Larachi) their knowledge about the physico-chemical phenomena taking place in TBRs. However, in spite of considerable research in the past 40 years, TBR mass transfer is still not well understood and general correlations of mass transfer parameters are still out of grasp. Hence, it is well recognized that Achilles' heel of the currently available TBR design tools lies in their lack of generality inherent partly to the narrow experimental windows upon which validation of most correlations/models is carried out, and partly to biased analysis and inappropriate mathematical expressions. Yet a decade ago, a French initiative led to the so-called Ellman TBR correlations (Ellman et al., 1988,1990; Wild et al., 1992) which were considered among the best empirical correlations as they covered the broadest database at that time (ca 5000 measurements). Unfortunately, lack of success of these correlations was repeatedly pinpointed in the recent literature (Ratnam and Varma, 1992; Benkrid et al., 1997; AndreH , 1997; Chen, 1998; Al-Dahhan et al., 1998; Larachi et al., 1998a). In response, a renewed e!ort to reach better predictability of TBR gas}liquid mass transfer and hydrodynamic parameters was launched by us with the endeavor of elaborating the most comprehensive two-phase #ow databases based on the worldwide literature published over the last half century on cocurrent packed beds. There is a twofold goal behind 0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 1 2 9 - 3 5634 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 this initiative: (i) The "rst goal is to assess and to critically evaluate all available design tools, whether empirical or theoretical; and (ii) while the second is to eventually re-engineer these tools through sound approaches which will lead to the most robust constitutive TBR design predictors. We thus compiled over 30,000 experimental data on #ow regime transitions, two-phase pressure gradients, liquid (external, dynamic, static) holdups, gas} liquid interfacial areas, and volumetric liquid- and gasside mass transfer coe$cients. Only with comprehensive operating ranges covering every recess of the #ow operating map of two-phase #ow in packed beds, can state-ofthe-art correlations tangibly useful for industry scale-up purposes be developed. Our approach rests on combining dimensional analysis with neural networks to train neural network models based on huge data sets and then make predictions based on such models. Two recent articles illustrate the possibilities of such an approach for packed bubble columns (Bensetiti et al., 1997; Larachi et al., 1998b). This work aims at providing researchers and engineers with uni"ed, yet most accurate gas}liquid mass transfer explicit and whole-#ow-regime correlations for interfacial areas, volumetric liquid-side and gas-side mass transfer coe$cients in trickle-bed reactors based on beyond 3200 mass transfer data published in the literature between 1963 and 1998 (a comprehensive bibliography on TBR mass transfer consisting of over 70 references is included in this report). The e!ectiveness of the developed neural correlations will be discussed through comparisons against most popular literature mass transfer correlations. The methodology leading to these neural network correlations is similar to the one already employed by Bensetiti et al. (1997). Therefore, for the sake of brevity and to avoid repetitions, we will spare the reader all the details which may be found in Bensetiti et al. (1997) and Larachi et al. (1998b). 2. Need for new, improved gas}liquid mass transfer correlations the reader is invited to consult the References section where a meticulous report of the whole gas}liquid mass transfer is given. Table 1 lists the ranges of variation of the overall mass transfer parameters, #uid properties, operating conditions, particle and bed geometrical properties, liquids and gases belonging to this database. The di!erent mass transfer parameters are obtained using operating conditions typical of cocurrent down#ow trickle beds, packed absorption as well as desorption columns. The corresponding solids inventories include few cm size packings (Raschig and Pall rings, Intalox, Berl saddles) of high bed porosity (e up to 94%), and few mm size packings (porous and nonporous spheres, extrudates and pellets) of moderate bed porosity (e)45%). The super"cial #uid velocity ratio, which is a measure of gas}liquid interfacial slip and thus intensity of interaction, spans four-order-of-magnitude ranges for each mass transfer parameter. These latter in turn vary by about the same amplitudes. The gas}liquid interfacial area includes conditions of partially (a(a ) to fully wetted (a*a ) Q Q packings. It is worth mentioning that the database encompasses the unusual conditions where gas-side mass transfer resistance exceeds its liquid-side counterpart. 2.2. Dimensional analysis From considerations stated elsewhere (Bensetiti et al., 1997), it is proposed to analyze the impact of #uid velocities, densities, viscosities, di!usivities, surface tension, gravitational acceleration, particle size and shape, bed diameter and porosity, via their combinations in the various dimensionless groups that may a!ect the gas}liquid interfacial mass transfer parameters. Many hundreds of sets of dimensionless groups were thus tested by trial and error with the ultimate objective of identifying the optimal sets of groups best describing each of the gas}liquid interfacial areas, a (via ad /(1!e)), the volF umetric liquid-side mass transfer coe$cients, k a (via * Sh ), and the volumetric gas-side mass transfer coe$* cients, k a (via Sh ). The choice of the best sets rests on % % the ful"llment of the following criteria: 2.1. Data base compilation The neural network gas}liquid mass transfer correlations were derived based on an extended mass transfer database containing more than 3200 measurements compiled from about 70 references in the open literature between 1963 and 1998. This database includes 52 gas}liquid systems, more than 60 packing sizes and geometries, 17 column diameters, high-pressure data, data for coalescing, non-coalescing and pseudoplastic nonNewtonian aqueous and organic liquids, and data for low and high interaction regimes (trickle, pulse, bubble and dispersed bubble #ows, foaming and foaming-pulsing #ows). To avoid burdening the text with references, E The optimal set must contain a minimum number of selected dimensionless groups. E Each group must be highly cross-correlated with the corresponding mass transfer parameter group (output to be predicted). E The optimal set must lead to the best output prediction, i.e. minimal absolute average relative error (AARE) and variance. E The neural network architecture must be of minimal complexity, i.e. the least number of hidden neurons giving the smallest errors both on the learning (70% of the database) and the generalization "les (the remaining database). I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 5635 Table 1 Description of database Fluid physical properties Operating conditions 805)o )1450 * 6.32;10\)k )4.72;10\ * 1.06;10\)p )7.77;10\ * 0.937)o )57.46 % 0.1)P)5.1 MPa 19)¹)30.53C 3;10\)< )1.488;10\ 1* 1.289;10\)< )4.5 1% < k a: 6.3;10\) 1%)6.5;10 * < 1* 1.66;10\)k )2.6;10\ % Limits of gas}liquid mass transfer parameters 2.13;10\)k a)7.04 * 4.76;10\)D )4.0;10\ * 6.6;10\)D )1.6;10\ % Geometrical properties of packings and columns Particle diameter, d (m) N Column diameter, d (m) A Bed porosity, e Shape factor, Particle material Particle shape < k a: 8;10\) 1%)1.8;10 % < 1* < a: 0.23) 1%)1.5;10 < 1* 2.36;10\)k a)6.94 % 23.4)a)9070 5.4;10\)d )2.64;10\ N 2.3;10\)d )3.0;10\ A 0.263)e)0.94 0.133) )1.0 Glass, ceramics, porous alumina, carbon, stainless, polyethylene, polypropylene, CuO}ZnO catalyst Spherical, cylindrical, extrudates, Raschig and Pall rings, Intalox, Berl saddles Cylindrical Column geometry Liquids H O, H O#C H , H O#NaOH[0.1}2 N], H O#Na SO [0.8 M], H O#Na SO [1. M], H O#Na SO [0.5 M]#Co>, H O#Na SO [0.8 M]#CoSO [5;10\ M], H O#NaOH [0.5}2 N]#Na SO , H O#K CO [0.8}1.3 M]#KHCO [0.65}1.2 M], H O#Na S O , H O#MEA [0.25}0.33 M], H O#DEA [1.5}2 M], H O#DIPA [2.4 M], H O#DEA [1.5 M]#ETG [20}40%], H O#40% CaCl , H O#naphthalene, H O#CHA [0.227}1.177 M]#toluene#10%IPA, H O#EtOH#MEA, EtOH#MEA [0.2}0.7 M], EtOH#DEA [0.6 0.8 M], IPA#toluene#CHA [0.1}0.7 M], toluene#10% IPA#DIPA, p-xylene#10% i-PrOH#CHA, n-C H OH#MEA, H O#0.1% CMC, H O#0.5% CMC, H O#1.0% CMC Gases He, air, air#CO , air#SO , air#O , air#moisture, N #CO , N #O , CO Common liquids (Lide, 1993); mixtures (Grunberg and Nissan method, Reid et al., 1987). Macleod and Sugden method (Reid et al., 1987). Ideal gas law ()0.1 MPa), if *0.1 MPa (L'Air Liquide, 1976). Pure gases (L'Air Liquide, 1976); mixed gases (Wilke method: Reid et al., 1987). Wilke and Chang method (Reid et al., 1987). Takahashi method (Reid et al., 1987). Finally, the most relevant dimensionless groups are: E For Sh : liquid inertia-to-viscous forces ratio (Re ), * * liquid inertia-to-capillary forces ratio, (=e ), gas-to* liquid inertia forces ratio (X ), capillary forces ac% counted for via a Morton number (Mo ), momentum * di!usivity-to-mass di!usivity ratio (Sc ), and the bed * correction function (S ). @ E For Sh : Re , X , Sc , S , gas inertia-to-capillary for% * % % @ ces ratio (=e ), and liquid viscosity-to-gravity forces % ratio (St ). * E For ad /(1!e): Re , =e , X , S , gas inertia-to-visF * * % @ cous forces ratio (Re ), gravity-to-capillary forces ratio % (Eo ), and inertia-to-gravity liquid forces ratio (Fr ). K * Cross-correlation coe$cients (a ) between the gas} NO liquid mass transfer parameters and the di!erent dimen- sionless groups are listed in Table 2. This table shows that: Sh increases as Re , =e , X and S increase * * * % @ and decreases with increasing Mo and Sc ; Sh in* * % creases as Re , =e , Sc , X and S increase and de* % % % @ creases with increasing St ; ad /(1!e) increases as * F Re , Re , Eo , X and S increase and decreases with * % K % @ increasing =e and St . It is interesting to note that * * (i) bed/particle geometrical properties, i.e. S , a!ect @ strongly the gas}liquid mass transfer groups, and (ii) X % a!ects Sh and Sh the least, and so does Fr for * % * ad /(1!e). F 2.3. Neural regression A three-layer arti"cial neural network model was designed, using NN"t software (Cloutier et al., 1996), to 5636 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 Table 2 Cross-correlation coe$cients of gas}liquid mass transfer parameters to dimensionless groups Dimensionless group Cross-correlation to Sh (%) * Cross-correlation to Sh (%) % Cross-correlation to ad /(1!e) (%) F Re * Re % =e * =e % X % St * Eo K Fr * Mo * Sc * Sc % S @ 55.7 } 37.1 } 7.2 } } } !8.9 !10.4 } 64.3 72.6 } } 92.1 17.5 !19.2 } } } } 66.5 91.3 35.5 49.0 !21.0 } 18.0 } 32.9 !10.1 } } } 81.4 derive dimensionless correlations for the gas}liquid mass transfer parameters. The neural architecture is described by Eqs. (1) and (2) (Table 3) that correlate the network normalized output, S, to a set of normalized input variables, ; . In these equations, ; and H de"ne the input G and hidden layer vectors, and H and ; are the (> '> bias constants set equal to 1, u and u are the weights or GH H the "tting parameters of the neural network, and J is the number of hidden nodes. The network weights are unknown a priori. They have to be determined using a training algorithm by performing a nonlinear leastsquares regression over known pseudo-random set of inputs/outputs (learning "le, ca. 70% of the database, i.e., 2240 data). The weights are set to minimize the training error on the training set using a quadratic objective function which was minimized by the quasiNewton}Broyden}Fletcher}Goldfarb-Shanno algorithm (Press et al., 1992). A good measure for the extrapolation performance of a well-trained neural network is given by the generalization error which should be close to the training error in the case of inputs/outputs not presented during the learning step of the neural network (generalization "le, ca. 30% remaining data set, i.e., 960 data). The number of hidden neurons, J, was varied from 3 to 15. Hidden layers with 8 neurons (for Sh ), 13 % neurons (for Sh ) and 11 neurons [for ad /(1!e)] were * F found to be the optimal neural architectures leading to the smallest average absolute relative errors (AARE) and standard deviations on the learning as well as the generalization "les. The complete sets of the neural network equations for the gas}liquid mass transfer parameters are given in Table 3, and Table 4 lists the "tted weights of each neural correlation. The detailed form of the three correlations is freely accessible from the net at the following web address: http://www.gch.ulaval.ca/&#arachi. 2.4. Performance of the neural network correlation, comparison with most general correlations Figs. 1}3, respectively, are parity plots of the dimensionless overall liquid-side, gas-side mass transfer coe$cient and interfacial area correlations over the learning and test sets from the database. The respective scatters between neural network predictions and experimental values are summarized in Table 5 for the learning "le, the generalization (or test) "le, and the whole database. As shown in these "gures, agreement between the experimental results and those predicted by the neural network correlations is very good. Hence, respectively 55% (Fig. 1a, and b), 75% (Fig. 2a and b) and 50% (Fig. 3a and b) of the mass transfer data fell within the $15% limits of the Sh , Sh and ad /(1!e) correlations. Also, we compared * % F the experimental data with the predictions from the majority of the literature correlation (AndreH , 1997). Table 6 excerpts, among these literature correlations, the ones which exhibited the lesser scatters (AndreH , 1997). AAREs given by the neural network correlations (Table 5) and by the most general literature correlations (Table 7), indicate that prediction of gas}liquid mass transfer parameters were improved noticeably. The former outperforms the latter by up to a factor eight for Sh , a factor nine for Sh % * and a factor xve for gas}liquid interfacial area. Despite gas}liquid mass transfer parameters are strongly dependent on #ow regimes, the present correlations are capable of predictions of these mass transfer parameters regardless of the prevailing #ow regime. 3. Closing remarks Based on the largest gas}liquid interfacial mass transfer database (beyond 3200 data), new, state-of-art I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 5637 Table 3 Set of equations for the neural network correlations 1 S" 1#exp [!(>u H ] H H H (1) 1 H" H 1#exp [!'>u ; ] G GH G Sh (I"6, J"13) * sh * log 0.3359 S" 5.2428 (2) (3) Re =e X * * % log log log 1.994;10\ 1.851;10\ 2.636;10\ , ; " , ; " ; " 4.898 6.298 4.918 Mo Sc S * * @ log log log 2.545;10\ 44.33 2.552 ; " , ; " , ; " , ; "1 10.114 4.042 1.9011 (5) Sh (I"6, J"8) % Sh % log 1.311;10\ S" 6.752 (6) Re St =e * * % log log log 2.089;10\ 4.323;10\ 1.711;10\ , ; " , ; " ; " 2.6751 3.615 6.8823 X Sc S % % @ log log log 8.288;10\ 2.328;10\ 1.740 ; " , ; " , ; " , ; "1 0.55765 4.359 2.0205 ad /(1!e) (I"7, J"11) F ad /(1!e) F log 9.952;10\ S" 4.741 (4) (7) (8) (9) Re Re =e * % * log log log 1.007;10\ 1.709 1.275;10\ ; " , ; " , ; " 4.077 3.4213 5.2032 (10) Fr X Eo * % K log log log 1.088;10\ 1.078;10\ 2.674;10\ , ; " , ; " ; " 5.0172 3.651 4.906 S @ log 1.655 ; " , ; "1 2.1742 explicit and whole-#ow-regime dimensionless correlations for gas}liquid mass transfer parameters in trickle beds were derived upon combination of dimensional analysis and arti"cial neural networks. The overall (11) (12) result was a signi"cant improvement in predicting overall liquid-side and gas-side volumetric mass transfer coe$cients and gas}liquid interfacial area. Similarly to any other available correlation in literature, ad /(1!e) F u GH 1 2 3 4 5 6 7 8 u G Sh % u GH 1 2 3 4 5 6 7 u H Sh * u GH 1 2 3 4 5 6 7 u H 1 1.5435 2.2434 2.5155 2.5649 0.9739 1.4736 3.0631 3.8628 1 3.0432 1 !1.6356 2.1719 !1.4329 0.0279 !3.7197 1.9894 0.6121 1 !13.571 1 1.7352 3.7209 !3.1528 10.8069 !5.7494 9.2444 !5.0819 1 5.2505 2 !3.9356 2.5744 0.3614 0.1710 !1.7651 !8.0268 !4.1966 2.4074 2 5.0432 2 0.4413 !4.7885 4.2847 !4.7665 10.2979 !13.042 0.7693 2 !4.4635 2 !1.0859 4.3527 !5.9518 0.3045 !0.8630 1.2997 5.1608 2 !3.9571 3 4.1974 !0.5456 5.6068 !8.1754 0.4768 !6.6128 1.4328 1.4903 3 5.3856 3 !2.6556 3.9519 !0.1984 !2.2429 9.0856 2.0753 !2.0236 3 !4.4251 3 4.4131 !0.9842 1.4652 2.5158 6.0466 10.0231 !6.9573 3 7.6703 4 2.1391 11.0825 !8.5112 !5.0699 !10.376 !10.457 2.5269 9.3200 4 !1.9445 4 !1.6555 !3.0385 !3.2826 !4.6367 0.3069 3.3017 0.7602 4 8.4609 4 5.99 93 2.2940 !5.1562 4.6663 3.2448 8.7118 !3.3028 4 4.3998 Table 4 Fitting parameters of the neural network correlations 5 1.8422 1.0471 8.6948 !12.646 !2.8720 !7.1529 !2.2898 7.5124 5 !5.7894 5 5.1509 !1.4101 !7.2576 6.8145 !0.5302 1.5895 !0.8027 5 5.1391 5 5.53 25 !1.2809 !0.7164 !3.2695 2.0916 !5.8084 3.9598 5 9.9828 6 7.4930 !14.600 0.0311 !6.3510 5.3100 !1.8612 !5.9076 !2.9321 6 !8.4580 6 1.2263 3.4532 !5.5895 4.7365 0.5461 !2.1867 !2.9046 6 8.0094 6 !0.85 89 1.5063 !0.6652 4.2675 !7.2309 !5.6044 5.6439 6 !8.1581 7 7.4055 !11.867 11.3668 !6.5566 11.0910 !1.7484 !2.1967 !9.1011 7 !6.6317 7 8.0269 !2.0732 !8.6778 10.6797 !0.9721 !4.2163 !2.7202 7 !10.884 7 2.7195 !2.1694 !1.2966 !4.6230 0.4930 2.3693 2.6890 7 6.3469 8 !4.6897 !28.205 11.0779 17.1914 32.2031 !1.1837 7.3281 !17.957 8 !1.1868 8 7.1496 !3.7079 !3.8304 7.2395 !4.8951 !3.5211 1.5878 8 8.8342 8 1.8965 5.1352 4.2572 !3.7013 !1.9482 11.4437 !5.2396 8 !4.3963 9 !8.8114 6.4693 12.4214 !0.4853 1.9989 !1.8698 9.4666 !0.2705 9 !8.2298 9 0.9308 9 !0.4475 2.4182 !1.2258 3.0663 0.1645 9.7706 !1.6727 9 !7.0899 10 !3.4613 !6.2165 !1.4482 2.9275 !5.9464 !5.2761 !3.3217 !0.0944 10 5.0896 10 !1.7098 !3.1443 0.5253 !0.7606 4.6749 !6.4817 !2.3656 10 3.4881 11 !4.2452 !5.0921 16.6859 !3.8874 9.3558 1.3218 15.0035 !6.0079 11 4.9539 11 1.9772 !7.2618 !4.1405 0.1795 2.0291 3.1763 4.6354 11 !6.1047 12 3.4090 12 !1.8640 6.3021 !2.4334 2.5706 1.1673 4.8084 !1.7145 12 !4.3143 13 6.8217 7.4821 2.5210 0.0143 0.6759 8.9547 1.2650 13 5.5141 14 !4.4515 5638 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 5639 Table 5 Statistical tests of neural regression of gas}liquid mass transfer parameters Gas}liquid mass transfer dimensionless number Neural regression stage Statistical parameter AARE (%) p (%) Sh * Learning data Generalization data Whole data Learning data Generalization data Whole data Learning data Generalization data Whole data 22.0 22.9 22.3 10.1 13.1 10.9 27.8 29.1 28.1 24.9 26.4 25.3 8.9 13.5 10.4 39.0 34.0 37.0 Sh % ad /(1!e) F Fig. 1. Neural network predictions versus experimental liquid Sherwood numbers: (a) training set; (b) comparison with other data (test set). Dotted lines represent $15% envelopes. Fig. 2. Neural network predictions versus experimental gas Sherwood numbers: (a) training set; (b) comparison with other data (test set). Dotted lines represent $15% envelopes. 5640 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 Table 6 The most general gas}liquid mass transfer literature correlations Gas}liquid mass transfer dimensionless number Sh * Correlation Flow regime a d Q F Sh "2.8;10\ XRe=eSc * % * * * 1!e a d Q F Sh "0.091 XRe=eSc * % * * * 1!e Transition Wild et al. (1992) Low interaction High interaction and transition a d Q F Sh "0.067 XRe=eSc % % * % % 1!e a d Q F Sh "0.123 XRe=eSc % % * % % 1!e d Sh "0.049(a d )\ReReSc N % Q N % * % d A a/a Q Low interaction a d Q F Sh "0.45 XRe=eSc * % * * * 1!e Sh % Reference a a d Q F "10 X Re\=e % * * 1!e a Q High interaction Wild et al. (1992) All regimes YamK ci (1985) Low interaction Transition High interaction a d \ a Q F "21.3 X Re\=e % * * 1!e a Q a a d \ Q F "1550 X Re\=e % * * 1!e a Q Wild et al. (1992) Table 7 Statistical tests of most general literature correlations Gas}liquid mass transfer dimensionless number Correlation Sh * Wild et al. (1992) Sh % Wild et al. (1992) a/a Q YamK ci (1985) Wild et al. (1992) Flow regime Low interaction Transition High interaction Low interaction Transition High Transition All regimes Low interaction Transition High interaction Statistical parameter AARE (%) p (%) 119.0 196.0 137.0 89.4 41.0 37.2 54.9 148.0 71.6 70.8 233.0 421.0 272.0 266.0 65.0 167.4 141 356.0 83.0 71.1 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 5641 Notation a a Q gas}liquid interfacial area, m/m external area of particles and wall per unit reactor volume, ("6(1!e)/ d #4/d ), m/m N A AARE average absolute relative error d A d F d N D ? EoK K Fr * g H J ka ? Mo * N P Re ? S S @ Sc ? Sh ? Sh % St * ¹ ; G v 1% v 1* X % y Fig. 3. Neural network predictions versus experimental dimensionless interfacial areas ad /(1!e): (a) training set; (b) compaF rison with other data (test set). Dotted lines represent $15% envelopes. w =e ? Greek letters a a NO the neural network correlations proposed here are basically interpolation correlations. Hence, to prevent unacceptable deviations, it is suggested to verify a priori that the conditions to be predicted fall within the validity range of the dimensionless groups shown in Table 1. (y !y ) G G "(1/N), y G G column diameter, m Krischer and Kast hydraulic diameter ("d (16e/9n(1!e)) N grain equivalent diameter, diameter of sphere having same volume as grain, m di!usivity in a-phase, m/s modi"ed EoK tvos number ("o gd e/ * N p (1!e)) * liquid Froude number ("v /gd ) 1* N gravitational acceleration, m/s hidden-layer vector number of nodes in hidden layer a-phase side volumetric mass transfer coe$cient, s\ liquid Morton number ("gk/o p) * * * number of data pressure, MPa a-phase Reynolds number ("v o d /k ) 1? ? N ? network output bed correction function ("a d /(1!e) Q F a-phase Schmidt number, ("k /D o ) ? ? ? a-phase Sherwood number ("k ad/D ) ? F ? modi"ed gas-phase Sherwood number ("k ad /a D ) % N Q % liquid Stokes number ("k v /o gd) * 1* * N temperature, 3C normalized input variables super"cial gas velocity, m/s super"cial liquid velocity, m/s Lockhart}Martinelli number ("v o/v o) 1% % 1* * gas}liquid mass transfer parameter (y"k a, k a,a) * % parameter a-phase Weber number ("v d o /p ) 1? N ? * subscript meaning gas (G) or liquid (L) cross-correlation coe$cient between column p and column q of the database, a " NO , (w N!w N ) (w O!w O ) G L G (, (w N!w N )(, (w O!w N ) G G G G e bed void fraction 5642 k ? u o ? p I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 sphericity factor a-phase dynamic viscosity, kg/ms weights a-phase density, kg/m standard deviation, p" , G p * y !y G G !AARE /(N!1) y G surface tension, N/m Subscripts calc exp G ¸ calculated experimental gas liquid Abbreviations CHA cyclohexylamine CMC carboxymethylcellulose DEA diethanolamine DIPA diisopropanolamine DMA dimethylamine ETG ethylene glycol EtOH ethanol IPA isopropanolamine MEA monoethanolamine i-PrOH isopropanol Acknowledgements Financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fonds pour la Formation de Chercheurs et d'Aide à la Recherche (QueH bec) is gratefully acknowledged. Part of this work was done in the frame of the `CoopeH ration scienti"que franco-queH becoisea (Programme Conception assisteH e par ordinateur - GeH nie des ProceH deH s). The "nancial support of the Ministère des A!aires Etrangères (France), the Ministère des Relations Internationales (QueH bec, Canada) and the organizational help of Prof. Carrière are gratefully aknowledged. We also express our appreciation to Dr. Z. Bensetiti and Ms A. AndreH for the collection of the database. We are also indebted to many contributors who provided us with theses and reports, among them we are thankful to Profs A. Lakota and J. Levec from University of Ljubljana (Slovenia), Prof. W. P. M. van Swaaij from Twente University (The Netherlands) and Drs K. Tahraoui and W. J. A. Wammes. The author would also like to acknowledge use of the following literature: Azzaz, 1984; Bakos et al., 1980; Blok et al., 1984; Boyes et al., 1995; Charpentier, 1976,1986; Dodds et al., 1960; Frank, 1996; Fukushima and Kusaka, 1977a,1977b,1978; Gianetto et al., 1970,1973; Goto and Smith, 1975; Goto et al., 1975; Guangda and Dudukovic, 1993; Hirose et al., 1974; Iliuta, 1996; Iliuta and Thyrion, 1997; Iliuta et al., 1997; Lakota, 1990; Larachi, 1991; Larachi et al., 1992, 1997; Lara-MaH rquez et al., 1992; Mahajani and Sharma, 1979,1980; Martin et al., 1980; Merchuk, 1980; Midoux et al., 1984,1986; Mitchell and Perona, 1979; Morsi et al., 1980a,1980b; Morsi, 1982; Morsi et al., 1982,1984; Morsi, 1989; Nagel and KuK rten, 1972; Patil and Sharma, 1981,1983; Purwasasmita, 1985; Ratnam and Varma, 1991; Ratnam et al., 1994; Reiss, 1967; Sato et al., 1972; Satter"eld, 1975; Seira" and Smith, 1980; Shende and Sharma, 1974; Shiying et al., 1989; Sylvester and Pitayagulsarn, 1975; Tahraoui, 1990; Tahraoui et al., 1992; Turek and Lange, 1981; U!ord and Perona, 1973; Versteeg, 1987; Versteeg and van Swaaij, 1988; VivarieH , 1981; Wammes, 1990; Wammes et al., 1991; Wammes and Westerterp, 1991; Wang et al., 1994,1997; Wen et al., 1963; YamK ci et al., 1985; YamK ci et al., 1988. References Al-Dahhan, M. H., Khadilkar, M. R., Wu, Y., & Dudukovic, M. P. (1998). Prediction of pressure drop and liquid holdup in highpressure trickle-bed reactors. Industrial and Engineering Chemistry Research, 37, 793. AndreH , A. (1997). Construction de banques de donne& es sur les e& changes de matie% re dans un re& acteur triphasique a% co-courant vers le bas. De& veloppement d'une corre& lation neuronale. M.Sc. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Azzaz, M. S. (1984). Re& acteurs gaz}liquid}solide a% lit xxe: Re& actions catalytiques, hydrodynamique et transfert de matie% re. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Bakos, M., Arva, P., & Szeifert, F. (1980). Interfacial area in packed bed gas}liquid reactors with co-current downward #ow. Hungarian Journal of Industrial Chemistry, 8, 383. Benkrid, K., Rode, S., & Midoux, N. (1997). Prediction of pressure drop and liquid saturation in trickle-bed reactors operated in high interaction regime. Chemical Engineering Science, 52, 4021. Bensetiti, Z., Larachi, F., Grandjean, B. P. A., & Wild, G. (1997). Liquid saturation in cocurrent up#ow "xed-bed reactors: A state-of-the-art correlation. Chemical Engineering Science, 52, 4239. Blok, J. R., Koning, C. E., & Drinkenburg, A. A. H. (1984). Gas}liquid mass transfer in "xed-bed reactors with cocurrent down#ow operating in the pulsing #ow regime. The American Institute of Chemical Engineers Journal, 30, 393. Boyes, A. P., Chugtai, A., Khan, Z., Raymahasay, S., Sulidis, A. T., & Winterbottom, J. M. (1995). Cocurrent down#ow contactor (CDC) as a "xed bed and slurry reactor for catalytic hydrogenation. Journal of Chemical Technology and Biotechnology, 64, 55. Charpentier, J. C. (1976). Recent progress in two-phase gas}liquid mass transfer in packed beds. Chemical Engineering Journal, 11, 161. Charpentier, J. C. (1986). Mass transfer in "xed-bed reactors. In A. Gianetto, & P. Silveston, Multiphase chemical reactors: Theory, design, scale-up. Washington, DC: Hemisphere Publishing Corporation. Chen, M. (1998). Les re& acteurs triphasiques a% lit xxe a% co-courant vers le bas. E! tablissement de corre& lations ge& ne& ralise& es de la transition ruisselant-pulse& . M.Sc. thesis, Laval University, QueH bec, Canada, 1998. I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 Chen, Y. W., & Tsai, M. C. (1997). Hydrodrodesulfurization of atmospheric gas oil over NiMo/aluminum borate catalysts in a tricklebed reactor. Industrial and Engineering Chemistry Research, 36, 2521. Cheng, S., & Chuang, K. T. (1992). Simultaneous methanol removal and destruction from wastewater in a trickle-bed reactor. Canadian Journal of Chemical Engineering, 70, 727. Chou, S. H., Chen, S. C., Tan, C. S., & Wang, W. H. (1997). Hydrogenation of dicyclopentadiene in a trickle-bed reactor. Journal of the Chinese Insttitute of Chemical Engineers, 28, 175. Cloutier, P., Tibirna, C., Grandjean, B. P. A., & Thibault, J. (1996). Nn"t, logiciel de reH gression utilisant les reH seaux à couches. http://www.gch.ulaval.ca/&nn"t. Dodds, W. S., Stutzman, L. F., Sollami, B. J., & McCarter, R. J. (1960). Cocurrent gas absorption mass transfer. The American Institute of Chemical Engineers Journal, 6, 197. Ellman, M. J., Midoux, N., Laurent, A., & Charpentier, J. C. (1988). A New, improved pressure drop correlation for trickle-bed reactors. Chemical Engineering Science, 43, 2201. Ellman, M. J., Midoux, N., Wild, G., Laurent, A., & Charpentier, J. C. (1990). A New, improved liquid hold-up correlation for trickle-bed reactors. Chemical Engineering Science, 45, 1677. Frank, M. J. W. (1996). Mass and heat transfer phenomena in G-L(-S) reactors relevant for reactive distillation. Ph.D. thesis, Twente University, Enschede, The Netherlands. Fukushima, S., & Kusaka, K. (1977a). Interfacial area and boundary of hydrodynamic #ow region in packed column with cocurrent downward #ow. Journal of Chemical Engineering of Japan, 10, 461. Fukushima, S., & Kusaka, K. (1977b). Liquid-phase volumetric and mass transfer coe$cient, and boundary of hydrodynamic #ow region in packed column with cocurrent downward #ow. Journal of Chemical Engineering of Japan, 10, 468. Fukushima, S., & Kusaka, K. (1978). Boundary of hydrodynamic #ow region and gas-phase mass transfer coe$cient in packed column with cocurrent downward #ow. Journal of Chemical Engineering of Japan, 11, 241. Gianetto, A., Baldi, G., & Specchia, V. (1970). Absorption in packed towers with concurrent high velocity #ows. I } interfacial areas. Quaderni dell Ingegnere Chimico Italiano, 6, 125. Gianetto, A., Specchia, V., & Baldi, G. (1973). Absorption in packed towers with concurrent downward high-velocity #ows. II } mass transfer. The American Institute of Chemical Engineers Journal, 19, 916. Goto, S., & Smith, J. M. (1975). Trickle-bed reactor performance. The American Institute of Chemical Engineers Journal, 21, 706. Goto, S., Levec, J., & Smith, J. M. (1975). Mass transfer in packed beds with two-phase #ow. Industrial and Engineering Chemistry Process, Design and Development, 14, 473. Guangda, G., & Dudukovic, M. P. (1993). Mass transfer and pressure drop in trickle beds with small particles. Journal of Chemical Engineering Chinese Universities, 7, 29. Hirose, T., Toda, M., & Sato, Y. (1974). Liquid phase mass transfer in packed bed reactor with cocurrent gas-liquid down#ow. Journal of Chemical Engineering of Japan, 7, 187. Iliuta, I. (1996). Hydrodynamics and mass transfer in multiphase xxed bed reactors. Ph.D. thesis, UniversiteH Catholique de Louvain, Belgium. Iliuta, I., & Thyrion, F. C. (1997). Gas}liquid mass transfer in "xed beds with two-phase cocurrent down#ow: Gas/Newtonian and nonNewtonian liquid systems. Chemical Engineering Technology, 20, 538. Iliuta, I., Iliuta, M. C., & Thyrion, F. C. (1997). Gas}liquid mass transfer in trickle-bed reactors: gas-side mass transfer. Chemical Engineering Technology, 20, 589. Jiang, Y., Khadilkar, M. R., Al-Dahhan, M., Dudukovic, M. P., Chou, S. K., Ahmed, G., & Kahney, R. (1998). Investigation of a complex reaction network: II. Kinetics, mechanism and parameter 5643 estimation. The American Institute of Chemical Engineers Journal, 44, 921. Khadilkar, M. R., Jiang, Y., Al-Dahhan, M., Dudukovic, M. P., Chou, S. K., Ahmed, G., & Kahney, R. (1998). Investigation of a complex reaction network: I. Experiments in a high-pressure trickle-bed reactor. The American Institute of Chemical Engineers Journal, 44, 921. L'Air Liquide (1976). Encyclope& die des Gaz. Amsterdam, The Netherlands: Elsevier. Lakota, A. (1990). Hydrodynamics and mass transfer characteristics of trickle-bed reactors. Ph.D. thesis, University of Ljubljana, Ljubljana, Slovenia. Landau, M. V., Herskowitz, M., Givoni, D., Laichter, S., & Yitzhaki, D. (1998). Medium severity hydrotreating and hydrocracking of Israeli shale oil } II. Testing of novel catalyst systems in a trickle-bed reactor. Fuel, 77, 3. Larachi, F. (1991). Les re& acteurs triphasiques a% lit xxe a% e& coulement a% co-courant vers le bas et vers le haut de gaz et de liquide. E! tude de l 'inyuence de la pression sur l'hydrodynamique et le transfert de matie% re gaz}liquide. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Larachi, F., Laurent, A., Wild, G., & Midoux, N. (1992). Pressure e!ects on gas}liquid interfacial area in cocurrent trickle-#ow reactors. Chemical Engineering Science, 47, 2325. Larachi, F., Cassanello, M., Laurent, A., Midoux, N., & Wild, G. (1997). Gas}liquid interfacial areas in three-phase "xed bed reactors. Chemical Engineering Process, 36, 497. Larachi, F., Cassanello, M., & Laurent, A. (1998a). Gas}liquid interfacial mass transfer in trickle-bed reactors at elevated pressures. Industrial and Engineering Chemistry Research, 37, 718. Larachi, F., Bensetiti, Z., Grandjean, B. P. A., & Wild, G. (1998b). Two-phase frictional pressure drop in #ooded-bed reactors: A stateof-the-art correlation. Chemical Engineering Technology, 21, 887. Lara-MaH rquez, A., Larachi, F., Wild, G., & Laurent, A. (1992). Mass transfer characteristics of "xed beds with cocurrent up#ow and down#ow. A special reference to the e!ect of pressure. Chemical Engineering Science, 47, 3485. Lide, D. R. (1993). Handbook of Chemistry and Physics (73rd ed.) CRC Press. Mahajani, V. V., & Sharma, M. M. (1979). E!ective interfacial area and liquid side mass transfer coe$cient in trickle bed reactors. Chemical Engineering Science, 34, 1425. Mahajani, V. V., & Sharma, M. M. (1980). Mass transfer in packed columns: Cocurrent (down#ow) operation: 1 in. and 1.5 in. metal pall rings and ceramic Intalox saddles: Multi-"lament gauze packings in 20 cm and 38 cm I. D. columns. Chemical Engineering Science, 35, 941. Martin, J. M., Combarnous, M., & Charpentier, J. C. (1980). Physical gas}liquid mass transfer for co-current #ow through porous medium with low liquid and gas #ow rates corresponding to the conditions of enhanced oil recovery. Chemical Engineering Science, 35, 2366. Merchuk, J. C. (1980). Mass transfer characteristics of a column with small plastic packings. Chemical Engineering Science, 35, 743. Midoux, N., Morsi, B. I., Purwasasmita, M., Laurent, A., & Charpentier, J. C. (1984). Interfacial area and liquid side mass transfer coe$cient in trickle bed reactors operating with organic liquids. Chemical Engineering Science, 39, 781. Midoux, N., Wild, G., Purwasasmita, M., Laurent, A., Charpentier, J. C., & Martin, H. (1986). Zum FluK ssigkeitsinhalt und zum WaK rmeuK bergang in Rieselbettreaktoren bei hoher Wechselwirkung des Gases und der FluK ssigkeit. Chemie-Ingenieur Technik MS 1445/86, 142. Mitchell, M. G., & Perona, J. J. (1979). Gas}liquid interfacial areas for high porosity tower packings in concurrent downward #ow. Industrial and Engineering Chemistry Process Design and Development, 18, 316. 5644 I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 Morsi, B. I., Midoux, N., Laurent, A., & Charpentier, J. C. (1980a). Hydrodynamique et aire interfaciale des eH coulements gaz}liquide à co-courant vers le bas en lit "xe. In#uence de la nature du liquide. Entropie, 16, 38. Morsi, B. I., Laurent, A., Midoux, N., & Charpentier, J. C. (1980b). Interfacial area in trickle bed reactors: Comparison between ionic and organic liquids and between Raschig rings and small diameter particles. Chemical Engineering Science, 35, 1467. Morsi, B. I. (1982). Hydrodynamique, aires interfaciales et coezcients de transfert de matie% re gaz}liquide dans les re& acteurs catalytiques a% lit xxe arrose& : Les re& sultats obtenus en milieu liquide aqueux acade& mique sont-ils encore repre& sentatifs en milieu organique industriel? Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Morsi, B. I., Midoux, N., Laurent, A., & Charpentier, J. C. (1982). Hydrodynamics and interfacial areas in downward cocurrent gas}liquid #ow through "xed beds. In#uence of the nature of the liquid. International Chemical Engineering, 22, 142. Morsi, B. I., Laurent, A., Midoux, N., Barthole-Delanauy, G., Storck, A., & Charpentier, J. C. (1984). Hydrodynamics and gas}liquid}solid interfacial parameters of co-current downward two-phase #ow in trickle-bed reactors. Chemical Engineering Communications, 25, 267. Morsi, B. I. (1989). Mass transfer coe$cients in a trickle-bed reactor with high and low viscosity organic solutions. Chemical Engineering Journal, 41, 41. Nagel, O., KuK rten, H., & Sinn, R. (1972). Sto!austausch#aK che und Energiedissipationsdichte als Auswahlkriterien fuK r Gas/FluK ssigkeits-Reaktoren. Chemie-Ingenieur Technik, 44, 367. Patil, V. K., & Sharma, M. M. (1981). Packed tube columns: Hydrodynamics and e!ective interfacial area: Pall rings and multi-"lament wire gauge packings. Canadian Journal of Chemical Engineering, 59, 606. Patil, V. K., & Sharma, M. M. (1983). Hydrodynamics and mass transfer characteristics of co-current down#ow packed tube columns. Canadian Journal of Chemical Engineering, 61, 509. Pintar, A., Bercic, G., & Levec, J. (1997). Catalytic liquid-phase oxidation of aqueous phenol solutions in a trickle-bed reactor. Chemical Engineering Science, 52, 4143. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1992). Numerical recipes in Fortran. The art of scientixc computing (2nd ed.). Cambridge, MA, USA: Cambridge University Press. Purwasasmita, M. (1985). Contribution a% l'e& tude des re& acteurs gaz}liquide a% lit xxe fonctionnant a% co-courant vers le bas a% fortes vitesses du gaz et du liquide. Hydrodynamique, transfert de matie% re et de chaleur pour des liquides aqueux et organiques. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Ratnam, V. G. S., & Varma, Y. B. G. (1991). E!ective interfacial area in gas}liquid cocurrent down#ow through packed beds. Bioprocess Engineering, 7, 29. Ratnam, G. S. V., & Varma, Y. B. G. (1992). Liquid holdup in gas}liquid cocurrent down#ow through packed beds. Canadian Journal of Chemical Engineering, 70, 580. Ratnam, V. G. S., Narasaiah, V. D., & Varma, Y. B. G. (1994). A correlation for interfacial area in cocurrent gas}liquid down#ow through packed beds. Bioprocess Engineering, 10, 53. Ravindra, P. V., Rao, D. P., & Rao, M. S. (1997). A model for the oxidation of sulfur dioxide in a trickle-bed reactor. Industrial and Engineering Chemistry Research, 36, 5125. Reid, R. C., Prausnitz, J. M., & Poling, B. E. (1987). The properties of Gases and Liquids (4th ed.). New York: McGraw-Hill. Reiss, L. P. (1967). Cocurrent gas}liquid contacting in packed beds. Industrial and Engineering Chemistry Process Design Devevelopment, 6, 486. Sato, Y., Hirose, T., Takahashi, F., & Toda, M. (1972). Performance of "xed-bed catalytic reactor with cocurrent gas}liquid #ow. PACHEC'72, Session 8, Reaction Eng. (pp. 187}196). Satter"eld, C. N. (1975). Trickle-bed reactors. The American Institute of Chemical Engineers Journal, 21, 209. Seira", H. A., & Smith, J. M. (1980). Mass transfer and adsorption in liquid-full and trickle beds. The American Institute of Chemical Engineers Journal, 26, 711. Shende, B. W., & Sharma, M. M. (1974). Mass transfer in packed columns: Cocurrent operation. Chemical Engineering Science, 29, 1763. Shiying, G., Yunsheng, C., & Pangsheng, L. (1989). Study of gas-phase mass transfer coe$cients in trickle beds with small particles. Journal of East China Institute of Chemical Technology, 15, 565. Sylvester, N. D., & Pitayagulsarn, P. (1975). Mass transfer for twophase cocurrent down#ow in a packed bed. Industrial and Engineering Chemistry Process Design Development, 14, 421. Tahraoui, K. (1990). Hydrodynamique, Transferts de Matiere, Mise en 0uvre et Mode& lisation d 'une Re& action Catalytique dans un Re& acteur Triphase& Verlixx Muni d'un Venturi a% jet. Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. Tahraoui, K., Ronze, D., & Zoulalian, A. (1992). Hydrodynamique et transfert gaz}liquide dans un reH acteur Verli"x rempli de diffeH rents garnissages. Canadian Journal of Chemical Engineering, 70, 636. Turek, F., & Lange, R. (1981). Mass transfer in trickle-bed reactors at low Reynolds number. Chemical Engineering Science, 36, 569. U!ord, R. C., & Perona, J. J. (1973). Liquid phase mass transfer with concurrent #ow through packed towers. The American Institute of Chemical Engineers Journal, 19, 1223. Versteeg, G. F. (1987). Mass transfer and chemical reaction kinetics in acid gas treating processes. Ph.D. thesis, Twente University, Enschede, The Netherlands. Versteeg, G. F., & van Swaaij, W. P. M. (1988). Absorption of CO and H S in aqueous alkanolamine solutions using a "xed-bed reactor with cocurrent down#ow operation in the pulsing #ow regime. Chemical Engineering Process, 24, 163. VivarieH , A. (1981). E! tude de l 'hydrodynamique et des aires interfaciales gaz}liquide associe& es a% des e& coulements diphase& s a% co-courant vers le bas dans un re& acteur pilote a% garnissage. Comparaison avec les re& sultats de la litte& rature obtenus a% l 'aide de travaux avec des colonnes de laboratoire. CNAM thesis, Conservatoire National des Arts et MeH tiers de Paris, Nancy, France. Wammes, W. J. A. (1990). Hydrodynamics in a cocurrent gas}liquid trickle-bed reactor at elevated pressures. Ph.D. thesis, Twente University, Enschede, The Netherlands. Wammes, W. J. A., Middelkamp, J., Huisman, W. J., de Baas, C. M., & Westerterp, K. R. (1991). Hydrodynamics in a cocurrent gas}liquid trickle bed at elevated pressures, Part 1: gas}liquid interfacial areas, Part 2: liquid holdup, pressure drop, #ow regimes. The American Institute of Chemical Engineers Journal, 37, 1849. Wammes, W. J. A., & Westerterp, K. R. (1991). Hydrodynamics in a pressurized cocurrent gas}liquid trickle-bed reactor. Chemical Engineering Technology, 14, 406. Wang, R., Mao, Z., & Chen, J. (1994). Hysteresis of gas}liquid mass transfer in a trickle bed reactor. Chinese Journal of Chemical Engineering, 2, 236. Wang, R., Luan, M., Mao, Z., & Chen, J. (1997). Correlation between hysteresis of gas}liquid mass transfer and liquid distribution in a trickle bed. Chinese Journal of Chemical Engineering, 5, 135. Wen, C. Y., O'Brien, W. S., & Fan, L. T. (1963). Mass transfer in packed beds operated cocurrently. Journal of Chemical Engineering Data, 8, 42. Westerterp, K. R., & Wammes, W. J. A. (1992). Three-phase trickle-bed reactors. In Principles of chemical reaction engineering and plant design, vol. B4. Ullmans Encyclopedia of Industrial Chemistry (5th ed., p. 309). Wild, G., Larachi, F., & Charpentier, J. C. (1992). Heat and mass transfer in gas}liquid}solid "xed bed reactors. In M. Quintard & I. Iliuta et al. / Chemical Engineering Science 54 (1999) 5633}5645 M. Todorovic, Heat and mass transfer in porous media (pp. 616}632). Amsterdam, The Netherlands: Elsevier. WuK bker, S.-M., Laurenzis, A., Werner, U., & Friedrich, C. (1997). Controlled biomass formation and kinetics of toluene degradation in a bioscrubber and in a reactor with a periodically moved trickle bed. Biotechnology and BioEngineering, 55, 686. YamK ci, W. (1985). Mise au point de nouveaux syste% mes d 'absorption gaz}liquide avec re& action chimique en milieux liquides aqueux et organique en vue de leur application a% la de& termination par me& thode chimique de la conductance de transfert de matie% re en phase gazeuse dans un re& acteur catalytique a% lit xxe arrose& . 5645 Ph.D. thesis, Institut National Polytechnique de Lorraine, Nancy, France. YamK ci, W., Laurent, A., Midoux, N., & Charpentier, J. C. (1985). DeH termination des coe$cients de transfert de matière en phase gazeuse dans un reH acteur catalytique à lit "xe arroseH en preH sence de phases liquides aqueuses et organiques. Bulletin de la Societe Chimique de France, 6, 1032. YamK ci, W., Laurent, A., Midoux, N., & Charpentier, J.-C. (1988). Determination of gas-side mass transfer coe$cients in trickle-bed reactors in the presence of an aqueous or an organic liquid phase. International Chemical Engineering, 28, 299.