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596 When a man blames others for his failures, it’s a good idea to credit others with his successes. Howard W. Newton The multiphase reactors to be discussed in this chapter are those in which gas and liquid phases are contacted with a solid catalyst. The reaction generally takes place between the gas and the liquid on the catalyst surface. However, in some reactions the liquid phase is an inert medium for the gas to contact the solid catalyst. The latter situation arises when a large heat sink is required for highly exothermic reactions. In many cases the catalyst life is extended by these milder operating conditions. u The two types of three-phase reactors to be discussed are the slurry reactor and the trickle bed reactor. In the slurry reactor the catalyst is suspended in the liquid and the gas is bubbled through the liquid. The slurry reactor may be operated in either the semibatch or continuous mode. The trickle bed reactor is essentially a vertical packed (fixed)-bed reactor in which the liquid and gas flow cocurrently down the reactor. Trickle beds saw their first use in the removal of organic material from wastewater streams. Here, aerobic bacteria would attach themselves to stones or other supports over which the wastewater was “trickled” and contacted with air. Since this first application the trickle bed reactor has been used for a wide variety of reactions (see Table 12-1). The range of operating flow rates in commerical trickle bed reactors are 0.8 to 25 kg/m?.s for liquids and 0.013 to 1.97 kg/m?-s for gases. For pilot-plant operation the corresponding flow rates range from 0.08 to 2.5 kg/m’-s for liquids and 0.0013 to 0.197 kg/m?-s for gases. 1“ edition Uses of a slurry reactor 597 TaBLe 12-1. APPLICATIONS OF THREE-PHASE REACTORS 1. Slurry Reactor A. Hydrogenation 1. of fatty acids over a supported nickel catalyst. 2. of 2-butyne-1,4-diol over a Pd-CaCQy catalyst. 3. of glucese over a Raney nickel catalyst B. Oxidation 1. of C3Hg in an inert liquid over a PdCl)-carbon catalyst 2. of SO in inert water over an activated carbon catalyst C. Hydroformation of CO with high-molecular-weight olefins on either a cobalt or ruthenium complex bound to polymers D. Ethynylation Reaction of acetylene with formaldehyde over a CaCl,-supported catalyst Il. Trickle Bed Reactors A. Hydrodesulfurization Removal of sulfur compounds from crude oil by reaction with hydrogen on Co-Mo on alumina B. Hydrogenation 1. of aniline over a Ni-clay catalyst 2. of 2-butyne-1,4-diol over a supported Cu-Ni catalyst 3, of benzene, @-CH; styrene, and crotonaldehyde 4, of aromatics in napthenic lube oil distillate C. Hydrodenitrogenation 1. of lube oil distillate 2. of cracked light furnace oil D. Oxidation 1. of cumene over activated carbon 2. of SO, over carbon Source: C. N. Satterfield, A/ChE J., 2/, 209 (1975); P. A. Ramachandran and R. V. Chaudhari, Chem. Eng., 87(24), 74 (1980); R. V. Chaudhari and P. A. Ramachandran, A/ChES., 26, 177 (1980). R12.1 Slurry Reactors In recent years there has been an increased emphasis on the study of slurry reactors in chemical reactor engineering.’ A slurry reactor is a multiphase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles, The solution may be either a reactant, as in the case of the hydrogenation of methyl linoleate, or an inert, as in the Fischer-Tropsch synthesis of methane. Slurry reactors may be operated in a batch or continuous mode. One of the main advantages of slurry reactors is that temperature control and heat recovery are easily achieved. In addition, constant overall catalytic activity can be maintained by the addition of small amounts of catalyst with each reuse during batch operation or with constant feeding during continuous operation. TSee the journal review “Three phase slurry reactors” by R. V. Chaudhari and P. A. Ramachandran, A/ChE J, 26, 177 (1980). 1" edition 599 Bubble Particle Figure 12-2 Steps in a slurry reactor. with methyl linoleate, L, to form methyl oleate, O. Methyl oleate then diffuses out of the pellet into the bulk liquid. 12.1.1 Rate of gas absorption The rate of absorption of H; per unit volume of linoleate oil is (12-2) where k, = mass-transfer coefficient for gas absorption,’ dm/]s a, = bubble surface area, dm?/(dm* of solution) C; = H, concentration at oil-H, bubble interface, mol/(dmy C, = bulk concentration of Hy in solution, mol/(dmy> Ral=] dm dm? mol _ mol Atl“? "s \dmi of solution] dm? (dm? of solution)-s Equation (12-2) gives the rate of H, transport from the gas-liquid interface to the bulk liquid. R12.1B Transport to catalyst The rate of mass transfer of H) from the bulk solution to the external surface of catalyst particles is —————————— = Ra = keacm(Cs—C,) | (12-3) where 4, = mass-transfer coefficient for particles, dm/s a, = external surface area of particles, dm/g m = mass concentration of catalyst (g of catalyst/dm? of solution); the parameter im is also referred to as the catalyst loading C; = concentration of H, at external surface of catalyst pellet, mol/({dm)* Ra{=](emjom {smo _ mol “ s } g \dm of solution/dm’ (dm? of solution)-s ‘Correlations for k,a, for a wide variety of situations can be found in the review article “Design parameters estimations for bubble column reactors,” by Y. T. Shah et al., AIChE 4, 28, 353 (1982). 1“ edition 600 12.1.3 Diffusion and reaction in the catalyst pellet In Chapter 11 we showed that the internal effectiveness factor was the ratio of the actual rate of reaction, —r‘,, to the rate —r’,, that would exist if the entire inte- rior of the pellet were exposed to the reactant concentration at the external surface, C4;. Consequently, the actual rate of reaction per unit mass of catalyst can be written 1 TTA (11-38) Multiplying by the mass of catalyst per unit volume of solution, we obtain the rate of reaction per volume of solution: Ra = mny(—r'as) (12-4) Ral] g of catalyst i mol — mol AU" dmé of solution\ 1 /(g of cat):s (dm? of solution)-s 12.1.4 The rate law The rate law is first order in hydrogen and first order in methyl linoleate. However, since the liquid phase is essentially all linoleate, it is in excess and its concentration, C,, remains virtually constant at its initial concentration, Cz», for small to moderate reaction times: ary = K'CypC = kC (12-5) The rate of reaction evaluated at the external pellet surface is =r, = kC, (12-6) where C, = concentration of hydrogen at the external pellet surface, mol/dm’ k = specific reaction rate, dm°/g cat-s 12.1.5 Determining the limiting step Since, at any point in the column, the overall rate of transport is at steady state, the rate of transport from the bubble is equal to the rate of transport to the catalyst surface, which in turn is equal to the rate of reaction in the catalyst pellet. Then Ra = kyay(C; — Cy) = kema.(Cy — C,) = mn(—r'gs) Equations (12-2) through (12-6) can be rearranged in the form Rs 6,6, Kyay B__o,-c, kag Rae mkyn 1“ edition Finding the limiting resistance 602 Slope = top = Fy, Fe Ola Diffusional resistance to and within pellet Yb Th Gas absorption resistance 1. [ams m \ gm Figure 12-3 Plot to delineate controlling resistances. diffusional resistance to and within the pellet at a particular catalyst loading m is absorption resistance sr, _—_—_intercept x m diffusion resistance —_r,,(1/m) slope Suppose it is desired to change the catalyst pellet size (to make them smaller, for example). Since gas absorption is independent of catalyst particle size, the inter- cept will remain unchanged. Consequently, only one experiment is necessary to determine the combined diffusional and reaction resistances r,,. As the particle size is decreased, both the effectiveness factor and the mass-transfer coefficient increase. As a result, the combined resistance, r,,, decreases, as shown by the decreasing slope in Figure 12-4a. In Figure 12-4b we see that as the resistance to gas absorption increases the intercept increases. The two extremes of these con- ‘trolling resistances are shown in Figure 12-5. Figure 12-5a shows a large intercept {r,) anda small slope (7, + r,), while Figure 12-5b shows a large slope (r, + r,) and a small intercept. To decrease the gas absorption resistance, one might consider changing the sparger to produce more gas bubbles of smaller diameter. Now that we have shown how we learn whether gas absorption r, or diffu- sion-reaction (r, + r,) is limiting by varying the catalyst loading, we will focus on the case when diffusion and reaction combined are limiting. The next step is to learn how we can separate r, and r, to learn whether 1. External diffusion is controlling, 2. Internal diffusion is controlling, or 3. Surface reaction is controlling. To learn which of these steps controls, one must vary the particle size. After deter- 1" edition If diffusion controls, decrease particle size, use more catalyst If gas absorption controls, might want to change the sparger to get smaller bubbles Combined external and internal resistances Surface reaction rate is independent of particle size 603 Decreasing _«— particle size increasing y resistance fo gas absorption 1 \ ™m m (a} (b) Figure 12-4 (a) Effect of particle size; (b) effect of gas absorption. i ™m (b e 3 Figure 12-5 (a) Gas absorption controls; (b) diffusion and reaction control. mining r,, from the slope of C;/R versus 1/m at each particle size, one can con- struct a plot of r,, versus particle size, d,. 1 1 lor = =—— + — 12-16 Kae * nk ( ) a. Very small particles: It has been shown in Chapter 11 (see Figure 11-5) that as the particle diameter becomes small, the surface reaction controls and the effectiveness factor approaches 1.0. For small values of & (reaction control) lor = kb Consequently, r,, and r, are independent of particle size and a plot of In r,, as a function of Ind, should yield a zero slope for this condition of surface reaction limitations. b. Small to moderate-size particles: For large values of the Thiele modulus 1" edition For external diffusion control resistance varies with square of particle size for small particles and + power of particle size for large particles Algorithm to determine reaction- limiting step 605 Case 2: Shear between Particles and the Fluid. If the particles are sheared by the fluid motion, one can neglect the 2 in the Fréssling correlation between the Sherwood number and Reynolds number, and Sh = 2 + 0.6Re!/*Se!/? (10-40) becomes Sh & Rel? Then kedy .. (dpU\'" Dap v or y'2 Sap and 1/2 Kee © __ al | re = ana} (12-21) 1 l Another correlation for mass transfer to spheres in a liquid moving at a low velocity! gives Sh? = 4.0 + 1.21(ReSc)*? (12-22) From which one obtains, upon neglecting the first term on the right-hand side, r= ad) If it is found that if the combined resistance varies with d, from the 1.5 to 1.7 power, then external resistance is controlling and the mixing (stirring speed) is important. Figure 12-6 shows a plot of the combined resistance r,, as a function of particle diameter d, on log-log paper for the various rate-limiting steps. Given a set of reaction rate data, we can carry out the following procedure to determine which reaction step is limiting: 1, Construct a series of plots of C;/R as a function of 1/m. 2. Determine the combined resistance from the slopes of these plots for each corresponding particle diameter. 3. Plot r,, as a function of d, on log-log paper. From the slope of this plot determine which step is controlling. The slope should be 0, 1, 1.5, 1.7, or 2. 4. If the slope is in between any of these values, say 0.5, this suggests that more than one resistance is limiting. tSatterfield, Mass Transfer in Heterogeneous Catalysis (Cambridge, Mass.: MIT Press, 1970), p. 114. 1" edition 606 External-diffusion Slope = 1.5 to 2.0 limited a Slope = 1 Internal-diffusion limited Slope = 0, reaction limited dp Figure 12-6 Effect of particle size on controlling resistance. The variables that influence reactor operation under each of the limiting conditions just discussed are shown in Table 12-2. Example 12-1 Determining the Controlling Resistance The catalytic hydrogenation of methy! linoleate’ was carried out in a laboratory- scale slurry reactor in which hydrogen gas is bubbled up through the liquid and catalyst. Unfortunately, the pilot-plant reactor did not live up to the laboratory reactor expectations. The catalyst particle size normally used is between 10 and 100 wm. In an effort to deduce the problem, the experiments listed in Table E12-1.1 were carried out on the pilot-plant slurry reactor at 121°C. Taste E12-1.1 Partial Size of Pressure Solubitin® Catalyst Catalyst Hy Rate of of Hy of Hy Particles Charge Reaction, —Fy. Run (atm) (kmol/m?) (um) (kg/m) (kmolfm+ min) 1 3 0.007 40.0 5.0 0.0625 2 6 0.014 40.0 0.2 0.0178 3 6 0.014 80.0 0.16 0.0073 “Henry's law: H"Py, = Cy, with H’ = 0.00233 mol H,/atm-dm’. a. What seems to be the problem (i.c., major resistance) with the pilot- plant reactor and what steps should be taken to correct the problem? Support any recommendations with calculations. 'W. A. Cordova and P. Harriott, Chem, Eng. Sci., 30, 1201 (1975). 1“ edition 608 Figure E12-1.1 TasLe E12-1.2 jm (m*/kg) Run C;/R; (min) 1 0.112 0.20 0.787 3.00 6.25 2 1.92 From the slope of the line corresponding to the 40-ym particle size, the combined external and internal diffusion and reaction resistance is 0.787 — 0.112 = 0.140 minskg (E12-1.1) m Tert40.0 xm) = 300-02 For the 80.0-um particle size, we obtain 1.92 — 1.00 = 0.283 mike (E12-1.2) m Tor m) = (004m) = 953.00 Comparing equations (E12-1.2) and (E12-1.1) gives us Tee(go) _ 9-283 _ 2.02 Perigo) 0-140 We see that when the particle size is doubled, the resistance is also doubled. Tor Ay Since the combined resistance is proportional to the particle diameter 1“ edition 609 to the first power, internal diffusion is the controlling resistance of the three resistances. To decrease this resistance a smaller catalyst particle size should be used, For the 80.0-z2m particle size at a catalyst charge of 0.4 kg/m}, the overall resistance at 1/m = 2.5 is 0.84 min (see Figure E12-1.2). percent gas absorption resistance = ae x 100 = 9.5% percent internal diffusion resistance = ard x 100 = 90.5% 2.07- 1B 16h lab = 80 5 h2p zm =| = 1.0- Ole 40 pm 0.84 a a | | 4 5 6 7 8B A m Figure E12-1.2 12.1.6 Slurry reactor design In the material above we have discussed the transport and reactor steps and developed an equation for the overall resistance. A rearrangement of equation (12-7) gives = Cc, ~ Ukady + 1fm(] Kea. + 1[nk) To design slurry reactors one simply couples this rate law with the appropriate mole balance! (see Chapters 1 and 2). Ry =—rn (12-23) TAn interesting example ofa slurry reactor modeled as.a plug-flow reactor for Fischer- Tropsch synthesis is given by D. Stern, A. T. Bell, and H. Heinemann, Chem. Eng. Sci., 38, 597 (1983). 1“ edition 
