Turbulent Mixing and Chemical Reaction in Stirred Tanks

Transcription

1 Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational Fluid Mixing (CFM) model. The blend time prediction how good agreement with an experimental correlation. Calculation for turbulent, time dependent mixing of two chemical, exhibiting a competitive pair of reaction, are compared with experimental reult. The effect of the poition of the inlet feed tream in the turbulent flow field are tudied. It i concluded that proce problem with turbulent chemical reactor can be avoided by incorporating the reult of CFM imulation in the deign tage. Keyword: Mixing, Chemical Reaction, Computational Modeling, Stirred Tank, Turbulent Flow. Publihed in The Online CFM Book at (c) 1998 André Bakker Updated: February 15, 2000

2 2 THE ONLINE CFM BOOK INTRODUCTION Blending of chemical reactant i a common operation in the chemical proce indutrie. Blend time prediction are uually baed on empirical correlation. When a competitive ide reaction i preent, the final product ditribution i often unknown until the reactor i built. The effect of the poition of the feed tream on the reaction byproduct are uually unknown. Alo, the cale up of chemical reactor i not traightforward. Thu, there i a need for comprehenive, phyical model that can be ued to predict important information like blend time and reaction product ditribution, epecially a they relate to cale and feed poition. The objective of thi paper i to invetigate the extent to which Computational Fluid Mixing (CFM) model can be ued a a tool in the deign of indutrial reactor. The commercially available program Fluent i ued to calculate the flow pattern and the tranport and reaction of chemical pecie in tirred tank. The blend time prediction are compared with a literature correlation for blend time. The product ditribution for a pair of competing chemical reaction i compared with experimental data from the literature. MODEL The flow pattern i calculated from conervation equation for ma and momentum, in combination with the Algebraic Stre Model (ASM) for the turbulent Reynold tree, uing the Fluent V3 olver. Thee equation can be found in numerou textbook and will not be reiterated here. Once the flow pattern i known the mixing and tranport of chemical pecie can be calculated from the following model equation: Here X i i the ma fraction of chemical pecie I and R i i the rate of creation or depletion by chemical reaction. For a ingle tep, firt order reaction like A + B -> R the reaction rate i given by: Here C and C (upper cae) denote the mean molar concentration of reactant A and B while c A B A and c (lower cae) denote the local concentration fluctuation that reult from turbulence. When the B pecie are perfectly mixed the econd term on the right hand ide, containing the correlation of the concentration fluctuation, will approach zero. Otherwie, if the pecie are not perfectly mixed, thi term will be negative and will reduce the reaction rate. The etimation of thi correlation term i not traightforward and numerou model are available. An excellent dicuion on thi ubject wa given by Hannon [1]. The model ued here i a lightly modified verion of the tandard Fluent model [2]. Two poible reaction rate are calculated, the kinetic reaction rate R ki and a econd reaction rate R mi that

3 MIXING AND CHEMICAL REACTION 3 i controlled by the turbulent mixing. The kinetic reaction rate for pecie I i calculated a: The turbulent mixing limited reaction rate for pecie I i calculated a: The "minimum" function give the minimum value of (ρ.x j/ν j.m j) of all the reactant j taking part in thi reaction. Finally the reaction rate R i i calculated a the product of the molar toichiometry ν i of pecie I and the minimum of R ki and R mi: Here M i i the molecular weight of pecie I and A mn i an empirically determined model contant for reaction n. In the reaction ytem tudied here, ν i i +1 for reactant and -1 for product. K i the kinetic rate contant of the reaction. The idea behind thi model i that in region with high turbulence level the eddy lifetime k/ε will be hort, mixing fat and a a reult the reaction rate i not limited by mall cale mixing. On the other hand, in region with low turbulence level, mall cale mixing may be low and limit the reaction rate. Figure 1 Flow field in 30 liter reactor. Figure 2 Predicted X v. A for A equal infinity. m1 m2 Thirty liter reactor at 100 RPM.

4 4 THE ONLINE CFM BOOK RESULTS REACTION MODELING The following competitive-conecutive reaction ytem wa tudied: Thi i the reaction ytem ued by Bourne et al. [3] and Middleton et al. [4]. The firt reaction i much fater than the econd reaction: K 1 = 7300 m.mole. v. K 2 = 3.5 m.mole.. The experimental data publihed by Middleton et al. were ued to determine the model contant A mn. Two reactor were tudied, a 30 l reactor equipped with a D/T=1/2 D-6 impeller and a 600 l reactor with a D/T=1/3 D-6 impeller. A mall volume of reactant B wa intantaneouly added jut below the liquid urface in a tank otherwie containing reactant A. A and B were added on an equimolar bai. The tranport, mixing and reaction of the chemical pecie were then calculated uing the flow pattern in Figure 1 a a bai. Experimental data were ued a impeller boundary condition. The product ditribution X i then calculated a: In the reaction model ued here it wa aumed that mall cale mixing only affected the firt reaction and that once thi reaction had occurred, the pecie were locally well mixed. A a reult, Figure 9 - X a a function of RPM. Model prediction compared with data from Middleton et al. [4]. Figure 10 - X a a function of feed location. 600 Liter Veel at 100 RPM. A m1 = 0.08 and A m2 equal infinity.

5 MIXING AND CHEMICAL REACTION 5 Figure 6 The local ma fraction in the 2-D reaction imulation after 0, 1, 2, 4, 10 and 20 econd.

6 6 THE ONLINE CFM BOOK mall cale turbulent mixing did not affect the econd reaction. Thi wa achieved by uing different value of A for both mn reaction. For the econd reaction A wa m2 et to infinity. The value for A wa then m1 varied, to tudy the effect on the predicted final product ditribution. Figure 2 how the predicted X a a function of A for the 30 l reactor at 100 m1 RPM. Decreaing A low down the firt m1 reaction and increae the formation of the econdary product S. A a reult the predicted X decreae with increaing A m1. It wa found that A = 0.08 gave the bet m2 prediction, when compared to the experimental data from Middleton et al. Figure 3 how a comparion between the experimental data from Middleton et al. and the current model prediction for both Figure 5 Ma fraction of R and S and product ditribution X a a function of time, normalized with final value. the 30 l and the 600 l reactor. X i plotted a a function of RPM. Thi graph how that the model predict the effect of cale and impeller rotational peed correctly, and i uually within 10% of the experimental reult. The effect of inlet poition of the feed tream on the formation of the econdary by-product S wa tudied. Figure 4 how value of X for variou feed location. X varie only lightly when the inlet i located in the fluid bulk. However, when the feed i injected directly above the impeller, uch that the feed tream immediately pae through the highly turbulent impeller zone, local mixing i much fater and doe not limit the rate of the firt reaction. A a reult there i le reaction by-product S and the final X i only 50% of what it would be if the feed were located away from the impeller. Thi qualitatively agree with the experimental reult of Tipni et al. [5]. Tipni et al. ued a different et of reaction and different tank geometrie but alo found that injection near the impeller reult in a lower X than injection farther away from the impeller and that the relative difference are imilar to thoe found in thi tudy. Figure 5 how the concentration of R and S and the product ditribution X a a function of time for the feed location jut above the impeller. The value are normalized with repect to the final value. R and S increae teadily with time. X increae at firt, reaching a local maximum jut before the pecie are mixed by the impeller. The improved quality of the mixture favor the firt reaction and X drop, until it reache a local minimum. At thi point there i enough R preent to allow the econd reaction to occur even in relatively well mixed region, and X increae again until it aymptotically reache a final value. Figure 6 how the local concentration of pecie A, R and S a a function of time for the 600 l tank at 100 RPM.

7 MIXING AND CHEMICAL REACTION 7 Figure 7 The HE-3 flow pattern. Figure 8 Uniformity a a function of time. Figure 9 The concentration field in the 3-D blending imulation at 0, 4, 10 and 20.

8 8 THE ONLINE CFM BOOK BLEND TIME The mixing of two non-reacting pecie in a tank equipped with a high efficiency impeller (Chemineer HE-3) impeller wa calculated uing Fluent V3. The tank diameter wa T = 1 m. Furthermore, Z/T = 1; D/T = 0.33; C/T = 0.32 and RPM = 58. The flow pattern in thi tank i hown in Figure 7. Experimental data were ued a impeller boundary condition. Figure 8 how the uniformity of the mixture a a function of time. The model prediction are compared with the reult of the experimental blend time correlation of Faano and Penney [6]. Thi graph how that for a uniformity above 90% there i excellent agreement between the model prediction and the experimental correlation. Figure 9 how the concentration field at t = 0, 4, 10 and 20 econd repectively. After 80 the pecie are homogeneouly mixed. DISCUSSION The model preented here correctly predict blend time and reaction product ditribution. The reaction model correctly predict the effect of cale, impeller peed and feed location. Thi how that uch model can provide valuable tool for deigning chemical reactor. Proce problem may be avoided by uing CFM early in the deign tage. When deigning an indutrial chemical reactor it i recommended to determine the value of the model contant on a laboratory cale. The reaction model can then be ued to optimize the product converion on the production cale varying agitator peed and feed poition. However, the range of validation of the reaction model wa limited. Only one impeller type and one reaction ytem were tudied. Future work ha to concentrate on teting the model for a wider range of geometrie and reaction ytem, and if neceary modify the model to increae it' range of validity. REFERENCES [1] Hannon, J. (1992) Mixing and Chemical Reaction in Tubular Reactor and Stirred Tank Ph.D. Thei, Cranfield Intitute of Technology, U.K. [2] Fluent V3.03 Uer Manual (1990) Fluent Inc., Lebanon NH, USA [3] Bourne, J.R., Kozicki, F., Ry, P. (1981) Mixing and Fat Chemical Reaction - I; Tet Reaction to Determine Segregation Chem. Eng. Sci., 36(10)1643 [4] Middleton, J.C., Pierce, F., Lynch, P.M. (1986) Computation of Flow Field and Complex Reaction Yield in Turbulent Stirred Reactor and Comparion with Experimental Data, Chem. Eng. Re. De., Vol 64, January 1986, pp

9 MIXING AND CHEMICAL REACTION 9 [5] Tipni, S.K., Penney, W.R. Faano, J.B. (1993) An Experimental Invetigation to Determine a Scale-Up Method for Fat Competitive Parallel Reaction in Agitated Veel, AIChE Annual Meeting, November 1993, St. Loui [6] Faano, J.B., Penney, W.R. (1991) Avoid Blending Mix-Up, Chemical Engineering Progre, October 1991, NOTATION Amn Model contant for reaction n... (-) -3 Ci Concentration of pecie I... (mole m ) 2-2 k Turbulent kinetic energy denity... (m ) K Reaction rate contant... (m mole ) Mi Molecular weight pecie I... (-) -3-1 Ri Production/depletion pecie I... (kg m ) -3-1 Rki Kinetic reaction rate pecie I... (kg m ) -3-1 Rmi Mixing limited reaction rate for pecie I... (kg m ) Sct Turbulent Schmidt number... (-) t Time... () -1 ui Velocity in direction I... (m ) xi Spatial coordinate in direction I... (m) X Product ditribution... (-) Xi Ma fraction pecie I... (-) 2-3 ε Turbulent kinetic energy diipation rate denity... (m ) -1-1 µ t Turbulent vicoity... (kg m ) -3 ρ Liquid denity... (kg m ) νi Stoichiometry pecie I... (-)