SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Experimental methods for finding rates 1) Differential reactor ~To consider the rate to be constant at all points within the reactor ~Reasonable only for small conversions or for shallow small reactors as rates are concentration-dependent ~Applicable for slow reactions where reactors are large or for zero- order kinetics where composition change can be large ~Plug flow performance equation ∫ X A,out X A,in ∫ X A,out X A,in ~Each run gives directly a value for the rate at the average concentration in the reactor 2) Integral reactor ~Used when the variation in reaction rate within a reactor is so large ~Large variations are expected as they are concentration-dependent and the composition of reactant changes while passing through the reactor

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Experimental methods for finding rates (cont’d) ~Analyzing by integrating ∫ X A,out X A,in 3) Mixed flow reactor ~Requires a uniform composition of fluid throughout ~Difficult with gas solid system or ~Each run gives a value of the rate at the composition of the exit fluid

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Comparison of experimental reactors ~Integral reactor can have significant temperature variations ~Integral reactor is useful for modeling the operations of larger packed bed unit with all their heat and mass transfer effects ~Differential and mixed flow reactors are useful in analyzing complex reacting system ~Small conversion in differential reactors require more accurate measurements of composition ~Recycle reactor with large recycle acts as a mixed flow reactor ~Basket, recycle and batch gas-solid reactors are more suited for finding the limits for heat effects and for studying the kinetics of the reactions ~Batch gas-solid reactor gives cumulative effects  useful for multiple reactions ~Mixed flow reactor is the most attractive device for studying the kinetics of solid catalyzed reactions ~Difficult to interpret data at low/intermediate recycle ratio ~High recycle ratio provides a way of approximating mixed flow

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS 4) Batch reactor ~Most experimental reactors use a batch of catalyst and a batch of fluid Comparison of experimental reactors ~Change in composition will be followed and the result will be interpreted with the batch reactor equation ∫ XAXA 0 ∫ XAXA 0 ~The procedure is analogous with the homogeneous batch reactor ~The composition of fluid must be uniform throughout the system at any instant Catalyst, W Rapid circulation of reactant Uniform composition Follow change of composition with time

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression 1) Differential reactor A4R The is ran at 3.2 atm and 117 o C in a plug flow reactor which contains 0.01 kg of catalyst and uses a feed consisting of the partially converted Product of 20 liter/h of pure unreacted A. The results are as follows; Run 1234 C A,in (mol/l) C A,out (mol/l) Find a rate equation to represent the reaction Solution: ~Since the maximum variation about the mean concentration is 8 % (run 1), consider it a differential reactor C Ao =N Ao /V=P Ao /RT= 3.2 atm = 0.1 mol/l (0.082 l-atm/mol-K)(390 K) and, F Ao =C Ao V=(0.1 mol A/l)(20 l/h) = 2 mol/h

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression ~Because the density changes during the reaction, concentrations and conversions are related by; C A /C Ao =(1-X A )/(1+  A X A ) or X A =(1-C A /C Ao )/(1+  A C A /C Ao ) Where  A = (4-1)/1 = 3 (based on pure A) ~Plotting –r’ A vs C A gives a straight line through the origin indicating a first order decomposition -r’ A = -(1/W)(dNA/dt) = (96 l/h-kg cat )(C A, mol/l)

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression 2) Integral reactor A4R C Ao =0.1 mol/l,  A =3 F Ao =2 mol/h The reaction is studied in a plug flow reactor using various amounts of catalyst and 20 l/h of pure A feed at 3.2 atm and 117 o C. The concentration of A in the effluent stream is recorded Run 1234 Wcat (kg) C A,out (mol/l) a) Find the rate expression for this reaction using the integral method b) Repeat (a) using the differential method Solution: a) Concentration varies during the run  integral reactor ∫ XAXA 0 -r’ A =k’C A (first order)

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression And with  A, C Ao and F Ao values The two terms in parenthesis should be proportional to each other with k’ as the constant of proportionality Linear plot  first order rate equation satisfactorily fit the data -r’ A = (95 l/h-kg cat )(C A, mol/l)

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression b) Differential reactor equation shows that the rate is given by the slope of the X A vs W/F Ao curve

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression The linear relation between –r’ A and C A in the figure then gives the rate equation -r’ A = (93 l/h-kg cat )(C A, mol/l)

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression 3) Plug flow reactor size from a rate equation A4R Using the rate equation found for this reaction, determine the amount of catalyst needed in a packed bed reactor (assume plug flow) for 35% of A to R for a feed of 2,000 mol/h of pure A at 3.2 atm and 117 o C Solution: The amount of catalyst needed is given by the first-order rate expression for plug flow Replacing all known values (X A =0.35)

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression 4) Mixed flow reactor For the same reaction, determine the amount of catalyst needed in a packed bed reactor with a very large recycle rate (assume mix flow) for 35 % conversion of A to R for a feed rate of 2,000 mol/h of pure A at 3.2 atm and 117 o C (take –r’ A = 96 C A, mol/kg cat -h) Solution: At 35 % conversion, the concentration of reactant is For mixed flow

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression 5) Plug flow reactor size from rate concentration data For the same reaction, suppose the following concentration data are available C A (mol/l) -r’ A (mol A/h-kg cat ) Directly from this data and without using a rate equation, find the size of packed bed needed to treat 2,000 mol/h of pure A at 117 o C to 35 % conversion all at 3.2 atm Solution: To find the amount of catalyst needed, a graphical integration of the plug flow performance equation is required ∫

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression The needed 1/(-r’ A ) versus X A data are determined and are plotted. Integrating graphically then gives ∫ so

SCHOOL OF CHEMICAL ENGINEERING, UNIVERSITI SAINS MALAYSIA EKC 334/3 ANALYSIS & OPERATION OF CATALYTIC REACTORS Determination of rate of reaction/expression