Continuous Stirred Tank Reactor Design - Weebly

1 Continuous Stirred Tank Reactor Design CHEMICAL REACTION RATE The rate of a chemical reaction is the rate of formation or transformation of a participant in a chemical reaction. It is expressed as the number of mass or mole of material converted per unit volume of Reactor per unit time. Thus, the rate of appearance or disappearance of a chemical species i in a homogeneous reaction is (Levenspiel, 2003): ( / )=iid n Vrdt eq 5-1 If i is a reactant, the negative sign is used to signify depletion with time. Whereas, the positive sign is used if it s a product. Where in is the number of moles of component i, V is the Reactor volume and t is the reaction time. For a constant volume reaction, 1=iiidndCrV dtdt eq 5-2 As expressed in the Law of Mass Action, the rate of a chemical reaction is proportional to the active masses of participating reactants.

2 Therefore, the rate is dependent on the concentration of the participating reactants. In elementary reaction, the stoichiometric coefficient of the reactants is equal to the order of the reactions. This order becomes the power to which the reactant is raised. If the given chemical reaction is aA bB cCdD eE eq 5-3 then, the rate of reaction for the disappearance of reactant A is AAABCdCrkC C Cdt eq 5-4 Again, except in elementary reactions, the order of the reaction is not equal to the stoichiometric coefficients as ina, b, and c. k is the rate constant of the reaction. CSTR Design 2 Elementary and Non-Elementary Reactions Elementary Reaction Elementary reaction occurs only in a single step.

3 Example: 1. AProduct eq 5-5 2. A+BProduct eq 5-6 Non-elementary Reaction Non-elementary reaction occurs in two or more steps of reactions and there is no direct correspondence between the stoichiometric coefficient and the rate expression of the reaction. Mechanism of Non-Elementary Reaction (Levenspiel, 2003) Non-chain reaction mechanism Reactants (intermediates)* eq 5-7 (intermediates)*Products eq 5-8 Chain Reaction Mechanism Reactants (intermediates)* eq 5-9 (intermediates)* + Reactant (intermediates)* + Product eq 5-10 ( intermediates)* Product eq 5-11 REACTION RATES OF DIFFERENT MECHNISMS Reversible Reactions First Order Reversible Reactions 12kkAR eq 5-12 The rate expression for substance A and R are written as AA1A2 Rnetnet-dCr=k C -k Cdt eq 5-13 CSTR Design 3 R1A2 RnetnetdC=k C -k CdtRr eq 5-14 At equilibrium rnet = 0.

4 Therefore, 1Ae2 Rek C =k C eq 5-15 Re1C2 AeCkk ==kC eq 5-15 After establishing the material balance and upon integration, the final working equation in terms of fractional conversion is: A2 CAeXln 1-=- k k +1 tX eq 5-16 Irreversible Reactions in Parallel 1kAR assumed desired product eq 5-17 2kAT unwanted product eq 5-18 3kAS unwanted product eq 5-19 The rate equation is for reactant A AA123A-dCr == (kkk )Cdt eq 5-20 Integration gives 123-(k +k +k )tAAoC = Ce eq 5-21 Irreversible Reactions in Series (Consecutive Reactions) Consider the unimolecular first order reaction 12kkABR eq 5-22 The rate equation for component A A1A-dC=k Cdt eq 5-23 CSTR Design 4 Rearranging and integrating.

5 1-k tAAoC = C e eq 5-24 B1A2 BdC=k C -k Cdt eq 5-25 Homogeneous Catalyzed Reactions In the homogeneous catalyzed type of reactions, the overall rate is the sum of rates of both the uncatalyzed and catalyzed reactions. The uncatalyzed reaction is 1kAR eq 5-26 and the catalyzed reaction is 2kA + CR C eq 5-27 The rate expression of component A is A1A2AC-dC= k C + k C Cdt eq 5-28 The concentration of the catalyst (CC) is assumed to be constant. A12CA-dC= (k +k C )Cdt eq 5-29 Integration gives A12 CAoCln= (k +k C ) tC eq 5-30 Autocatalytic Reactions An autocatalytic reaction is a reaction in which one of the products of reaction acts as a catalyst. For an uncatalyzed reaction: 1kAR eq 5-31 For which the equation rate is.

6 AAAR-dCr ==k C Cdt eq 5-32 CSTR Design 5 The corresponding catalyzed reaction where product R acts as a catalyts is 1kA + RR + R eq 5-33 the rate equation is AAAR-dCr ==k C Cdt eq 5-34 Establishing the material balance and upon integration, the final rate expression is oAAoooAoAC -CCln=C ktC -CC eq 5-35 CLASSIFICATION OF REACTORS Although the purpose of this chapter is to present the determination of CSTR specifications, Batch and Plug flow reactors will be briefly described Batch Reactor Batch reactors are usually simple in Design with minimum auxiliary and instrumentation requirements.

7 It is commonly employed for small scale production, testing of new productions, manufactured of expensive and easily contaminated system. High conversion could be easily obtained by increasing the reaction time, although production output is reduced correspondingly. It is usually not applicable for large industrial scale production where labor cost would be high and production output is low compared to Continuous flow reactors. In batch Reactor there is neither inflow nor outflow of both reactants and products while the reaction is in progress. Plug Flow Reactors (PFR) In Plug flow Reactor , reactant continually flows through a cylindrical vessel or pipe. The reactant diminished along the length, and there is no radial variation in concentration.

8 This type of Continuous flow reactors are simple in Design and practically has no power requirement. reactat product Figure 5-1. Plug Flow Reactor . CSTR Design 6 reactan productow Continuous - Stirred Tank Reactor (CSTR) CSTR is commonly used for industrial production. It is assumed of having no spatial variation in concentration and temperature. As name implies the Reactor is well mixed, allowing the assumption of same concentration at any point within the Reactor and the product. It is also called Backmix Reactor (Fogler, 1999). Even a well designed and operated CSTR will produce lower conversion per unit Reactor volume against Plug Flow type reactors.

9 In this chapter, Design of Continuous Stirred Tank Reactor will be discussed. Most homogeneous liquid phase reactions employs CSTR. Figure 5-2. Continuous Stirred Tank Reactor . CSTR Design EQUATIONS Space Time and Space Velocity concept The space time, , is the time required to process one Reactor volume of feed and is given by the following equation: AoAooC VVFv eq 5-36 where CAo is the initial concentration V is the volume of the Reactor , FAo is the molal flowrate of component A and, vo is the volumetric flow rate. CSTR Design 7 Whereas, space velocity (S) refers to the number of Reactor volumes of reactant fed into the Reactor per unit time and is given by the following equation: 1 AooAoFvSC VV eq 5-37 Overall Material Balance Volume element reactant leaves Reactant disappears by reaction Reactant accumulates Reactant enters Volume element reactant leaves Reactant disappears by reaction Reactant accumulates Reactant enters Figure 5-3.

10 Over-all Material Balance. rate of reactant rate of reactant rate of disappearance due rate of accumulation offlow into element = flow out of element + to chemical rxn within + reactant in element of volumeof volume of volume the element of volume eq 5-38 Input = output + rate of disappearance + rate of accumulation of A At steady- state process, rate of accumulation of reactant = 0 FAo = FA + (-rA) V eq 5-39 However, FA = FAo FAo XA eq 5-40 Then, -AAAoXVrF eq 5-41 CSTR Design 8 Where XA is the fractional conversion of reactant A In terms of space time -AoAACXr eq 5-42 REACTION RATES AND SPACE TIME Zero Order irreversible chemical reaction A-----------Product eq 5-43 (-rA) = k eq 5-44 substituting ( rA) into space time equation, AoACXk eq 5-45 First Order irreversible chemical reaction A-----------Product eq 5-46 (- )