chbi502-Chapter_2 - CONVERSION AND REACTOR SIZING...

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1 Objectives: CONVERSION AND REACTOR SIZING • Define conversion and space time. • Write the mole balances in terms of conversion for a batch reactor, CSTR, PFR, and PBR. • Size reactors either alone or in series once given the molar flow rate of A, and the rate of reaction, -r A , as a function of conversion, X . Conversion: Choose one of the reactants as the basis of calculation and relate the other species involved in the rxn to this basis. Space time: the time necessary to process one reactor volume of fluid based on entrance conditions (holding time or mean residence time)
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2 CONVERSION AND REACTOR SIZING 1. Conversion Consider the general equation dD cC bB aA + + We will choose A as our basis of calculation. D a d C a c B a b A + + The basis of calculation is most always the limiting reactant. The conversion of species A in a reaction is equal to the number of moles of A reacted per mole of A fed. 0 0 ) ( ) ( A A A A F F X N N X = = Batch Flow 0 0 A A F N X = Moles of A reacted Moles of A fed For irreversible reactions , the maximum value of conversion, X, is that for complete conversion, i.e. X = 1.0. For reversible reactions , the maximum value of conversion, X, is the equilibrium conversion, i.e. X = X e .
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3 Batch Reactor Design Equations: reacted A of Mole A o Mole A of Moles 2. 2. Design Equations Design Equations = fed A of Moles Moles fed of Moles consumed reacted ) ( [] 0 A N = X [1] Now the # of moles of A that remain in the reactor after a time t, N A can be expressed in terms of N A0 and X; [ ] [ ] ) 1 ( 0 0 0 X N N X N N N A A A A A = = [2] V r dt dN mixing prefect V r dt dN A A A A = = ) ( [3] For batch reactors, we are interested in determining how long to leave the reactants in the reactor to achieve a certain conversion X. dX dt dX N dt dN A A = 0 0 (Since N A0 is constant) [4] V r dt dX N V r dt N A A A A = = 0 0 Batch reactor design eq’n (in differential form) [5]
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4 For a constant volume batch reactor: (V = V 0 ) = = A A A dt dC dt V N d dt dN V 0 0 ) / ( 1 From [3] = = = X A A A A A V dX N t V r dX N dt r dt dC 0 0 From [5] Constant volume batch reactor Batch time, t, required to achieve a A r 0 conversion X. X t As t X Flow Reactor Design Equations: reacted A of moles fed A of moles For continuous-flow systems, time usually increases with increasing reactor volume. A A A A F X F F fed A of moles time X F = = 0 0 0 inlet molar flow rate Molar flow rate at which A is consumed within the system Outlet flow rate 0 0 0 0 ) 1 ( v C F X F F A A A A = = moles /volume volume / time (volumetric flow rate, dm 3 /s)
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5 For liquid systems, C A0 is usually given in terms of molarity (mol/dm3) For gas systems, C A0 can be calculated using gas laws.
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chbi502-Chapter_2 - CONVERSION AND REACTOR SIZING...

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