2021-08-31 CHBE 456 Heterogeneous Catalysis and Advanced Reactor Design 1. Isothermal Reactor Design Kevin J. Smith Room 223 - CHBE kjs@mail.ubc.ca 1 The General Mole Balance Equation F0 F; V N A + VBB > VCC + VDD (1) We consider an arbitrary reactor of volume V, with component j entering the volume at a steady-state flow rate of Fomol.s-1, with N, moles of component j in the control volume. The arbitrary reaction (1) is assumed to occur at a rate r; mol/(m3.s) - note that we define the rate in terms of moles of component j produced. A simple mole balance on component j, then yields the equation: 2 ~ 1
2021-08-31 F0 V - Ni A + VBB > vcC + VDD (1) dNi Fi - Fj + rdV = dt Molar flow in - Molar flow out + mole generated per unit time = accumulation Depending on the mixing pattern in the reactor we can obtain useful design equations as follows: CSTR: Steady-state so that dt dNi = 0 Perfectly mixed: there is no concentration/temperature profile within the reactor volume (complete back-mixing): { r}dV = r) { dV = rV Hence: F) - Fj + rV = 0 or -rj V _ FÅ-Fj 3 F0 V N Fj A + VBB > VCC + VDD (1) dNj Fi - Fj + |rdV = dt Molar flow in - Molar flow out + mole generated per unit time = accumulation PFR: Steady-state so that dt di = 0 Plug-flow: zero mixing between independent plugs flowing through the reactor (or zero back-mixing); there is a concentration/temperature profile within the reactor volume: { r}dV # rj § dV Hence: F) - Fj + JndV = 0 or by differentiation dFj df j = rj dV 4 2
2021-08-31 F0 V N - A + VB > VCC + VDD (1) dNi F0 - Fj + |rdV = dt Molar flow in - Molar flow out + mole generated per unit time = accumulation Batch reactor: No inlet or outlet flow: F = Fj = 0 Not at steady-state dj + 0 dt Perfectly mixed: there is no concentration/temperature profile within the reactor volume (complete back-mixing): { r}dV = rj § dV = rV Hence: ¡v =aNj or t = rjV - dNj Assuming constant volume then: dc =rj or t = [ dc; 5 Fj V N A + VBB > vCC + VDD (1) In terms of conversion of component A (VA = - 1): X = PAFA CSTR: V = Fix - YA PFR: V = FA fax dx -TA Batch: t = NA S dx -TAV 6 3