Question

2. A first order reaction ( - A = kC ) takes place in an isothermal trickle bed reactor with volume of V which is shown in figure below. There is an agitator in the reactor to provide uniform mixing. Reactants and products are pumped to another pipeline with a centrifugal pump. At the pump outlet, a portion of the stream is sent to the reactor as a recycle. By performing unsteady state and steady state material balances, find the transfer function G(s). HINT: G(s) C(s) C':(S) T 19 C: (0 NIE с (a+1) 9 Ti C (1) 9

Answer 1

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cr q, C; Lq C Cdor q a accumulation in (xpl Q Writing molar balance for the reactor: out - consumption {ci im to a 9 +669)} - flex=)ący - (UEG d[vc) q ci + Gag - 4+1) qc - VkC= v dc at steady state dt dt as dt q Cig Cist ça q -(6+1) qGs - VK 6 = wdę q ti أن - (أ) dt variable q ( Ci - Ci] + aq(6-6)-(4+)4 (C-6) - vk (C-C) : vd(C-6) (writing in terms of deviation 9 C + a96! - (+qc'- vkl = vde: Applying Laplace qC118 + 094473) – (at)qc's) - VkC'() = Vs C's) dt acé transform.

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Z C' (5) fra Vs+Vk) qCirs) + a age(s) (vs + V6+6+)q) e'rs qei'cs) + ta) Writing material balance et Pumpa 9+c9503) 1 în (x+1) 910 applying haplace transform. to the desibeon variable . out qq taqq to the deviation variable. (a + q c'(s) = qe;(s) + oq G'(s) From eqn(A) (2+1) q q el(s) + x ta q G=(s) (&+) q (9C+(1+89605) (6+Dq+ Vs T Vk Assuming Ci > is kept constant; C:'(s) = 0 (x +) 4 (aq) (19) q c'(s) + aq G'(s) t us + Vk (at)aqa ('(s) aq Gars) = qeils) Vs+ Vk s'ls) q els) (ax +1) 9. + VS +Vk Txal) q q+ (x+1) q x

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