A reactor converts reactant BC to product CB by heating the material in the presence of an
Question:
A reactor converts reactant BC to product CB by heating the material in the presence of an additive A (mole fraction = xA). The additive can be injected into the reactor, while steam can be injected into a heating coil inside the reactor to provide heal. Some conversion can be obtained by heating without addition of A, and vice versa. The product CB can be sold for $50 per lb-mol. For 1 lb-mol of feed, the cost of the additive (in dollars per lb-mol feed) as a function of XA is given by the formula 2.0 + l0xA + 20x2A. The cost of the steam (in dollars per lb-mal feed) as a function of S is 1.0 + 0.003S + 2.0 ? 10-6S2 (S = lb steam/lb-mol feed). The yield equation is yCB?= 0.1?+ 0.3 xA?+ 0.0001S ? 0.0001xAS.
(a) Formulate the profit function (basis of 1.0 lb-mol feed) in terms of xA and S.
f = income ? costs
(b) Maximize f subject to the constraints
0 ? xA?? 1 ?S ? 0
Step by Step Answer:
Process Dynamics And Control
ISBN: 978-0471000778
2nd Edition
Authors: Dale E. Seborg, Thomas F. Edgar, Duncan A. Mellich