Page 111 - Analysis, Synthesis and Design of Chemical Processes, Third Edition

ρ = 875 kg/m 3
C = 2000 J/kg°C
p
2
U = 420 W/m °C
A = 10 m 2

Solving for the unknown time, we get t = 4215 s = 70.3 min.

The distillation is performed using a still with three theoretical stages (N = 3), a boil-up rate, V = 30
kmol/h, and a reflux ratio, R = 4.5. The volatilities of each component relative to the product are given as
follows:
α = 3.375
AP
α = 2.700
BP
α = 1.350
SP
α = 1.000
PP

The solution methodology involves a numerical integration using the method of Sundaram and Evans [1].

The overall material and component balances are given by

or in finite difference form,

(E3.1m)

or in finite difference form,

(E3.1n)

where W is the total moles in the still; x and x are the mole fractions of component i, at any time t, in
Di Wi
the overhead product and in the still, respectively; k is the index for time in the finite difference
representation; and Δt is the time step. These equations are solved in conjunction with the sum of the gas
phase mole fraction equaling unity and the Fenske-Underwood-Gilliland method for multicomponent
distillation. This leads to the following additional equations: