Page 91 - Separation process engineering

(2-52)

where ΔT drum is the change in T drum from trial to trial,

(2-53)
and dE /dT drum is the variation of E as temperature changes. Since the last two terms in Eq. (2-51) do not
k
k
depend on T drum , this derivative can be calculated as

(2-54)

where we have used the definition of the heat capacity. In deriving Eq. (2-54) we set both dV/dT and
dL/dT equal to zero since a sequential convergence routine is being used and we do not want to vary V
and L in this loop. We want the energy balance to be satisfied after the next trial. Thus we set E k+1 = 0.

Now Eq. (2-52) can be solved for ΔT drum :

(2-55)

Substituting the expression for ΔT drum into this equation and solving for T drum k+1 , we obtain the best guess

for temperature for the next trial,

(2-56a)

In this equation E is the calculated numerical value of the energy balance function from Eq. (2-51) and
k
dE /dT is the numerical value of the derivative calculated from Eq. (2-54).
k drum
The procedure has converged when

(2-56b)

For computer calculations, ε = 0.01°C is a reasonable choice. For hand calculations, a less stringent limit
such as ε = 0.2°C would be used. This procedure is illustrated in Example 2-3.
It is possible that this convergence scheme will predict values of ΔT drum that are too large. When this

occurs, the drum temperature may oscillate with a growing amplitude and not converge. To discourage
this behavior, ΔT drum can be damped.

(2-57)