Page 252 - Separation process engineering

be done using any standard matrix inversion routine. The particular matrix form shown in Eq. (6-13) is a
tridiagonal matrix, which is particularly easy to invert using the Thomas algorithm (see Table 6-1)
(Lapidus, 1962; King, 1980). Inversion of the ABC matrix allows direct determination of the component
liquid flow rate, l , leaving each contact. You must construct the ABC matrix and invert it for each of the
j
components.

Table 6-1. Thomas algorithm for inverting tridiagonal matrices

The A, B, and C terms in Eq. (6-13) must be calculated, but they depend on liquid and vapor flow rates

and temperature (in the K values) on each stage, which we don’t know. To start, guess L, V, and T for
j
j
j
every stage j! For ideal systems the K values can be calculated for each component on every stage. Then
the A, B, and C terms can be calculated for each component on every stage. Inversion of the matrices for
each component gives the l . The liquid-component flow rates are correct for the assumed L, V, and T.
j
j
j
i,j
6.3 Initial Guesses for Flow Rates and Temperatures
A reasonable first guess for L and V is to assume CMO. CMO was not assumed in Eqs. (6-1) to (6-13).
j
j
With the CMO assumption, we can use overall mass balances to calculate all L and V.
j
j
To start the calculation we need to assume the split for non-key (NK) components. The obvious first
assumption is that all the light non-key (LNK) exits in the distillate so that x LNK,bot = 0 and Dx LNK,dist =
Fz LNK . And all heavy non-keys (HNK) exit in the bottoms, x HNK,dist = 0 and Bx HNK,bot = Fz HNK . Now we
can do external mass balances to find all distillate and bottoms compositions and flow rates. This was
illustrated in Chapter 5. Once this is done, we can find L and V in the rectifying section. Since CMO is
assumed,

(6-14)

At the feed stage, q can be estimated from enthalpies as

(6-15)
or q = L /F can be found from a flash calculation on the feed stream. Then and are determined from
F