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or alternatively, n 1 equations such as equation (7.11) and one overall material bal-
ance, given by
F L 1
L 2
=
0
(7.12)
Additionally, n equilibrium equations can be written which describe the equality of the
fugacities of components in each phase, where
1
2
i are the activity coefficients
of component i and x i and x i are the mole fractions of component i in phases 1 and
2, respectively:
γ
i and
γ
1
i x i
i x i
2
γ
− γ
=
0
(7.13)
An overall energy balance,
h F F + Q h L 1 L 1
h L 2 L 2
= 0
(7.14)
completes a set of 2 n + 1 equations.
Most decantation processes are carried out isothermally, and the heat associated
with solute moving between phases is usually negligible, thus eliminating the need
for equation (7.14) and reducing the number of unknowns to 2 n when the pressure
is specified. This is reflected in the block's input forms, where the only allowable
specifications are temperature and pressure. As in the Flash3 block, care must be
taken to specify the key component in the second liquid product, which should be
the heavier phase. The feed from Flash3Example was used to create an example of
the use of a Decanter block, which may be found in Examples/DecanterExample. It
would be useful to compare results of Flash3 and Decanter since both are carried out
at the same conditions: 1 psia and 62 F. The Flash3 specification is V/F =
0 . 1, which
produces a temperature of 61 . 9 F, which is close enough for a comparison. Figure 7.9
shows the data sources for the Uniquac parameters, which are LLE data compared
to VLE data for Flash3. This is an example of a conundrum. Which data produce
the correct answer? Both seem reasonable. Aspen Plus has solved the appropriate
equations, but it is up to the user to select the correct result. Perhaps some laboratory
work will be required.
The block also permits an alternative formulation of the basic equations as a Gibbs
free energy minimization problem. This formulation and some methods of solution are
described by Walas (1985). Additional details are provided in Chapter Ten.
An interesting aspect of the Decanter block is the possibility of its use to simulate a
batch extraction process. The describing equations are identical to those of a continuous
decanter if the flows per unit time are replaced with a batch charge as a feed and the
batch removal of the two products. A common practice in industry is to place a solvent
A containing a quantity of C, the product desired, into a vessel. Following this, the
solvent B is charged to the vessel. After agitation the products are allowed to settle. This
is the equivalent of feeding both streams as a mixture to the decanter, producing the
products L 1 and L 2 . Common industrial practice is to remove the equilibrium B stream,
now containing extracted C, and recharging the vessel with fresh B. This process is
easily simulated with several Decanter blocks in series, as shown in Figure 7.10.
The combined feeds are repeatedly settled, the extract and raffinate removed, and the
resulting product sent to the next stage. Each stage represents the same vessel one
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