Page 213 - Separation process principles 2

178 Chapter 5 Cascades and Hybrid Systems

This approach to separation process design was developed
by Kwauk [8], and a modification of his methodology forms
the basis for this discussion.
Typically, the variables in a separation process are inten- Equilibrium stage
sive variables such as composition, temperature, and pres-
sure; extensive variables such as flow rate or the heat-transfer .I=: L~~~ '1 N
rate; and equipment parameters such as the number of equi-
librium stages. Physical properties such as enthalpy or Figure 5.20 Equilibrium stage with heat addition.
K-values are not counted because they are functions of the
intensive variables. The variables are relatively easy to enu- these variables and NE are
merate, but to achieve an unambiguous count of NE it is nec-
essary to carefully seek out all independent relationships due Equations Number of Equations
to material and energy conservations, phase-equilibria restric- Pressure equality 1
tions, process specifications, and equipment configurations.
Pvom = PLOUT
Separation equipment consists of physically identifiable equality, 1
elements (equilibrium stages, condensers, reboilers, etc.) as
Tvow = TLOW
well as stream dividers and stream mixers. It is helpful to
Phase equilibrium relationships, C
examine each element separately, before synthesizing the
( Y I ) v ~ ~ = KI(XL)LOUT
complete system. Component material balances,
C-1
LIN(x~)LIN + VIN(Y~)V~~ Lo~(xi)~ouT
=
Stream Variables
+ VOUT(Y~) VOUT
For each single-phase stream containing C components, a Total material balance, 1
complete specification of intensive variables consists of C LIN + VIN = LOUT + VOUT
mole fractions (or other concentration variables) plus temper- Energy balance, 1
=
ature and pressure, or C + 2 variables. However, only C - 1 Q + ~L~NLIN hvIN VIN = ~L~~LOUT
of the feed mole fractions are independent, because the other + h vow VOUT
mole fraction must satisfy the mole-fraction constraint: Mole fraction constraints in entering 4
and exiting streams
r
mole fractions = 1.0
i=l
Thus, only C + 1 intensive stream variables can be speci-
fied. This is in agreement with phase rule, states Alternatively, C, instead of C - 1, component material bal-
that, for a single-phase system, the intensive variables are ances can be written. The total material balance is then a
specified by c - g + 2 = c + 1 variables. T~ this number dependent equation obtained by summing the component
can be added the total flow rate of the stream, an extensive material balances and applying the mole-fraction constraints
variable. Although the missing mole fraction is often treated to the (5-67)7
implicitly, it is preferable for completeness to include the ND=(4C+13)-(2C+7)=2C+6
missing mole fraction in the list of stream variables and then
Notice that the coefficient of C is equal to 2, the number of
to include in the list of equations the above mole-fraction
constraint. Thus, associated with each stream are C + 3 vari- streams entering the stage.
ables. For example, for a liquid-phase stream, the variables Several different sets of design variables can be specified.
are liquid mole fractions XI, x2, . . . , xc; total molar flow A typical set includes complete specification of the two en-
rate L; temperature T; and pressure P. tering streams as well as the stage pressure and heat transfer
rate.
Adiabatic or Nonadiabatic Equilibrium Stage
Variable Specification Number of Variables
For a single adiabatic or nonadiabatic equilibrium stage
Component mole fractions, (xi)L1,
with two entering streams and two exit streams, as shown in
Total flow rate, LIN
Figure 5.20, the variables are those associated with the four
Component mole fractions, (yi)vw
streams plus the heat transfer rate to or from the stage. Thus:
Total flow rate, Vm
Temperature and pressure of Lm
Temperature and pressure of Vm
The exiting streams VOUT and LoL1~ are in equilibrium, so Stage pressure, (PvouT or PLOW)
there are equilibrium restrictions as well as component ma-
Heat transfer rate, Q
terial balances, a total material balance, an energy balance,
and mole fraction constraints. Thus, the equations relating