Information Technology Reference
In-Depth Information
The basic equilibrium equations for component i ,onstage j ,are
y i
= K i x i
(11.4)
When the independent variables and equations (11.2) are substituted into (11.4), we
obtain
= K i (v i ,l i ,T j ,P j ) l i k = 1 ,m v k
v i
(11.5)
k = 1 ,m l k
There are nm equilibrium equations.
The enthalpy per mole of liquid and vapor flows H j and h j refer to the vapor and
liquid leaving stage j , respectively. For each stage, one energy balance, given by
H F
k =
+ H j 1
k =
+ h j + 1
k =
H j
k =
v k h j
k =
f k
l j + 1
k
v j 1
m
l j m
1 ,m
1 ,m
1 ,m
1 ,m
1 ,m
h j
k = 1 ,m
S j
+ Q j
= 0
(11.6)
may be written, where S j represents the total molar flow of a sidestream. The
enthalpy/mole of a sidestream depends on its source and may be written as either H j
or h j , depending on the state of the sidestream. If there are no feeds, sidestreams, or
heat exchangers associated with stage j ,the F , S ,and Q terms disappear. There are
n energy balance equations.
Models usually do not include stage pressure calculations, and pressures are nor-
mally assigned a priori. The summation of equations for a distillation column is as
follows:
Material balances
nm
Equilibrium equations
nm
Energy balances
m
Total
m( 2 n +
1 )
In the absence of sidestreams or interstage heat exchangers, a count of unknowns
for a column with a condenser and a reboiler is as follows:
Componential vapor flows
nm
Componential liquid flows
nm
Stage temperatures
m
Condenser and reboiler duties
2
Total
m( 2 n + 1 ) + 2
Thus, there are typically two degrees of freedom, which correspond to the column's
end specifications. These may be reboiler and condenser duty specifications. Other
specifications that can be used, such as product rate and reflux ratio, require minor
modifications to the basic equations.
Each sidestream adds one degree of freedom; therefore, it is necessary to provide
two end specifications for each sidestream, plus a specification such as a sidestream
flow rate.
Search WWH ::




Custom Search