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Nonisothermal case: adiabatic approach
Prof. Dr. Marco Mazzotti - Institut fr Verfahrenstechnik
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1. Approach
Therefore two new concepts become important:
1. Energy balances
2. Changes of L and G within the column
In the adiabatic approach energy balances are calculated under following assumptions:
There is no heat exchange through the walls of the column
The gas and liquid stream leaving a stage are at the same temperature
Calculating changes of L and G within the column are important when dealing with large solute
fractions. This is often the case when calculating non-isothermal columns.
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Once, pressure and initial composition and temperature of the solvent are set we can consider them as data. This
is a list of known variables:
Specifications
y1Gas final composition, y1
Gn+1
TG
n+1
Data and set values
yn+1
x0Pressure,p
Gas flow rate, Gin
Gas initial composition, yn+1
Solvent initial composition,x0
Equilibrium data, y=f(x,T)
p
y = f(x,T)
TL0
Gas Temp. at inlet TG1
Liquid Temp. at inlet, TL2
Ln
TLn
Unknowns
xn
Solvent flow rate at inlet, L2
Number of stages, n
Solvent final composition,xn
G1 L0
n
Solvent flow rate outlet, L1
TG1
Gas Temp. at outlet TG2
Gas Temp. at outlet TL1
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2. Balances
Material Balance of column:
T)f(x,y
yGxLyGxL
GLGL
11nn1n1n00
1n1n0
The amount of liquid increases from the bottom to the top of the column. It is calculated by adding up the
amount of solvent and the amount of absorbed solute. The same way the amount of gas is calculated. It
deacreases from the top to the bottom of the column as the solute absorbs to the liquid.
Energy Balance of column
)T(TcpHH
H)T(TcpHH
HGHLHGHL
0
G
0
GG
S
0
L
0
LL
G11Lnn1Gn1nL00
HS represents the molar enthalpy of mixing or the integral heat of solution, at the prevailing concentrationand at the base temperature T0
J/(mol K)Heat capacitycp
J/molChange of solute enthalpy
between liquid and gas
phase
Hs
J/molEnthalpy at reference stateH0
J/molEnthalpyH
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To solve the problem the gas outlet temperature and the amount of liquid solvent have to be estimated or
calculated by a nother method, e.g. the isothermal approach
3. Solution of the system
Now all necessary values of the bottom of the column can be calculated by the energy and mass
balances.
From the bottom of the column a new set of mass and material balances can be made including the first
stage. (green canvas) From these balances all unknowns of the first stage can be calculated. This is
repeated including one more stage every time until the required specification is reached.