Topic 9: Absorption, Stripping and Distillation in Packed Columns Flashcards
what is given in a typical design problem for packed bed absorption?
specified gas feed rate and composition
target outlet gas purity
avaialable solvent with initial composition (often xT=0)
what do we want to solve from a typical design problem for packed bed absorption?
the required flow rate of solvent
height of packing
diameter of the column
what is the notation for packed bed absorption
V': solute free molar gas flow rate L': solute free molar gas liquid flow rate Y: mole ratio of solute in gas phase X: mole ratio in liquid phase J: molar flux of solute from gas to liquid Ac: cross sectional area of column a: packing surface area per unit volume h: height H: total height of packing
what is Ja?
Ja is the rate of mass transfer from gas to liquid per unit volume
what is the solute balance for packed bed absorption
the steady state gas-phase solute balance ina horizontal slice of packing of height dh is:
V’.Y = V’(Y+dY) + (Ja).Ac.dH
based on the solute balance for packed bed absorption, what is the differential equation that can be used to determine the total packing height H?
-V’ (dY/dh)= (Ja). Ac
where J positive for flux from gas to liquid
what are the boundary conditions for the differential equation for packed bed absorption?
boundary conditions:
h=0 h=H Y=Yb Y=Yt X=Xb X=Xt
what is the difference between the analysis of the absorption column and stripping column?
the analysis for a stripping column is almost identical to absorption
however, in this case, the flux is from liquid to gas and the differential equation has the opposite sign
V’(dY/dh)= (Ja).Ac
what is the differential equation for the stripping column
V’(dY/dh)= (Ja).Ac
where J positive for flux from liquid to gas
how is the packing height obtained for a absorber/stripper?
the packing height in an absorber/stripper may be obtained by integrating the respective differential equation
-V'(dY/dh)= (Ja).Ac absorber V'(dY/dh)= (Ja).Ac stripper
what boundary conditions are the differential equations used to obtain the packing height iin absorber/stripper subjected to?
h=0 Y=Yb X=Xb h=H Y=Yt X=Xt
what is the solute flux from gas to liquid?
J=KOG=(Y-Y*)
where:
KOG is the overall mass transfer ccoefficient in the gas phase for mole-ratio driving force
Y* is the hypothetical gas-phase mole ratio that would be in equilibrium with the bulk liquid composition X at a given height in the column
use the differential equation and expression for solute flux from gas to liquid to integrate for the packing height for an absorber
dh=(-V’/KOG.a.Ac)dY/Y-Y*
an so by integration from bottom to top we obtain
H=V’/AC sum[ dY/ KOG.a(Y-Y*) ]
top limit Yb, bottom limit Yt, limits reversed to eliminate the minus sign
what is the expression for solute fluc from liquid to gas?
J=KOG(Y*-Y)
where:
KOG is the overall mass transfer coefficient in the gas phase for mole-ratio driving force
Y* is the hypothetical gas-phase mole ratio that would be in equilibrium with the bulk liquid composition X at a given height in the column
use the differential equation and expression for solute flux from liquid to gas to integrate for the packing height for a stripper
dh=(V’/KOG.a.Ac)dY/Y-Y*
an so by integration from bottom to top we obtain
H=V’/Ac. sum[ dY/ KOG.a(Y-Y*) ]
top limit Yt, bottom limit Yb, limits are not reversed
what is HOG?
HOG has dimensions of height and is called the height of the gas phase transfer unit (HTU)
HOG= V’/(KOG.a).AC for stripper/absorber
where:
V’ is the solute free molar gas flow rate
KOG.a is the overall gas phase volumetric mass transfer coefficient, for mole-ratio driving force
Ac is the internal cross-sectional area of the column
KOG.a is typically obtained from a semi theoretical mass-transfer model with parameters fitted to laboratory/plant data
what is NOG?
NOG is dimensionless and is called the number of gas phase transfer units (NTU)
NOG= sum [dY/(Y-Y*)] for absorber top limit Yb, bootom limit Yt
NOG= sum [dY/(Y-Y*)] for stripper top limit Yt, bootom limit Yb
NOG expressions are obtained by combining the operating line with the equilibrium curve to obtain Y* as a function of Y
note that the integrations start at the dilute end of the column
when can the expressions for packing height be factorised for an absorber or stripper
if KOG is constant the expressions can be factorised
H=V’/AC sum[ dY/ KOG.a(Y-Y*) ]= HOG. NOG
this is the absorber equation
if KOG is constant/ non-constant what do the expressions for the packing height look like?
if KOG is constant, the packing height is the product of HOG and NOG
if KOG is non-constant then the packing height needs to be integrated from the given H differential
what is the operatinG line for an absorber
the operating line of a packed bed absorber is obtained the same way as a trayed tower
component balance around the top
V’.Y+L’Xt=V’Yt+L’X
Y=[Yt’(L’/V’).Xt]+(L’/V’)X
the operating line of a packed bed stripper is obtained the same way as a trayed tower
component balance around the bottom
V’.Yb+L’X=V’Y+L’Xb
Y=[Yb’(L’/V’).Xb]+(L’/V’)X
what is the slope of the operating lines?
the slope of the line connecting(Xt,Yt) and (Xb,Yb) is L’/V’
how are minimum flow rates of gas or liquid determined?
the minimum flow rates of gas or liquid are determined from pinch points as before
how do we calculate Y*(Y) for an absorber?
the operating line relates X and Y for passing streams at ehight h in the column
the equilibrium curve, expressed as Y(X) yields the values of Y, i.e. the mole ratio of the vapour thta would be in equilibrium with the liquid in the column at height h
hence, Y(Y) is determined from the equilibrium curve and the operating line at the same values of X