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
why do we need to compute Y*(Y)?
we need Y*(Y) to calculate NTU
how do we calculate Y*(Y) for a stripper?
the method of obtaining Y*(Y) for the stripper is analogous
in this case the operating line is below the equilibrium curve so that Y*>Y
how do you graphically determine NOG?
Y(Y) is determined from the equilibrium curve and operating lines
for an absorber, plot (Y-Y)^-1 against Y
NOG is the area under this curve betweenYt and YB
area can be found graphically or by the trapezium rule
how do you numerically determine NOG
NOG can be determined for numerical integration which may be more accurate
on slide 20 for stripping and absorption formulae
how do the variables change for dilute solutes in stripping and absorption?
Y = y
V’ =V
m=K
KOG=KOG
how does HOG change for dilute solutes in stripping and absorption
the variables change for dilute solutes in stripping and absorption,
then express HOG in terms of mole fraction, total molar flow rate and ,mass transfer coefficients for mole-fraction driving force
HOG=(V/Ac)(KOG.a)^_!=(V/AC)[(KG.a)^-1=K(KL.a)^-1]
does an analytical method exist for dilute systems
as with plate columns, an analytical solution can be found for dilute systems in which the equilibrium relation is linear
the solution is developed here in terms of mole fractions (rather than mole ratios)
the key requirement is that the equilibrium line be linear i.e. y=Kx with K= constant
the operating line is linear in any case
it then follows that y*(y) is a linear function of y and hence the integral for NIG may be evaluated analytically
unlike the analytical solutions for plate columns, the analytical method for packed columns does not require the feed solvent (absorber) or strippin gas (stripper) to be solute free
what is NOG as a result of the analytical method
NOG= (y1-y2)/ delta[yLM]
where y1 and y2 denote gas-phase mole fractions at the top and bottom of the column
and delta[yLM] is the log mean fraction difference given by
delta[yLM]=(deltay1-deltay2)/ln(deltay1/y2)
conventionally 1=bottom and 2=absorber for an absorber and the reverse for a stripper (however the labels can be reversed
can NOG for packed bed be related to N in a plate column?
the number of gas phase mass transfer units NOG, is not the same as the number of theoretical stages N required in a plate column
however in dilute systems these quantities are related
in a dilute system what is NOG for a stripper and absorber in terms of N?
for the absorber with xT=0,
NOG=(AlnA/A-1).N
[A =/ 1, if A=1 then NOG=N]
for the stripper with yB=0
NOG=(lnS/S-1).N
[S =/ 1, if S=1 then NOG=N]
what is the relation between NOG and N based on?
this is based on the expressions for NOG and the kremser equations for N:
N=ln[1+(A-1)(yB/yT)]/lnA-1
N=ln[1+(S-1)(xT/xB)]/lnS-1
how is HOG related to N in dilute solutions for absorption and stripping
H=HOG(AlnA/A-1).N
H=HOG(lnS/S-1).N
what is the height equivalent of a single theoretical plate (HETP,HTP)
HTP=HOG(AlnA/A-1)HOG(lnS/S-1)
since S=1/A the two forms are identical
what is HETP used for in packed columns?
more generally, HETP is often used to quantify the mas-transfer efficiency of packed columns by referene to some ‘standard’ or typical absorption/stripping processes
if A or S = 1 then HTP = HOG
when is HTP=HOG
if A=1 or S = 1 then HTP = HOG
what is the diffusion process in bninary distillation
EMD
outline disillation and the mass transfer in packed columns
in binary distillation ,the diffusion process is EMD
analysis is in terms of mole fractions and total molar flow rates
flux is the MVC fromliquid to gas is KOG(y*-y)
since there are two operating lines (below and above the feed), each section of the column is treated separately
additionally, the overall gas-phase mass transfer coefficient KOG can vary significantly across the column for two reasons:
- (1/KOG)=(1/KG0+(m/KL), where m= slope of equilibrium curve which varies with the composition
- the individual mass transfer coefficients KG and KL depend upon physical proprties of the phases, which vary across teh column, and the flow rates, which generally differ in the two sections of teh column
however, we will use a simplified analysis in which KOG.a is assumed to have a constant value throughout each section of the column
how is the packing height obtained for distillation?
the packing height H is obtained as HB and Ht
HB=Vb/(KOG.a).Ac . sum[dy/(y*-y) top limit yf, bottom limit yb
HT=Vt/(KOG.a).Ac . sum[dy/(y*-y) top limit yt bottom limit yf
VB vapour total molar flow rate in the stripping (bottom) section
VT vapour total molar flow rate in the top (rectifying) section
yB vapour composition leaving the reboiler
yF vapour composition where the q-line crosses the operating lines
yT=xD= distillate composition ( total condenser assumed)
KOG=overall gas-phase mass transfer coefficient
is the reboiler a theoretical stage in packed bed distillation?
the reboiler stilll functions as a theoretical stage in packed bed distillation
is KOG constant throughout the distillation column?
KOG is assumed to be constant within each section of the column, but may be different in the two sections
