Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
J3. GAS ABSORPTION
J3.1. INTRODUCTION
Gas absorption involves the removal of a soluble component from an inert gas by contacting
the mixture with an appropriate solvent. The solvent must be chosen such that it has a very
high affinity to dissolve the solute with the inert gas practically insoluble in it. The solvent
must have reasonably high boiling point to remain in the liquid state at the specified operating
temperature during the absorption process. The separation process is highly influenced by the
solubility of the solute in the solvent and is very much dependent on the equilibrium
concentration at a given pressure and temperature. The rate by which absorption proceeds
depends on the contacting area, the resistance to mass transfer and the driving force which is
the difference between the concentration of the solute in the gas phase and the equilibrium
concentration existing at the liquid interface as described by the two-film theory of mass
transfer. The concentration at the interface depends on the solubility of the solute in the liquid
phase that describes the equilibrium concentration.
J3.2. PHASE EQULIBRIA IN GAS ABSORPTION
The system involves three components, the solute (A), the solvent (B) and the inert gas (I). If
we apply the Gibb’s Phase Rule,
 CP2
(J3 - 1)
with  as the number of degrees of freedom, C the number of components and P the number
of phases, the degrees of freedom obtained is three. Usually, in the operation of a gas
absorber, the pressure is fixed. This gives two more conditions to be specified. Thus, to
simplify the analysis, the temperature is also fixed at a constant value. In this case, since the
concentration of the liquid is fixed, there will only be one possible concentration that can be
obtained in the gas phase at equilibrium. This variation in the equilibrium concentration is
provided by the solubility data, which is the basis of determining equilibrium concentration.
J3.2.1. SOURCES OF EQUILIBRIUM CONCENTRATION
1. Solubility Data or Solubility Curves. These information can be obtained from various
references especially Perry’s Handbook. A specified total pressure and temperature, the usual
data given involve values of the partial pressure of the solute in the gas phase, p A in mm Hg
corresponding to the solubility in the liquid phase represented by cA’ in mass of A per 100
mass units of the solvent B. To express these concentrations in terms of the mole fraction, the
following relationships can be applied,
J3 - 1
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
p
yA  A
PT
cA' / M A
and xA  '
cA / M A  100 / M B
(J3 – 2)
2. Henry’s Constants. If the mixture is somewhat dilute such that Henry’s Law can be
applied, the equilibrium concentrations can be related in terms of the Henry’s constant, HA.
yA 
HA
xA  mxA
PT
(J3 – 3)
3. Vapor Pressure. If the solution can be considered and ideal solution, Raoult’s Law can be
applied in determining the partial pressure of A from the vapor pressure pAo, thus
p A p Ao
yA 

xA
PT
PT
(J3 – 4)
The vapor pressure-temperature data can easily be obtained from references or the Antoine
Equation may be used to estimate this value.
4. Distribution Coefficients. If the other sources mentioned are not available for the system
under consideration and the distribution coefficient, KA is known, the equilibrium relationship
can also be obtained using the equation
y A  K A xA
(J3 – 5)
J3.3. EQUIPMENT FOR GAS ABSORPTION
In the operation of the gas absorber the rate of mass
transfer must be maintained high, in order to reduce
the size of the equipment, at the same time reduce
energy requirements by maintaining low-pressure
drop and efficient contact of liquid and gas within
the column. To increase the rate of mass transfer, a
high concentration gradient, high mass transfer area
and low resistance to mass transfer must be
maintained. A counter-current flow can maintain
high concentration gradients compared to cocurrent flow besides using the natural flow of the
phases. Low resistance to mass transfer can be
induced by increasing eddy diffusion or turbulence
in the flow system. One important consideration is
the mass transfer area which is very much
dependent on the hydrodynamics and method of
J3 - 2
Lean Gas
V', V2
Y2, y2
Solvent
L', L2
V'
ZT
Gas
V', V1
Y1, y1
L'
dZ
Solution
L', L1
X1, x1
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
contact between the two phases. Two types will be considered here. A packed column,
composed of random or structured packings, and a plate column such as sieve trays or bubble
caps.
For packed column, the design problem involves the determination of the volume or height of
the packed column while for plate columns, the problem is to determine the number of
theoretical stages needed for the separation. In both cases, ideal conditions are assumed. The
actual design values can be obtained by considering the efficiency of the column.
J3.4. PACKED COLUMNS
Let us consider the packed column shown in Fig. 1 with the flow rates and concentration of
the streams indicated. Two types of flow and concentrations are used, based on the total and
based on the solute-free component, as indicated by a prime for flow rates and capital letters
for concentration. The convert from one type to the other, the following equations can be
applied
V '  V (1  y)
L'  L(1  x)
(J3 – 6)
x
1 x
(J3 – 7)
X
1 X
(J3 – 8)
Y
y
1 y
X
y
Y
1 Y
x
J3.4.1. Mass Transfer Equations.
Referring to Fig. 2, which represents the two-film theory
of mass transfer, it is possible to generate two mass
transfer equations, one for the gas phase and the other for
the liquid phase.
Gas Phase
PA
A. Gas Phase
 dNTA G
 kG
p
A
 p Ai
(dNA)G
 dA
(J3 – 9)
since the interfacial area dA is usually very inconvenient
to measure, it can be expressed in terms of the element of
volume of the packed section
dA  aSdZ
(J3 – 10)
J3 - 3
interface
Liquid Phase
PAi
(dNA)L
CAi
CA
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
where a is the interfacial area provided by the packing per unit volume. This property can be
determined depending on the type of packing used. Also, the partial pressure in Eq. (J3 - 9)
can be expressed in terms y, the mole fraction of A. Thus, Eq. (J3 - 9) can be written in the
form
 dNTA G
 kG aPT
 y  yi  SdZ
(J3 – 11)
or, if we let kya = kGaPT, the equation becomes,
 dNTA G
 k y a  y  yi  SdZ
(J3 – 12)
B. Liquid Phase
For the liquid phase, similar equations can be derived,
 dNTA  L


 k L cAi  cA dA
 dNTA L
 kL a m  xi  x  SdZ
 k x a  xi  x  SdZ
(J3 – 13)
J3.4.2. Determination of Height of Packed Column
The volume or height of the packed column can be evaluated from these mass transfer
equations. For brevity, only the derivation based on the gas-phase mass transfer equation will
be shown and a similar equation for the liquid phase can be generated.
Solving for Z from Eq. (J3 – 13), we get
Z 

y2
y1
( dNTA )G
k y aS ( y  yi )
(J3 – 14)
A material balance around the element of volume SdZ gives,
 dNTA G  V 'dY
(J3 – 15)
expressing in terms of mole fraction, Eq. (J3 – 15) becomes,
 y 
dy
dNTA  V 1  y  d 
 V
1 y
 1 y 
(J3 – 16)
substituting this in Eq. (J3 – 14) and simplifying by just getting the arithmetic mean of the gas
flowrate and the mass transfer coefficient, we get
J3 - 4
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
V / S 
y2
dy
Z 


 k a  y1 (1  y )( y  y )
i
 y ave
(J3 – 17)
Equation (J3 – 17) may be split in terms of height of a transfer unit, HTU or HG, and the
number of transfer units NTU or NG given by
Z  H G x NG
(J3 – 18)
Similarly, if the same mathematical operation is done on the liquid-phase mass transfer
equation, the following equations will be obtained
x2
 L/S 
dx
Z 
 H Lx NL
 x1
(1  x)( xi  x)
 k x a ave
(J3 – 19)
in both cases, the number of transfer unit NG and NL are evaluated by numerical or graphical
integration. The values of the bulk concentrations and the corresponding interfacial
concentrations are obtained from a plot of the operating line using a material balance around
the column, the equilibrium curve obtained from the solubility data and slope of the tie-line
obtained from the mass transfer equations.
J3.4.3. Procedure in the Evaluation of N G or N L
(1) Using the coordinates in terms of mole fraction of the solute in the liquid, x and the mole
fraction of the solute in the gas phase, y, first plot the equilibrium curve by converting the
solubility data to these units. These equilibrium values are referred to as y* versus x. Here the
asterisk indicate equilibrium concentration.
(2) Plot the operating line from the solute balance around the element of volume and
integrating this from the inlet conditions to any point in the column.
dN A  V ' dY  L' dX
integrating
N A  V ' Y1  Y   L'  X1  X 
(J3 – 20)
(J3 – 21)
expressing Eq ( ) in terms of the mole fraction
 y1
x1
y 
x 
'
V '


  L

 1  y1 1  y 
 1  x1 1  x 
J3 - 5
(J3 – 22)
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
It is seen that the operating line if plotted using a coordinate system in terms of mole fraction
will not necessarily generate a straight line unless the gas and liquid phase solutions are very
dilute. However, if the coordinates used are in terms of mole ratios, that is, X and Y, the
operating line obtained is a straight line with a slope of L’/V’ which represents the liquid to
gas ratio on solute-free basis.
(3) The equation of the tie line is obtained by equating the mass transfer rates in both phases
since there is no accumulation of solute at the interface.
dN A  G
 dN A  L
(J3 – 23)
EC
slope= -kya/kxa
TL
substituting Eqs. ( J3 -12 ) and ( J3 -13 ), we get
y
k y a  y  yi  SdZ  kx a( xi  x)SdZ
(J3 – 24)
OL
y
yi
y*
re-arranging this equation, we obtain
y  yi
k a
 x
x  xi
k ya
(J3 – 25)
x
xi
x*
x
and the slope of the tie line is given by
Slope  
kxa
kya
(J3 – 26)
If a tie line is drawn from any point along the operating line at x and y, this line which is
slanting to the left, since the slope is negative, will intersect the equilibrium curve at xi and yi
as shown in Fig. J3 - 2. Since several parallel tie lines can be drawn, then various values of y
vs yi or x versus xi can be obtained to evaluate the values of NG or NL numerically or
graphically.
It is important to note that the driving force in the gas phase is represented by the vertical
distance from y to yi while the distance from yi to y* may be considered to represent the
driving force in the liquid phase in terms of concentrations based on the gas-phase. Similar
interpretation can be done with the difference between xi and x, to represent the driving force
in the liquid phase while xi – x* represents the driving force in the gas-phase based on the
liquid phase concentration. The relative distance of yi to y and xi to x will depend on the slope
of the tie line which can also be interpreted as the ratio of the mass transfer resistance in the
gas phase to the mass transfer resistance in the liquid phase. If the resistance to mass transfer
in the gas phase is controlling, the tie line tends to be vertical and yi is almost equal to y*.
Similarly if the resistance in the liquid phase is controlling, the tie line tends to become
horizontal, making the xi approach x*.
J3 - 6
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
The above rigorous procedure may be simplified depending on the prevailing requirements of
design. There are cases when approximate methods can be applied due to certain conditions
such as strong or weak solubility, the solutions are dilute and the data or correlations available
do not warrant very precise calculations.
J3.4.4. Simplified Equations
In Terms of the Over-all Driving Force. One way of simplifying the design procedure is to
use the over-all driving force (y – y*) instead of the interfacial driving forces. In this case the
resistance that should be considered will now be the combination of the gas and liquid phase
resistances by calculating the equivalent over-all mass transfer coefficient, Kya or Kxa, this
time defined by the mass transfer equations as
(dN A )G  K y a( y  y*)SdZ
(J3 – 27)
(dN A ) L  K x a( x *  x)SdZ
(J3 – 28)
Eq. (J3 - 27) may be written in the equivalent form
(dN A )G  K y a[( y  yi )  ( y *  yi )]SdZ
(J3 – 29)
by combining this with Eq. (J3 – 27) and if we assume that (y – yi) = m (xi – x), where m is the
slope of the equilibrium curve, it can easily be shown that
1
1
m


K y a k y a kxa
(J3 – 30)
Similarly, for the liquid phase over-all resistance to mass transfer can be expressed in terms of
the individual resistances by
1
1
1


K x a k x a mk y a
(J3 – 31)
From Eqs. (J3 – 27) and (J3 – 28), the height of the packed section can be derived as
V S
Z 
K a
y




 ave
dy
 1  y   y  y 

 L S
dx
Z 

 K x a  ave  1  x  x   x

J3 - 7

 H OG  N OG
 H OL  N OL
(J3 – 32)
(J3 – 33)
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
Although NOG and NOL will still require graphical or numerical integration, however, the
procedure is reduced by one step since the slope of the tie-line is no longer needed. The tielines used here are either vertical, for gas phase, or horizontal for liquid phase.
(a) For Very Dilute Solutions. If the solutions are very dilute such that (1 – y) = 1 or
(1 – x) = 1, the above equations can be simplified further to
V S
Z 
K a
y


 V '/ S
dy


  y  y
 K a
y



dY

  Y Y *

(J3 – 34)
For very dilute solutions, the operating line is linear, however, if the equilibrium curve is also
linear, the log-mean driving force may be applied instead of integration. That the equation for
NOG can be written as
N OG 
where
y  y 

y1  y 2
y  y

(J3 – 35)
,
ln
y  y   y  y 
y  y 
ln
y  y 


ln


1
2
(J3 – 36)

1

2
(b) If solution is concentrated and EC and OL are linear within limits,
V S 
y1  y 2
1
Z 

 K a

y  y
 y  ave 1  y  ave
ln


(J3 – 37)
(c) For very soluble solutes (gas phase resistance is controlling)
Slope of Tie Line   k x a   since k x a  k y a
k ya
yi  y  ; N G  N OG ;
Kya  Kya
(J3 – 38)
(d) For very slightly soluble solutes (liquid phase resistance is controlling)
Slope of Tie Line  0
since k x a  k y a
xi  x  ; N L  N OL ; k x a  k y a
J3 - 8
(J3 – 39)
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
(e) Approximate Integration of MTE
The mass transfer equation in terms of partial pressure driving force may be written in the
form
 dN A G
 KG a  p  p  SdZ
(J3 – 40)
To approximate the design calculations, the logarithmic mean of the driving force may be
applied. Thus,
N A  KG a  p  p  SZ
ln
(J3 – 41)
J3.5. PLATE COLUMNS
For plate columns, contacting of gas and liquid
are facilitated using bubble caps or sieve trays
identical to those used in stagewise distillation
columns. The design problem, therefore, involves
the determination of the number of plates, which,
can be based on the assumption of ideal or
theoretical stages. That is, the gas and liquid
leaving a particular stage is considered to be in
equilibrium with each other.
To determine the theoretical number of stages, the
following procedure may be applied:
a. plot the equilibrium curve (EC) based
on the solubility data or equilibrium
equation derived,
b. plot the known concentrations of either
gas or liquid
c. plot the operating line (OL) using the material balance equation around the column
or use the slope which represents the liquid to gas ratio.
d. From the point x2,y2 draw a step up lines between the OL and EC until the point x1,
y1 are reached. The theoretical number of stages is equivalent to the number of
triangles formed.
J3 - 9
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
If operating line (OL) and the equilibrium curve (EC) are linear, apply the Absorption Factor
Method or the Tiller-Tour Equation, given by
y1  y1*
y2  y2*

y y
log 1* 2*
y1  y2
log
Ntheo
x1  x1*
x2  x2*

x x
log 1* 2*
x1  x2
(J3 – 42)
log
Ntheo
(J3 – 43)
J3.6. LIMITING FLOWRATES
In the operation of the absorption columns, certain limiting flow conditions should be
determined so that these flow rates can be avoided to insure that the conditions specified in
the performance of the equipment is achieved. These limiting flow rates are based on flooding
conditions and the solubility of the solute in the liquid phase.
J3.6.1. Based on Flooding Conditions:
When a gas flows counter current with a
liquid in a packed column, pressure drop
J3 - 10
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
along the column is induced. This pressure drop is very much dependent on the liquid to gas
ratio, the physical properties of the streams, the characteristics of the packing and the crosssectional area of the column. If the pressure drop is plotted with gas flow rate in a log-log
graph, a straight line is generated with a slope of approximately two as shown in Fig. 1. When
the gas flow rate is further increased, at a given liquid flow rate, the slope changes and tends
to approach a very high value. This is the point where phase inversion starts to occur and
further increase in the gas rate, the liquid flow is arrested due to high pressure generated by
the gas. At this condition, flooding occurs and the efficiency of the column is drastically
reduced. To determine the flooding velocity of the gas, the Generalized Pressure Drop
Correlation (GPDC) chart may be used as shown in Fig. 4. Flooding may be assumed to occur
at a pressure drop of 1.5 in. H2O. A chart that can be used to determine the flooding condition
indirectly is found in Foust, et al (19__).
When the flooding velocity is determined, the actual velocity can be evaluated as a fraction of
this maximum value. Design heuristics suggest that 50 per cent of flooding may be a good
estimate. From the actual velocity of the gas and the fixed volumetric flow rate of the inlet
gas, the cross-sectional area may be calculated which will then determine the diameter of the
column.
J3.6.2. Based on Equilibrium Conditions
The flow rate of either gas or liquid may be limited based on the extent by which the solute
can dissolved in the liquid phase defined by the solubility or equilibrium conditions. Consider
the graph shown in Fig. J3-5. The operating line can be adjusted in such a way that it can
intersect the equilibrium curve to generate a minimum slope. At this condition, the driving
force at the top of the column is zero. This will then require an infinitely tall tower or infinite
number of stages. Thus the limiting slope is a minimum given by
 L' 
Y1  Y2

 ' 

V
X

 min
1  X2
(J3 – 44)
If the gas flow rate is fixed, the liquid flow rate becomes minimum and therefore, in order not
to operate an infinitely tall tower, the specified liquid flow rate must be greater that the
minimum. Heuristics suggest between 1.5 to 2.0 times the minimum. Of course, this will have
to be checked for consistency with the flooding conditions.
On the other hand, if the conditions at the bottom of the tower are fixed, an operating line
with a maximum slope becomes the limiting condition. From this slope, it is now possible to
determine which becomes the limiting flow rate.
J3 - 11
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
NOMENCLATURE

A
a
C
c’A
HG
HA
K
KA
kGa
kxa
kya
L
L’
M
m
N
NTA
P
pA
PT
S
V
V’
X
x
Y
y
Z
number of degrees of freedom
mass transfer area
interfacial area per unit volume of packing
number of components
concentration of A in the solution
height of a transfer unit
Henry’s constant
over-all mass transfer coefficient
distribution coefficient of A
individual gas phase mass transfer coefficient
individual liquid phase mass transfer coefficient
individual gas phase mass transfer coefficient
flow rate of solution
flow rate of solvent,
molecular weight
slope of a linear equilibrium curve
number of transfer units
total moles of A transferring
number of phases
partial pressure of A
total pressure
cross-sectional area of the column
total gas flow rate,
inert gas flow rate,
mole solute/mole solvent
mole fraction of solute in solution
mole solute/mole inert gas
mole fraction of solute in gas
height of the packing in the column
J3 - 12
[-]
[ft2] or [m2]
[-]
gm A/100 gm of B
[m]
[-]
[lb mole/hr]
[lb mole/hr]
gm/gm-mole
[-]
lb mol/hr
[-]
mm Hg or atm
mm Hg or atm
[ft2] or [m2]
[lb mole/hr]
[lb mole/hr]
[-]
[-]
[-]
[-]
[ft] or [m]
Philippine Handbook
in Chemical Engineering
Gas Absorption
by Servillano Olaño, Jr.
Gas Absorption, J3 – 1
absorption factor method, J3 - 10
distribution coefficients, J3 - 2
equilibrium concentration, sources of, J3 - 1
NG or NL evaluation, J3 - 5
gas absorption, J3 - 1
gas absorption, equipment for, J3 - 2
gas absorption, phase equilibria in, J3 - 1
Gibb’s Phase rule, J3 - 1
height of a transfer unit, HTU, J3 - 5
Henry’s constants, J3 - 2
limiting flowrates, J3 - 10
limiting flowrates, based on equilibrium conditions, J3 - 11
limiting flowrates, based on flooding conditions, J3 - 10
mass tranfer equations, J3 - 3
number of transfer units, NTU, J3 - 5
packed column, determination of height of, J3 - 4
packed columns, J3 - 3
plate columns, J3 - 9
solubility curves, J3 - 1
Tiller-Tour equation, J3 - 10
vapor pressure, J3 - 2
J3 - 13