Graphical Methods for Analyzing Multistage Cascades

1
Graphical Methods for Analyzing Multistage
Cascades
Last lecture Extended our analysis of
separations techniques to include use of group
methods for analyzing multistage equilibrium
separation processes. We also extended the
degree of freedom analysis for multistage systems.
This lecture will focus on Extending our
analysis of separations techniques to include use
of graphical methods for analyzing multistage
equilibrium separation processes. We also
described the algebraic method for analyzing
multistage separations.
2
Absorption and Stripping of Dilute Mixtures
Absorption and stripping are common methods to
a) remove of impurities from gas (absorption) or
b) remove of impurities from a liquid
(stripping). This is done by flowing a liquid
absorbent countercurrent to a vapor mixture
(absorption) or a vapor stripper countercurrent
to a liquid mixture (stripping).
Stripping
Absorption
L0 (absorbent)
V1
VN
LN1 (liquid to be separated)
1
N
2
N1
N1
2
1
N
VN1 (vapor to be separated)
LN
V0 (stripper)
L1
Vapor stripping agent preferentially vaporizes
certain components of the liquid stream.
Liquid absorbent absorbs certain components of
the vapor stream preferentially.
Although the arrows are drawn to indicate the
mass transfer of species in absorption and
stripping, generally mass transfer of components
from the absorbent or stripping streams will
occur in the opposite direction as well.
3
Absorption
Generally, if the absorption factor AL/KV is
greater than 1 for a component, then any degree
of separation can be achieved. The larger A is
the fewer stages (or trays) are required to
achieve a given level of separation, although
the absorbent flow rate may become too large.
For the absorption process considered in
example 5.3, notice that the exiting vapor stream
has had almost all of the most volatile species
removed and transferred into the absorbent
stream. The amounts of each component left in
each stream was determined using the group
method.
Typical Absorption Process
Lean gas
Absorbent oil 90F
L0 lbmol/hr n-butane
0.05 n-pentane 0.78 Oil 164.17
L0165.00
V1 lbmol/hr Methane 155.0 Ethane
323.5 Propane 155.4 n-butane
3.02 n-pentane 0.28 V1 637.3
1
2
6
Notice almost all of the methane remains in the
vapor stream.
VN1 lbmol/hr Methane 160.0 Ethane
370.0 Propane 240.0 n-butane
25.0 n-pentane 5.0 LN800.0
LN lbmol/hr Methane 5.0 Ethane
46.5 Propane 84.6 n-butane
22.0 n-pentane 5.5 LN327.7
Notice almost all of the n-pentane was
transferred to the absorbent stream.
4
Absorption and Stripping Equipment
Trayed Tower
Packed Column
Spray Tower
Vapor out
Vapor out
Liquid in
Liquid in
Vapor out
Liquid in
1
2
N1
N
Liquid out
Liquid out
Vapor in
Vapor in
Liquid out
Vapor in
Bubble Column
Vapor out
Centrifugal Contactor
Liquid in
Liquid in
Vapor out
Vapor in
Liquid out
Vapor in
Liquid out
5
Absorption and Stripping Equipment
Trayed Tower
Tray Configuration
Vapor out
Liquid in
Weir
1
2
cap
slots
cap
N1
N
Liquid out
Vapor in
leg
plate
riser
plate
plate
Weir
Three type of tray openings perforation, valve
cap and bubble cap.
Plate
Liquid flow shown by blue arrows. Vapor flow by
red arrows.
The vapor-liquid flow regimes for a contacting
tray include spray, froth, emulsion, bubble, and
cellular foam.
6
Phase Contact on a Contacting Tray
Vapor streams (shownin red) bubble up
throughfroth. Liquid stream flowsthrough froth
and over weir.
The froth conditions can be varied depending on
the vapor-liquid flow regimes to Include spray,
froth, emulsion bubble, and cellular foam.
7
Design Considerations
Specifications 1. Entering gas or liquid flow
rate, composition, temperature and pressure 2.
Degree of separation desired 3. Choice of
absorbent (or stripping) agent 4. Operating
pressure and temperature and allowable pressure
drop 5. Minimum absorbent (or stripping) flow
rate 6. Number of equilibrium stages 7. Heat
effects and need for cooling 8. Type of absorber
(stripper) equipment 9. Height of absorber
(stripper) 10. Diameter of absorber (stripper)
Absorbent should 1. Have a high degree of
solubility for the solute (minimizes absorbent
required) 2. Have low volatility (increases
solute recovery and reduces absorbent loss) 3. Be
stable (reduces need to replace absorbent) 4. Be
noncorrosive (reduces need for corrosion
resistant equipment) 5. Have low viscosity
(reduces pressure drop and pump requirements,
increase mass flow) 6. Be nonfoaming when in gas
contact (reduces size of equipment) 7. Be
nontoxic and nonflammable (safety) 8. Be
available from the process (reduces cost, reduces
need for external source)
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Graphical Method for Equilibrium Stage Trayed
Towers
Countercurrent Absorption Trayed Tower Operating
Conditions A) Isobaric B) Isothermal C)
Continuous D) Steady flow
Absorption
X0, L (absorbent)
Y1, G
1
2
Assume equilibrium between vapor and liquid flow
streams leaving a tray and that the only
component transferred from one phase to the other
is the solute.
n
N
L molar flow rate of solute-free absorbent
(constant through the tower) G molar flow rate
of solute-free gas (constant through the tower) X
mole ratio of solute to solute-free absorbent
in the liquid Y mole ratio of solute to
solute-free gas in the vapor
XN, L
YN1, G
To convert from mole fractions to ratios
Mole ratio of solute in solute free basis
Moles of solute N
Total moles excluding solute N
Mole fraction of solute N
Using the above relationship between mole
fraction and mole ratios on a solute free basis
we substitute into the equilibrium condition
between the liquid and vapor to find
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Graphical Method for Equilibrium Stage Trayed
Towers
Absorption
L molar flow rate of solute-free absorbent
(constant through the tower) G molar flow rate
of solute-free gas (constant through the tower) X
mole ratio of solute to solute-free absorbent
in the liquid Y mole ratio of solute to
solute-free gas in the vapor
X0, L (absorbent)
Y1, G
1
2
A mass balance around the first n stages (where
n is an arbitrary interior stage) gives
n
Solute out stage n
Solute in stage 1
N
XN, L
YN1, G
Solute out stage 1
Solute in stage n
Solving for Yn1 gives the operating line
Bottom
Y
Slope L/G
Operating line is above the equilibrium line
because for each stage there is more solute in
the vapor than the equilibrium amount for any
given liquid solute concentration.
Top
Equilibrium
Y1 (gas out)
Y1-X0(L/G)
X
X0 (liquid in)
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Graphical Method for Equilibrium Stage Trayed
Towers
L molar flow rate of solute-free absorbent
(constant through the tower) G molar flow rate
of solute-free gas (constant through the tower) X
mole ratio of solute to solute-free absorbent
in the liquid Y mole ratio of solute to
solute-free gas in the vapor
Stripping
XN1, L
YN, G
N
A mass balance around the first n stages (where n
is an arbitrary interior stage and we have
numbered from the bottom) gives
n
Solute out stage 1
Solute in stage N
2
1
Solute out stage n
Solute in stage 0
X1, L
Y0, G
Y
Equilibrium
Top
Slope L/G
Operating line is below the equilibrium line
because for each stage there is more solute in
the liquid than the equilibrium amount for any
given vapor solute concentration.
Bottom
Y0 (gas in)
X
X1 (liquid out)
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Minimum Absorbent
To achieve a desired degree of separation there
is a minimum amount of absorbent that must be
used.
A material balance around the entire absorber
gives
Solving for L
Solving for Lmin requires substituting in XN
from the equilibrium relationship. Doing this we
obtain
Infinite Absorbent
Bottom
Operating lines
Y
Slopes L/G
Y1 (gas out)
Top
Equilibrium
Y1-X0(L/G)
So the minimum amount of absorbent to achieve a
desired degree of separation depends on the
fraction of solute removed, the flow rate of the
vapor, and the distribution coefficient.
X
X0 (liquid in)
12
Determination of the Equilibrium Number of Stages
Xn-1
Yn
Xn-1
Yn
n
n
Xn
Xn
Yn1
Yn1
Y
Bottom
Mass Balance
YN1
Stage 3
Equilibrium
Operating Line
Slope L/G
Stage 2
Passing Streams
Top
Y1 (gas out)
Exiting Streams
Stage 1
Y1-X0(L/G)
XN
X
X0 (liquid in)
13
Graphical Determination of N for Absorption
Absorption
Y1, G
X0, L (absorbent)
1
2
Bottom
Y
Operating Line
n
YN1
Stage 3
N
XN, L
YN1, G
Stage 2
Slope L/G
Top
Equilibrium
Y1 (gas out)
Stage 1
Y1-X0(L/G)
XN
X
X0 (liquid in)
14
Graphical Determination of N for Stripping
Stripping
XN1, L
YN, G
N
n
Y
2
YN1
1
Equilibrium
X1, L
Y0, G
Slope L/G
Operating Line
Stage 3
Stage 2
Top
Stage 1
Y0 (liquid in)
Bottom
Y1-X0(L/G)
XN
X1 (gas out)
X
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Algebraic Method for Trayed Towers

• The graphical procedure for determining the
  number of equilibrium stages is convenient,
• and easy to follow. However, often
• the number N becomes large, or
• N is specified rather than the desired purity,
• or more than one solute is being absorbed,
• or the operating conditions are being optimized,
• or the concentrations are high or low such that
  multiple diagrams are needed.
• In these cases the algebraic method becomes
  useful. Here we rely on the development of the
  Kresmer
• Group Method developed for cascades (Seader
  Section 5.4)

Previously we derived two recovery fractions
Note that here we include the species designation
and remove the designation for effective
absorption and stripping factors.
The inverse of a recovery fraction is the
fraction of solute absorbed (or stripped)
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Absorption of Hydrocarbons by N-Decane
Example 5.3
A vapor hydrocarbon mixture is to be absorbed by
a liquid absorbant of heavy oil (assume K0.0001)
and trace amounts of n-butane and n-pentane.
Givens Cascade pressure P2760kPa N6
stages Vapor stream in consists of Methane 160
lbmol/hr Ethane 370 Propane 240 n-butane
25 n-pentane 5 Vapor enters at T105F
Entering liquid is n-butane 0.05
lbmol/hr n-pentane 0.78 Heavy Oil 164.17 Liquid
enters at T90F
Liquid Heavy Oil absorbs nonvolatile components
preferentially.
17
Absorption of Hydrocarbons by Heavy Oil
1) Assume T is the average of the entering stream
temperatures 2) Read off the K-values from the
Depriester charts. 3) For the heavy oil assume
that it has a very small K-value (e.g. 0.0001) 4)
Use the entering stream flow rates with the
K-values to determine A and S. 5) Determining the
absorption and stripping fractions using N6. 6)
Determine the composition of the exiting streams
from the entering compositions and absorption
and stripping factors.
Depriester
Ki A S psiA psiS VN1 L0 V1 L8 methane 6.65 0.031
32.242 0.969 0.000 160 0 155.04 4.96 ethane 1.64
0.126 7.952 0.874 0.000 370 0 323.47 46.53 propane
0.584 0.353 2.832 0.647 0.001 240 0 155.35 84.65
n-butane 0.195 1.058 0.945 0.120 0.168 25 0.05 3.0
4 22.01 n-octane 0.0713 2.893 0.346 0.001 0.655 5
0.78 0.27 5.517 heavy oil 0.0001 2062.5 0.0005 0.0
00 0.9995 0 164.17 0.08 164.09
Given
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Summary
This lecture We described the graphical
construction for analyzing multistage adsorption
and stripping.  We used a combination of
algebra and graphs to describe the change in
compositionstage by stage in a process to
determine the number of equilibrium stages, the
minimum adsorbent, etc. We described how to
use the graphical construction to understand an
equilibriumprocess.
Next lecture well begin discussion of binary
distillation and the McCabe Thiele method.