24 - enthalpy based distillation models
TRANSCRIPT
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ENTHALPY-BASED DISTILLATION MODELING
PONCHON-SAVARITT ANALYSIS
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PONCHON-SAVARIT ANALYSIS
• ENTHALPY CONCENTRATION EQUILIBRIUM DIAGRAM – POINTS REPRESENT CONCENTRATION, x
OR y, AND ENTHALPY, Hy OR hx.
– ANALYSIS INCLUDES CHANGES IN V/L AS A FUNCTION OF ΔHvap.
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ENTHALPY EQUILIBRIUM DIAGRAM
http://www.hyper-tvt.ethz.ch/images/enthalpy.jpg
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FORM OF SIMULATION DIAGRAM
XB XF XD
HB
HD
HF
H’D
H’B
-qC/D
qr/D
Hy1
x,y
HSATURATED VAPOR LINE
SATURATED LIQUID LINE
EQUILIBRIUM TIE LINES
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ENTHALPY CONCENTRATION
COORDINATE SYSTEM
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
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ENTHALPY CONCENTRATION RECTIFICATION
SECTION
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
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ENTHALPY CONCENTRATION
STRIPPING SECTION
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
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OPTIONS
• DATA FOR MIXTURE VALUES NOT READILY AVAILABLE
• CAN ASSUME IDEAL MIXTURES AND USE PURE COMPONENT DATA AT TERMINAL POINTS - THEN CONNECT WITH STRAIGHT LINE.
• EQULIBRIUM TIE LINES, LINK EQUILIBRIUM LIQUID & VAPOR CONCENTRATIONS ON EACH ENTHALPY LINE. SHOWN AS DASHED LINES FIG 11.6-1
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SIMPLIFIED P-S DIAGRAM
XB XF XD
HB
HD
HF
H’D
H’B
-qC/D
qr/D
Hy1
x,y
H
SATURATED VAPOR LINE
SATURATED LIQUID LINE
EQUILIBRIUM TIE LINES
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ENTHALPY BALANCES
• OVERALL
• CONDENSERB
qHH
D
qHH
BHDHFhBDF
rBB
cDD
BDF
''
''
Dnnnn DxxLyV 11
DLV nn 1
CDnLn
nVn
qDHHL
HV
,
1,1
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CONSTRUCTION FOR GRAPHICAL MODEL
• ENTHALPY RIGOROUS EQUATION OR DATA
• SIMPLIFIED VERSION
• EQUILIBRIUM DATA
FROM VLE DATA
H kJ/mol
V
L
T1T2
T3T4
T5x1 x2 x3x4
x5
y1 y2y3
y4y5
)]()[1()]([
)()1()(
00
00
TTcyTTcyH
HTTcxTTcxh
PvBBAPvAAA
SOLNPlBAPlAA
BABA
BBAA
BBAA
HHhh
HHHyH
hhhxh
)(
)(
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EQUILIBRIUM DATA TRANSFER
H kJ/mol
A
V
L
T1T2
T3T4
T5x1x2 x3x4
x5
y1 y2 y3 y4 y5
Tb(B)T
xA=1
Tb(A)
V
L
xA=0
T5T4T3T2T1
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REBOILER HEAT BALANCE
• REBOILER
• OVERALL
Brmmmm BhqhBVHV )( 111
cFBDr qFhBhDhq
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LOCATION OF FEED LINE• BASED ON FEED CONC. &
ENTHALPY - RELATIVE TO q VALUES ON McCABE-THEILE– SAT'D LIQ., q = 1, ON SAT'D LIQ.
ENTHALPY LINE– SAT'D VAPOR, q = 0, SAT'D VAP.
ENTHALPY LINE– PARTIAL SAT'D VAPOR, 0 < q < 1,
BETWEEN SAT'D ENTHALPY LINES WITH CONCENTRATION IN EACH PHASE BASED ON EQUILIBRIUM TIE LINES.
– SUPERCOOLED LIQ, q > 1, BELOW SAT'D LIQ. ENTHALPY LINE AT xF.
– SUPERHEATED VAP., q < 1, ABOVE SAT'D VAP. ENTHALPY LINE AT xF
x
V
Lq=0
q=1
q<1
q>1
0<q<1
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COMPLETION OF DIAGRAM• FEED POINT, POINTS H’D
AND H’B LIE ON A COMMON LINE TO CLOSE THE ENTHALPY BALANCE
• PRODUCT ENTHALPIES– LOCATION OF H'D IS
BASED ON REFLUX RATIO:
– LOCATION OF H’B IS BASED ON BOILUP RATIO
H kJ/mol
x
V
L
H’B
xF xD
H’D
xBDy
yDad HH
HH
D
LR
1
1'
Byb
BBbB HH
HH
B
VR
'
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LIMITING CASES• TOTAL REFLUX
– CONSTRUCTION HAS STEPS THAT ASSUME H’D IS LOCATED AT ∞ SO VERTICAL OPERATING LINES
– START AT ONE PRODUCT AND GO TO THE OTHER– RED LINES FOLLOW EQUILIBRIUM VALUES
x
V
L
H kJ/mol
xDxB
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LIMITING CASES• INFINITE STAGES - RdMIN,
– LINE THROUGH FEED POINT FOLLOWS EQULIBRIUM LINE
– INTERSECTS WITH H’DMIN AT VERTICAL EXTENSION THROUGH PRODUCT CONCENTRATION
H kJ/mol
x
V
L
H’BMIN
xF xD
H’DMIN
xB
Dy
yDMINdMIN HH
HHR
1
1'
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ACTUAL NUMBER OF STAGES
• RdDZN > RdMIN SO H’D > H’Dmin
• CONSTRUCTION PASSES THROUGH H’D AND H’B– STAGES ARE CALCULATED ABOVE &
BELOW FEED H kJ/mol
x
V
L
H’B
xF xD
H’D
xB
H kJ/mol
x
V
L
H’B
xF xD
H’D
xB
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COMPARISON WITH M-T• P-S ANALYSIS CAN BE
TRANSFERRED TO M-C– OPERATING LINE IS
ADJUSTED TO ALLOW FOR CHANGES IN ΔHvap
– RESULTING NUMBER OF STAGES CAN DIFFER FROM STRAIGHT OPERATING LINE CALCULATIONS
• SEE FIGURE 11.6-3 FOR EXAMPLE
– M-T EQUILIBRIUM LINES ARE VERTICAL
– LINES AND POINTS ARE INTERCHANGED BETWEEN THE TWO METHODS.
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ACTUAL STAGE COUNT FACTORS
• INTERSECTIONS OF OPERATING LINE WITH ENTHALPY LINES REPRESENT ACTUAL STAGE CONCENTRATIONS
• EQUILIBRIUM CONCENTRATIONS ON EACH STAGE ARE REPRESENTED BY EQUILIBRIUM TIE LINES
• MURPHREE EFFICIENCY– STAGE TO STAGE CONSTRUCTION IS
ADJUSTED SO THE ACTUAL CONCENTRATION CHANGE IS A FRACTION OF THE IDEAL
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ADDITIONAL DESIGN FACTORS
• FEED LOCATION– IDEAL LOCATION IS ON A TRAY WHERE:
• TRAY CONCENTRATION = FEED CONCENTRATON
• FEED TEMP = SATURATION TEMP
– DEVIATIONS FROM THIS EQUALITY RESULTS IN SOME LOSS IN EFFICIENCY
• IT IS MINOR • IS INEVITABLE
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TRAY DESIGN• COMPONENTS
– TRAYS– DOWNCOMERS– SUPPORTS
• TYPES - USED FOR GAS LIQUID CONTACTING– CAP– VALVES– SIEVES
Douglas L. Bennett and Kenneth W. Kovak, Optimize Distillation Columns, Chemical Engineering Progress, May 2000
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TRAY HYDRODYNAMICS• PRESSURE DROPS (ENERGY LOSSES)AFFECT
EQUILIBRIUM AND SYSTEM ENERGY DEMANDS• LIQUID ΔP
– COMPENSATED BY GRAVITY– FRICTION LOSSES
• THROUGH DOWNCOMER• UNDER DOWNCOMER• OVER DOWNCOMER
– INERTIAL LOSS - CHANGE IN FLOW DIRECTION ON TRAY
– CONTRACTION/EXPANSION LOSSES DUE TO CHANGE IN FLOW CROSS-SECTION AREA
– EDDY LOSSES• AT WALLS• AT CAPS OR VALVES
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TRAY HYDRODYNAMICS• VAPOR ΔP IS ALL THAT IS NORMALLY
CONSIDERED:
• hLIQUID HEAD
– BASED ON LIQUID LEVEL ON TRAY– RELATED TO RESIDENCE TIME OF THE
BUBBLE IN THE LIQUID – BASED ON WEIR HEIGHT LEVEL PLUS
HEIGHT OF LIQUID FLOW OVER WEIR
h h h HEAD LIQUIDORIFICETOTAL
IGHTOVERFLOWHEWEIRHEIGHTLIQUIDHEAD hhh
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CORRELATION EQUATIONS• FLOW OVER A WEIR (FRANCIS EQN.)
• ORIFICE DROP– SIEVE TRAYS
323
443
/
)(
min)/(.)(
mL
mqmmh
W
LHEIGHTOVERFLOW
AREADOWNCOMERA
AREAPLATETOTALAAAAREAPLATEACTIVEA
AREAHOLEPLATETOTALACOEFFICENTORIFICEC
A
A
C
smuliqmmh
d
da
OO
a
O
L
V
O
OORIFICE
2
1512
2
2
,
)/()(
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CORRELATION EQUATIONS
• BUBBLE CAPS ARE OF THE FORM
• VALVE TRAYS HAVE SIMILAR FORMS– SEE PERRY’S Pp. 14-11 THROUGH 14-38
FOR TRAYS AND 14-38 – THROUGH 14-58 FOR PACKING
VELOCITYVAPORMAXIMUMU
CONSTANTNCORRELATIOK
UKh
VC
C
L
VVCCBC
2
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LIQUID-IN-VAPOR ENTRAINMENT
• CONTROLLED THROUGH DESIGN OF:– TRAY SPACING– VAPOR VELOCITY– LIQUID HEIGHT– VAPOR DENSITY– LIQUID SURFACE TENSION– HOLE DIAMETER
• VAPOR-IN-LIQUID ENTRAINMENT (FOAMING) CAN RESULT IN VAPOR BEING CARRIED DOWN THE THE LOWER TRAYS OR LIQUID AS BUBBLES BEING CARRIED TO THE TRAY ABOVE
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TRAY EFFICIENCY
• CONTROLLING VARIABLES:– PATH LENGTH– BACKMIXING – BUBBLE FORMATION MECHANISM AND
PHASE CONTACT• ORIFICE SIZE• FREE AREA FOR BUBBLING
– RELATIVE VAPOR/LIQUID RATES
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CORRELATIONS OF EMPIRICAL DATA
• USE PECLET NUMBER
– AIChE STANDARD METHOD (1958) FOR BUBBLE CAPS– GENERAL DIMENSIONLESS FORM USES AS POSSIBLE
VARIABLES: • VAPOR & LIQUID DENSITY, VISCOSITY AND DIFFUSIVITY• LIQUID SURFACE TENSION
– GENERAL FORM– ≈ + 12% ACCURACY
TRAYONTIMERESIDENCELIQUIDtYDIFFUSIVITEDDYD
PATHFLOWOFLENGTHZtD
ZPe
LE
LLE
L
2
EC
LL
L
B
vLM Du
A
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SUMMARY OF COLUMN DESIGN• COLUMN
– OPERATING PRESSURE AND TEMPERATURE– REFLUX RATIO– NUMBER OF TRAYS– FEED AND DRAW-OFF LOCATIONS– COLUMN DIAMETER– TRAY SPACING
• TRAY– TYPE AND ARRANGEMENT– ACTIVE AREA– DOWNCOMER TYPE, AREA & CLEARANCE– MATERIALS OF CONSTRUCTION