Download - 24 - ENTHALPY BASED DISTILLATION MODELS
ENTHALPY-BASED DISTILLATION MODELING
PONCHON-SAVARITT ANALYSIS
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.
ENTHALPY EQUILIBRIUM DIAGRAM
http://www.hyper-tvt.ethz.ch/images/enthalpy.jpg
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
ENTHALPY CONCENTRATION
COORDINATE SYSTEM
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
ENTHALPY CONCENTRATION RECTIFICATION
SECTION
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
ENTHALPY CONCENTRATION
STRIPPING SECTION
From: Treybal, R.E., Mass-Transfer Operations, 2nd Ed., McGraw-Hill, 1968
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
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
ENTHALPY BALANCES
• OVERALL
• CONDENSERB
qHH
D
qHH
BHDHFhBDF
rBB
cDD
BDF
''
''
Dnnnn DxxLyV 11
DLV nn 1
CDnLn
nVn
qDHHL
HV
,
1,1
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
)(
)(
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
REBOILER HEAT BALANCE
• REBOILER
• OVERALL
Brmmmm BhqhBVHV )( 111
cFBDr qFhBhDhq
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
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
'
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
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'
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
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.
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
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
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
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
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
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
,
)/()(
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
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
TRAY EFFICIENCY
• CONTROLLING VARIABLES:– PATH LENGTH– BACKMIXING – BUBBLE FORMATION MECHANISM AND
PHASE CONTACT• ORIFICE SIZE• FREE AREA FOR BUBBLING
– RELATIVE VAPOR/LIQUID RATES
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
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