The Enthalpy-Concentration Method Ponchon-Savarit Graphical Method 1.
[ H i , hi − xi , yi ]The Enthalpy-Concentration diagram
The Enthalpy-Concentration Diagram •
Bubble point curve
•
Dew point curve
•
Tie lines
•
Superheated vapor
•
Sub cooled liquid 1
•
Two phase region
2.
Drawing of saturated liquid enthalpy curve
•
Enthalpies of i , j at their boiling points
T i ,T j
hi = mic pi (Ti − T ref )
h j = m jc pj (T j − T ref ) •
Enthalpy of liquid mixture:
hmix = xi c pi (T − Tref ) +(1 − xi ) c pj ( T −Tref ) + ∆Hsol
3.
Drawing of saturated vapor enthalpy curve
Vapour Enthalpies of i , j at their boiling points
T i ,T j
H i = hi + λ i H j = h j + λ j Enthalpy of vapour mixture
H mix = y i [λi + c pyi (T −T ref )] + (1 − y i )[ λ j +c pyj (T −T ref )]
2
4.
Drawing of Tie Lines
3
RECTIFICATION SECTION
Material balance: V n +1 = L n + D V n +1 y n +1 = L n x n + Dx D ( L n + D ) y n +1 = L n x n + Dx D Ln D
=
x D − y n +1 y n +1 − x n
Energy balance: V n +1H n +1 = L n h n + Dh D + Q c ( L n + D )H n +1 = L n h n + D ( h D + L n D
=
(h D +
Qc D
Qc D
)
) − H n +1
H n +1 − hn
Combining by equating the reflux ratio 4
Ln D
expressions:
x D y n
−
yn
1
+
xn
1 −
+
Qc ) − H n D H n 1− hn
( h D =
+
1
+
+
The equation represents three relationships for stages :
Qc x D , (hD + D )
n
and
n +1
, [ y n +1 , H n +1 ] , [ x n , h n ] ,
Q The point x D , (hD + c ) has a constant value. D
The equation represents a set (family) of straight lines on the Q [ H , h − x i , y i ] diagram all out of the point x D , (hD + c ) represented D
by symbol O D referred to as the “UPPER OPERATING POINT”.
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Ponchon-Savarit Graphical method
1. Locate
x D , x = x D , y 1 = x D . h D and H D
2. Read the enthalpies of distillate λ D
3. Draw O D at x D , (hD
+
Qc D
H D
=
−
h
D
) , notice that O D lies a distance
Qc D
above h D . 4. For a total condenser :
Qc = λDV 1 = λ D D (R + 1) Qc D
=
λ D R+ λ D
5. Notice that O D lies a distance R λ D above H D Construction procedure: •
Equilibrium tie-line from y 1 locates x 1 .
•
x 1 joined to
O D locates
y 2 ( operating relationship,
straight line O D x 1 fixes position of y 2 ) •
Equilibrium tie-line from y2 locates x2 .
•
x2 joined to
O D locates y3 ( operating relationship,
straight line O D x 2 fixes position of y3 ). •
…and so on ….. y n locates straight
line
x n by equilibrium and the
O D x n locates y n +1
relationship. 6
by
the
operating
•
•
..this continues until a tie-line falls on or passes x F the feed composition. .. in this way the equilibrium stages are determined (each tie line represent an equilibrium stage).
Ponchon-Savarit Graphical method
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STRIPPING SECTION
Material balance:
V m +1 = L m −W V m +1 y m +1 = L m x m −Wx w ( L m −W ) y m +1 = L m x m −Wx w L m W
=
y m +1 − x w y m +1 − x m
Energy balance:
V m +1 H m +1 = L m h m −W hw + Q b Q ( L m −W )H n +1 = L m h m −W (hw − b ) W Q H m +1 − ( hw − b ) L m W = W H m +1 − hm 8
Qb W Energy added to the reboiler per unit bottoms product
Combining by equating the ratio
y m +1 − x w y m +1 − x m
=
Lm W
expressions:
H m +1 − (hw −
Qb ) W
H m +1 − h m
The equation represents three relationships for all values of m and m +1 :
Qb − x , ( h w w W
) ,
[ y m +1 , H m +1 ]
,
[ x m , hm ]
Qb − x , ( h ) has a constant value. The point w w W The equation represents a set (family) of straight lines on the [ H , h − x i , y i ]
diagram
all
represented by the symbol
out
of
the
point x w , ( hw
−
Qb ) W
OW referred to as the “LOWER
OPERATING POINT”.
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Construction procedure: 1. Locate
x
w
at intersection of x = xw and the bubble point
curve. 2. The reboiler N + 1 is an equilibrium stage, hence are in equilibrium. The tie lie from
x
w
x
w
and y N +1
locates. y N +1 .
3. Straight line joining y N +1 with the lower operating point locates
x
N
OW
on the saturated liquid bubble point curve.
4. xN locates y N by equilibrium tie line relationship. 5. Straight line joining y N to the operating point OW locates x N −1 .
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6. …and so on using tie line and operating point relationships for number of equilibrium stages until x F is reached or crossed by a tie line.
Ponchon-Savarit Graphical method
THE FRACTIONATOR
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Material balance:
F Material balance
=
Fx F
D + W =
Dx D + Wx w
( D +W ) x F= Dx D+ Wx W D
=
w
x D −x F x F −x w
F H F + Qb = Qc + DhD + Whw ( D + W ) H F + Qb = Qc + DhD + Whw D H F + W H F = D( h D +
Qc D
) + W ( hw −
Qb W
Qc ) − H F W D = Q D H F − ( hw − b ) W ( h D +
Combining by equating the ratio
W expressions D 12
)
x D − x F x F − x w
Qc ) − H F D = Q H F − ( hw − b ) W ( h D +
Here a relationship between three points:
Qc Qb − x , ( h ) x , ( h + , w w W D D D ) , x F , H F
x F , H F is the feed point represented by the symbol F . The equation, thus, represent a straight line OW FOD joining the operating points F , OW , O D . By drawing the line OW FO D from any two of the three operating points the third will be located. The equilibrium stages for the whole fractionator will be determined as shown in the following steps:
1. Locate x iD and extend upwards 2. Calculate
λ D
= ( H D − h D )
3. Locate O D at a distance R λ D above H D 4. Fix the feed point F from knowledge of x iF and H F 5. extend the line O D F to intersect the vertical line x = x iw at OW 6. Start construction of equilibrium stages starting from y 1 using tie lines and upper operating pointO D one after the other until the feed point F is passed. 7. After that the lower operating pointOW is used with x to give y
, followed by tie line from give y and so on …….
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y
to give x , then x with OW to
8. Construction stops when x iw is reached or passed.
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