Lecture 12 1 Mass and Energy Balances – Stripping Section and Partial Reboiler The previous mass and energy balances apply only to the enriching section. At some point down the column, we will have a feed to one of the equilibrium stages – the feed stage. At this feed stage, the enriching section of the column ends. At the feed stage we have the introduction of additional liquid and/or vapor depending upon the nature of the feed stream. Liquid from the feed stream will flow down the column and vapor from the feed stream will rise up the column. Consequently, the ratio of vapor to liquid in the enriching section above the feed stage is generally different than that in the stripping section below the feed stage because of the feed between these two sections.
Transcript
Lecture 12 1
Mass and Energy Balances – Stripping Section and Partial Reboiler
The previous mass and energy balances apply only to the enriching section.
At some point down the column, we will have a feed to one of the equilibrium stages – the feed stage. At this feed stage, the enriching section of the column ends.
At the feed stage we have the introduction of additional liquid and/or vapor depending upon the nature of the feed stream.
Liquid from the feed stream will flow down the column and vapor from the feed stream will rise up the column.
Consequently, the ratio of vapor to liquid in the enriching section above the feed stage is generally different than that in the stripping section below the feed stage because of the feed between these two sections.
Lecture 12 2
Feed Stage
Stripping Section
Enriching or Rectifying Section
Lecture 12 3
Mass and Energy Balances – Stripping Section and Partial Reboiler
While we have designated the vapor and liquid streams in the enriching section as L and V, we will designate the vapor and liquid streams in the stripping section using an “underline” or V and L (in place of the “overbar” in the text) to delineate them from those in the enriching section.
L/V < 1 in the enriching section.
Conversely, L/V > 1 in the stripping section.
Let’s look at the mass and energy balances for the stripping section of the column with a partial reboiler.
Lecture 12 4
Stage N-2
Stage N-1
Stage N
Stage N+1
∙∙∙
Stage N- n
Stage N-3
1NV NL
Partial Reboiler
RQ
N V
2N L
1N L
B
1N V
2N V
3N L
nN L
1N V n
Stage N-2
Stage N-1
Stage N
Stage N+1
∙∙∙
Stage N- n
Stage N-3
1NV NL
Partial Reboiler
RQ
N V
2N L
1N L
B
1N V
2N V
3N L
nN L
1N V n
Lecture 12 5
Mass and Energy Balances – Stripping Section and Partial Reboiler
Total Component Energy Mass Balance Mass Balance Balance Stage (Partial Reboiler)
Just as we did for the enriching section, we will assume that for every mole of liquid that vaporizes at an equilibrium stage, an equivalent amount of vapor condenses, then the LN-n’s are constant and the VN-m+1’s are constant in the column – the CMO assumption.
We can then rewrite the component mass balance as:
BNN1N1N BxxLyV nnnn
BN1N xB xLy V nn (CMO) or rearranging
BN1N xV
B x
V
Ly nn (CMO)
Lecture 12 7
Indices Let’s do an indices substitution. If we let
k = N-n-1; then k = N+1, N, N-1, N-2, … then the previous equation can be rewritten as:
Note that this allows us to arrive at the indices used by Wankat, e.g., Eq. (5-14), which we can derive from this equation.
B1 xV
B x
V
Ly kk
Lecture 12 8
Stripping Section Operating Line
Just as we did for the enriching section, we can also drop the indices from the CMO equation for the stripping section noting that the vapor and liquid compositions, yk and xk-1, represent the vapor and liquid compositions at equilibrium at stage k.
Just as we derived the enriching section operating line (OL) from the mass balances and assuming CMO, this equation is the OL for the stripping section.
B xV
B x
V
Ly
Lecture 12 9
Stripping Section Operating Line
The stripping section operating line (OL) for a distillation column (assuming CMO) is a linear equation with:
slope L/V andy-intercept –(B/V)xB
Note that the L/V ratio for the stripping section of a distillation column will always be greater than one, L/V > 1, since there will be a greater amount of liquid than vapor in the stripping section below the feed stream.
B xV
B x
V
Ly Stripping Section OL
Lecture 12 10
Alternative Stripping Section OL – Liquid to Vapor Ratio
Stripping Section OL:
BxV
Bx
V
Ly
From a mass balance around the reboiler, VLB
1V
L
V
B
and substituting into the previous stripping section OL yields:
Bx1V
Lx
V
Ly
Eq. (5-22)
Lecture 12 11
Stripping Section OL and y = x Intersection
If we substitute y = x into any of these OL’s, including Eq. (5-22), we find that Bxxy This is the intersection of the Stripping Section OL and the y = x line, which is xB, the composition of the bottom stream.
Lecture 12 12
Distillation Column – Stripping Section Operating Line
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1.0
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
x mole fraction
y m
ole
fra
cti
on
Equilibrium Curve
Stripping Section OL
y-int = -(B/V)xB
= - (L/V-1)xB
y = x
xB
Slope = L/V
Lecture 12 13
Feed Stage At some point down the column, we introduce the feed at the
feed stage.
The phase and temperature of the feed affects the vapor and liquid flow rates in the column.
If the feed is a liquid, then L > L.
If the feed is a vapor, then V > V.
The feed may also be flashed into the column yielding both vapor and liquid – remember flash distillation!
Remember, however, L/V < 1 and L/V >1.
Let’s look at the feed stream and how we handle it…
Just as we did for the enriching and stripping sections, we will assume CMO for the feed stage and drop the indices. We also add the liquid and vapor designations for our enthalpies in the energy balance.
Total Mass Balance VLVLF Eq. (5-15) Component Mass Balance VyxLyVLxFzF Energy Balance VLVLF VHhLHVLhFh Eq. (5-16)
Lecture 12 17
Handling Feed Stream Conditions
Since the nature (both phase and temperature) of the feed affects the column’s liquid and vapor flows, we need to derive a method for handling these various types of possible feeds.
It would be useful to derive such a method that allows us to readily incorporate a parameter that accounts for the condition of the feed stream.
We will start with the total mass and energy balances around the feed stage…
Lecture 12 18
Some Manipulations…The energy balance, Eq. (5-16) can be rearranged to: 0V)HV()hLL(Fh VLF
If we solve the mass balance, Eq. (5-15), for V – V FLLVV and substitute into the previous equation, we have, after some rearranging, )hF(HL)hL(L)HL( FVLV
or )hF(H)hL)(HL( FVLV
and one final rearrangement yields the relationship:
LV
FV
hH
hH
F
LL
Eq. (5-17)
Lecture 12 19
“Quality” qWe define the left-hand side of Eq. (5-17) as the “quality”, q
LV
FV
hH
hH
F
LLq
Eq. (5-17)
It can also be shown from the previous material balances that
plate feed on theenthalpy liquidplate feed on theenthalpy vapor
enthalpy feedplate feed on theenthalpy vapor q
The quality, q, is the fraction of feed that is liquid. This is analogous to the q that we saw defined for flash distillation – remember that we assume that the feed is adiabatically flashed to the column pressure!
Lecture 12 20
OL Intersection
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x mole fraction
y m
ole
fra
cti
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Equilibrium Curve
Stripping Section OL
Enriching Section OL
Lecture 12 21
Another Mass Balance –OL Intersection
At the feed stage, the enriching section OL and the stripping section OL must intersect. These OL’s can be written as: DDxLxVy Enriching Section OL Eq. (5-26) BBxxLyV Stripping Section OL Eq. (5-27) We can represent this point of intersection by subtracting the stripping section OL from the enriching section OL (essentially a simultaneous solution). Doing so and grouping terms yields: BD BxDx)xL(L)Vy(V Eq. (5-29)
Lecture 12 22
Some Further Manipulations – General Feed Line
The component mass balance around the column yields FBD FzBxDx Substituting this mass balance into the difference of the OL’s yields, upon rearrangement,
Fz)V(V
Fx
)V(V
)L(Ly
Feed Line Eq. (5-30)
This equation is linear and in the form of an operating line. It is one of the various forms, as we shall see, of the feed line and is the most general form.
Lecture 12 23
Some Further Manipulations – Another Feed Line
The total mass balance around the feed stage yields VLVLF Combining this mass balance with the previous feed line yields, upon rearrangement,
Fz
FLL
1
1x
1F
LLF
LL
y
or, from the definition of quality, q:
Fzq1
1x
1q
qy
Feed Line Eq. (5-35)
Lecture 12 24
Feed Line The previous equation is the feed line for the column in terms of
quality q.
This should look familiar – it is the same as the operating line that we obtained from the mass balances for flash distillation!
We can use the conditions of the feed to determine q from its enthalpy relationship:
Fzq1
1x
1q
qy
Feed Line Eq. (5-35)
LV
FV
hH
hH
F
LLq
Eq. (5-17)
Lecture 12 25
Feed Line Equations
By inspection from the results of our flash distillation operating lines, the feed line can also be expressed in terms of fraction of feed vaporized, f = V/F. This, as well as the other feed line equations, are summarized below:
Fz)V(V
Fx
)V(V
)L(Ly
Eq. (5-30)
Fzq1
1x
1q
qy
Eq. (5-35)
Fzf
1x
f
f1y
Eq. (5-34)
Lecture 12 26
Feed Line and OL Intersection
Remember that we derived these feed line equations from the intersection of the enriching section and stripping section OL’s.
It can be shown that the feed line also intersects the OL’s at their intersection – all three lines intersect at the same point.
We will need to use this intersection point in our solutions…
Lecture 12 27
OL and Feed Line IntersectionSimultaneous solution of the enriching section and stripping section OL’s and feed line yields their intersections, xI and yI:
VL
VL
x1VL
xVL
1
xBD
I
DII xV
L1x
V
Ly
qVL
1q
zxVL
11qx
FD
I
/DLq
1
/DLqx
z
y
0
0
DF
I
Eq. (5-38)
Lecture 12 28
Possible Feed Stream Conditions
We assume that the incoming feed is adiabatically flashed to the column pressure, Pcol.
We can have 5 possible feed stream conditions for a given feed composition zF:
Subcooled liquid feed if TF < Tbp
Saturated liquid feed if TF = Tbp
Two-phase feed if Tbp <TF < Tdp
Saturated Vapor if TF = Tdp
Superheated Vapor if TF > Tdp
Lecture 12 29
Saturated Liquid Feed – Given TF = Tbp
1F
L)F(L
F
LLq
or since hF = hL
1h0
h0
hH
hHq
L
F
LV
FV
Note that q = 1.
Lecture 12 30
Saturated Vapor Feed – Given TF = Tdp
0F
LL
F
LLq
or since HV = hF,
0hH
HH
hH
hHq
LV
VV
LV
FV
Note that q = 0.
Lecture 12 31
Two-Phase Feed – Given f
f is the fraction of feed vaporized.
F
L
F
L)L(L
F
LLq FF
F
V1
F
)VV(V1
F
VV1q FF
f1F
V1q F
Note that 0 < q < 1.
Lecture 12 32
Two-Phase Feed – Given TF
Since we assume CMO, all HV’s and hL’s are constant.
liquid) dL(sat' vapor)dV(sat'
temp)F(feed vapor)dV(sat'
LV
FV
hH
hH
hH
hHq
all determined at zF. Note that HV > hF > hL, 0 < q < 1.
