Mass and Energy Balances

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.

2
Enriching or Rectifying Section
Feed Stage
Stripping Section
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 lt 1 in the enriching section.
• Conversely, L/V gt 1 in the stripping section.
• Lets look at the mass and energy balances for
  the stripping section of the column with a
  partial reboiler.

4
(No Transcript)
5
Mass and Energy Balances Stripping Section
and Partial Reboiler
6
Constant Molar Overflow (CMO) Assumption
Stripping Section

• 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-ns are
  constant and the VN-m1s are constant in the
  column the CMO assumption.
• We can then rewrite the component mass balance
  as

7
Indices

• Lets do an indices substitution. If we let
• k N-n-1 then k N1, 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.

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.

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 and
• y-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 gt 1, since there will be a greater
  amount of liquid than vapor in the stripping
  section below the feed stream.

10
Alternative Stripping Section OL Liquid
to Vapor Ratio
11
Stripping Section OL and y x Intersection
12
Distillation Column Stripping Section
Operating Line
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 gt L.
• If the feed is a vapor, then V gt V.
• The feed may also be flashed into the column
  yielding both vapor and liquid remember flash
  distillation!
• Remember, however, L/V lt 1 and L/V gt1.
• Lets look at the feed stream and how we handle
  it

14
(No Transcript)
15
Mass and Energy Balances Feed Stage
16
Constant Molar Overflow (CMO) Assumption
Feed Stage

• 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.

17
Handling Feed Stream Conditions

• Since the nature (both phase and temperature) of
  the feed affects the columns 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

18
Some Manipulations
19
Quality q
20
OL Intersection
21
Another Mass Balance OL Intersection
22
Some Further Manipulations General Feed
Line
23
Some Further Manipulations Another Feed
Line
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

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

26
Feed Line and OL Intersection

• Remember that we derived these feed line
  equations from the intersection of the enriching
  section and stripping section OLs.
• It can be shown that the feed line also
  intersects the OLs at their intersection all
  three lines intersect at the same point.
• We will need to use this intersection point in
  our solutions

27
OL and Feed Line Intersection
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 lt Tbp
• Saturated liquid feed if TF Tbp
• Two-phase feed if Tbp ltTF lt Tdp
• Saturated Vapor if TF Tdp
• Superheated Vapor if TF gt Tdp

29
Saturated Liquid Feed Given TF Tbp
30
Saturated Vapor Feed Given TF Tdp
31
Two-Phase Feed Given f
32
Two-Phase Feed Given TF
33
Subcooled Liquid Feed Given c
c
34
Subcooled Liquid Feed Given TF lt Tbp
c
35
Superheated Vapor Feed Given v
v
36
Superheated Vapor Feed Given TF gt Tdp
v
37
Possible Feed Lines
38

• End of Lecture 12