Source: A Working Guide to Process Equipment

CHAPTER 12
Bubble Point and
Dew Point
Equilibrium Concepts in
Vapor-Liquid Mixtures

O
ur work as process engineers and operators is based on three
principles:

• Hydraulics—when the velocity of water in a pipe goes up, its

pressure goes down.
• Heat balance—condensing steam gives up latent heat, or sensible
heat, to increase the temperature in the feed preheater.
• Vapor-liquid equilibrium—a boiling liquid is at its bubble point,
and a condensing vapor is at its dew point.

12.1 Bubble Point

The purpose of this chapter is to explain what is meant by the terms
bubble point and dew point, and how we can use these ideas to improve
the operation of the distillation tower. To begin, we will derive the bubble-
point equation from the basic statement of vapor-liquid equilibrium:
y1 = K1 × x1 (12.1)

where y1 = concentration of the first component in the vapor

x1 = concentration of the first component in the liquid
K1 = an equilibrium constant

We really should use mole fraction, and not concentration, in our

description of y and x, but for our work, we will just say that the term
concentration refers to the percent of a component that the operator
would see in the gas-chromatographic (GC) results, as reported by

137
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 Bubble Point and Dew Point

138 A Working Guide to Process Equipment

the lab. The equilibrium constant, assuming the ideal-gas law applies,
is defined as
PV ,1
K1 =
(12.2)
PT
where PV ,1 = vapor pressure of the first component, at the temperature
we are working at, in psia (see Fig. 12.1 for chart of
vapor pressures used here)
PT = total pressure in psia (psia = psig + 14.7)

If you do not recall the meanings of mole fraction or the ideal-gas law,
don’t worry—it is not necessary to recall these in order to understand
bubble points, or dew points. Substituting Eq. (12.2) in Eq. (12.1), we obtain
PV ,1 x1 (12.3)y1 =
PT
Let’s assume that we have three components in the vessel shown
in Fig. 12.2. Then we could write
PV ,1 x1 PV ,2 x2 PV ,3 x3
y1 + y 2 + y 3 = + + (12.4)
PT PT PT
But if we add up the concentration of the three components in the
vapor phase on the left side of Eq. (12.4), we would get 100 percent.

1000

e
an
op
Vapor pressure psia (log scale)

Pr

e
tan
Bu
100

ne
n ta
Pe

10

100 150 200 250

Temperature, °F

FIGURE 12.1 Vapor-pressure chart.

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 Bubble Point and Dew Point

Chapter 12: Bubble Point and Dew Point 139

FIGURE 12.2
Calculating bubble-
point pressure. P=?

Dew
point
150°F

Feed

Bubble
point

20% propane
40% butane
40% pentane

The fractions on the right side of Eq. (12.4) all have the same deno-
minator (i.e., PT), so they can be also added together:

PV ,1 x1 + PV ,2 x2 + PV ,3 x3
100% = (12.5)
PT

Recalling that 100 percent of anything is the whole thing or, in

other words, equals unity or one, if we cross-multiply both sides of
this equation by PT , we have
PT = PV,1 x1 + PV,2 x2 + PV,3 x3 (12.6)
This is the bubble-point equation for a three-component system.

12.1.1 Using the Bubble-Point Equation

Are we missing the pressure PT in the flash drum shown in Fig. 12.2?
Let’s calculate this pressure, using the bubble-point equation and the
vapor pressure chart shown in Fig. 12.1:
Vapor Partial
pressure at Concentrating pressure,
Component 150°F, psia mol% in liquid, % psia
Propane 330  20  66
Butane 105  40  42
Pentane 35  40  14
Vessel  122
pressure

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 Bubble Point and Dew Point

140 A Working Guide to Process Equipment

The term partial pressure, meaning part of the total pressure created
by each component, is important. The partial pressure of a component
divided by the total pressure is the concentration of the component in
the vapor phase. For example, the concentration of propane in the
vapor leaving the drum shown in Fig. 12.2 is
66 psia
= 54%
122 psia
What is the concentration of pentane in the vapor? (Answer:
14 ÷ 122 = 13 percent.)

12.1.2 Adjusting Temperature to Meet

a Product Specification
A new set of product specifications has just been issued to your shift.
The liquid from the flash drum shown in Fig. 12.3 has too much
propane. The new liquid specification is

• Propane: 10 percent
• Butane: 40 percent
• Pentane: 50 percent

The pressure in the drum is still fixed at 122 psia. So, it seems as if
we will have to run the drum hotter. But how much hotter? Suppose we
raise the drum temperature to 160°F, and repeat our bubble-point
calculation:

FIGURE 12.3
Calculating a
temperature to
meet a new
specification. 122
psia
Temp. = ?

10% propane
40% butane
50% pentane

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 Bubble Point and Dew Point

Chapter 12: Bubble Point and Dew Point 141

Vapor Partial
pressure at Concentrating pressure,
Component 160°F, psia mol% in liquid, % psia
Propane 380  10  38
Butane 130  40  52
Pentane 40  50  20
Calculated  110
vessel
pressure

Apparently, our guess of 160°F was wrong. If we had guessed the

correct temperature, the calculated vessel pressure would have been
122 psia, not the 110 psia. Try to work this problem yourself1 by
guessing a new flash drum temperature (answer: 168°F).
This seems to be a potentially good application for computer
technology. For example, an operator is running a debutanizer and
finds that she has too much isobutane in her isopentane bottoms
product. She enters the most recent gas chrome result from the lab in
the computer, with the corresponding tower pressure and reboiler
outlet temperature. Next, she enters the isobutane specification she
would like to achieve in the tower’s bottoms product. The computer
then tells her to raise the reboiler outlet temperature by 17°F, to get
back on spec (specification) quickly. This is a lot better than guessing
at the reboiler temperature, lining out the tower, and waiting half the
shift for the lab GC result, before making your next move.

12.2 Dew Point

12.2.1 Dew-Point Calculations
We now derive the dew-point equation from the same basic statement of
vapor-liquid equilibrium, starting with Eq. (12.3) in the previous section:
PV ,1 x1
y1 = (12.3)
PT
Now let’s multiply both sides of this equation by PT/PV ,1
y1 PT
= x1
PV ,1
Again, let’s assume we have three components:
y1 PT y 2 PT y 3 PT
+ + = x1 + x2 + x3 (12.7)
PV ,1 PV ,2 PV ,3
However, if we add up the concentration of the three components
in the liquid phase on the right-hand side of Eq. (12.7), we would get
100 percent, which is unity or equal to one as before:
y1 PT y 2 PT y 3 PT
+ + = 1.0 (12.8)
PV ,1 PV ,2 PV ,3

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 Bubble Point and Dew Point

142 A Working Guide to Process Equipment

Next, we divide both sides of the equation by PT, the vessel pressure:
y1 y y 1
+ 2 + 3 = (12.9)
PV ,1 PV ,2 PV ,3 PT

This is the dew-point equation for a three-component system.

12.2.2 Using the Dew-Point Equation

Is science really this easy? Much of the science applied to process
engineering is straightforward. In order to show you how to calculate
the temperature of the vapor leaving the depropanizer, in Fig. 12.4,
we will use the dew-point equation.
This time, we know that the tower-top pressure is 175 psig, or
190 psia. We also know that the composition of the overhead vapor is

• Propane: 80 percent
• Butane: 15 percent
• Pentane: 5 percent

It is normal to assume that the vapor leaving the top of a tower is

at its dew point. That is, it is at equilibrium with the liquid on the top
tray of the tower. Unfortunately, this assumption falls apart if the tower
is flooding and liquid is being entrained overhead from the column
with the vapor. However, assuming a normal, nonflooded condition,
we will guess that the tower-top temperature is 140°F. Using the vapor-
pressure curves provided in Fig. 12.1, we would calculate as follows:

Temp. = ?
190 psia

80% propane
15% butane
1 5% pentane

15

FIGURE 12.4 Calculating a dew-point temperature.

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 Bubble Point and Dew Point

Chapter 12: Bubble Point and Dew Point 143

Vapor
pressure at
140°F, psia, Concentration
Component PV in vapor y y ÷ PV
Propane 300 0.80 0.00267
Butane 90 0.15 0.00166
Pentane 30 0.05 0.00167
Sum of quotients 0.00600
y ÷ PV

According to Eq. (12.9), the sum of the quotient of y ÷ PV ought to

equal 1/PT :

1
0.00600 =
PT

Solving for PT , we find the calculated tower-top pressure equals

167 psia. But the actual tower-top pressure is 190 psia. Evidently, we
guessed too low a temperature. Try the calculation again yourself
with a better guess for the tower-top temperature (answer: 146°F).
For this tower, the composition of the overhead vapor is the same
as the overhead liquid product made from the reflux accumulator.

12.2.3 Revised Product Specification

It seems that the depropanizer overhead composition specification
has been changed. Our new operating orders are to produce

• Propane: 90 percent
• Butane: 8 percent
• Pentane: 2 percent

The tower-top pressure is still 190 psia. The tower-top temperature

will have to be reduced. Let’s guess that it will be reduced to 130°F:

Vapor
pressure at Concentration
Component 130°F, psia in vapor y y ÷ PV
Propane 270 0.90 0.00333
Butane 80 0.08 0.00100
Pentane 26 0.02 0.00077
Sum of quotients 0.00510
y ÷ PV

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 Bubble Point and Dew Point

144 A Working Guide to Process Equipment

Referring again to Eq. (12.9), we can solve for PT , the tower pressure:
1
0.00510 =
PT

or PT = 196 psia. But this is the calculated tower pressure. The actual
tower pressure is only 190 psia. Try to repeat this calculation to get
the correct tower-top temperature (answer: 128°F).
Again, this seems to be a rather nice application for computer
technology. Even a good-quality programmable calculator can store
a number of vapor-pressure curves. At least for hydrocarbons, equations
for these curves can be extracted from the API (American Petroleum
Institute) data book. Also, a programmable calculator can perform bubble-
point and dew-point calculations, with over 10 components, without
difficulty.
Dear reader, if you have skipped most of this chapter because of
the equations and the math, please consider the following:

• Most graduate chemical engineers cannot do these

calculations without the aid of a computer.
• Imagine the pleasure you will get if you’re an operator
explaining how to execute bubble-point and dew-point
calculations to your unit engineer. Possibly you might observe,
“Didn’t they teach you this in your first year of chemical
engineering at the university?”
• If you are a chemical engineer, you will have to admit that we
all learned the rules of vapor-liquid equilibrium during our
freshman year.

For me, it’s easy to remember how to do bubble-point and dew-

point calculations. I carry a pocket-size vapor pressure chart in my
wallet. When I’m out in the plant troubleshooting, that’s all I need to
check temperatures versus pressures for light hydrocarbon systems.

Reference
1. American Petroleum Institute, API Technical Data Book, vol. I, sec. 5, “Vapor
Pressures,” Aug. 1964, fig. 5A 1.1, p. 5-3.

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