Page 53 - Separation process engineering

liquid in equilibrium with the actual bulk gas of mole fraction y , and the term “a” is the interfacial area
A
3
2
2
3
per unit volume (m /m or ft /ft ).
By definition, at equilibrium we have y * = y and x * = x . Note that as y →y * and x →x * the
A
A
A
A
A
A
A
A
driving forces in Eqs. (1-5) approach zero and mass transfer rates decrease. In order to be reasonably
close to equilibrium, the simplified model represented by Eqs. (1-5) shows that we need high values of
K and K and/or “a.” Generally speaking, the mass transfer coefficients will be higher if diffusivities are
x
y
higher (details are in Chapter 15), which occurs with fluids of low viscosity. Since increases in
temperature decrease viscosity, increasing temperature is favorable as long as it does not significantly
decrease the differences in equilibrium concentrations and the materials are thermally stable. Mass
transfer rates will also be increased if there is more interfacial area/volume between the gas and liquid
(higher “a”). This can be achieved by having significant interfacial turbulence or by using a packing
material with a large surface area (see Chapter 10).
Although some knowledge of what affects mass transfer is useful, we don’t need to know the details as
long as we are willing to assume we have equilibrium stages. Thus, we will delay discussing the details
until we need them (Chapters 15 through 18).

1.4 Problem-Solving Methods

To help develop your problem-solving abilities, an explicit strategy, which is a modification of the
strategy developed at McMaster University (Woods et al., 1975), is used throughout this book. The seven
stages of this strategy are:
0. I want to, and I can

1. Define the problem
2. Explore or think about it

3. Plan
4. Do it

5. Check

6. Generalize
Step 0 is a motivation and confidence step. It is a reminder that you got this far in chemical engineering
because you can solve problems. The more different problems you solve, the better a problem solver you
will become. Remind yourself that you want to learn how to solve chemical engineering problems, and
you can do it.

In step 1 you want to define the problem. Make sure that you clearly understand all the words. Draw the
system and label its parts. List all the known variables and constraints. Describe what you are asked to
do. If you cannot define the problem clearly, you will probably be unable to solve it.

In step 2 you explore and think about the problem. What are you really being asked to do? What basic
principles should be applied? Can you find a simple limiting solution that gives you bounds to the actual
solution? Is the problem over- or underspecified? Let your mind play with the problem and chew on it,
and then go back to step 1 to make sure that you are still looking at the problem in the same way. If not,
revise the problem statement and continue. Experienced problem solvers always include an explore step
even if they don’t explicitly state it.

In step 3 the problem solver plans how to subdivide the problem and decides what parts to attack first.
The appropriate theory and principles must be selected and mathematical methods chosen. The problem
solver assembles required resources such as data, paper, and calculator. While doing this, new