Optimization in Plant Design and Economics

is the process of selecting the best feasible solution among several alternatives, based on a defined objective and subject to constraints

Optimization

depends on the goal

best

physically possible and acceptable

feasible

limits that must be obeyed

constraints

The quantity that can be changed or selected

Decision Variable

The quantity to be minimized or maximized

Objective

The limits the design must satisfy

Constraints

A design decision usually affects

• capital cost or investment cost

• operating cost

• maintenance cost

• profitability

The best design is often the one that gives:

• minimum total annual cost

• maximum annual profit

The optimum design is often found where the

combined cost is minimum

An _______________ is the mathematical expression of the goal of the optimization problem.

objective function

General form of an objective function

Optimize f(x)

f(x)

Objective function

x

design variable

These equations help determine which design is economically best

Total Annual Cost = Annual Capital Cost + Annual Operating Cost

or

Profit = Revenue −Total Cost

TRUE or FALSE

For a required flowrate, more than one pipe diameter may be feasible

TRUE

smaller diameter gives ________ velocity

higher velocity

higher velocity causes _______ friction loss

greater friction loss

greater friction loss leads to ______ pressure drop

higher pressure drop

higher pressure drop requires ______ pumping power

more pumping power

Larger diameter gives

less velocity

lower velocity reduces ____________

pressure drop

lower pressure drop reduces ____________________

pumping requirement

The optimum pipe diameter is the diameter that gives the ________________

lowest overall annual cost

It is the pipe size that gives the best economic balance

optimum pipe diameter

As pipe diameter increases:

• installed pipe cost increases

• pumping power cost decreases

• total cost first decreases, reaches a minimum, then increases

The diameter corresponding to the lowest total cost is the

optimum economic pipe diameter

Annual Pipe Cost

• Pipe diameter

• Cost

Annual Pipe Cost

• increases as pipe diameter increases

• larger pipes cost more to purchase and install

Annual Pumping Cost

• Pipe diameter

• Cost

• decreases as pipe diameter increases

• larger pipes reduce friction loss and pumping requirement

In the diagram, Pipe cost goes _______ with diameter

upward

In the diagram, Pumping cost goes __________ with diameter

downward

A simplified model for total annual cost is:

The _______________ is the condition that gives the best overall result based on a chosen objective.

optimum operating condition

The optimum condition usually arises from a

trade-off

A common trade-off in equipment design in larger equipment

• higher capital cost

• lower operating cost

• better performance in some cases

A common trade-off in equipment design in smaller equipment

• lower capital cost

• higher operating cost

• lower performance in some cases