Pipework is a large part of the cost of a process plant. Plant designers need to minimize the total cost of this pipework across the lifetime of the plant. The total overall cost is a combination of individual costs relating to the following:
•

energy costs for pumping

This application uses the approach described in the reference to find the pipe diameter that minimizes the total overall cost. The method involves the iterative solution of an empirical equation using Maple’s fsolve() function (the code is in the Startup code region)
Bear in mind that the empirical parameters vary as economic conditions change. Those used in this application are correct for 1998 and 2008 (as given in the reference)
The economical optimal pipe diameter (as given in the reference) is given by an iterative solution of the following equation (Generaux Equation).
$Qequals;{\left(\frac{{\mathrm{D}}^{4.84plus;n}nXE\left(1plus;F\right)\left(Zplus;\left(aplus;b\right)\cdot \left(1\mathrm{\Phi}\right)\right)}{\left(1plus;0.794\mathrm{Le}apos;\mathrm{D}\right)\left(0.000189YK{\mathrm{rho;}}^{0.84}{\mathrm{mu;}}^{0.16}\right)\left(\left(1plus;M\right)\left(1\mathrm{\Phi}\right)plus;\frac{Z\cdot M}{aapos;plus;bapos;}\right)}\right)}^{\frac{1}{2.84}}$
The empirical parameters are given in the following tables.
a

Fractional annual depreciation on pipeline (dimensionless)


n

Exponent in pipecost equation $Cequals;X{\mathrm{D}}^{n}$(dimensionless)

b

Fractional annual maintenance on pipeline (dimensionless)


P

Installation cost of pump and motor ($/hp)

a'

Fractional annual depreciation on pumping installation (dimensionless)


Q

Fluid flow rate (ft^{3}/s)

b'

Installed cost of pipeline, including fittings ($/ft)


S

Cross sectional area (ft^{2})

C

Inside pipe diameter (ft)


V

Velocity (ft/s)

D

Inside pipe diameter (ft)


X

Cost of 1 ft of 1 ft diameter pipe ($)

E

Combined fractional efficiency of pump and motor (dimensionless)


Y

Days of operation per year (at 24 hours per day)

F

Factor for installation and fitting


Z

Fractional rate of return of incremental investment (dimensionless)

K

Energy cost delivered to the motor ($/kWh)


F

Factor for taxes and other expenses (dimensionless)

Le'

Factor for friction in fitting, equivalent length in pipe diameter per length of pipe (1/ft)


r

Flow density (lb/ft^{3})

M

$\frac{\left(a\'\+b\'\right)\left(EP\right)}{17.9KY}$
Factor to express cost of piping installation, in terms of yearly cost of power delivered to the fluid (dimensionless)


m

Fluid viscosity (cP)


