A SIMPLE EXAMPLE
To illustrate the application of the method developed in the previous section, an
example using realistic parameter values is presented in this section. In addition, the
results obtained are compared to those obtained by using a common rule of thumb.
Before we can proceed with the calculation of the parameters, we need to define the
economic and technical assumptions upon which our solution is based.
The assumptions concerning economic conditions of an application are the most
controversial in an analysis of this type. Here, we will endeavor to select conditions
that are felt to be representative of the majority of applications rather than any
specific application. The analysis is quite sensitive to these economic assumptions,
so the reader is cautioned that specific information must be obtained before
applying these results. This can not be overemphasized.
The most significant cost to be considered is the capital cost of the piping system.
This cost is also highly variable, depending on the piping system used and, above
all, the site conditions. Our pipe cost equation is from Phetteplace (1981) and has
been adjusted for inflation from 1980 to 1988 using factors from R.S. Means Co.
Cp = 218 L + 2180 Ld.
The capital costs of pumps is also taken from Phetteplace (1981), with cost ad-
justments made as indicated above to arrive at
Cpumps = 1060 np + 0.242 ∆Pd m d/ρd.
The present value factors (PVF's) are assumed to be equal for electrical cost, heat
cost, and maintenance and repair costs. As noted earlier, these PVF's could be
modified to allow for escalation of energy, labor or material costs and could even be
modified to allow for increasing heat loss over the life of the system. For simplicity,
however, such modifications are not made here. We assume an interest rate of 10%
per annum and a system lifetime of 25 years in calculating the PVF's using the
PVF = [1 (1+i)n]/i = [1 (1.10)25]/0.10 = 9.08.
We assume that both heat and electricity costs are constant over the year,
although the formulation allows for varying rates over the yearly cycle. Again, these
costs are highly variable, dependent mainly on the sources of the energy and the
values given are not for a specific application, although it is felt that they are
representative. The assumed costs are
Ce = 7.0 105 $/Wh (
Ch = 3.4 105 $/Wh (/106Btu).
The rate of maintenance and repair on the system is also taken from Phetteplace
(1981) as 2% of the capital cost per year. This factor is assumed to apply to both the
piping system and the pumps. Again, note that maintenance and repair increasing
with component age could be easily accounted for using escalation factors to adjust
PVFm&r , although this is not done here.