Table 4 for each optimal diameter and the discrete diameters found when using the

rule of thumb based design method. Pressure drops at maximum flow conditions

are also given in Table 4. Note that these are unchanged from those in Table 1, since

the maximum flow condition remains the same. Thus, the rule of thumb based

design would remain the same and a 12-in. nominal diameter pipe would be

required. The cost saving of the optimal discrete design increases slightly once the

consumer model is added. Now the rule of thumb based design is 19% more costly

than the optimal discrete design. Also, note that the total life cycle costs are reduced

in all cases when the consumer model is added. Since it is important to have accurate

cost predictions when comparing district heating to alternatives, these seemingly

minor changes in total life cycle cost can be significant. For instance, the total life

cycle cost of our optimal discrete diameter design decreases 4% with the addition of

the consumer model. This is a very significant cost reduction. In our example 1-km-

long pipe segment with a design capacity of 25 MW, this refinement in predicted life

cycle cost amounts to ,000. Note that since our optimal discrete diameter is

unchanged by the addition of the consumer model, the capital cost of this design is

unchanged as well. Thus, the optimal discrete design still represents a 30% reduc-

tion in capital costs from the rule of thumb based design.

Before leaving the topic of the consumers, let's consider the constraints that they

place on the design. The consumers of heat place two very basic requirements on the

heat supply system:

1. That the delivered temperature of the heat be high enough to meet their

requirements.

2. That their heat demand be met at all times.

The first requirement will simply result in the following inequality constraint

(3-27)

where *T*s,i is the supply temperature at the heat consumer *i *(C) and *T*smin,i is the

minimum supply temperature required by heat consumer *i *(C).

Satisfaction of the second requirement will result in an equality constraint that

must be obeyed at each heat consumer. This constraint will be based on the model

developed in the previous section. The load placed on the system by the consumer

will be known, expressed as a fraction of the load under the design condition, i.e.,

exchanger then becomes our constraint on the return temperature. Equation 3-17 is

modified slightly by removing the 2 subscript, the unsubscripted values now

representing the actual operating condition

2/*n*1

2

.

(3-28)

There is also an additional equality constraint on the mass flow rate that results

from eq 3-21

˙ ˙

(3-29)

In the next chapter, we will examine how these and other constraints interact

when multiple consumer designs are considered.

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