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.
HEAT CONSUMER CONSTRAINTS
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
Ts,i ≥ Tsmin,i
(3-27)
where Ts,i is the supply temperature at the heat consumer i (C) and Tsmin,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.,
q/q0. The supply temperature will also be known. The model for the consumer heat
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/n1
Tr = Ta (Ts - Ta )-1(Tmg )0 (q / q0 )
2
.
(3-28)
There is also an additional equality constraint on the mass flow rate that results
from eq 3-21
˙ ˙
m / m d = (q/qd)(Ts Tr )d/(Ts Tr).
(3-29)
In the next chapter, we will examine how these and other constraints interact
when multiple consumer designs are considered.
31
Previous Page
