Environmental Engineering Reference
In-Depth Information
The maximum difference between the available hot loads and cooling capacities from the
heat balances of these intervals is
- 550 kW.
This deficiency in heat will be supplied via an
outside hot utility.
This value will be the input (from the top of the first interval) and the same
heat balance calculation conducted above will be repeated to produce the energy
balanced
thermal cascade
diagram below.
Balanced Thermal Cascade Diagram
Minimum Heating Utility = 550 units
0.0
400
1
150
1300
1300
2
150
100
150
3
100
750
4
750
100
100
200
5
Pinch Point
0.0
50
0
6
Minimum Cooling Utility = 50 units
Figure 12. Thermal Cascade Diagram (Balanced)
With the completion of this step, the minimum heating utility and minimum cooling
utility required are 550 kW and 50 kW respectively.
T
ARGETING
U
SING
M
ATHEMATICAL
P
ROGRAMMING
M
ETHOD
The algebraic method mentioned above can be generalized using optimization techniques.
A very famous approach is the “transshipment model formulation as we mentioned in the first
module.
Mathematical programming at a Glance:
Let us consider the following constrained problem;
Min f(x)
s.t. h(x) =0.0
g(x) ≤ 0.0
x є
R
Where: f(x) is the objective function
h(x) = 0.0 is the set of (m) equations in variables x
g(x) ≤ 0.0 is the set of r inequality constraints.
