Energy Targeting Using Mathematical Programming Method
The algebraic method illustrated above can be generalized using optimization techniques.
Any mathematical programming “optimization” model can be written in the following
g(x) ≤ 0.0 is the set of r inequality constraints.
In general, the number of variables, n, will be greater than the number of equations, m, and the difference between (n-m) is commonly denoted as the number of degrees of freedom of the optimization problem. If we want to maximize a function this is equivalent to minimizing the negative of that function.
Now for the heating and cooling utilities minimization problem, let us go back to our
simple problem solved algebraically before using pinch technology and use FCP of the cold
streams of 19 and 2 kW/ºC respectively. The new problem can be easily solved using
mathematical programming model. We can write our objective function not only including
heating and cooling utilities loads but also including heating and cooling utilities costs;
formulate our model/constraints using the cascade approach; and then solving the
optimization problem using any commercial solver.
Define the loads of heating and cooling utilities in each temperature interval and the surplus from each interval as we did before in the algebraic method through the development of temperature interval diagram, tables of exchangeable loads and un-balanced thermal cascade diagram.
The model equations are heat balance around each temperature interval in the thermal
cascade graph shown below.
The energy consumption targets obtained graphically or algebraically or using
mathematical programming, give an idea about the potential utility needs of any industrial
facility using streams data only.
To get a better idea in terms of utility types needed, we need to construct a diagram known as the grand composite curve (GCC) and use it for defining the kind of utilities we need and how much we need. We can then utilize these findings to compare the current facility needs with the minimum utility needs calculated before to define the gap needed to be tackled. This step will help us evaluate potential savings upon the heat integration for certain process area.
Such exercise can be carried out to any existing facility to define rigorous energy
consumption targets before conducting and plant retrofit. It can also be used while
reviewing process and utility design of any grassroots plant to the design of the facility
from energy efficiency point of view.