*Energy Targeting Using Mathematical Programming Method*

*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*

*forms:*

*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.*

*Objective Function*

*Objective Function*

*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.*