1. Heat exchanger network synthesis PAULI HILTUNEN LUCAS BÄCKMAN ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

2. Lecture contents LP basics Introduction to MINLP Heat exchangers The HEN model ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

3. Linear programming

4. Convex and concave functions A function is convex, if a linear interpolation between two points of the function doesn’t get a lower value than the function between those points A function is concave, if a linear interpolation between two points of the function doesn’t get a higher value than the function between those points

5. Convex and non-convex sets A set is convex if a line drawn between any two points of the function does not cross the boundaries of the set In convex sets a local optimum is always also a global optimum Non-convex sets have multiple local optima and sometimes it may be difficult to define wich one is the global optimum

6. Mixed integer nonlinear programming - Contains discrete and continuous variables - Of the objective function and the constraint, at least one is nonlinear - General form: Example: ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

7. Constraints n variables -> n dimensions A MINLP HEN model has many more variables and constraints ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

8. Heat exchangers - A device used to transfer thermal energy between fluids ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

9. What is HEN? - Used when several hot and cold streams need to be cooled and heated simultaneously - Commonly used in chemical processes, such as petro-chemical plants and waste water treatment facilities - The goal is to reduce energy usage ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

10. Constructing the model The model has k temperature locations st(k)=k-1 stages i hot streams j cold streams Hot streams heat cold streams and are used in cold utilities W Cold streams cool hot streams and are used in hot utilities S ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

11. SYNHEN model ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

12. Thank you [presenting the homework] ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

15. Constraints: ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P