ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Heat exchanger network synthesisPAULI HILTUNEN

LUCAS BÄCKMAN

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Lecture contents•LP basics

•Introduction to MINLP

•Heat exchangers

•The HEN model

Linear programming•An LP model has a linear objective function and linear constraints

•Objective function: Min f(x) or Max f(x)

•Constraints limit the solution to some feasible area

•Example

• S.t.

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

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

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

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

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

Heat exchangers - A device used to transfer thermal energy between fluids

Heat capacity flow

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

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

Constructing the model•The model has k temperature locations

•st(k)=k-1 stages

•i hot streams

•j cold streams

•Hot streams heat coldstreams and are used in cold utilities W

•Cold streams cool hotstreams and are usedin hot utilities S

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

SYNHEN model•The objective of the model is to minimize costs of the heat exchanger network.

•The costs of the network consist of investment costs of the heat exchangers and costs of the hot and cold streams.

•A heat exchanger’s investment cost is dependent on the heat exchanging area of the heat exchanger:

α=area cost coefficient, β=cost exponent and A=area of the exchanger.

• The completed model includes 8 sets of continuous variables, 3 sets of binary cariables and 7 sets of constraints.

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Thank you [presenting the homework]

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Q=the exchanged heat, =heat exchanging coefficient and =logarithmic mean temperature difference.

Logarithmic mean temperature difference can be approximated with.

are the temperature differences of the streams before and after the heat exchanger at the stage st(k).

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

The costs of the hot and cold streams are calculated:

=cost of hot stream, =cost of cold stream, =hot stream used in utility W and =cold stream used in utility S.

The objective function of the model:

Area and area cost coefficient of the heat exchanger between hot stream i and cold stream j at stage st(k) are and .

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Constraints: Overall heat balances for each stream:

Heat capacity flow of the hot stream i , Temperature drop of i

Heat capacity flow of the cold strem j , temperature increase of j

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Heat balances of each stream at the stage st(k):

=temperature drop at the stage st(k)

=temperature increase at the stage st(k)

Heat balances at the utilities W and S:

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Inlet temperatures:

Temperatures at the stage st(k):

Temperatures before the utilities:

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Logical constrait at the stage st(k):

Binary variable determines, if the heat exchanger i,j,k exists.

If =0, heat is not changed between streams i and j at the stage st(k) (=0). Heat exchanged at any stage cannot be higher than and .

Logical constraints at the utilities W and S:

Binary variables and tells, if there is a heat exchangers i,W and j,S.

ENE-59.4310 SPECIAL COURSE IN ENERGY FOR COMMUNITIES P

Temperature approaches: