2 replies to this topic

[newbieneedshelp]

I want to solve the following optimization problem from Optimization of Chemical processes:

 841.PNG   46.2KB   7 downloads

 

Here is what I have done so far:

 

- Assume wcp is constant for all streams

 

- Contraints can be derived from the equations of heat: Q=wcp*dT_cold=wcp*dT_hot=U*A*dT_LM

Where dT_cold & dT_hot are the change in temperature of each cold and hot stream in a heat exchanger. And dT_LM=(dT₁-dT₂)/ln(dT₁/dT₂).

A clearer representation of this can be seen in the following image:

 hx.png   12.62KB   5 downloads

 

- With that the objective function is specified as: A_total = A₁+A₂+A₃

 

- Some linear equilibrium constraints can be made as follows:

From the heat equation dT_cold=dT_hot, from that I got:

T₁+T₅=400

-T₁+T₂+T₄=400

-T₂+T₃=100

 

-The inequality linear constraints can be set as:

T₁<T₂

T₂<T₃

T₁<T₄

 

-Lower and upper bounds for the variables are somewhat irrelevant, given the constraints, either way I specified them as: 

0<A_1,2,3<Inf

100<T₁<300

100<T₂<400

100<T₃<600 

100<T₄<400

100<T₅<300

 

-Lastly, some non-linear constraints were specified as:

U*A*dT_LM-wcp*dT_cold=0

Could have used dT_cold or dT_hot, but should be the same if the other contraints hold.

 

Coded that into Matlab (and I have checked multiple times that everything is coded as described above), but I get very inconsistent results, a slight change in the initial guess of the estimated parameters leads to a different answer every time. Is there something wrong with my approach? 

[breizh]

Hi,

Did you try Excel and solver ?

Your set of equations seems correct .

Initialization step :T1,T2,T3,T4,T5

Calculation step :  Q1 ,Q2,Q3  then  A1 ,A2,A3  

Optimization step  Min (A1+A2+A3) by changing T1,T2,T3,T4,T5 with associated constraints .

 

Good luck

Breizh 

[Bobby Strain]

You have only two variables. So it's simple enough to use trial and error. Track overall area, then pick the smallest. Best if you use VBA. Better still, code it in VB.NET or C#.

 

Bobby