Using Optimization to Design a Heat Exchanger in a Chemical Plant

Authors: Dr. Alison Cozad and Dr. Cara Touretzky

Picture this. You’re an engineer for an international oil company, and you’ve just been tapped to design a simple heat exchanger that will be installed at a chemical plant.

Given that heat exchangers can run anywhere from \$100,000 to$1,000,000 and beyond, it’s important that you choose one that keeps things cool—while keeping costs low. And your leaders are eager to break ground, so they need your design yesterday.

What’s the best way to approach a scenario like this? Or other familiar chemical engineering equations?

Many of us may be tempted to dive into a spreadsheet and brute force our way through it. But there’s a better way. It’s called mathematical optimization.

What is optimization?

People often associate optimization with industrial engineering or transportation, which tend to have more linear applications. But there are plenty of ways to use optimization in scenarios with nonlinear variables, too. And with Gurobi, you have the benefit of proving global optimality for nonlinear non-convex problems as well.

As we like to say, if you can model it, you can optimize it. To figure out if your scenario is ripe for optimization, consider these questions:

• Do you have a problem that involves a complex, interconnected set of decisions?
• Can you quantify and compare the outcomes of your decisions?
• Do you want to find new ways to use your resources more efficiently?
• Do you work in a constantly changing business environment?

The case of the heat exchanger

Let’s go back to our scenario with the heat exchanger. Here’s an example of how you might design your model. In this scenario, you have one hot stream (H1) and two cold streams (C1 and C2). The lines depict several possible paths where you might consider laying pipe.

In this example, there are at least five combinations to play with, given the constraints of your space and the liquids you’re working with. The questions are: Which of these options is most cost-effective and efficient? And what size should the exchangers be in order to meet the process requirements?