Improving bulk solid processing with smarter thermal modelling

Solex explores new paths to drive greater efficiency in heat transfer design 

Author: Jamie Zachary 

Whether it's heating chemicals or cooling biosolids, effectively managing heat within bulk solids is crucial to many industrial processes. Accurate heat transfer modelling allows engineers to predict the behaviour of materials under varying conditions. This, in turn, allows them to create systems that are safer, more energy-efficient and cost-effective. 

Yet the science of heat transfer to and from bulk solids is complex. It involves the use of advanced mathematical equations to simulate how heat flows through materials. 

To do so effectively, engineers must account for a number of differing factors that range from particle size and flow rate to temperature variations over time. These kinds of details are critical to creating systems that will be efficient and dependable in real-world conditions. 

Solex Thermal Science has successfully put these details to the test for more than 30 years. The company’s moving bed heat exchangers (MBHEs) have been used in more than 50 countries to indirectly heat and cool bulk solids by having the material flow slowly through vertically oriented banks of stainless-steel pillow plates while a heat transfer fluid moves inside the plates to enhance heat transfer. 

During that time, the company has continually sought ways to optimize the performance and design of its heat exchange solutions. This recently led to the company’s Calgary-based processing engineering team embarking on a new initiative to further improve the accuracy and efficiency of Solex’s MBHEs by developing an alternative method for handling the thermal model – an improvement that has the potential to deliver cost savings to customers. 

Advancing heat exchanger design with improved modelling 

Carlos Elorza Casas, Junior Process Engineer (EIT) at Solex, explains their primary goal was to improve the processes of solving complicated equations – otherwise known as complex partial differential equations, or PDEs – that describe how heat is exchanged between the fluid and solid materials in an MBHE. These equations are coupled, meaning changes to either the fluid or solid sides affect the other – requiring them to be solved simultaneously to determine how temperature is distributed throughout the system. 

A better/more efficient understanding of this dynamic can help lead to more precise designs – which, in turn, means less heat exchanger area is required, and leads to lower manufacturing costs. Furthermore, a more efficient design can reduce utility consumption, thereby lowering operational costs for clients.  

"If you don’t have an accurate model, you often have to build in large safety factors just to be sure you meet the design requirements,” says Casas. 

"That can mean oversizing the heat transfer area, just to compensate for the uncertainty. And that has a big impact on cost.” 

A new approach with real-world benefits 

Casas notes that the traditional approach to solving these equations has been to apply something known as the Laplace transform. This approach converts complicated equations with variation in space into a simpler form to make them easier to solve. While effective, Laplace can be limiting when applied to more complex system setups such as those that Solex regularly encounters.  

So, the Solex team theorized that it could apply the generalized integral transform (GITT) technique to tackle this problem. The technique, first developed by Brazilian mechanical engineer and researcher Renato Machado Cotta, transforms PDEs into ordinary differential equations, or ODEs, which are easier to work with when using standard mathematical tools.  

A key advantage of using the GITT technique is its computational efficiency. Because the technique simplifies equations to a form that can be solved more quickly and accurately, engineers can more easily iterate between different heat exchanger design options. This rapid feedback loop makes it possible to explore numerous configurations, identify those that meet the desired thermal performance and then concentrate on solutions that provide lower capital and operational costs. 

Furthermore, Casas notes this more robust and flexible approach can then be extended to account for even more challenging scenarios. For example, it can incorporate spatial variations in the inlet temperature of the solids. It can also account for heat generation within the solids themselves, such as if radioactive materials were involved. 

Validating the new modelling approach 

The findings were recently highlighted in a published paper titled Counter-Current Parallel-Plate Moving Bed Heat Exchangers: Analytical Solution Via Integral Transforms that was presented at the 10th Thermal and Fluids Engineering Conference in Washington, D.C. 

The paper was able to demonstrate that the GITT approach could successfully solve the problem, yielding the same solutions for the solid and fluid temperature functions as those previously found in the literature using Laplace transforms.  

Casas says this confirms the validity of the GITT technique for this specific problem and paves the way for future extensions to address more complex problems using the same approach. 

“What’s exciting is that this approach provides us with the ability to simplify analytical modeling in ways that make advanced thermal system design more accessible and adaptable to our customers’ needs,” he says. 

Interested in knowing more about how Solex can accurately and efficiently solve your bulk material thermal processing needs? Contact us today to speak with one of our heat exchange experts.