UA and pinch point temperature difference modeling — Finding the best heat exchanger schemes

Abstract

Process models using simplified heat exchanger (HE) models are often analyzed using methods based on derivatives or optimization procedures, where even small numerical errors can cause algorithms to fail. This article explores the use of numerical approximations for calculating pinch temperature and UA-value, including novel high-order polynomial methods using equidistant and Chebyshev grids. The results show that the mainstream methods, where LMTD and pinch temperature are calculated from grid values, are 2–5 times slower than the high-order methods if requiring accuracy better than 1%. If a 0.01% accuracy is needed high-order methods are often 10–20 times faster. Numerical errors in high-order schemes with pure fluids converge quickly to zero when increasing the grid size, and schemes with more than 30 grid points generate errors less than 1E-4%. High-order methods were less successful for fluid mixtures, where a novel hybrid high and low-order pinch temperature scheme is recommended.