Analysis of the Influence of Minimum Temperature Difference in a Heat Exchanger Under Fouling on the PID Temperature Controller Settings

Fouling is one of the most troublesome constraints in heat exchanger operation; it reduces heat duty and, as deposits grow, changes the exchanger dynamics, causing PID temperature controllers tuned for clean conditions to lose performance. This study examines whether the minimum temperature difference (ΔTmin) chosen at the design stage can limit this effect. A dynamic model of a shell-and-tube crude oil preheater (220 t/h) was implemented in MATLAB/Simulink R2025b, and closed-loop responses, control-quality indices and stability margins were compared for ΔTmin = 50 K and 10 K for clean and fouled (Rf = 0.00138 m2K/W) exchangers with Ziegler–Nichols PID settings. At ΔTmin = 50 K, fouling increased the set-point ISE by 75%, the settling time from 92 s to 231 s, and the overshoot from 57% to 65%, while reducing the phase margin from 25.7° to 15.8°; retuning was necessary and restored the phase margin to 27.8°. At ΔTmin = 10 K, the corresponding changes were much smaller (ISE increased by 27%, settling time increased from 107 s to 159 s, overshoot increased from 40% to 44%, and phase margin decreased by only 3.4°), so the original settings could be retained. Disturbance-rejection ISE grew 2.2-fold at 50 K versus 1.6-fold at 10 K. A lower ΔTmin is therefore a practical design guideline for reducing fouling-induced controller retuning.