Fouling in heat transfer applications affects process efficiency, safety, emissions, and economics. Models of different predictive accuracy, data requirement, and computational feasibility are available to quantify its effects on individual exchangers and whole networks, and the benefits of mitigation techniques. A key question is how much model detail is required for which use. This article compares two dynamic thermo-hydraulic models for heat exchanger networks under fouling: a high-fidelity model (A) suitable for simulation and a simpler model (B) suitable for optimization. It identifies conditions where the two models are broadly equivalent and presents a parameter estimation scheme to match them, and a validation methodology. A detailed comparison for 37 exchangers in 8 networks shows that the simpler model (with parameters fitted as indicated) can approximate well the high-fidelity model for relatively long periods. The simpler Model B is then successfully used to simultaneously optimize cleaning schedule and flow distribution of an industrial preheat train. This solution is validated against Model A, with a difference in predicted operational cost of 1.4% over 1 year. Results indicate that the simpler model and fitting procedure can be confidently used in a closed loop nonlinear model predictive control strategy.