Fouling is a challenging, longstanding, and costly problem affecting a variety of heat transfer applications in industry. Mathematical models that aim at capturing and predicting fouling trends in shell-and-tube heat exchangers typically focus on fouling inside the tubes, while fouling on the shell side has generally been neglected. However, fouling deposition on the shell side may be significant in practice, impairing heat transfer, increasing pressure drops, and modifying flow paths. In this paper, a new model formulation is presented that enables capturing fouling on the shell side of shell-and-tube heat exchangers including the effect of occlusion of the shell-side clearances. It is demonstrated by means of an industrial case study in a crude oil refinery application. The model, implemented in an advanced simulation environment, is fitted to plant data. It is shown to capture the complex thermal and hydraulic interactions between fouling growth inside and outside of the tubes, the effect of fouling on the occlusion of the shell-side construction clearances, and to unveil the impact on shell-side flow patterns, heat transfer coefficient, pressure drops, and overall exchanger performance. The model is shown to predict the fouling behavior in a seamless dynamic simulation of both deposition and cleaning operations, with excellent results.