We present a pragmatic computational model, which can be employed as a physics-based digital twin, and is used to simulate Alcoa's aluminium reduction cell. The model predicts the evolution of dissolved and particulate alumina in the electrolytic bath. In addition, we may solve for passive tracer distribution and the bath temperature. The model also includes simplified treatment of anode effects and loss of alumina due to sludge formation. The bath flow in the model is based on a detailed magnetohydrodynamic CFD simulation that is corrected to be mass conserving. The model predictions, using relevant initial conditions and operational settings (e.g., feeding patterns), are compared with detailed measurements of dissolved alumina and tracer during two industrial measurement campaigns. The comparison of the spatial and temporal evolution of tracer predicted by the model matches quite well with the experimental data. The model is able to predict the experimental observations of dissolved alumina by using a sludging coefficient. The simulations also indicate that the sludging and a corresponding self-feeding mechanism is a very local and very slow transient phenomena. The model has also been used to simulate the evolution of representative bath temperatures in the cell. Despite the simplifications, the model has been shown to be able to reliably model an industrial aluminium reduction cell at a low computational overhead.