Two new Non-Intrusive Reduced Order Modelling approaches to estimate time varying, spatial distributions of variables from arbitrary unseen inputs are introduced. One is a generalization of an existing'dynamic' approach which requires multiple surrogate evaluations to model the solutions at different time instances, the other is a'steady-state' approach that evaluates all time instances simultaneously, reducing the local approximation error. The ability of these approaches to estimate the water saturation distributions expected during a gas flood through a 2D, dipping reservoir is investigating for a range of unseen input parameters. The range of these parameters has been chosen so that a range of flow regimes will occur, from a gravity tongue to a viscous dominated Buckley-Leverett displacement. A number of practically relevant model error measures were employed as opposed to the standard L2 (Euclidean) norm. The influence of the number and the structure of training simulations for the model was also investigated, by employing two simple experimental design methods. The results show that POD based NIROM approaches are prone to significant deviations from the true model. The main sources of error are due to the non-smooth variation of system responses in hyperspace and the transient nature of the flows as well as the underlying dimensionality reduction. Since the first two sources are properties of the physical system modelled it may be expected that similar problems are likely to arise independently of the interpolation method and the reduction process used.