Modelling and state estimation for a two-dimensional moving boundary problem

The five-spot waterflooding problem has been modelled as a two-dimensional moving boundary problem with a sharp interface separating the water and oil regions. The Galerkin method was used to solve for the shape and movement of the interface, as well as for the pressures in the reservoir. Having obtained a working model, the extended Kalman filter was then used to estimate the interfacial position when using corrupted pressure measurements from a single sensor in the field.