MODELLING AND STATE ESTIMATION OF THE WATERFLOODING PROCESS IN OIL RESERVOIRS.

摘要

The process of waterflooding has been modelled for one- and two-dimensional reservoirs. Two approaches were taken in doing this. In the first model, a sharp interface is assumed to exist between the displacing phase and the displaced phase. The partial differential equations that trace the moving interface and the pressures in the reservoir are then solved. This approach, while adequate for favourable mobility ratios, is inadequate for the general case where the interface is diffuse. However, the moving boundary problem also has wide applications in other scientific areas such as the melting of solids, spreading of oil spills, casting of metals, etc.;A common problem that arises in many industrial situations is the need to estimate the states and parameters of a system from a limited number of measurements, in the prescence of process and measurement noises. This is especially true in oil fields, where the only measurements available are corrupted pressure measurements at a few injection and production wells and these have to be used to obtain an estimate of the system state over the whole reservoir. For linear problems, the Kalman Filter is one of the most popular estimation algorithms, as it gives the optimal estimates with respect to just about any reasonable criterion, if the noises are Gaussian and white. For our nonlinear problem, we have used an extended form of the Kalman Filter. Good estimates of the system states were obtained for most of the cases studied.;The study carried out here should go a long way in helping to carry out the process of secondary recovery in an optimally controlled fashion.;The second type of model used is the popular black oil model. Here, the state of the process is characterized by the simultaneous flow of both the oil and the water in the same portions of the field. The process is then governed by nonlinear partial differential equations whose solution gives the saturation and pressure profiles in the reservoir. Typical relative permeability curves are used, and these equations have been successfully solved using the weighted residual method of Galerkin.