Application of Kalman filter to pressure interference test analysis

We present a method to analyze multiwell variable flow rate interference tests by the Kalman filter. A line source solution using the principle of superposition is employed to express the pressure change at a observation well. This solution is utilized as a measurement equation in the Kalman filtering. Since the measurement equation is nonlinear with respect to the parameters of transmissivity and storativity which are to be identified, the extended Kalman filter is adopted. The results of an interference test with four production wells has been analyzed for transmissivity and storativity. In this analysis, these parameters are updated at every moment when the pressure data at the observation well is obtained. The results of analysis indicate that the most likely values of parameters can be estimated as early as at the middle of the test duration.