Analysis of Pressure Interference Test Using Kalman Filter

A method to analyze interference tests for a case of multiwell with variable flow rate using the Kalman filtering is presented. The line source solution is superposed to express the pressure change at an observation well. This solution is used as a measurement equation to form the Kalman filtering. Nonlinealities in the measurement equation with respect to the parameters to be identified are linealized according to a method developed by Sen (1984). The method is applied to analyze the results of interference tests in which pressure decline caused by producing fluid with four wells was measured at one observation well (McEdwards and Benson, 1981). In this analysis, two parameters, transmissivity and storativity, are updated at every moment when the pressure data at the observation well is obtained. Reliability of the final estimates depends on the initial values of these parameters. The reliability of the parameters, however, can be improved by iterating whole procedure of filtering by giving the final estimates as the initial values. Thus, most probable estimates can be obtained within several iteration even if discrepancies between the initial and the true values are in the order of two to three.