Development of Analysis Method for Geothermal Pressure Interference Test Using Kalman Filtering

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Kalman filtering has been applied to develop methods to analyze pressure interference tests of multiple-well, multiple-rate problems. Two different reservoir systems are considered in this study : an infinite porous reservoir and a porous reservoir with a presence of a hydraulic boundary. Pressure change observed in an observation well under the situations above can be expressed by applying the principle of superposition to the line source solution. These analytical solutions are nonlinear with respect to parameters to be identified : transmissivity and storativity. Therefore, two different methods are adopted to linealize the solutions : one is taking the ordinary logarithm, and another is to approximate the nonlinear function with Taylor's series expansion. Then, Kalman filtering is formed using these linealized equations, and two parameters are estimated at every moment when observation pressure value is obtained.Characteristics of the analysis method depending on the way of linealization are :1)For the logarithmic case, estimated values never diverge during the estimation procedure even if the discrepancy between the initial estimates and the most probable values is greater by several orders of magnitude. Therefore, this method is particularly effective when no prior information on the parameters is available.2)For Taylor's expansion case, reasonable values of parameters can be estimated at early stage of the estimation procedure under conditions that the initial estimates are given within a difference of one order of magnitude compared with the most probable values. Thus, more quick estimation is possible compared with the method above.