Gladfelter Deconvolution

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Abstract
The Gladfelter (Gladfelter, Tracy, and Wilsey1) deconvolution method has been used for the last three decades for determining the constant rate behavior of the well-reservoir system from simultaneously measured downhole flow rate (afterflow) and pressure data. The success of the Gladfelter deconvolution method depends on the behavior of the downhole flow rate. It is shown that the method works only if the downhole flow rate varies linearly with time. It is also shown that the commonly assumed first semilog straight line due to the Gladfelter deconvolution is instead a tangential line that is parallel to the final semilog straight line. The validity of the Gladfelter deconvolution method is investigated for different wellbore geometries such as line, cylindrical, and spherical source wells, as well as fractured wells. Some useful asymptotic solutions are presented for the interpretation of simultaneously measured downhole flow rate and pressure.