The Fenske Conservation Method for Pressure Transient Solutions With Storage

Abstract

Abstract A method for determining pressure transient solutions for wells with storage (and skin) is presented; this method is based on an approach developed by Fenske1 in the groundwater literature. By specifically conserving the entire mass of the system, including the wellbore or wellbores, it is possible to generate many common type curves. The procedure can be developed in an exact manner, in which case it is equivalent to existing techniques; however, a simple approximation step makes possible the generation of common solutions without recourse to numerical or ornate analytical techniques. In some cases, the approximation provides equivalent solutions with substantially less computation; in other cases, the solutions are significantly in error, although perhaps still usable. The achievement of computationally rapid, closed-form solutions is of significant advantage for current developments in computerized interpretation. The evaluation of a solution can be hastened by three orders of magnitude over conventional methods in some cases. Examples given in this paper demonstrate the application of the approximate Fenske method and its exact generalization. The approximate method gives agreement within 2% of the standard single-well, storage, and skin type curves. However, as the storage becomes small, as for example in the cylindrical wellbore case (where it is zero), the accuracy becomes unacceptable at early time. As an example of how the method can be applied to configurations other than those developed by Fenske, the derivation of the method for the slug test problem is demonstrated. The slug test solution obtained by the approximate method is within acceptable accuracy. The Fenske method is applicable to a wide variety of problems with storage and skin, probably including problems as yet unsolved. An approximate form is available for fast calculation, and die more correct form is equivalent to standard analytical methods.