Vertical Single-Well Pulse Testing of a Three-Layer Stratified Reservoir

Abstract

Abstract A new mathematical model is developed for analyzing single-well pulse test data from a reservoir consisting of two permeable zones separated by a less permeable zone. The model considers well-bore storage and skin effects and allows the three zones to have different rock properties. The line-source assumption used in developing the analytic solution is validated via comparison of results with another model also developed in this work. This latter model assumes identical rock properties for the two permeable zones but allows the wellbore radius to be finite. The numerical Laplace inversion methods available in the literature are evaluated with respect to some simple functions and the analytic Laplace space solution of the problem of interest. It is found that the Fourier-series and Zakian's methods can serve as alternatives to the well-known Stehfest algorithm. The effects of wellbore storage and skin on single-well pulse testing of layered reservoirs are investigated. Consistent with the findings in the literature for multiwell pulse testing, it is shown that the influence of wellbore storage and skin is to reduce the response amplitude and to increase the time lag of the pulse response. Among the wellbore storage and skin factors involved in a single well pulse testing, the skin associated with the observation interval is least influential on the pressure response. Using field data, it is shown that the mathematical model presented can be used, in conjunction with an optimization subroutine, to estimated the parameters of interests. It is further shown numerically that neglecting the effects of wellbore storage and skin could result in an underestimation of the formation permeabilities of interest. The problem of non-uniqueness of solution for parameter estimation using optimization techniques is also discussed for the subject problem.