The Use of Attenuation and Phase Shift to Estimate Permeability Distributions from Pulse Tests

Abstract

Abstract In this work, attenuation and phase shift information acquired from pressure pulse tests at multiple frequencies was used to estimate the permeability distribution of reservoirs. By preprocessing the time series pressure data at the active well and the observation well, not only are the sizes of both the time and frequency conditioning data reduced tremendously, but also there is no need to know the flow rate. However, to put this method into practice and to know its limits, an investigation was conducted under various reservoir conditions to resolve the issues of detrending (removing transient upward trends in the pressure data) and to develop the Fourier transform procedures that are necessarily involved with this approach. In addition to estimate horizontal heterogeneous permeability from a radial multicomposite reservoir, the method utilizing multiple frequency attenuation and phase shift information was applied to a partially penetrating well in a multilayered reservoir with crossflow to reveal the heterogeneous vertical permeability distribution. The performance of the frequency method was investigated in comparison to straightforward pressure history matching. Quasi-Newton line-search optimization with gradient information was used for both methods. In addition, we investigated the sensitivity of the permeability estimation to perturbation in both pressure data and attenuation and phase shift information. A heuristic method for detrending was devised which helps in obtaining accurate attenuation and phase shift information. Cases with different values of storage, skin, and boundary conditions were considered. The impact of varying the number of periods and the sampling rate were checked to determine the sensitivity of Fourier transformation.