Analytical modeling of linear flow with variable permeability distribution in tight and shale reservoirs

It is demonstrated herein that the calculated LFP corresponds to a weighted average of permeabilities (and fracture half-lengths); different parts of the reservoir contribute differently to the LFP at different production times. The LFP is influenced most strongly by permeabilities at a distance y=0.056(kt)ϕμct. The derived weighting functions during CTR and CTP production can be applied in inverse mode for determining LFP distribution near the hydraulic fractures. This is particularly useful in evaluating the effectiveness of hydraulic fracturing operations and assessing the performance of different fracturing techniques in unconventional reservoirs. In addition, this work gives significant insight into the concept of distance of investigation (DOI) in tight and shale reservoirs, and the differences when producing under CTR and CTP conditions.