Rate transient analysis using log-log plots of rate-normalized pressure (RNP) and its derivative (RNP') versus material balance time have proven helpful in providing estimates of shale matrix permeability and SRV drainage volumes in multiple transverse fracture wells (MTFW's) (Samandarli et al. 2012). The calculation of these properties requires the accurate detection and definition of the "end of linear flow" (telf) – the time at which hydraulic fractures begin to draw down upon their neighbors, causing the onset of what Song and Ehlig-Economides (2011) have described as "pseudo pseudo steady state" flow. The definition of telf is currently ambiguous, and in this study, we quantify and clarify the numerical definition of telf and the physical mechanisms behind its use as a permeability and drainage volume estimator.
We have constructed an analytical model of MTFW's that accurately predicts individual fracture flow performance for both constant and variable rate and constant bottom hole pressure inner boundary conditions. Using this model, we can accurately compute the pressure disturbance and rate change seen at the whole well and for individual fractures to quantify the degree of interference between fractures for any number of parallel, equally-spaced, and equally-sized fractures. This model has been validated by simulation using a commercial simulator. With both this analytical model and a series of numerical simulations, we investigated the fundamental mechanisms of flow in MTFW's and how the estimation of telf may be improved.
Previous authors have represented the progression of flow regimes in MTFW's as a linear flow period that transitions to a pseudo steady state (or apparently boundary-dominated) flow regime. We show that the same flow response is exhibited by a fully-infinite linear system, calling into question the nature of the "stimulated reservoir volume" (SRV) as a bounded reservoir system. In addition, we show telf can be detected and interpreted as the beginning of the onset of this fracture interference using the "limit of detectability" concept.