It is well established within the Industry that injection of (produced) water almost always takes place under fracturing conditions. Particularly when large volumes of very contaminated water are injected -either for voidage replacement or disposal-large fractures may be induced over time. The current paper aims to provide a methodology for Injection Fall-Off (IFO) test analysis of fractured (produced) water injection wells. Some essential elements of IFO for fractured water injectors are: Closing fracture, (early) transient elliptical reservoir fluid flow, finite (changing) fracture conductivity, and fracture face skin.
An exact semi-analytical solution is presented to the fully transient elliptical fluid flow equation around a closing fracture with changing finite conductivity, fracture face skin, and multiple mobility zones in the reservoir surrounding the fracture. Based on this solution, type curves of the dimensionless bottom-hole pressure as a function of dimensionless time are provided covering both the period during fracture closure and the period after fracture closure. The shape of these type curves is studied as a function of the different relevant parameters, in particular the fracture closure time, fracture compliance, wellbore storage, fracture conductivity, fracture skin, mobility ratio, and injection period. The type curves are compared in detail with pressure transient (build-up/fall-off) behaviour known from the literature, particularly with the aim to identify the well-known "storage", "linear", "bilinear" and "radial" flow regimes.
Furthermore, based on the conceptual results presented in this paper, a number of different methods to determine fracture length from fall-off tests are discussed.
Finally, these concepts are applied to two field examples, where the dimensions of the induced fractures are derived from the analysis of the IFO data.