Dimensions and Degree of Containment of Waterflood-Induced Fractures from Pressure Transient Analysis

Summary 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. This paper aims to provide a methodology for injection-falloff (IFO) test analysis of fractured (produced) water-injection wells. Some essential elements of IFO for fractured water injectors include the closing fracture, (early)transient elliptical reservoir-fluid flow, finite fracture conductivity, and fracture face skin. An exact semianalytical solution is presented to the fully transient elliptical fluid-flow equation around a closing fracture with finite conductivity, fracture face skin, and multiple mobility zones in the reservoir surrounding the fracture. This solution also captures the case that during closure, the fracture is generally shrinking from adjacent geological layers under higher in-situ stress. Based on this solution, type curves of the dimensionless bottomhole pressure as a function of dimensionless time are provided, covering both the period during fracture closure/shrinkage 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 compliance, the height of in-situ stress contrasts, fracture face skin, fracture closure time, and injection period. It is shown how the fracture length and height and the degree of fracture containment (in combination with the heights of the stress contrasts) can be derived from these types of curves. It is also demonstrated that the analyses based on the storage flow and linear formation flow regimes need to be integrated into one analysis method to obtain consistent results. Finally, the concepts developed in this paper are applied to a number of field examples, in which the dimensions and degree of containment of the induced fractures are derived from the analysis of the IFO data. Introduction IFO test analysis offers one of the cheapest ways to determine the dimensions of induced fractures. Unfortunately, hardly any work has been carried out to date to provide a methodology for interpreting the pressure-transient data of fractured water-injection wells. This contrasts with the vast amount of work that has been carried out in the area of pressure-transient analysis for wells with propped fractures. Both pressure-transient tests during hydraulic fracture stimulation (called"minifrac tests"; see Ref. 1) and pressure-transient tests during production after stimulation (i.e., buildup tests; see Refs. 2 through 5) have been studied extensively. The theories as developed in Refs. 1 through 5 by now are well-accepted "textbook" methodologies. This paper deals with the subject of pressure-falloff analysis on fractured water-injection wells. In this area, the situation is entirely different from the one above in the sense that until recently, there existed no practical methodology dedicated to pressure-falloff analysis on fractured water injectors. The very limited interest in falloff-test analysis on fractured water injectors may well be related to the fact that historically, most operators have been unaware that their water injectors are fractured. Only in recent years has this situation started to change. Unfortunately, one of the consequences of the lack of a dedicated method of analysis is that falloff tests on injectors are generally interpreted in the wrong way, even if one realizes that they are fractured. Typically, such interpretations lead to wellbore-storage coefficients that can be up to orders of magnitude too high, and to fracture lengths based only on analysis of the linear formation flow period (see Ref. 10). The objective of our study is to fill the gap as described above (i.e., to provide a dedicated interpretation methodology for falloff tests on fractured water injectors). In a recent paper, we presented a novel interpretation methodology for falloff tests on fractured water injectors. This methodology is based on exact 2D solutions to the problem of pressure falloff around fractured water injectors for different boundary conditions. The most important stepforward of Ref. 6 is that it allows the determination of fracture length from a consistent combined analysis of the storage and linear-to-pseudo radial formation flow periods, and of fracture height from a consistent combined analysis of the storage and pseudoradial flow periods. Thus, uncertainties in the determination of fracture dimensions from falloff-test analysis are reduced. In the course of analyzing a variety of field cases, we found, based on the signature of field falloff-test data, that in many cases, the induced fractures must have penetrated into adjacent higher-stress zones. Therefore, the methodology as developed in Ref. 6 was extended to cater to this effect, with the objective being to enable derivation of local in-situ stress contrasts from falloff-test interpretation. This extension forms the main subject of the current paper. The paper is organized as follows. The next section presents the pressure-transient solution for a closing and shrinking water-injection fracture, including a brief recap of the main concepts presented in Ref. 6. The third section presents in some detail the shape of the pressure-transient type curves for a closing/shrinking fracture as a function of the different relevant parameters, such as the fracture compliance and the height of in-situ stress contrasts. Subsequently, this method is applied to four field examples. Finally, the last section presents our conclusions.