Simulation of Produced Water Reinjection Under Fracturing Conditions

Abstract

Summary An essential difference between conventional waterflood fracturing and unfiltered produced water reinjection (PWRI) under fracturing conditions is that in the latter case, the fracture conductivity cannot be assumed infinite anymore as a result of fracture fillup with injected solids. This relates to the important PWRI issue of where the injected solids go. Using numerical model calculations, we show that the pressure drop over a finite conductivity fracture can lead to a significant increase in fracture volume without necessarily leading to a significantly higher injection pressure. Thus, a picture emerges in which the fracture conductivity "adjusts" itself in order to accommodate injected solids. This picture allows the computation of well injectivity as a function of total injected water volume, solids loading, etc. This concept can also be used to qualitatively explain the PWRI field observation that injectivity appears to be partially or fully reversible as a function of water quality. A field example from the Middle East is presented. The effect of parameters such as water quality, formation stiffness, and filter cake permeability on well injectivity and fracture size is discussed. It is shown that for most practical applications, an approximate analytical formulation for the computation of well injectivity and fracture size provides good results. Introduction Field experience of produced water reinjection (PWRI) under fracturing conditions (for example, Refs. 1-3) has shown that well injectivity depends a.o. on injection water quality and temperature. One key uncertainty in well injectivity relates to the issue of where injected solids go.1 PWRI field experience shows that several fracture volumes of solids can be injected without significant loss of injectivity.1–3 To date, no explanation exists for this observation. This paper discusses several aspects of simulating unfiltered PWRI under fracturing conditions. A numerical model has been developed that fully couples the reservoir engineering and fracture mechanics aspects of the problem, and includes features such as finite, nonuniform fracture conductivity, fracture growth, external filter cake buildup on the fracture face, impairment of the formation around the fracture by deep penetration of oil and solids, and backstresses resulting from pore pressure inflation, and formation cooling. An essential difference with conventional simulators for waterflood-induced fracturing is that owing to fracture fillup with injected solids the fracture conductivity cannot be assumed to be infinite any more. Using our model, we are able to show that the pressure drop over a finite conductivity fracture can lead to "ballooning," i.e., a significant width increase. As a result, the fracture volume can become several times larger. The results also show that fracture ballooning does not necessarily lead to a significant injection pressure increase. Thus, a picture emerges in which the fracture conductivity "adjusts" itself in order to accommodate injected solids. This picture allows the computation of well injectivity as a function of total injected water volume, solids loading, etc. A field example from the Middle East is presented, where highly contaminated produced water was successfully injected at rates around 6000 m3/d. The computed results (wellhead injection pressure (WHP) and fracture size as a function of injection rate) appear to be in good agreement with initial measurements. The model has also been used for long-term (20 year) predictions of fracture size and well injectivity. The sensitivity of the results on a number of relevant parameters (injection water temperature and quality, degree of formation impairment, formation Young's modulus) has been studied. It appears that well injectivity strongly depends on formation Young's modulus and external filter cake permeability (skin). Well injectivity also depends on the assumed permeability profile within the fracture. Fracture size strongly depends on external filter cake permeability. Although Young's modulus may be estimated from laboratory measurements, representative values for external filter cake permeability can only be obtained from in-situ injection tests. A simple method is proposed to extrapolate results from water injection trials into the long-term future. Description of Numerical Model gives a short description of the numerical model, and compares the results for infinite conductivity "square" fractures with a recent radial model for water injection above fracturing pressure.4 Field Example: Simulation and Sensitivities presents and discusses results for finite conductivity fractures. These results have been computed as part of a PWRI study for a field in the Middle East. Analytical Model of Fracture With Tip Plug discusses an analytical approximation for fractures with low-permeability tip plugs. Finally, conclusions are presented in the last section. Description of Numerical Model This model is an extension of Koning's model for waterflood-induced fracturing. 5 The fracture is assumed to fully penetrate a permeable layer which is bounded by impermeable layers on top and bottom. The fracture is surrounded by four elliptically shaped zones (see Fig. 1 for a plan view): an impaired zone where oil and/or solids have penetrated (to be discussed below), a cooled (cold water) zone, a zone flooded by injected water which has warmed up, and an oil zone. Note that if produced water is injected into a separate (waterbearing) disposal formation, the "oil zone" becomes a warm water zone. Each zone is characterized by its own temperature, water (oil) viscosities, and relative permeabilities. The extent of the zone boundaries is calculated from the injected volume, and from the heat capacities of the water and formation rock by the method of Ref. 5. The fracture face is covered by an external filter cake consisting of injected oil and solids that have not penetrated into the formation. Eventually, the fracture may be filled with solids (oil) that have not penetrated into the formation, leading to a finite fracture conductivity. Note that the damage zone, external filter cake and finite fracture conductivity were not included in Koning's model.5

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