Available PWRI Fracturing Models

It is evident from the foregoing discussion that there are some unique challenges for modeling hydraulic fracturing during water injection operations. Various models and modeling philosophies are available or have been used. These will be described subsequently, but first, it is necessary to summarize the basic physical mechanisms that need to be considered. First, recall the differences that are important between produced water reinjection under matrix conditions and under fracturing conditions.

Suppose that injection is into an intact wellbore. For the sake of argument, consider that flow is radial (ignoring anisotropy). Field experience, laboratory measurements and analytical and numerical modeling all indicate that there will be the development of internal and external filter cakes. This will cause progressive development of skin. This causes a progressive and often precipitous decline in the injectivity (the injection rate divided by the difference between the injection pressure and the average formation pressure). On the other hand, if there is a fracture present, internal and external filter cakes will develop along the surfaces and ahead of the fracture. This causes a progressive increase in the efficiency and can ultimately facilitate discrete additional fracture propagation until a new equilibrium situation is reached. In combination with damage to the fracture face and in the formation, mass balance requires contaminant deposition in the fracture. Depending on the particulars, it is suspected that this leads to plugging of the tip of the fracture and/or reduction in conductivity of the fracture itself. It also needs to be remembered that there is a larger surface area for development of the cake and there are important velocity differences between the linear and radial cases.

The applicability of many of the matrix impairment events that have been described in the literature is relatively secondary for fracturing. For produced water reinjection under fracturing conditions, the most relevant stage of matrix type impairment is where an external filter cake has already started to build up. The real unknowns at this stage are the external filter cake's permeability and the external filter cake's thickness. The permeability is needed to assess the amount of fluid leaving the fracture and the thickness is required for mass balance considerations in evaluating how much "fill" is in the fracture itself. As is known from the hydraulic fracturing and drilling literature, it is presumed that the characteristics of a filter cake developed under fracturing conditions are different from those for a cake forming during matrix injection because of the linear flow geometry and shear rate effects leading to an equilibrium cake. The message is that filtration mechanics developed for radial flow models should be cautiously applied for fracturing scenarios.

As a result, even the most rudimentary fracturing model must account for movement of fluids and particulates into the adjoining formations, development of filter cake, and tip plugging or fracture conductivity impairment. The models should ultimately also account for erosional features associated with dynamic fluid loss mechanisms. The large injection volumes and common temperature differences absolutely require consideration of poro- and thermoelastic effects. The entire perspective of the reservoir must be considered for sweep efficiency considerations and for interaction with offset injectors and producers. The model must be able to represent more than one-dimensional fluid flow in the reservoir and have the capability to model discrete, albeit long-term injection events.

The models available for representing produced water fracturing range from modified stimulation simulators, through analytical two-dimensional produced water models, pseudo-three dimensional produced water models, and coupled or partially coupled reservoir simulators.

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