Abstract The character of fluid flow in and around wellbores, cavities, and fractures in pore-elastic media can significantly affect resource extraction operations in underground reservoirs. Reasonable estimations of hydraulic fracture profiles and propagation rates cannot be made without considering propagation rates cannot be made without considering fluid exchange, especially for high leak-off; well production rates greatly depend on the flow rates into fractures; and reservoir properties are often strongly stress-sensitive.
In this paper, the fluid loss and the subsequent "backstress" (i.e. induced reservoir stress) caused by it are characterized for stationary and propagating fractures, and the model is applied to three cases:a single fluid in the reservoir and fracture;
two fluids: a reservoir fluid and a fracture fluid that has penetrated some distance into the reservoir;
a production model where the crack has been propped and the reservoir fluid flows out of the well.
The fluid exchange between fracture and reservoir is found by solving an integral representation of the flow in the reservoir. Since the pressure distribution in the reservoir is governed by a diffusion process, the flow out of (or into) the fracture and the backstress are rather simply calculated by integrating along the fracture the influcence function for the pressure due to each component of fluid exchange, specifying the pressure at each point on the fracture or closing the system by some other means such as solving simultaneously the flow equations in the fracture, and solving for the fluid exchange inside the integral. Then backstress can then be found from the fluid exchange. Preliminary computational results for plane fractures Preliminary computational results for plane fractures have been obtained that compare well with existing special analytical and numerical solutions (e.g., those of Cinco and Samaniego). More general results are provided for moving fractures and induced stresses, and the broader capabilities of the methodology are outlined.
Introduction The study of diffusive processes and associated stresses has a broad range of applications. Classical analyses of beat conduction and thermal stresses are being continuously extended and implemented to understand and design for building structures and equipment; newer applications are always appearing, such as the extraction of heat from geothermal reservoirs. Analogous models may be used to describe the effects of more general (e.g. drying) shrinkage and solid-state diffusion. An area of more recent intense interest has been that of stresses induced by fluid flow in porous media-, especially in relation to fracturing processes; such problems, especially in the context of (hydraulic) fractures in underground reservoirs, are also the main concern of the work presented here. presented here. A variety of techniques have been developed for the analysis of diffusion, many especially for application to reservoir engineering, and some have been oriented toward fracture geometries (e.g. see ref. 6 for sample state of the art). There has been a predominant preference for volume discretisation techniques, especially finite difference (and more recently finite element) techniques: these work well for smoothly varying non-singular, allowably discontinuous fields and finite geometries, permitting efficient solution of banded matrices, and they facilitate incorporation of non-linearities, heterogeneities etc. In order to capture the behavior around typical reservoir structures, however, complicating factors are unavoidable such as severe mesh refinements, "infinite elements," and moving fracture surfaces; the last is especially difficult to incorporate accurately, and it even requires remeshing for arbitrarily curved trajectories. Such problems have motivated us to develop so-called surface integral equation (SIE) techniques, which deal effectively with their more difficult characteristics; we then take advantage of the best features in both methods, by surface integral and finite element hybrid techniques (SIFEH), which we are now developing.
Such integral equation approaches are certainly not new in heat conduction (e.g., ref. 7), nor even in this area of application.
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