A PKN hydraulic fracturing model, capable of delineating the impacts of pore pressure buildup, energy dissipation and elastic deformation of the fluid as well as the solid, is presented. This improvement on the current poroelastic PKN model may provide a better interpretation in simulating hydraulic fracturing operations where non isothermal conditions are manifest.
Un model de fracture hydraulique, PKN, capable de decrire l'impact des pressions du fluide, la dissipation d'energie, ainsi que les deformations elastiques du fluide et du solide, est presente. Cette modification du modele PKN poroelastique pourra fournir une meilleure interpretation des fractures hydrauliques effectuees dans des conditions non-isothermiques.
Ein PKN hydraulisch-frakturendes Modell, das den Effekt des Druckaufstiegs, der Energie-dissipation und der elastische Deformation der Fluessigkeit sowie des Körpers beschreiben kann, wird vorgestellt, Diese Verbesserung des gegenwartigen poroelastischen PKN Modells mag eine bessere interpretation fuer die Simulation del' hydraulisch-frakturenden Operation besorgen, wo nichtisothermatische Zustande offeubar sind.
The study of the thermomechanical response of fluid saturated media appears to be an important task in many research areas such as extraction of geothermal energy, storage of high-level nuclear waste and site remediation, enhanced hydrocarbon recovery using thermal flooding, and reservoir stimulation under non isothermal conditions. It is understood that these circumstances may result in strong coupling between heat transfer, interstitial fluid flow and solid matrix deformation. As a result of the temperature differences between the injected fluid and the surrounding rock mass, additional hydraulic gradients may be induced. The field measurement reveals that 1°C temperature change may introduce 1 MPa pressure variation (Pickens et aI., 1987). Even under an initially isothermal environment, hydraulic pressurization within the induced fracture may create heat transfer. A field test in western Canada indicated that 3°C temperature rise was directly related to a 30 MPa pressure increase in a pressurized well bore (Wang and Papamichos, 1994). The poroelastic effects have been identified in reservoir stimulation to cause a significant increase in fracturing pressure, which in turn may affect the dynamic changes of the induced fracture geometry (Abousleiman, 1991). The combined thermal hydraulic fracturing force can become an effective stimulation catalyst as either cold fluid is injected in hot reservoirs, or hot fluid is injected in the cold formations (Jensen, 1994). Cooling may result in tensile stress components that may reduce the internal fluid pressure required for fracturing. In contrast, heating may induce substantial compressive stresses near the borehole that may affect the stability of the well. Furthermore, the temperature fluctuation may significantly modify the shut-in pressure conventionally taken as equal to the value of the least principal stress (Stephens and Voight, 1982). As a result, the designed stimulation may create fracture geometries that differ unexpectedly from traditional isothermal environments. Aside from the temperature-dependent rock - fluid deformation, pore pressure variations can be affected by thermal transport via conduction, convection as well as radiation. While the transport phenomena in porous media are normally dominated through the first two factors, the heat convection may be negligible if the rate of fluid flow is low, such as occurring in low-permeable formations (Nguyen and Selvadurai, 1994). Paradoxically, the effect of thermal convection due to fluid circulation is prominent near the wellbore where the fluid velocity is relatively high (Bai and Roegiers, 1994). Therefore, omission of the thermal convection is frequently aimed at the convenience of invoking sequential solutions by circumventing the fully coupled fluid flow - thermal transport equations, with sacrifice of the conceptual, so as computational, accuracy. However, such an omission may be justifiable for the evaluation of a hydraulic fracturing operation, where the thermal effect could be substantially overweighed by the hydraulic impact. Considering the impact of geothermal gradients for deep reservoir or using hybrid thermo-hydraulic fracturing technique, the coupled phenomenon incorporating the effects of pressure buildup, energy dissipation and volumetric expansion of fluid and solid needs to be investigated. Different from current poroelastic PKN models, this paper presents an alternative thermoporoelastic PKN solution in which the fluid pressure field is conditioned by the variations of both temperature and deformation fields.