A new transient analytical model is presented to study the poro-thermal and poro-elastic stress transients during cold water injection into a hot reservoir. Earlier models have shown that pore pressure and temperature variations during a non-isothermal injection such as waterflooding or even drilling fluid invasion can influence the stress distribution in the field profoundly. Such effects are relatively easier to account for single phase flow or piston-like displacement cases.

In this work, a new solution is developed to further improve the coupling in the case of a non-isothermal Buckley Leveret type displacement. Thus we are able to account for the very important viscosity and relative permeability effects on the stress transients. In the model, first the transient saturation and temperature distributions are solved simultaneously and then transient pressure and stress fields are computed consecutively.

In order to decouple the equations for saturation and temperature from the equation for pressure incompressible fluid flow is assumed. Then, the pressure distribution in the system is obtained by superimposing pressure transient effects on a saturation profile known a priori with its mobilities and diffusivities. Then a plain strain model is developed to compute the poro-elastic and thermo-elastic stress transients for a non-isothermal Buckley-Leveret type displacement.

The results implied that the thermoelastic changes in the cooled zone could affect the surrounding stress fields in a profound manner. For instance for a porous medium with stiff material such as carbonate reservoirs owing to cooling by the injected cold water large scale tensile stresses arise and a major tangential stress concentration develops in front of the cooled zone. The thermally induced viscosity effects can dominate the near wellbore stresses at early times. The relative permeability also affects the stresses significantly in the invaded zone albeit to a lesser extent than viscosity.

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