Semi-analytical solutions for nonisothermal fluid injection including heat loss from the reservoir: Part 2. Pressure and stress

In this work semi-analytical solutions for saturation, temperature, pressure and in situ reservoir stress are found for immiscible nonisothermal injection into a radial porous medium. A model for advection-dominated, nonisothermal, two-phase flow from a previous work is used to estimate the reservoir pressure and stress that result from injection of cold CO2. Flow is assumed to be one-dimensional and purely advective, while temperature has radial advection in the reservoir and transverse diffusion into the surrounding media. A simplified thermal solution is developed to allow for easier analysis of the reservoir stress. Two pressure models are presented, one which requires numerical integration of the pressure in the two-phase region, and one which is fully analytical, but simplifies the pressure profile. Two models are used to calculate reservoir stress, one which uses the full pressure and temperature profiles and must be numerically integrated, and one which uses the simplified models and has a closed-form analytical solution. The resulting radial and tangential (hoop) stress profiles in the reservoir are compared and it is shown that the simplified model is adequate for estimating the reservoir stresses. The impact of outer boundary conditions on reservoir pressure and stresses is also explored.