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

• Published in: Advances in water resources 2014-11, Vol.73, p.242-253
• Main Authors: LaForce, T., Mijić, A., Ennis-King, J., Paterson, L.
• Format: Article
• Language: English
• Subjects: Carbon dioxide storage; Earth sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Estimating; Exact sciences and technology; Exact solutions; Hoops; Hydrogeology; Hydrology. Hydrogeology; Mathematical analysis; Mathematical models; Method of characteristics; Nonisothermal; Pollution, environment geology; Porous media; Reservoir pressure; Reservoirs; Stress in the reservoir; Stresses; Two-phase
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2014.08.009

•Semi-analytical saturation, pressure and stress profiles are constructed for radial flow.•In the example temperature has a much larger impact on stress than pressure.•For the example there is little chance of fracturing the reservoir.•The models provide a fast way to generate estimates of reservoir pressure and stress.•These models will be useful in early screening of field projects. 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.