In the fully-coupled thermoporoelastic wellbore stress modeling, pore pressure and temperature can be decoupled for a low-permeability shale and the decoupled equations can be solved analytically in the Laplace domain. For a high-permeability rock, such as sandstone or carbonate, the fully-coupled pore pressure and temperature can also be decoupled by assuming the pore fluid flow reaches steady-state. This assumption of steady-state fluid flow in a high-permeability rock is validated by solving the fully-coupled pore pressure equations. It is found that the assumption is valid as long as the dimensionless time exceeds a certain time. Under this assumption, the temperature equation can be decoupled and can be solved analytically in the Laplace domain for both injection and production conditions. Closed-form solutions for thermally-induced stresses are also presented in the Laplace domain. The undrained loading effect, which usually occurs at short time and small distances in a low-permeability formation, may be negligible for a high-permeability non-shale formation. Results show that the undrained loading effect can be ignored for a high-permeability non-shale formation when the pore fluid flow reaches steady state. Modeling results of near-wellbore temperature and stresses can be applied to injection well design (pressure and temperature of the injection fluid), wellbore stability analysis, and sanding prediction analysis.
1. INTRODUCTION
It has been demonstrated that thermal effects can be very important to both wellbore stability and injection design (Guenot and Santarelli, 1989 [1]; Paige and Murray, 1994 [2]; Charlez, 1997 [3]). Formation temperature and formation pore pressure are fully-coupled for fluid flow in porous media, such as in oil and gas drilling, injection, and production operations. The fully coupled thermoporoelastic equations and solutions for some initial and boundary conditions, and their applications in the petroleum industry, can be found in the literature (Kurashige, 1989 [4]; Wang and Papamichos, 1994 [5]). Theoretically, for any initial and boundary conditions, the fully coupled thermoporoelastic equations can be solved using the finite-difference method, but sometimes at the expense of computation time (Chen, 2001) [6]. In the meantime, the fully-coupled temperature and pore pressure can be partially or completely decoupled for various ranges of rock permeabilities.
The decoupled equations might be solved analytically in the Laplace domain as well as in the real time domain under certain initial and boundary conditions (Kurashige, 1989) [4]. For low-permeability (~nanodarcy, or ~1e-21 m2) shale formations, pore pressure, temperature and thermally-induced stresses can be determined analytically for a permeable wellbore boundary (Wang and Papamichos, 1994 [5]; Li et al., 1998 [7]; Chen et al., 2003 [8]) as well as for an impermeable wellbore boundary condition (Chen and Ewy, 2003) [9]. For intermediate and high permeability rocks, Wang and Dussault (2003) [10] presented temperature and pore pressure solutions for a permeable wellbore.
Once pore pressure and temperature solutions are determined, the pressure-induced and thermally-induced stresses around the wellbore can then be solved. Rock failure can also be determined by comparing stresses with rock strength using various failure criteria.
