Étude numérique du couplage thermohydromécanique dans les roches. Influence des termes de couplage non linéaires pour un matériau isotrope linéaire Numerical Analysis of a Thermohydromechanical Coupling in Rocks. Influence of Nonlinear Coupling Terms on a Linear Isotropic Material

• Main Authors: Henry J. P., Skoczylas F., Shahrour I.
• Format: Article
• Language: English
• Published: EDP Sciences 2006-11-01
• Series: Oil & Gas Science and Technology
• Online Access: http://dx.doi.org/10.2516/ogst:1992003
• ISSN: 1294-4475; 1953-8189

Nous présentons dans ce travail une étude numérique basée sur la méthode des éléments finis, du comportement thermoporoélastique de certaines roches. Les trois effets de couplage : déformabilité de la roche, pression interstitielle et température sont pris en compte simultanément dans la résolution numérique. Une application simple sur un puits pétrolier en conditions axisymétriques est finalement présentée afin de dégager en particulier l'influence du terme de couplage convectif non linéaire, obtenu dans l'équation de diffusivité thermique, sur l'évolution de la température et de la pression interstitielle autour du forage. <br> This article describes a finite-element method for solving the problem of nonlinear coupling between interstitial pressure and temperature during stress on a poroelastic rock. Such coupling phenomena occur during massive injection of cold water into a petroleum borehole for example. The implementation of such a numerical solution, used here with the assumption of small deformations, first requires a review of the behavior law of the material (Eq. 2. 2) and of the equations for hydraulic diffusivity (Eq. 2. 3) and thermal diffusivity (Eq. 2. 4). This last equation (2. 4) is the one containing the nonlinear coupling terms in Grad P Grad P and Grad T. Grad P. During simulation of flow at a high flow rate, these products can no longer be neglected as shown by the results in Fig. 2. The variational formulation of the problem is then determined in relation to the three equations for equilibrium, thermal diffusivity and hydraulic diffusivity. After geometric and temporal discretizations, this formulation leads to a finite-element calculating scheme resulting in the simultaneous solving of all three equations. This solution, based on the inversion of the system of equations (2. 15), requires the updating of the rigidity matrix at each time step to take nonlinear coupling into consideration. Calculations with an axisymmetrical model (Fig. 1) are then described and used for testing the influence of convective coupling. Boundary conditions simulate a cold-fluid injection (cold in relation to the rock) at a fixed pressure Pi inside a borehole in more or less high-permeabifity rocks. The results obtained clearly show the influence of convective coupling if the permeability is high, thus revealing a high fluid-flow rate. This influence is very appreciable on the way temperature evolves (Figs. 2 and 5) but without any effect of overpressure. If permeability is low, the influence of convective coupling becomes negligible because the fluid flow rate remains very low. Thermal shocks on the borehole wall are also calculated and shown in Fig. 12. These examples can be used to visualize the interstitial overpressure caused in the rock by a temperature variation and due to differences in the fluid-material expansion coefficients as well as to coupling effects. This type of calculating model, which is suitable for a more complex geometry, is also a tool that can simulate fluid flow due to the storage of thermally active wastes.