ANALYSIS OF COUPLED POROTHERMOELASTIC RESPONSE OF A WELLBORE BY USING A FEMLAB-BASED SIMULATOR

Coupled porothermoelastic response, one of the key problems for wellbore stability, is very complicated in petroleum engineering. Thusly, a coupled porothermoelastic model is presented first in a saturated linear thermoelastic medium，which incorporates cross-coupled fluid flow equation，energy conservation equation and mechanical equilibrium equation with many cross-coupling terms. A series of constitutive relations and cross-coupling relations between material properties and independent variables are defined in the model. Then the details of the coupled porothermoelastic model expressed in FEMLAB’s format are given. FEMLAB is the first engineering tool that performs partial differential equation-based multi-physical modeling in an interactive environment. Finally, a 2-D coupled porothermoelastic problem of a wellbore with known analytical results is simulated by using a FEMLAB-based simulator, in which pore pressure, displacements and temperature can be solved simultaneously. Cooling-induced pore pressure, tangential and radial stresses distribution along the radial direction away from the wellbore for various times are discussed in this example. The results reveal that coupled processes have significant effects on the stresses and wellbore stability. The good agreement of the numerical results with the analytical solutions indicates that the coupled porothermoelastic model and the FEMLAB’s based simulator are credible.