基于 FEMLAB 的钻井过程中流固热耦合响应分析

在石油开采等行业中,钻井过程中的渗流-变形-温度多场耦合作用非常复杂,它对井壁稳定分析具有重要意义。该文将在有关文献的基础上,首先建立一组饱和多孔岩体介质瞬态的流、固、热三场耦合方程组(其中包括固体变形、能量传输、流体流动三个相互耦合的过程,多物理场之间的交叉耦合还包括材料性质与独立变量之间的耦合关系);然后给出了该方程组在FEMLAB软件(基于偏微分方程组的多物理过程模拟工具)中的详细数学表达;最后以FEMLAB作为平台,着重分析了钻井过程中的流固热耦合作用过程,讨论了井壁温度发生突然降低后,井壁附近围岩的孔隙水压力、温度、应力的变化过程,为井壁稳定分析提出更为准确的应力分布。计算结果反映了耦合作用对井壁围岩应力的重要影响。该文的计算结果与解析解进行了比较,结果非常吻合,证明了耦合模型及求解方法的正确性。

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 firs 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 radiadirection 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.