We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on an hydrodynamical Drift Flux Model (DFM) combined with a No Pressure Wave approximation of the momentum equation. The focus of this work is on the design of a robust discretization accounting for slanted and multibranch wells with the ability to simulate both transient behavior such as well opening as well as coupled simulations at the time scale of the reservoir. It is based on a staggered finite volume scheme in space combined with a fully implicit Euler time integration. The construction of consistent and stable numerical fluxes is a key feature for a robust numerical method. It is achieved by combining a monotone flux approximation for the phase superficial velocities with an upwind approximation of the phase molar fractions, density and enthalpy. In order to facilitate the coupling of the well and reservoir models, the Newton linearization accounts for the elimination of the hydrodynamical unknowns leading to Jacobian systems using the same primary unknowns than those of the reservoir model. The efficiency of our approach is investigated on both stand alone well test cases without and with cross flow, and on a fully coupled well-reservoir simulation.

翻译：我们考虑一种用于模拟地热过程中井筒作业的非等温组分气液模型。该模型假设相变处于热力学平衡状态，基于水动力学漂移通量模型（DFM）并结合动量方程的无压力波近似。本工作重点设计一种鲁棒的离散化方法，适用于倾斜井和多分支井，能够模拟瞬态行为（如井口开启）以及储层时间尺度下的耦合模拟。该方法采用空间交错有限体积格式结合全隐式欧拉时间积分。构建一致且稳定的数值通量是实现鲁棒数值方法的关键特征，通过将相表观速度的单调解逼近与相摩尔分数、密度和焓的上风逼近相结合来实现。为便于井筒与储层模型的耦合，牛顿线性化中消去水动力学未知量，生成的雅可比矩阵系统采用与储层模型相同的主未知量。在无窜流和有窜流的独立井筒测试案例以及全耦合井-储层模拟中验证了该方法的效率。