报告人：孙树瑜教授

           阿卜杜拉国王科技大学(KAUST)

报告题目：Two-Phase Flow with Partial Miscibility: Modeling and Algorithms

报告时间：2016年07月07日下午15:00

报告地点：海韵数理楼661

学院联系人:陈黄鑫副教授

报告摘要：Two-phase and multi-phase flows are important and common phenomena in petroleum industry, where oil, gas and water are often produced and transported together.  In particular, engineers and researchers in reservoir engineering study drainage problems arising during the development and production of oil and gas reservoirs so as to obtain a high economic recovery, by developing, conducting, and interpolating the simulation of subsurface flows of reservoir fluids, including water, hydrocarbon, CO2, H2S for example in porous geological formation.  Field-scale (Darcy-scale) simulation has conventionally and routinely used for this purpose.  A number of parameters like relative permeability and capillary pressure are taken as given functions in Darcy-scale simulation.  To study these parameters as well as to obtain deep understanding of porous media flow and transport, researchers develop and utilize pore-scale simulation of two-phase, which has been shown to be a great research tool to understand the complex hydrodynamic behaviors of the flow systems.

In this work, we consider two-phase flow with partial miscibility at a pore scale.  Specifically, we study the modeling and simulation of possibly compressible, partially miscible, fully compositional two-phase hydrocarbon systems using a diffuse interface model together with Peng-Robinson Equation of State (EOS).  For multi-component two-phase fluid systems, most published results are limited to equilibrium condition in one spatial dimension based on the gradient theory and variational calculus, but we extend it to multiple spatial dimensions as well as to non-equilibrium transient conditions, based on the coupling of the Navier-Stokes equation for flow and a Cahn-Hilliard-like equation with Peng-Robinson chemical potentials for phase behaviors of hydrocarbon fluids.  For diffuse interface modeling of two-phase flow, most published results are limited to fully immiscible and fully incompressible two-phase flow, but we extend it to possibly compressible and partially miscible two-phase flow (and multi-phase flow); this extension is significant for engineering applications, particularly because partial miscibility is a crucial factor for petroleum fluid, for example in the CO2-decane two-phase fluid system.  This research has an eventual goal of applying to realistic modeling of petroleum and other reservoir fluids in pores or pore networks within geological formation.  Our modeling scheme utilizes molar densities as the order parameters, and the approach is based on the coupling of the Navier-Stokes equation for flow and a Cahn-Hilliard-like equation with Peng-Robinson chemical potentials for phase behaviors of hydrocarbon fluids.  Our modeling approach can be used to predict volumetric behaviors, solubility, miscibility, and interface tensions of common hydrocarbon liquid (oil) and vapor (gas) accurately.  Moreover, the entire modeling approach is self-consistent and complies with the principles of non-equilibrium thermodynamics including the second law of thermodynamics, the maximum entropy production principle (MEPP) and the Onsager reciprocity principle.  The continuum model is formulated mathematically in a coupled nonlinear partial differential equation (PDE) system, which usually does not have analytical solutions.  We thus propose an efficient numerical solution of the modeling system, focusing on discrete energy stability, local mass conservation and numerical accuracy.  For spatial discretization, we apply a finite volume-based method to turn the partial differential equations (PDE) into an ordinary differential equation (ODE) system.  For temporal discretization, the resultant ODE system is decoupled by using an asymmetric splitting scheme, and then integrated in time using a semi-implicit marching scheme.  In addition, targeting the specific features of each of the three terms in Peng-Robinson chemical potentials, we propose a convex splitting-based semi-implicit time scheme, which is proved to be unconditionally energy stable under certain conditions.  The proposed algorithm is capable of solving successfully the dynamically evolved and spatially heterogeneous two-phase systems with varied molar density profiles in multiple dimensional domains.  We compare our computational results with laboratory experimental data reported in the literature, which have good agreement.

This presentation is partially based on joint work with Kai Bao (SINTEF), Jie Chen (Xi’an Jiaotong U), Xiaolin Fan (KAUST), Abbas Firoozabadi (Yale U), Jisheng Kou (Hubei Eng. U.), Tiezheng Qian (HKUST), Zhonghua Qiao (HK PolyU), Xiao-Ping Wang (HKUST), Mary F. Wheeler (UT-Austin), and Hua Zhong (KAUST).

报告人简介：孙树瑜教授是数学学科和工程学科的双栖研究工作者，现在主要从事于工程和科学应用中各种数值模拟和计算方法的研究。孙树瑜教授是阿卜杜拉国王科技大学的创建教师之一，在该校地球科学与工程（ErSE）和应用数学和计算科学（AMCS）两个专业授课和指导博士和硕士研究生。孙树瑜教授的研究领域主要包括管道内单相多相流动，多孔介质渗流和对流扩散及反应的数值模拟及相关算法的数值分析。除了大量会议论文及技术报告外，其在相关领域国际学术杂志上发表了100余篇文章，目前孙树瑜教授是相关研究领域的7种国际杂志的编辑，嘉宾编辑，副编辑，或者编委会成员。

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