I present a novel computational framework for simulating flow in porous media for mixtures having an arbitrary number of phases. This framework is designed to keep a unified computational structure for different nonlinear formulations and complex physical models. That includes generic phase appearance/disappearance treatment, efficient linear solver typical for mixed types of unknowns, finite volume discretization using flexible spatial stencil etc. The behavior of components in any phase is computed using mixed phase equilibrium assumptions. This type of simulation is very important for modeling of natural and industrial processes, such as development of natural hydrocarbon resources, including gas-hydrates, CO2 injection into hydrocarbon reservoirs and saline aquifers, and for modeling of thermal processes. In this framework I use a Fully Implicit (FI) time approximation with general extension to the Adaptive Implicit Method (AIM) using flexible algebraic reduction. The framework is built on top of an Automatic Differentiation with Expression Templates Library (ADETL) which generates the corresponding derivatives for any nonlinear relation and helps to construct Jacobian matrix for the nonlinear solver. Phase behavior for the new framework is calculated using Compositional Space Parameterization (CSP) approach, which helps to improve both efficiency and robustness of the standard Equation of State (EoS) computations. Within this simulation framework, the nonlinear behavior of different variable sets, including both natural and mass-type variables is investigated. The general extension of two-phase variable substitution is used to handle the phase appearance and disappearance for systems with arbitrary numbers of phases. Examples will be presented including different types of CO2 injection in a hydrocarbon reservoir, such as miscible and immiscible two-phase CO2 injection, thermal injection of CO2+steam (three-phase), and cold CO2 injection (three phase with the second liquid CO2-rich phase).
|Title of host publication||Society of Petroleum Engineers - SPE Annual Technical Conference and Exhibition 2011, ATCE 2011|
|Number of pages||15|
|Publication status||Published - 2011|
|Event||SPE Annual Technical Conference and Exhibition 2011, ATCE 2011 - Denver, CO, United States|
Duration: 30 Oct 2011 → 2 Nov 2011
|Conference||SPE Annual Technical Conference and Exhibition 2011, ATCE 2011|
|Period||30/10/11 → 2/11/11|