Efficient integration of stiff kinetics with phase change detection for reactive reservoir processes

Abstract

We propose the use of implicit one-step Explicit Singly Diagonal Implicit Runge-Kutta (ESDIRK) methods for integration of the stiff kinetics in reactive, compositional and thermal processes that are solved using operator-splitting type approaches. To facilitate the algorithmic development we construct a virtual kinetic cell model. The model serves both as a tool for the development and testing of tailored solvers as well as a testbed for studying the interactions between chemical kinetics and phase behavior. As case study, two chemical kinetics models with 6 and 14 components, respectively, are implemented for in situ combustion, a thermal oil recovery process. Through benchmark studies using the 14 component reaction model the new ESDIRK solvers are shown to improve computational speed when compared to the widely used multi-step BDF methods DASSL and LSODE. Phase changes are known to cause convergence problems for the integration method. We propose 384 M. R. Kristensen et al. an algorithm for detection and location of phase changes based on discrete event system theory. Experiments show that the algorithm improves the robustness of the integration process near phase boundaries by lowering the number convergence and error test failures by more than 50% compared to direct integration without the new algorithm.

An Equation-of-State Compositional In-Situ Combustion Model: A Study of Phase Behavior Sensitivity

“…Of particular interest is the sensitivity to reservoir heterogeneity, the important question being how the formation and sustained propagation of an ISC combustion front is affected by heterogeneities in the reservoir rock. For multi-dimensional problems we need improved numerical methods, and we are currently working on a computational framework, which leverages on adaptive gridding and operator splitting techniques to address the multi-scale nature of ISC processes (Younis Gerritsen 2006;Nilsson et al 2005;Kristensen et al 2007b).…”

“…The Virtual Kinetic Cell (VKC) was developed in Kristensen et al (2007b) and further extended in Kristensen et al (2007a). The VKC is essentially a zero-dimensional version of the above-developed model, which allows us to study kinetics and phase behavior in an isolated setting.…”

“…Details can be found in Appendix B for completeness. The numerical model for the VKC was presented in Kristensen et al (2007b). For the VKC we developed specialized solvers for the stiff kinetics based on the ESDIRK subclass of Runge-Kutta methods (Butcher and Chen 2000;Kvaernø 2004).…”

“…In order to properly resolve the fine scale behavior of ISC reaction zones, both Christensen et al (2004) and Nilsson et al (2005) have developed adaptive gridding techniques. Temporal adaptivity was addressed by Younis Gerritsen (2006), who proposed a framework for integration of ISC processes based on operator splitting techniques, and by Kristensen et al (2007b), who developed a class of efficient integration methods for ISC kinetics. On the experimental side, the ISC literature is richer, recent contributions including the work by e.g.…”

Experimental Investigation and High Resolution Simulator of In-Situ Combustion Processes

“…The Virtual Kinetic Cell (VKC) was developed in [1] and further extended in [2]. The VKC models a porous media system with multiple fluid phases in thermodynamic equilibrium and kinetically driven chemical reactions.…”