Advanced nonlinear techniques for compositional reservoir simulation

Abstract

Reservoir simulation using high-fidelity fluid models is typically employed to study subsurface displacement processes that involve complex physics. Such processes are highly nonlinear and they occur at the interplay of phase thermodynamics (phase stability and split), and rock/fluid interaction (relative-permeability). Accurate modeling of these processes requires considerable storage and computational resources. In this work, we focus on improving the nonlinear behavior of compositional simulation using two approaches: (1) understanding the nonlinearities related to flow and transport of compositional models, and proposing a robust and efficient solver, and (2) improving the portrayal of the physics of compositional models by designing a consistent and robust relative permeability model. To better characterize the convergence failures of compositional nonlinear solvers, we study the analytical and discrete forms of the component flux functions for the transport problem. We focus on isothermal, two-hydrocarbon phase models in the presence of viscous forces. As described in the literature, our analysis shows that the component flux function exhibits both kinks and inflection points. We study the kinks due to the crossing of phase boundaries, and we show their impact on residual terms. We, then, investigate the location, direction, and evolution of the inflection loci inside the two phase region. Our findings suggest that these inflection loci may exhibit complex features, as a result of which an a priori determination of such loci is computationally prohibitive. We propose a nonlinear solver that detects phase boundaries and guides the Newton update to avoid crossing these boundaries. Our numerical results show that this phase change detection solver has superior performance in comparison with both standard Newton solver and Newton solver with Appleyard chop for a wide range of cases. Due to its nonlinearity, relative-permeability is an important constitutive of the conservation equations and has a significant impact on the performance of a simulation model. Dependence of the phase relative-permeability on fluid compositions, pressure, and temperature is well-documented. In compositional reservoir simulation, however, relative-permeability is typically modeled as a function of phase saturation. Such an approach may lead to serious discontinuities in relative-permeability. To alleviate this issue, several authors have proposed models based on phase state indicators (density, parachor, Gibbs Free Energy). However, such techniques cannot represent the complete degrees of freedom that are exhibited by compositional displacements. In this work, we present a relative-permeability model based on a parameterization of the compositional space. The model is independent of the hydrocarbon phase labeling as gas or oil. We show that our proposed model (1) applies regardless of the degrees-of-freedom of the compositional displacement problem, and (2) is guaranteed to yield a continuous relative-permeability function across the entire compositional space. We have implemented this model in our research simulator, and we present test cases using traditional relative-permeability models, as well as, numerical results that compare the nonlinear performance