Nonlinear Formulation Based on an Equation-of-State Free Method for Compositional Flow Simulation

Abstract

Summary Compositional simulation is necessary for modeling complex enhanced oil recovery (EOR) processes. For accurate simulation of compositional processes, we need to resolve the coupling of the nonlinear conservation laws, which describe multiphase flow and transport, with the equilibrium phase behavior constraints. The complexity of the problem requires extensive computations and consumes significant time. This paper presents a new framework for the general compositional problem associated with multicomponent multiphase flow in porous media. Here, adaptive construction and interpolation using the supporting tie lines are used to obtain the phase state and the phase compositions. For the parameterization of the full solution of a complex compositional problem, we need only a limited number of supporting tie lines in the compositional space. The parameterized tie lines are triangulated using Delaunay tessellation, and natural-neighbor interpolation is used inside the simplexes. Then, the computation of the phase behavior in the course of a simulation becomes an iteration-free, table look-up procedure. The treatment of nonlinearities associated with complex thermodynamic behavior of the fluid is based on the new set of unknowns—tie-line parameters that allow for efficient representation of the subcritical region. For the supercritical region, we use the standard compositional variable set based on the overall composition. The efficiency and accuracy of the method are demonstrated for several multidimensional compositional problems of practical interest. In terms of the computational cost of the thermodynamic calculations, the proposed method shows results comparable to those of state-of-the-art techniques. Moreover, the method shows better nonlinear convergence in the case of near-miscible gas-injection simulation.

Multiscale Reconstruction Of Compositional Transport

“…For an isothermal compositional system consisting of components and 2 hydrocarbon phases [26], the transport equation is given by: …”

“…The key to CSAT implementation is based on the fact that the phase state identification in a gas injection processes involves only a limited number of tie-lines. The proposed techniques not only accelerated the phase behavioral computations, but also provided the basis for development of fully EOS-free compositional simulation approach [26].…”

Operator-based Linearization for Non-isothermal Multiphase Compositional Flow in Porous Media

“…We chose this approach for its application simplicity in comparison with the approach proposed in Zaydullin et al (2013) for compositional systems with a large number of components. Both methods have comparable accuracy and performance when applied to systems with a limited number of degrees of freedom, see Weiser and Zarantonello (1988) for details.…”

“…Using the capabilities of ADETL, an Automatic Differentiation General Purpose Research Simulator (ADGPRS) was developed (Voskov and Tchelepi, 2012). ADGPRS is a unified reservoir simulation framework providing an extensive set of nonlinear formulations (Voskov, 2012;Zaydullin et al, 2013); flexible spatial discretization (Zhou et al, 2011); extended physics models (Iranshahr et al, 2013;Zaydullin et al, 2014a;Garipov et al, 2016); inverse capabilities (Kourounis et al, 2010;Volkov and Voskov, 2016); geothermal formulation (Wong et al, 2015). We use ADGPRS for the implementation and performance comparisons in this study.…”

“…The predecessor of the new method described in this work was the Compositional Space Parametrization (CSP) method proposed in Voskov and Tchelepi (2009) and fully developed for compositional simulation by Zaydullin et al (2013). In this approach, a complex thermodynamic phase behavior is described by a special set of nonlinear unknowns: pressure, phase fractions and tie-line parameters.…”