General nonlinear solution strategies for multi-phase multi-component EoS based simulation

D. V. Voskov, R. Younis, H. A. Tchelepi

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

27 Citations (Scopus)


We present a novel reservoir flow simulation framework built on top of an Automatic Differentiation with Expression Templates Library (ADETL). Given discrete algebraic expressions of the governing conservation equations, associated constraint relations, and equations of state, the ADETL library generates efficient computer code for the corresponding Jacobian matrix. The framework allows for complete flexibility in the specification of the independent variables, which leads to unified simulator for different formulations and solution strategies. We study the behavior of several widely used nonlinear formulations and solution strategies for general-purpose compositional simulation. The numerical behaviors using different variable sets, including the so called natural- and mass-type variables, are investigated. We also report on tie-line based parameterization strategies for compositional modeling. The focus is on the fully implicit method (FIM), where the full Jacobian (primary and secondary algebraic equations in terms of both the primary and secondary variables) is constructed. Schur-complement reduction of the full Jacobian is used to assemble the (reduced) Jacobian for the primary equations as a function of the primary unknowns only. The numerical challenges associated with the nonlinear hydrodynamic and thermo-dynamic interactions associated with compositional displacement processes are the focus of this investigation. These include phase appearance and disappearance, crossing into and out of the critical region, wide pressure variations in space and time. The behavior of the Newton iterations as a function of timestep size is analyzed for different variable sets, alignment of equations (including linear and nonlinear constraints), and nonlinear updating strategies. Comparisons are performed for several challenging multi-phase multi-component problems of practical interest.

Original languageEnglish
Title of host publicationSPE Reservoir Simulation Symposium 2009
Number of pages15
Publication statusPublished - 2009
Externally publishedYes
EventSPE Reservoir Simulation Symposium 2009 - The Woodlands, TX, United States
Duration: 2 Feb 20094 Feb 2009


ConferenceSPE Reservoir Simulation Symposium 2009
Country/TerritoryUnited States
CityThe Woodlands, TX


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