Efficient energy-stable dynamic modeling of compositional grading

Jisheng Kou, Shuyu Sun

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Compositional grading in hydrocarbon reservoirs caused by the gravity force highly affects the design of production and development strategies. In this paper, we propose a novel mathematical modeling for compositional grading based on the laws of thermodynamics. Different from the traditional modeling, the proposed model can dynamically describe the evolutionary process of compositional grading, and it satisfies the energy dissipation property, which is a key feature that real systems obey. The model is formulated for the two scales of free spaces without solids (laboratory scale) and porous media (geophysical scale). For the numerical simulation, we propose a physically convex-concave splitting of the Helmholtz energy density, which leads to an energy-stable numerical method for compositional grading. Using the proposed methods, we simulate binary and tenary mixtures in the free spaces and porous media, and demonstrate that compared with the laboratory scale, the simulation at large geophysical scales has more advantages in simulating the features of compositional grading.

Original languageEnglish (US)
Pages (from-to)218-242
Number of pages25
JournalInternational Journal of Numerical Analysis and Modeling
Issue number2
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Institute for Scientific Computing and Information.


  • Compositional grading
  • Dynamic modeling
  • Energy stability
  • Peng-Robinson equation of state

ASJC Scopus subject areas

  • Numerical Analysis


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