@Article{IJNAM-14-218,
author = {J.-S. Kou and S.-Y. Sun},
title = {Efficient Energy-Stable Dynamic Modeling of Compositional Grading},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2016},
volume = {14},
number = {2},
pages = {218--242},
abstract = {<p style="text-align: justify;">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 ternary 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/418.html}
}