Volume 14, Issue 2
Efficient Energy-Stable Dynamic Modeling of Compositional Grading

J.-S. Kou & S.-Y. Sun

Int. J. Numer. Anal. Mod., 14 (2017), pp. 218-242.

Published online: 2016-05

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  • Abstract

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.

  • Keywords

Compositional grading, dynamic modeling, energy stability, Peng-Robinson equation of state.

  • AMS Subject Headings

65N12, 76T10, 49S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-14-218, author = {}, 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 = {

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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/418.html} }
TY - JOUR T1 - Efficient Energy-Stable Dynamic Modeling of Compositional Grading JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 218 EP - 242 PY - 2016 DA - 2016/05 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/418.html KW - Compositional grading, dynamic modeling, energy stability, Peng-Robinson equation of state. AB -

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.

J.-S. Kou & S.-Y. Sun. (1970). Efficient Energy-Stable Dynamic Modeling of Compositional Grading. International Journal of Numerical Analysis and Modeling. 14 (2). 218-242. doi:
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