Numerical modeling of isothermal compositional grading by convex splitting methods
Type
ArticleAuthors
Li, Yiteng
Kou, Jisheng

Sun, Shuyu

KAUST Department
Computational Transport Phenomena LabEarth Science and Engineering Program
Physical Science and Engineering (PSE) Division
KAUST Grant Number
BAS/1/1351-01-01Date
2017-04-09Online Publication Date
2017-04-09Print Publication Date
2017-07Permanent link to this record
http://hdl.handle.net/10754/623875
Metadata
Show full item recordAbstract
In this paper, an isothermal compositional grading process is simulated based on convex splitting methods with the Peng-Robinson equation of state. We first present a new form of gravity/chemical equilibrium condition by minimizing the total energy which consists of Helmholtz free energy and gravitational potential energy, and incorporating Lagrange multipliers for mass conservation. The time-independent equilibrium equations are transformed into a system of transient equations as our solution strategy. It is proved our time-marching scheme is unconditionally energy stable by the semi-implicit convex splitting method in which the convex part of Helmholtz free energy and its derivative are treated implicitly and the concave parts are treated explicitly. With relaxation factor controlling Newton iteration, our method is able to converge to a solution with satisfactory accuracy if a good initial estimate of mole compositions is provided. More importantly, it helps us automatically split the unstable single phase into two phases, determine the existence of gas-oil contact (GOC) and locate its position if GOC does exist. A number of numerical examples are presented to show the performance of our method.Citation
Li Y, Kou J, Sun S (2017) Numerical modeling of isothermal compositional grading by convex splitting methods. Journal of Natural Gas Science and Engineering 43: 207–221. Available: http://dx.doi.org/10.1016/j.jngse.2017.03.019.Sponsors
This work is supported by the KAUST research fund awarded to the Computational Transport Phenomena Laboratory at KAUST through the grant BAS/1/1351-01-01.Publisher
Elsevier BVAdditional Links
http://www.sciencedirect.com/science/article/pii/S1875510017301397ae974a485f413a2113503eed53cd6c53
10.1016/j.jngse.2017.03.019