BAIL 2006 Book of Abstracts - Institut für Numerische und ...

H. WANG: A Component-Based Eulerian-Lagrangian Formulation for Compositional
Flow in Porous Media
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Figure 1: The ELLAM ((a)-(b)) and upwind ((c)-(d)) simulation at 5 and 20 years.
(a) The overall mole fraction of Methane (b) The molar amount of Methane in vapor
(c) The overall mole fraction of Methane (d) The molar amount of Methane in vapor
Discussion The numerical results show that the Eulerian-Lagrangian formulation generates
stable and accurate solutions (overall mole fractions) that have preserved physically reasonable
moving steep fronts, even if a large time step of ∆tel = 1 year is used. With the (largest
possible) fine time step ∆tup = 2 days, the upwind method generates qualitatively similar (but
much more diffusive) overall mole fraction. We observe a similar comparison in terms of the
normalized molar amounts in the vapor and liquid phases.
It is instructive to look at the computational efficiency. Although the Eulerian-Lagrangian
method uses more CPU time than the upwind method in solving the mass balance equations,
both simulators have to perform the same computations on the pressure system and the thermodynamic
flash calculations which consume a larger portion of the CPU time per iterative step
at each time step. These results indicate that the Eulerian-Lagrangian simulator uses less than
twice the CPU time an upwind simulator uses per time step. Therefore, the Eulerian-Lagrangian
method generates accurate and stable solutions with steeper fronts using much less CPU time.
References
[1] H. Aziz and A. Settari, Petroleum Reservoir Simulation, Applied Science Publishers, 1979.
[2] M.S. Espedal and R.E. Ewing, Characteristic Petrov-Galerkin sub-domain methods for twophase
immiscible flow, Comput. Meth. Appl. Mech. Engrg., 64, (1987) 113–135.
[3] R.E. Ewing, T.F. Russell, and M.F. Wheeler, Simulation of miscible displacement using
mixed methods and a modified method of characteristics, SPE 12241, (1983), 71–81.
[4] R. Helmig, Multiphase Flow and Transport Processes in the Subsurface, Springer Verlag,
Berlin, 1997.
[5] H. Wang, D. Liang, R.E. Ewing, S.L. Lyons, and G. Qin, An ELLAM-MFEM solution
technique for compressible fluid flows in porous media with point sources and sinks, J. Comput.
Phys., 159, (2000) 344–376.
Speaker: WANG, H. 20 BAIL 2006
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