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Probability Density Function Modeling of Multi-Phase Flow in Porous Media with Density-Driven Gravity Currents.
- Source :
- Transport in Porous Media; Mar2011, Vol. 87 Issue 2, p603-623, 21p, 3 Graphs
- Publication Year :
- 2011
-
Abstract
- probability density function (PDF) based approach is employed to model multi-phase flow with interfacial mass transfer (dissolution) in porous media. The joint flow statistics is represented by a mass density function (MDF), which is transported in the physical and probability spaces via Fokker-Planck equation. This MDF-equation requires Lagrangian evolutions of the random flow variables; these evolutions are stochastic processes honoring the micro-scale flow physics. To demonstrate the concept, we consider an example of immiscible two-phase flow with the non-equilibrium dissolution of single component from one phase into the other-a model for solubility trapping during CO storage in brine aquifer. Since CO-rich brine is denser than pure brine, density-driven countercurrent flow is set up in the brine phase. The stochastic models mimicking the physics of countercurrent flow lead to a modeled MDF-equation, which is solved using our recently developed stochastic particle method for multi-phase flow (Tyagi et al. J Comput Phys 227:6696-6714, ). In addition, we derive Eulerian equations for stochastic moments (mean, variance, etc.) and show that unlike the MDF-equation the system of moment equations is not closed. In classical Darcy formulation, for example, the mean concentration equation is closed by neglecting variance. However, with several one- and two-dimensional simulations, it is demonstrated that the PDF and Darcy modeling approaches give significantly different results. While the PDF-approach properly accounts for the long correlation length scales and the concentration variance in density-driven countercurrent flow, the same phenomenon cannot be captured accurately with a standard Darcy model. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 01693913
- Volume :
- 87
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Transport in Porous Media
- Publication Type :
- Academic Journal
- Accession number :
- 59291563
- Full Text :
- https://doi.org/10.1007/s11242-010-9704-7