Computational Geosciences

, Volume 22, Issue 1, pp 389–412 | Cite as

An efficient distribution method for nonlinear two-phase flow in highly heterogeneous multidimensional stochastic porous media

  • Fayadhoi Ibrahima
  • Hamdi A. Tchelepi
  • Daniel W. Meyer
Original Paper


In the context of stochastic two-phase flow in porous media, we introduce a novel and efficient method to estimate the probability distribution of the wetting saturation field under uncertain rock properties in highly heterogeneous porous systems, where streamline patterns are dominated by permeability heterogeneity, and for slow displacement processes (viscosity ratio close to unity). Our method, referred to as the frozen streamline distribution method (FROST), is based on a physical understanding of the stochastic problem. Indeed, we identify key random fields that guide the wetting saturation variability, namely fluid particle times of flight and injection times. By comparing saturation statistics against full-physics Monte Carlo simulations, we illustrate how this simple, yet accurate FROST method performs under the preliminary approximation of frozen streamlines. Further, we inspect the performance of an accelerated FROST variant that relies on a simplification about injection time statistics. Finally, we introduce how quantiles of saturation can be efficiently computed within the FROST framework, hence leading to robust uncertainty assessment.


Stochastic Buckley-Leverett Saturation Uncertainty propagation Distribution functions Two-phase flow Porous systems Heterogeneity Streamlines 


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Daniel Meyer is very thankful to Florian Müller who kindly provided the streamline code that was applied in this work. Fayadhoi Ibrahima is thankful to Per Pettersson for his constant support in the early stage of the manuscript and to Matthias Cremon for providing SGEMS simulations. The authors are also grateful to the SUPRI-B research group at Stanford University for their financial support.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institute for Computational & Mathematical EngineeringStanford UniversityStanfordUSA
  2. 2.Department of Energy Resources EngineeringStanford UniversityStanfordUSA
  3. 3.Institute of Fluid DynamicsETH ZürichZürichSwitzerland

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