Skip to main content
SpringerLink
Log in

Conditional simulations of water–oil flow in heterogeneous porous media

  • Original Paper
  • Published:
Stochastic Environmental Research and Risk Assessment Aims and scope Submit manuscript

Abstract

This study is an extension of the stochastic analysis of transient two-phase flow in randomly heterogeneous porous media (Chen et al. in Water Resour Res 42:W03425, 2006), by incorporating direct measurements of the random soil properties. The log-transformed intrinsic permeability, soil pore size distribution parameter, and van Genuchten fitting parameter are treated as stochastic variables that are normally distributed with a separable exponential covariance model. These three random variables conditioned on given measurements are decomposed via Karhunen–Loève decomposition. Combined with the conditional eigenvalues and eigenfunctions of random variables, we conduct a series of numerical simulations using stochastic transient water–oil flow model (Chen et al. in Water Resour Res 42:W03425, 2006) based on the KLME approach to investigate how the number and location of measurement points, different random soil properties, as well as the correlation length of the random soil properties, affect the stochastic behavior of water and oil flow in heterogeneous porous media.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  • Abriola L (1989) Modeling multiphase migration of organic chemicals in groundwater systems—a review and assessment. Environ Health Perspect 83:117–143

    Article  CAS  Google Scholar 

  • Abriola L, Pinder G (1985) A multiphase approach to the modeling of porous media contamination by organic compounds: 1: equation development. Water Resour Res 21(1):11–18

    Article  CAS  Google Scholar 

  • Chen M, Zhang D, Keller AA, Lu Z (2005) A stochastic analysis of steady state two-phase flow in heterogeneous media. Water Resour Res 41:w01006, doi:10.1029/2004WR003412

    Article  Google Scholar 

  • Chen M, Keller AA, Zhang D, Lu Z, Zyvoloski GA (2006) A Stochastic analysis of transient two-phase flow in heterogeneous porous media. Water Resour Res 42:W03425, doi:10.1029/2005WR004257

    Article  Google Scholar 

  • Dagan G (1982) Stochastic modeling of groundwater flow by unconditional and conditional probabilities: 1. Conditional simulation and the direct problem. Water Resour Res 18(4):813–833

    Article  Google Scholar 

  • Dagan G (1989) Flow and transport in porous formations. Springer, New York

    Google Scholar 

  • Gelhar W (1993) Stochastic subsurface hydrology. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • van Genuchten M (1980) A closed form solution for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44: 892–898

    Article  Google Scholar 

  • Ghanem R, Dham S (1998) Stochastic finite element analysis for multiphase flow in heterogeneous porous media. Transport Porous Media 32:239–262

    Article  Google Scholar 

  • Ghanem R and Spanos D (1991) Stochastic finite elements: a spectral approach. Springer, New York

    Google Scholar 

  • Guadagnini A, Neuman SP (1999a) Nonlocal and localized analyses of conditional mean steady-state flow in bounded, randomly nonuniform domains: 1. Theory and computational approach. Water Resour Res 35(10):2999–3018

    Article  Google Scholar 

  • Guadagnini A, Neuman SP (1999b) Nonlocal and localized analyses of conditional mean steady-state flow in bounded, randomly nonuniform domains: 2. Computational examples. Water Resour Res 35(10): 3019–3039

    Article  Google Scholar 

  • Karhunen K (1947) Uber lineare methoden in der wahrschein-lichkeitsrechnung. Am Acad Sci, Fennicade, Ser. A, I, Vol 37, 3–79, (Translation: RAND Corporation, Santa Monica, California, Rep. T-131, August 1960)

  • Loeve M (1948) Fonctions aleatorires du second ordre, supplement to P. Levy. Processus Stochastic et Mouvement Brownien, Paris, Gauthier, Villars

  • Lu Z, Neuman SP, Guadagnini A, and Tartakovsky DM (2002) Conditional moment analysis of steady state unsaturated flow in bounded, randomly heterogeneous soils. Water Resour Res 38(4) doi:10.1029/2001WR000278

  • Lu, Z and Zhang D (2004) Conditional simulations of flow in randomly heterogeneous porous media using a KL-based moment-equation approach. Adv Water Resour 27:859–874

    Article  Google Scholar 

  • Tartakovsky DM, Neuman SP, and Lu Z (1999) Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff transformation. Water Resour Res 35(3):731–745

    Article  Google Scholar 

  • Yang J, Zhang D, and Lu Z (2004) Stochastic analysis of saturated–unsaturated flow in heterogeneous media by combing Karhunene–Loeve expansion and perturbation method. J Hydrol 29: 418–38

    Google Scholar 

  • Zhang D (2002) Stochastic methods for flow in porous media: coping with uncertainties. Academic, San Diego ISBN: 012-7796215

    Google Scholar 

  • Zhang D, and Lu Z (2004) Evaluation of higher-order moments for saturated flow in randomly heterogeneous media via Karhunen–Loeve decomposition. J Comput Phys 194(2):773–794

    Article  Google Scholar 

Download references

Acknowledgment

The authors would like to acknowledge the funding from the oil shale project cooperated between Chevron Energy Technology Company and Los Alamos National Laboratory.

Author information

Authors and Affiliations

  1. Hydrology & Geochemistry Group (EES-6), Los Alamos National Laboratory, Los Alamos, NM, USA

    Mingjie Chen, Zhiming Lu & George A. Zyvoloski

Authors
  1. Mingjie Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiming Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. George A. Zyvoloski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mingjie Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, M., Lu, Z. & Zyvoloski, G.A. Conditional simulations of water–oil flow in heterogeneous porous media. Stoch Environ Res Risk Assess 22, 587–596 (2008). https://doi.org/10.1007/s00477-007-0178-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00477-007-0178-2

Keywords

Search

Navigation