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Title: Stochastic Analysis of Immiscible Displacement of the Fluids with Arbitrarily Viscosities and its Dependence on Support Scale of Hydrological Data

Abstract

Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterizemore » the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow.« less

Authors:
; ;
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
912256
Report Number(s):
INEEL/JOU-03-01482
TRN: US200801%%699
DOE Contract Number:  
DE-AC07-99ID-13727
Resource Type:
Journal Article
Journal Name:
Advances in Water Resources
Additional Journal Information:
Journal Volume: 27; Journal Issue: 12
Country of Publication:
United States
Language:
English
Subject:
13 - HYDRO ENERGY, 54 - ENVIRONMENTAL SCIENCES, 58 - GEOSCIENCES; ANALYTICAL SOLUTION; CORRELATION FUNCTIONS; PERMEABILITY; SIMULATION; STABILITY; STATISTICS; TRANSPORT; VISCOSITY; heterogeneity; immiscible displacement; stochastic analysis

Citation Formats

Tartakovsky, A M, Meakin, P, and Huang, H. Stochastic Analysis of Immiscible Displacement of the Fluids with Arbitrarily Viscosities and its Dependence on Support Scale of Hydrological Data. United States: N. p., 2004. Web. doi:10.1016/j.advwatres.2004.09.003.
Tartakovsky, A M, Meakin, P, & Huang, H. Stochastic Analysis of Immiscible Displacement of the Fluids with Arbitrarily Viscosities and its Dependence on Support Scale of Hydrological Data. United States. https://doi.org/10.1016/j.advwatres.2004.09.003
Tartakovsky, A M, Meakin, P, and Huang, H. 2004. "Stochastic Analysis of Immiscible Displacement of the Fluids with Arbitrarily Viscosities and its Dependence on Support Scale of Hydrological Data". United States. https://doi.org/10.1016/j.advwatres.2004.09.003.
@article{osti_912256,
title = {Stochastic Analysis of Immiscible Displacement of the Fluids with Arbitrarily Viscosities and its Dependence on Support Scale of Hydrological Data},
author = {Tartakovsky, A M and Meakin, P and Huang, H},
abstractNote = {Stochastic analysis is commonly used to address uncertainty in the modeling of flow and transport in porous media. In the stochastic approach, the properties of porous media are treated as random functions with statistics obtained from field measurements. Several studies indicate that hydrological properties depend on the scale of measurements or support scales, but most stochastic analysis does not address the effects of support scale on stochastic predictions of subsurface processes. In this work we propose a new approach to study the scale dependence of stochastic predictions. We present a stochastic analysis of immiscible fluid–fluid displacement in randomly heterogeneous porous media. While existing solutions are applicable only to systems in which the viscosity of one phase is negligible compare with the viscosity of the other (water–air systems for example), our solutions can be applied to the immiscible displacement of fluids having arbitrarily viscosities such as NAPL–water and water–oil. Treating intrinsic permeability as a random field with statistics dependant on the permeability support scale (scale of measurements) we obtained, for one-dimensional systems, analytical solutions for the first moments characterizing unbiased predictions (estimates) of system variables, such as the pressure and fluid–fluid interface position, and we also obtained second moments, which characterize the uncertainties associated with such predictions. Next we obtained empirically scale dependent exponential correlation function of the intrinsic permeability that allowed us to study solutions of stochastic equations as a function of the support scale. We found that the first and second moments converge to asymptotic values as the support scale decreases. In our examples, the statistical moments reached asymptotic values for support scale that were approximately 1/10000 of the flow domain size. We show that analytical moment solutions compare well with the results of Monte Carlo simulations for moderately heterogeneous porous media, and that they can be used to study the effects of heterogeneity on the dynamics and stability of immiscible flow.},
doi = {10.1016/j.advwatres.2004.09.003},
url = {https://www.osti.gov/biblio/912256}, journal = {Advances in Water Resources},
number = 12,
volume = 27,
place = {United States},
year = {Wed Dec 01 00:00:00 EST 2004},
month = {Wed Dec 01 00:00:00 EST 2004}
}