A Stochastic Model for Two-phase Flow in Heterogeneous Porous Media PDF Download
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Author: Michael B. Butts
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Michael B. Butts
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: David W. Dean
Publisher:
ISBN:
Category : Multiphase flow
Languages : en
Pages : 16
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Presents a stochastic differential equation approach to multiphase flow, a typical example of which is flow in the unsaturated domain. Specifically, a two phase problem is studied which consists of a wetting phase and a nonwetting phase. The approach given results in a nonlinear stochastic differential equation describing the position of the non-wetting phase fluid particle.
Author:
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ISBN:
Category :
Languages : en
Pages : 13
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The effects of subsurface heterogeneity on two-phase flow can be observed from the characterization functions of field-scale effective relative permeability and capillary pressure with respect to mean saturation. Numerical experiments were used to evaluate such effective properties of two-phase flow in a heterogeneous medium with properties representing the Borden Aquifer, and compared with the results of stochastic analysis developed using a spectral perturbation technique that employs a stationary, stochastic representation of the spatial variability of soil properties. Arbitrary forms of the relative permeability and capillary pressure characteristic functions with respect to saturation can be used in the theoretical analysis and numerical code. A statistical scaling procedure, which is a generalization of Leverett scaling, was developed for the relationship between intrinsic permeability and two capillary parameters. The procedure for estimating the effective properties of two-phase flow using numerical simulation consists of three-steps. Firstly, a local-scale heterogeneous system with random fields of intrinsic permeability and two capillary parameters was generated. Secondly, numerical simulation of single-phase flow in the system, with different sets of flow boundary conditions for different directions, was performed; the field-scale effective saturated hydraulic conductivity tensor was calculated on the basis of the mean Darcy law. The tensor obtained numerically is very close to that determined using the generalized spectral-perturbation approximation. Finally, a number of numerical experiments on two-phase flow in the system were conducted with different infiltration rates of DNAPL; the field-scale effective relative permeability and capillary pressure functions were obtained. In each experiment, a highly heterogeneous saturation field was obtained, leading to large variations of actual nonwetting phase permeability (combination of intrinsic permeability and its positively correlated relative permeability). Both stochastic and numerical analyses produced very similar results of effective properties of multiphase flow. The vertical effective relative permeability is significantly lower than the homogeneous one found using mean capillary parameters, particularly at low mean DNAPL saturation (low mean capillary pressure). On the other hand, the effective capillary pressure function differs only slightly from the homogeneous case. Various statistical properties of local-scale NAPL saturation, capillary pressure and relative permeability and their relationships with intrinsic permeability and capillary parameters were analyzed in detail.
Author: Gedeon Dagan
Publisher: Springer Science & Business Media
ISBN: 9780792316169
Category : Mathematics
Languages : en
Pages : 312
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Book Description
This book contains a selection of articles presented at an International Workshop on `Mathematical Modeling for Flow and Transport Through Porous Media'. The major topics of the meeting were free and moving boundary problems, structured media, multiphase flow, scale problems, stochastic aspects, parameter identification and optimization problems. The volume also represents a few contributions on the incorporation of chemical and biological processes in mathematical models for transport in porous media. The book is directed at researchers active in porous media, mathematical modeling, petroleum and geotechnical engineering and environmental sciences.
Author: Mingjie Chen
Publisher:
ISBN: 9780542612817
Category :
Languages : en
Pages : 258
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We present a novel approach to modeling stochastic multiphase now problems, for example NAPL flow, in a heterogeneous subsurface medium with random soil properties. A stochastic numerical model for steady state and transient two-phase and three-phase flow in a random soil property field is developed using the Karhunen-Loeve Moment Equation (KLME) approach and is numerically implemented. An exponential model and van Genuchten model are adopted to define the constitutive relationship between phase relative permeability and capillary. The log-transformed intrinsic permeability, soil pore size distribution, and van Genuchten fitting parameter are assumed to be Gaussian random functions with a separable exponential covariance function. We demonstrate the validity of the proposed KLME model by favorably comparing up to second-order approximations to Monte Carlo simulations, which are considered "true" solutions. The significant computational efficiency of the KLME approach over Monte Carlo simulation is also illustrated.
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Category : Power resources
Languages : en
Pages : 782
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Author: Maren Paul
Publisher:
ISBN: 9783933761231
Category :
Languages : de
Pages : 143
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Author: Dongxiao Zhang
Publisher: Elsevier
ISBN: 0080517773
Category : Mathematics
Languages : en
Pages : 371
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Book Description
Stochastic Methods for Flow in Porous Media: Coping with Uncertainties explores fluid flow in complex geologic environments. The parameterization of uncertainty into flow models is important for managing water resources, preserving subsurface water quality, storing energy and wastes, and improving the safety and economics of extracting subsurface mineral and energy resources. This volume systematically introduces a number of stochastic methods used by researchers in the community in a tutorial way and presents methodologies for spatially and temporally stationary as well as nonstationary flows. The author compiles a number of well-known results and useful formulae and includes exercises at the end of each chapter. - Balanced viewpoint of several stochastic methods, including Greens' function, perturbative expansion, spectral, Feynman diagram, adjoint state, Monte Carlo simulation, and renormalization group methods - Tutorial style of presentation will facilitate use by readers without a prior in-depth knowledge of Stochastic processes - Practical examples throughout the text - Exercises at the end of each chapter reinforce specific concepts and techniques - For the reader who is interested in hands-on experience, a number of computer codes are included and discussed
Author: David W. Dean
Publisher:
ISBN:
Category : Fluids
Languages : en
Pages : 12
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This paper is a follow-up to Dean and Russell's in which the formulation of a model of NAPL (Non-Aqueous Phase Liquid) flow in heterogeneous porous media is based on the traditional argument of developing a Fokker-Planck equation for a diffusion process and then modifying this equation to handle the behavior of the fluid particle at an interface between sands of different permeabilities. In this paper, an attempt is made to accomplish the same result starting with a theory of stochastic processes that allows jumps.--Authors' abstract.
Author: Alaa El-din Ahmed Abdin
Publisher:
ISBN:
Category : Hydraulic engineering
Languages : en
Pages : 424
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