Stochastic Methods for Flow in Porous Media: Coping with Uncertainties

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

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 for describing flow in complex porous media under uncertainties. Amongst the methods discussed are perturbative expansions, Green's function method, spectral methods, adjoint state method, Adomian decomposition, and closure approximations. The potential and limitations are discussed for each method, and solution techniques and illustrative examples are presented for some selected ones.Features:

• Surveys a broad range of stochastic methods used by researchers in the community
• Introduces the various methods in a tutorial way
• Presents methodologies for spatially and temporally stationary as well as nonstationary flows
• Covers a wide variety of flows, from steady state to transient flow, from saturated, unsaturated to two-phase flow, and from nonfractured to fractured porous flow
• Compiles a number of well known results and useful formulae
• Includes exercises at the end of each chapter