The Mathematics of Fluid Flow Through Porous Media

Master the techniques necessary to build and use computational models of porous media fluid flow

In The Mathematics of Fluid Flow Through Porous Media, distinguished professor and mathematician Dr. Myron B. Allen delivers a one-stop and mathematically rigorous source of the foundational principles of porous medium flow modeling. The book shows readers how to design intelligent computation models for groundwater flow, contaminant transport, and petroleum reservoir simulation.

Discussions of the mathematical fundamentals allow readers to prepare to work on computational problems at the frontiers of the field. Introducing several advanced techniques, including the method of characteristics, fundamental solutions, similarity methods, and dimensional analysis, The Mathematics of Fluid Flow Through Porous Media is an indispensable resource for students who have not previously encountered these concepts and need to master them to conduct computer simulations.

Teaching mastery of a subject that has increasingly become a standard tool for engineers and applied mathematicians, and containing 75 exercises suitable for self-study or as part of a formal course, the book also includes:

• A thorough introduction to the mechanics of fluid flow in porous media, including the kinematics of simple continua, single-continuum balance laws, and constitutive relationships
• An exploration of single-fluid flows in porous media, including Darcy's Law, non-Darcy flows, the single-phase flow equation, areal flows, and flows with wells
• Practical discussions of solute transport, including the transport equation, hydrodynamic dispersion, one-dimensional transport, and transport with adsorption
• A treatment of multiphase flows, including capillarity at the micro- and macroscale

Perfect for graduate students in mathematics, civil engineering, petroleum engineering, soil science, and geophysics, The Mathematics of Fluid Flow Through Porous Media also belongs on the bookshelves of any researcher who wishes to extend their research into areas involving flows in porous media.