# Review of Geological Fluid Dynamics; Sub-surface flow and Reactions By O.M. Phillips

Reviewed by John L. Nieber, Department of Bioproducts and Biosystems Engineering, University of Minnesota

The book Geological Fluid Dynamics by O.M. Phillips provides an excellent reference for researchers and professional working on environmental problems involving groundwater flows, especially flows at large spatial scales that are incited by natural forcing functions. The author presents background material from a very fundamental perspective using physical and mathematical arguments. The book is presented in six chapters consisting of 1) Introduction, 2) Basic Principles, 3) Patterns of Flow, 4) Flows with Buoyancy Variations, 5) Patterns of Reaction with Flow, and 6) Extensions and Examples. The Introduction chapter lays out the approach used in the book and summarizes the topics given in each of the subsequent chapters.

The Basic Principles chapter describes the properties of porous media, the fundamental properties of porosity and permeability, the conservation of mass principle, the stream function, derivation of Darcy's equation, the buoyancy term in the expression for the total potential, the thermal energy balance and chemical balances. A unique feature of this book is that it presents two theorems established by Helmholtz, the uniqueness theorem and the minimum dissipation theory, both of which play important roles in describing phenomena involving flow in porous media.

The chapter on Patterns of Flow describes flow phenomena in both homogeneous and heterogeneous geological formations. It presents the Laplace equation and provides a list of properties of the equation that are directly translated into practical terms. Regional groundwater flow processes are described qualitatively and applications of the Laplace equation to solve for flow patterns are presented. The effect of random heterogeneity of permeability on the flow patterns and ultimately the hydrodynamic dispersion is discussed and analyses given and related to predictions of hydrodynamic dispersion estimated from field scale experiments like the well-known Cape Cod field tracer experiment. The interaction between flows in matrix blocks and adjoining fractures is analyzed to quantity the nature of the flow field as well as solute transport distribution. The chapter ends with a discussion of pressure transients in porous media, either matrix, or media composed of matrix and fracture elements.