In this paper, theoretical and experimental approaches to flow, hydrodynamic dispersion, and miscible and immiscible displacement processes in reservoir rocks are reviewed and discussed. Both macroscopically homogeneous and heterogeneous rocks are considered. The latter are characterized by large-scale spatial variations and correlations in their effective properties and include rocks that may be characterized by several distinct degrees of porosity, a well-known example of which is a fractured rock with two degrees of porosity---those of the pores and of the fractures. First, the diagenetic processes that give rise to the present reservoir rocks are discussed and a few geometrical models of such processes are described. Then, measurement and characterization of important properties, such as pore-size distribution, pore-space topology, and pore surface roughness, and morphological properties of fracture networks are discussed. It is shown that fractal and percolation concepts play important roles in the characterization of rocks, from the smallest length scale at the pore level to the largest length scales at the fracture and fault scales. Next, various structural models of homogeneous and heterogeneous rock are discussed, and theoretical and computer simulation approaches to flow, dispersion, and displacement in such systems are reviewed. Two different modeling approaches to these phenomena are compared. The first approach is based on the classical equations of transport supplemented with constitutive equations describing the transport and other important coefficients and parameters. These are called the continuum models. The second approach is based on network models of pore space and fractured rocks; it models the phenomena at the smallest scale, a pore or fracture, and then employs large-scale simulation and modern concepts of the statistical physics of disordered systems, such as scaling and universality, to obtain the macroscopic properties of the system. The fundamental roles of the interconnectivity of the rock and its wetting properties in dispersion and two-phase flows, and those of microscopic and macroscopic heterogeneities in miscible displacements are emphasized. Two important conceptual advances for modeling fractured rocks and studying flow phenomena in porous media are also discussed. The first, based on cellular automata, can in principle be used for computing macroscopic properties of flow phenomena in any porous medium, regardless of the complexity of its structure. The second, simulated annealing, borrowed from optimization processes and the statistical mechanics of spin glasses, is used for finding the optimum structure of a fractured reservoir that honors a limited amount of experimental data.

Flow phenomena in rocks : from continuum models to fractals, percolation, cellular automata, and simulated annealing

Hydrocarbon production, gas recovery from shale, CO2 storage and water management have a common scientific underpinning: multiphase flow in porous media. This book provides a fundamental description of multiphase flow through porous rock, with emphasis on the understanding of displacement processes at the pore, or micron, scale. Fundamental equations and principal concepts using energy, momentum, and mass balance are developed, and the latest developments in high-resolution three-dimensional imaging and associated modelling are explored. The treatment is pedagogical, developing sound physical principles to predict flow and recovery through complex rock structures, while providing a review of the recent literature. This systematic approach makes it an excellent reference for those who are new to the field. Inspired by recent research, and based on courses taught to thousands of students and professionals from around the world, it provides the scientific background necessary for a quantitative assessment of multiphase subsurface flow processes, and is ideal for hydrology and environmental engineering students, as well as professionals in the hydrocarbon, water and carbon storage industries.

Multiphase Flow in Permeable Media: A Pore-Scale Perspective

A three-dimensional network model of a porous medium is used to compute relative permeabilities and capillary pressures in drainage and imbibition. In contrast, the invasion-percolation model of drainage with trapping does not make a sensible prediction for the relative permeability of either the displaced or injected phases since it fails to represent the fluid connectivity correctly. We describe two realistic trapping mechanisms which overcome this difficulty by representing the flow of the wetting phase along irregularities in the pore-gain surface. In imbibition, we simulate the rate-dependent competition between bulk filling of pores and film flow and show how different displacement mechanisms affect relative permeability. We verify percolation-theory results for the effects of buoyancy forces on trapped saturation by simulation and derive an expression for the correlation length in displacements perturbed by viscous forces. We can then demonstrate how relative permeabilities measured in quasistatic systems at capillary equilibrium are still meaningful in larger-scale displacements where viscous forces predominate.

Simulation and theory of two-phase flow in porous media

The application of percolation theory to porous media is closely tied to network models. A network model is a detailed model of a porous medium, generally incorporating pore-scale descriptions of the medium and the physics of pore-scale events. Network models and percolation theory are complementary: while network models have yielded insight into behavior at the pore scale, percolation theory has shed light, at the larger scale, on the nature and effects of randomness in porous media. This review discusses some basic aspects of percolation theory and its applications, and explores work that explicitly links percolation theory to porous media using network models. We then examine assumptions behind percolation theory and discuss how network models can be adapted to capture the physics of water, air and solute movement in soils. Finally, we look at some current work relating percolation theory and network models to soils.

Percolation theory and network modeling applications in soil physics

Direct numerical simulations of interface dynamics to link capillary pressure and total surface energy

We present experiments and computer simulations of slow drainage in a two-dimensional porous medium. The effect of gravity is systematically varied by tilting the system from the horizontal position. The width \ensuremath{\sigma} of the front between the fluids is found to scale with the dimensionless Bond number Bo (ratio between gravitational and capillary forces) as \ensuremath{\sigma}\ensuremath{\sim}${\mathrm{Bo}}^{\mathrm{\ensuremath{-}}0.57}$, as predicted by theory. The external perimeter of the invaded structure is shown to be fractal with the fractal dimension ${\mathit{D}}_{\mathit{e}}$\ensuremath{\simeq}1.34 for length scales smaller than the front width.

Gravity invasion percolation in two dimensions: Experiment and simulation.

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Gravity invasion percolation in two dimensions: Experiment and simulation.