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

http://www-personal.umich.edu/~kaviany/researchtopics/nam.pdf

Effective diffusivity and water-saturation distribution in single- and two-layer PEMFC diffusion medium

wide acceptance of the conclusion that most reservoirs are at wettability conditions other than VSWW. This conclusion has led to a resurgence of interest in satisfactory proce­ dures for measuring reservoir wettability and determining its effect on oil recovery, especially with respect to waterflooding. De­ termination of reservoir wettability and its effect on oil recovery by methods that in­ volve core samples will be referred to as ad­ vanced core analysis for wettability (ACAW). Reservoir wettability is not a simply de­ fined property. Classification of reservoirs as water-wet or oil-wet is a gross oversim­ plification. Various procedures for meas­ uring wettability have been proposed. Two methods of quantifying wettability based on rocklbrine/oil displacement behavior, the modified Amott test 2 and the USBM test, 3 are in common use. Each method depends on water saturation measurements and re­ lated capillary pressures or flow conditions to define a wettability scale. The tests show that reservoir wettability can cover a broad spectrum of wetting conditions that range from VSWW to very strongly oil-wet. With­ in this range, complex mixed-wettability conditions given by combinations of preferentially water-wet and oil-wet surfaces have been identified. In this paper, the 'adopted scales of reservoir wettability and their relationships to interface boundary con­ ditions are considered together with the dra­ matic effects that wettability can have on oil recovery.

Wettability and Its Effect on Oil Recovery

The mechanisms of displacement of one fluid by another are investigated in an etched network.Experiments show that both fluids are simultaneously present in a duct, the wetting fluid remaining in the extreme corners of the cross-section. Calculation of displacement pressures are in good agreement with experiments for drainage, imbibition and removal of blobs. The results may be related to some flow behaviour exhibited in porous media.

Mechanisms of the displacement of one fluid by another in a network of capillary ducts

A review of immiscible fluids in the subsurface: properties, models, characterization and remediation

Percolation theory of two phase flow in porous media

Displacement of oil from an initially oil-filled porous rock by water consists of advancement of menisci and rupture of oil connections. In displacements controlled by capillarity, which are typical of oil reservoir floods, these pore-level events are governed by the local pore geometry, pore topology, and fluid properties, but the pressure field initiates these pore-level events and integrates them with the externally imposed Darcy flow. This paper reports the physics of the pore-level and their integration on a computationally simple model of rock: a square network of pores. The novelty of the approach lies in keeping track of the evolution of the displacement front and in constructing an approximation of the entire pressure field that carries the information essential for predicting the evolution. The result gives insight into the state of the residual oil saturation and its dependence on pore geometry and the capillary number, N/sub ca/, of displacement. As the capillary number increases, the residual oil saturation decreases and the residual oil blobs tend to be smaller. As the pore size distribution becomes wider, the decrease of residual oil saturation with capillary number becomes smoother.

Physics of Oil Entrapment in Water-Wet Rock

Reaction and transport in disordered composite media: Introduction of percolation concepts

When one fluid displaces another by through a porous medium, the fraction of pore space occupied by trapped residual phase correlates with the ratio of viscos to capillary force in the flow. This dependence, heretofore unexplained, is derived from the mechanics of fluid blobs, the nature of pore strecture, and precolation theory. Pore space topology is shown to be as important as geometry in the statistical flow behaviour of large populations of fluid blobs in two-phase flow in porous media. Topology and geometry can each be modelled usefully by a single parameter characteristic of the pore space.

H. T. Davis

Papers

Percolation theory of two phase flow in porous media

Physics of Oil Entrapment in Water-Wet Rock

Reaction and transport in disordered composite media: Introduction of percolation concepts

Percolation theory of residual phases in porous media

Capillary dispersion in porous media at low wetting phase saturations