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

The effect of pore-structure upon two-phase relative permeability and capillary pressure of strongly-wetting systems at low capillary number is simulated. A pore-level model consisting of a network of pore-bodies interconnected by pore-throats is used to calculate scanning loops of hysteresis between primary drainage, imbibition and secondary drainage. The pore-body to pore-throat aspect ratio strongly influences the pattern of hysteresis. Changes in the patterns of hysteresis often attributed to consolidation can be understood in terms of changes in aspect ratio. Correlation between the sizes of neighboring pore-throats affects the shape of the relative permeability curves, while the width and shape of the pore-size distribution have only a minor influence.

The effect of pore-structure on hysteresis in relative permeability and capillary pressure: Pore-level modeling

This monograph describes recent progress in modelling the transport properties of sedimentary rock. Statistical descriptions are applied to the pore-space geometry and to the transport processes involving pore fluids. Fractals are used to quantify the pore geometry at length scales shorter than grain size. Percolation theory is applied to fluid flow. The permeability can be expressed in terms of a single effective pore diameter measured from mercury injection capillary pressure. This permeability relation is valid for essentially all porous rock and for a broad class of porous media. Mercury injection provides a powerful caliper of the geometry of a percolation cluster in a pore-space and supplies new information about pore space correlations and dynamics of fluid displacements. The statistical description of fluid transport in porous media has analogues in disordered electronic and magnetic materials. Future work may make substantial use of such analogues to solve more complex problems of direct...

The microgeometry and transport properties of sedimentary rock.

Globally, evaporation consumes about 25% of solar energy input and is a key hydrologic driver with 60% of terrestrial precipitation returning to the atmosphere via evapotranspiration. Quantifying evaporation is important for assessing changes in hydrologic reservoirs and surface energy balance and for many industrial and engineering applications. Evaporation dynamics from porous media reflect interactions between internal liquid and vapor transport, energy input for phase change, and mass transfer across air boundary layer. We reviewed recent advances on resolving interactions between soil intrinsic properties and evaporation dynamics with emphasis on the roles of capillarity and wettability affecting liquid phase continuity and capillary driving forces that sustain Stage I evaporation. We show that soil water characteristics contain information for predicting the drying front depth and mass loss at the end of Stage I and thus derive predictions for regional-scale evaporative water losses from soil textural maps. We discuss the formation of secondary drying front at the onset of Stage II evaporation and subsequent diffusion-controlled dynamics. An important aspect for remote sensing and modeling involves nonlinear interactions between wet evaporating surfaces and air boundary layer above (evaporation rate is not proportional to surface water content). Using pore scale models of evaporating surfaces and vapor transport across air boundary layer, we examined the necessary conditions for maintenance of nearly constant evaporation while the surface gradually dries and the drying front recedes into the soil. These new insights could be used to improve boundary conditions for models that are based on surface water content to quantify evaporation rates.

Advances in Soil Evaporation Physics—A Review

We consider the quasistatic displacement of a nonwetting fluid by a wetting one in a porous medium in the presence of buoyancy forces. A simple percolation model of this process is presented and analyzed both theoretically and by Monte Carlo simulation. It is shown that the fact that percolation is a critical phenomenon, with diverging correlation length at the critical point, has a significant effect on the physics of the system, in particular on the dependence of nonwetting phase residual saturation on the density contrast between the phases. An extension of these ideas to the case where the pressure field is generated by viscous rather than buoyancy forces is suggested.

Percolation model of immiscible displacement in the presence of buoyancy forces

The observable consequences of percolation models of immiscible displacement in porous media are discussed, with emphasis on the critical behavior. At the microscopic level, these include the fractal nature of the nonwetting fluid configuration at breakthrough in drainage, and the size distribution of the residual nonwetting clusters in imbibition. At the macroscopic level, it is suggested that percolation ideas are consistent with the usual multiphase Darcy equations, and critical behaviors of the relative permeability and capillary pressure curves are obtained. By using these results, predictions are made for the shape of the fluid saturation profiles near the percolation thresholds in the presence of buoyancy or viscous pressure gradients. Finally, it is pointed out that very close to the percolation thresholds, the diverging correlation length requires these macroscopic ideas to be modified. A simple way of doing this is suggested.

Percolation effects in immiscible displacement.

Resistance jumps in mercury injection in porous media.

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Percolation model of immiscible displacement in the presence of buoyancy forces

Percolation effects in immiscible displacement.

Resistance jumps in mercury injection in porous media.