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

In this literature survey, different aspects of dynamics of two-phase flow in porous media are discussed. This review is based on the results of developed dynamic pore-network models and their applications. Thus, those concepts of dynamics of two-phase systems are addressed that have been already discussed in previous studies. Since it is not always possible to study different aspects of laboratory experiments, dynamic pore-network models were developed to gain new insights into the process. This characteristic is the major advantage of pore-network models, which give a better understanding of the physics of a process at pore scale as well as at the scale of representative elementary volume. Dynamic pore-network models are reviewed under different classifications; structure, computational algorithm, and local rules and applications.

Analysis of Fundamentals of Two-Phase Flow in Porous Media Using Dynamic Pore-Network Models: A Review

The physics of liquids in porous media gives rise to many interesting phenomena, including imbibition where a viscous fluid displaces a less viscous one. Here we discuss the theoretical and experimental progress made in recent years in this field. The emphasis is on an interfacial description, akin to the focus of a statistical physics approach. Coarse-grained equations of motion have been recently presented in the literature. These contain terms that take into account the pertinent features of imbibition: non-locality and the quenched noise that arises from the random environment, fluctuations of the fluid flow and capillary forces. The theoretical progress has highlighted the presence of intrinsic length-scales that invalidate scale invariance often assumed to be present in kinetic roughening processes such as that of a two-phase boundary in liquid penetration. Another important fact is that the macroscopic fluid flow, the kinetic roughening properties, and the effective noise in the problem are all coupled. Many possible deviations from simple scaling behaviour exist, and we outline the experimental evidence. Finally, prospects for further work, both theoretical and experimental, are discussed.

Imbibition in disordered media

We describe the most important developments in the application of three theoretical tools to modeling of the morphology of porous media and flow and transport processes in them. One tool is percolation theory. Although it was over 40 years ago that the possibility of using percolation theory to describe flow and transport processes in porous media was first raised, new models and concepts, as well as new variants of the original percolation model are still being developed for various applications to flow phenomena in porous media. The other two approaches, closely related to percolation theory, are the critical-path analysis, which is applicable when porous media are highly heterogeneous, and the effective-medium approximation - poor man's percolation - which provides a simple and, under certain conditions, quantitatively correct description of transport in porous media in which percolation-type disorder is relevant. Applications to topics in geosciences include predictions of the hydraulic conductivity and air permeability, solute and gas diffusion that are particularly important in ecohydrological applications and land-surface interactions, and multiphase flow in porous media, as well as non-Gaussian solute transport, and flow morphologies associated with imbibition into unsaturated fractures. We describe new applications of percolation theory of solute transport to chemical weathering and soil formation, geomorphology, and elemental cycling through the terrestrial Earth surface. Wherever quantitatively accurate predictions of such quantities are relevant, so are the techniques presented here. Whenever possible, the theoretical predictions are compared with the relevant experimental data. In practically all the cases, the agreement between the theoretical predictions and the data is excellent. Also discussed are possible future directions in the application of such concepts to many other phenomena in geosciences.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1002/2017RG000558

Flow, Transport, and Reaction in Porous Media: Percolation Scaling, Critical‐Path Analysis, and Effective Medium Approximation

Direct pore-to-core up-scaling of displacement processes: Dynamic pore network modeling and experimentation

Models of two-phase flow and displacement in porous media developed so far typically involve one displacing (invader) and one displaced (defender) fluid. However, in many important applications of these phenomena at field scales, such as two-phase flow in fractured porous media, as well as in laboratory studies, require at least two invaders which also act as the defenders. The results of extensive Monte Carlo simulations of a novel model of such phenomena are reported. The porous medium is represented as a network of pore throats and pore bodies to which effective sizes are assigned that are selected from a given distribution. Both 2-D and 3-D networks are used. The simulation results indicate that the structure of the fluids` clusters is volatile, that is, it changes with the time t and length scale. Moreover, n{sub s}(S,t), the number of fluid clusters of size s, , the mean cluster size, and S(t), the saturation of the fluids all vary with t in a manner that resembles an oscillatory behavior. This behavior is caused by the dynamic breakup and recoalescence of the fluids` clusters, which is a result of simultaneous invasion of the two fluids. The flow effect of thin wetting fluids filmsmore » on the dynamics of the displacement is strong over a broad range of the capillary number. Novel dynamical scaling laws for the cluster-size distribution are obtained. Some results agree qualitatively with the experimental observations, while others provide rational explanations for some unexplained data.« less

Dynamics of two‐phase flow in porous media: Simultaneous invasion of two fluids

Percolation with Two Invaders and Two Defenders: Volatile Clusters, Oscillations, and Scaling

We report the results of extensive Monte Carlo simulations of a novel model of two-phase flow in porous media, recently proposed by us (Phys. Rev. Lett. 80 (1998) 3248), in which the two fluids act both as the invading as well as the defending fluids. The phenomenon is relevant to several multiphase flow problems in porous systems and, in particular, in fractured porous media. Our simulations show that the structure of the fluids’ clusters is volatile and changes with the time t and length scale. Moreover, n s , the number of clusters of size s , 〈 s 〉, the mean cluster size, and the fluids’ saturations all oscillate aperiodically with t , indicating the continuing breakup and recoalescence of the clusters. The effect of flow of thin films of the wetting fluid on the dynamics of the displacement is shown to be strong. Novel dynamical scaling laws for the cluster-size distribution are obtained. The results are in qualitative agreement with experimental observations.

Mehrdad Hashemi

Papers

Dynamics of two‐phase flow in porous media: Simultaneous invasion of two fluids

Percolation with Two Invaders and Two Defenders: Volatile Clusters, Oscillations, and Scaling

Monte Carlo simulation of two-phase flow in porous media: Invasion with two invaders and two defenders

Percolation with Two Invaders and Two Defenders: Volatile Clusters, Oscillations, and Scaling