1. Introduction to Reservoir Engineering. 2. The General Material Balance Equation. 3. Single-Phase Gas Reservoirs. 4. Gas-Condensate Reservoirs. 5. Undersaturated Oil Reservoirs. 6. Saturated Oil Reservoirs. 7. Fluid Flow in Reservoirs. 8. Water Influx. 9. The Displacement of Oil and Gas. 10. History Matching.

Applied Petroleum Reservoir Engineering

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

(1957). DARCY'S LAW AND THE FIELD EQUATIONS OF THE FLOW OF UNDERGROUND FLUIDS. International Association of Scientific Hydrology. Bulletin: Vol. 2, No. 1, pp. 23-59.

Darcy's law and the field equations of the flow of underground fluids

This paper examines and assesses predictive methods for the saturated hydraulic conductivity of soils. The soil definition is that of engineering. It is not that of soil science and agriculture, which corresponds to “top soil” in engineering. Most predictive methods were calibrated using laboratory permeability tests performed on either disturbed or intact specimens for which the test conditions were either measured or supposed to be known. The quality of predictive equations depends highly on the test quality. Without examining all the quality issues, the paper explains the 14 most important mistakes for tests in rigid-wall or flexible-wall permeameters. Then, it briefly presents 45 predictive methods, and in detail, those with some potential, such as the Kozeny-Carman equation. Afterwards, the data of hundreds of excellent quality tests, with none of the 14 mistakes, are used to assess the predictive methods with a potential. The relative performance of those methods is evaluated and presented in graphs. Three methods are found to work fairly well for non-plastic soils, two for plastic soils without fissures, and one for compacted plastic soils used for liners and covers. The paper discusses the effects of temperature and intrinsic anisotropy within the specimen, but not larger scale anisotropy within aquifers and aquitards.

Predicting the saturated hydraulic conductivity of soils: a review

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

A method is described for studying the flow of gas‐liquid mixtures through unconsolidated sands. Results are given for experiments on four sands of widely different permeabilities using carbon dioxide and water as the fluids. A relation between permeability and liquid‐saturation of the sand is found which permits the correlation of saturation and the steady state flow of the gas and liquid components. Generalization of these results for all unconsolidated sands seems permissible. The phenomena of equilibrium permeability and equilibrium liquid‐saturation are described and their significance discussed. It is believed that the experimental attack and type of analysis is applicable to the general problem of the flow of gas‐liquid mixtures through porous media.

R. D. Wyckoff

Papers

The Flow of Gas-Liquid Mixtures Through Unconsolidated Sands