Fundamental Principles Laminar Boundary Layer Flow Laminar Duct Flow External Natural Convection Internal Natural Convection Transition to Turbulence Turbulent Boundary Layer Flow Turbulent Duct Flow Free Turbulent Flows Convection with Change of Phase Mass Transfer Convection in Porous Media.

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Convection Heat Transfer

Principles and potential of the anaerobic digestion of waste-activated sludge

The flow of homogeneous fluids through porous media: analogies with other physical problems

The volumetric and thermodynamic functions correlated by Pitzer and co-workers analytically represented with improved accuracy by a modified BWR equation of state. The representation provides a smooth transition between the original tables of Pitzer et al. and more recent extensions to lower temperatures. It is in a form particularly convenient for computer use.

A generalized thermodynamic correlation based on three‐parameter corresponding states

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

A new solution to the kinetics of a fixed-bed adsorber in response to a step change in feed concentration is obtained for a linear equilibrium system, considering the resistance to mass transfer in both the mobile and stationary phases. The differential equations of continuity and mass transfer are integrated by simulating the intraparticle concentration profile with a parabola. The results agree with Rosen's rigorous but complex solution.

Kinetics of fixed‐bed adsorption: A new solution

A group contribution molecular model is developed for the thermodynamic properties of polar and nonpolar liquids and their solutions, including energy of vaporization, ρVT relations, excess properties, and activity coefficients. The model is based on the cell theory in which the repulsive forces of molecules are expressed with a modified cell partition function derived from the Carnahan-Starling equation of state for hard spheres. The attractive forces are made up of group pair interaction contributions. Group and interaction properties have been determined for methyl, methylene, hydroxyl, and carbonyl. Extensive comparisons are made of predictions of the model with data for pure liquids and their solutions.

A group contribution molecular model of liquids and solutions

A random network model of a porous medium with nonuniform pores has been constructed. Nonuniformity is achieved by assigning two-parameter distributions to pore radius and pore length. Statistical derivations result in expressions for bulk model properties which are consistent with known empirical behavior of porous media such as capillary pressure, hydraulic permeability, and longitudinal and transverse dispersion. A series of experiments is suggested whereby the parameters of porous media structure may be determined from observed macroscopic behavior by using the expressions developed in this paper.

A statistical model of a porous medium with nonuniform pores

An equation of state is obtained to describe the fluid state from the supercritical gas to subcritical vapor and liquid for small and large molecules of organic and inorganic substances. The perturbation theory of the fluid state is extended to include rotational contribution of molecular motion in addition to translational and the attractive force contributions. Three equation constants describe a substance and values are presented for 22 substances. Application is made to mixtures with emphasis on their phase equilibria.

Chain‐of‐rotators equation of state

This paper describes a preliminary study of the linear flow of a non-Newtonian fluid, a water solution of Dextra (a polysaccharide), in porous media. A modification of Darcy's law, which uses capillary rheology data, is developed to describe non-Newtonian flow in underground reservoirs. The generalization, in effect, replaces the porous media with a capillary of equivalent radius proportional to the square root of the ratio of permeability to porosity. The constant of proportionality αo should be independent of permeability and porosity for a given type of rock. This has been partially confirmed experimentally. In principle, a capillary rheogram and a single core test permit evaluation of αo. Then non-Newtonian flow can be predicted in this type of rock regardless of porosity, permeability, or flow rate.

Robert A. Greenkorn

Papers

Kinetics of fixed‐bed adsorption: A new solution

A group contribution molecular model of liquids and solutions

A statistical model of a porous medium with nonuniform pores

Chain‐of‐rotators equation of state

Non‐Newtonian flow in porous media