A. E. Sáez

The effective homogeneous behavior of heterogeneous porous media

The macroscopic equations that govern the processes of one- and two-phase flow through heterogeneous porous media are derived by using the method of multiple scales. The resulting equations are mathematically similar to the point equations, with the fundamental difference that the local permeabilities are replaced by effective parameters. The method allows the determination of these parameters from a knowledge of the geometrical structure of the medium and its heterogeneities. The technique is applied to determine the effective parameters for one- and two-phase flows through heterogeneous porous media made up of two homogeneous porous media.

Shear and extensional rheology of solutions of modified hydroxyethyl celluloses and sodium dodecyl sulfate

This work reports on the rheology of aqueous solutions of hydroxyethyl cellulose (HEC) and three derivatives, in the presence of sodium dodecyl sulfate (SDS). The polymers employed were: a hydrophobically modified hydroxyethyl cellulose (HMHEC) containing hexadecyl grafts, a cationically modified hydroxyethyl cellulose (cat-HEC), containing glycidyl-trimethyl-ammonium grafts, and a polymer with both modifications (cat-HMHEC). Rheological measurements were performed in simple shear flow, oscillatory shear flow, opposed-jets flow and flow through porous media. The addition of surfactant increases intermolecular interactions between HMHEC molecules due to the formation of mixed micelles that bridge hydrophobic side groups from different polymer chains. These interactions lead to phase separation in an intermediate SDS concentration range and, at higher surfactant concentrations when a homogeneous phase was obtained, to higher shear and apparent extensional viscosities. Further surfactant addition eventually inhibits hydrophobe interactions due to electrostatic repulsion between micelles, leading to shear viscosities that are even lower than that of the original polymer solution. Hydrophobe interactions are inhibited by the relatively strong nature of flow in opposed-jets. The addition of cationic side groups confers the polymer a polyelectrolytic nature, which translates into higher shear and apparent extensional viscosities. Interchain interactions are strengthened by the presence of surfactant by the formation of intermolecular cross-links between polymer chains.

Flow of polymer solutions through porous media

Abstract The molecular mechanism for viscosity enhancement during the flow of poly(ethylene oxide) solutions through porous media has been investigated. Random packed beds of uniform-size spheres have been used as porous media. Experiments were conducted for one-dimensional (uniform) flow, as well as for a particular three-dimensional (nonuniform) flow situation. A substantial increase in flow resistance with respect to that exhibited by Newtonian fluids has been observed in both cases. The results obtained suggest that, under the conditions employed in the present work, the mechanism that causes the increased flow resistance is related to the formation of transient networks of polymer molecules in the flow field. The nonuniform flow results indicate that the presence of the polymer induces a change in the macroscopic flow distribution within the porous medium.

Dynamic response of a packed bed thermal storage system—a model for solar air heating

Abstract A mathematical model for simulating the dynamic temperature response of a packed column to an arbitrary time-dependent inlet air temperature is developed. The model includes axial thermal dispersion as well as intra-particle conduction, features that have usually been neglected but can be important in solar energy applications. Solutions, presented in terms of moments of the temperature response to an impulse of heat at the inlet, can be evaluated by simple numerical quadrature. Results of the model compare favorably with experimental data found in the literature. The model is used to optimize heat storage in a rock bin system subject to a realistic transient inlet temperature.

Prediction of Effective Diffusivities in Porous Media using Spatially Periodic Models

Calculations of effective diffusivities in three-dimensional, spatially periodic porous media are performed. For isotropic systems, it is found that, for a given porosity, the predicted value of the effective diffusivity matches experimental results for randomly-packed beds of spheres. Furthermore, the three-dimensional geometry yields approximately the same results as previous calculations employing two-dimensional representations, indicating a relative insensitivity of the effective diffusivity to local geometry. Regarding anisotropic systems, for which two-dimensional modes fail, it is found that there is a significant improvement in the prediction of the effective diffusivity perpendicular to the bedding plane when the three-dimensional model is employed using one adjustable parameter. However, the three-dimensional model overestimates the effective diffusivity parallel to the bedding plane.

EFFECT OF OPERATING CONDITIONS ON GAS HOLDUP IN SLURRY BUBBLE COLUMNS WITH A FOAMING LIQUID

This work presents experimental data on gas holdup in slurry bubble columns with a foaming liquid. The effects of solids concentration, solid particle size, superficial phase velocities and column dimensions on the gas holdup are analyzed. At low superficial gas velocities (less than 4cm/s), for which the liquid does not foam, the presence of solids with small particle size does not affect the gas holdup whereas solids with large particle size induce foam formation and thus their presence increases the gas holdup. In the foaming regime, an increase of solids concentration decreases the gas holdup. The operating mode has a strong effect on the gas holdup: the semi-batch operating mode (stagnant liquid-solid suspension) increases the ability of the liquid to foam with respect to the continuous mode. Regarding the effect of column dimensions, the results presented show that the height of the bubble column does not affect at an appreciable extent the gas holdup in the range 6 < LID < 12. At high gas velocitie...

Macromolecular dynamics in extensional flows: 1. Birefringence and viscometry

Abstract The opposed jets apparatus is used to investigate the dynamics of the coil-stretch transition of polymer solutions in an idealized stagnation point extensional flow-field. A linear CCD detector allows optical retardation profiles to be recorded as the strain rate is varied. A numerical transformation enables true birefringence profiles to be produced, which enable the assessment of localized molecular orientation and stretching around the stagnation point. High molecular weight, closely monodisperse aPS and PEO are studied in θ and good solvents. Flow modification effects are apparent to extremely low concentration (≈c∗/100). Under θ conditions, the width of the transition is consistent with the residual polydispersity. Simultaneous measurements of flow resistance enable the determination of the effective extensional viscosity. The increase in extensional viscosity due to molecular stretching is found to be of the order of the number of equivalent flexible units in the chain, after correction is made for the area of high molecular extension.

Extensional behavior of hydroxypropyl guar solutions: Optical rheometry in opposed jets and flow through porous media

In this work we perform an experimental characterization of the rheology of hydroxypropyl guar (HPG) solutions. The flow situations investigated are shear rheometry, elongational flow in opposed jets, and flow through porous media. The results of the experiments show that hydroxypropyl guar behaves as a semiflexible molecule in aqueous solutions under elongational flow situations. In shear flows and under semidilute conditions, the HPG solutions have a shear‐thinning behavior, whereas in opposed‐jets flow they exhibit extension thickening. In porous media flows, semidilute solutions behave as shear thinning, but there is evidence that extension thickening is present. We have developed a technique in which a linear charged‐coupled device (CCD) array is used as a retardation detector to measure birefringence profiles in opposed‐jets flow. This technique has shown that HPG molecules are stretched in the flow field, which confirms that the HPG molecules are semiflexible. The addition of a cross‐linking agent ...

Effect of intermolecular cross links on drag reduction by polymer solutions

SummaryIn this work we explore the effect of a cross-linking agent on the drag reduction capability of hydroxypropyl guar and guar gum solutions in turbulent flow through horizontal pipes. The results show that the addition of a cross-linking agent (borax) to solutions with concentrations below those required for gel formation enhances drag reduction due to the increased dimensions of the macromolecules in the presence of intermolecular cross links. The flow-induced degradation of the polymers is not appreciably affected by the addition of cross-linking agent.

Macromolecular dynamics in extensional flows: 2. The evolution of molecular strain

Abstract The opposed jets apparatus has been used to investigate the dynamics of the coil-stretch transition of polymer solutions in an idealized stagnation point extensional flow field. Flow simulations generated fluid strain profiles for different geometries. Assuming a molecular uncoiling model, true birefringence profiles have been converted to molecular strains for closely monodisperse, high molecular weight aPS under θ-conditions. This has enabled macromolecular deformation to be followed as a function of position and residence time. Non-linear hydrodynamic friction FENE dumb-bell simulations give qualitative agreement. Initially, molecular uncoiling is non-affine, consistent with changing hydrodynamic screening on extension. Deformation in a good solvent is more affine. Results are compared with PEO/water to investigate the effect of molecular parameters. The effective extensional viscosity has been ascertained by correction for the area of high molecular extension. The increase in extensional viscosity due to molecular stretching is substantial, of the order of the number of equivalent flexible units in the chain.