••1997••

D.D. Joseph, 1997.
Technical Forum - Questions in fluid mechanics: Understanding foams and foaming,
J. Fluids Engineering, 119, 497-498.

Abstract

Foams are common, complex, and not well understood. Most of the common foams are a two-phase medium of gas and liquid with a particular structure consisting of gas pockets trapped in a network of thin liquid films and Plateau borders.

••1998••

J. Guitian, D. D. Joseph, 1998.
How bubbly mixtures foam and foam control using a fluidized bed,
Int. J. Multiphase Flow, 24(1), 1-16.

Abstract

In hydrocracking and other foaming reactors, the foam rises to the top because it has a higher gas fraction than the bubbly mixture from which it comes. The high gas hold-up in foams is undesirable in chemical reactors because it strongly decreases the liquid residence time and in hydrocracking reactors also promotes the formation of coke. To study foams we built a cold slit bubble reactor which when used with aqueous anionic surfactants gives rise to foam. This reactor reproduces the foaming processes which are characteristic of the commercial system CANMET from Petrocanada. We discovered a critical condition for foaming; when the gas velocity exceeds a critical value which depends on the liquid velocity, a foam interface appears at the top of the reactor, with foam above and bubbly mixture below. The interface is very sharp and it moves down the reactor as the gas velocity is increased at a constant liquid velocity. This is the way reactors foam, with the bubbly mixture being consumed by foam.

The foam may be destroyed by increasing the liquid velocity backing up against the foaming threshold. The reactor partitions into two phase, two phase ow with bubbly mixture below and foam above. The bubbly mixture is dispersed gas in water plus surfactant; the phase above is a foam through which large gas bubbles rise. Constant state theories for the bubbly mixture, the foam and the position of the foam interface are derived and semiempirical correlations are presented.

Foaming may be strongly suppressed by fluidizing hydrophilic particles in the bubbly mixture below the foam. The suppression is achieved by increasing the liquid hold-up by bed expansion; by increasing the wetted area of solid surface (walls and particles) and by decreasing the gas hold-up by increasing the effective density of liquid-solid mixture.

••1999••

C. Mata, D.D. Joseph, 1999.
Foam Control using a fludized bed of hydrophobic particles,
Int. J. Multiphase Flow, 25(1), 63-85.

Abstract

Applications of foams and foaming are found in many industries like the flotation of minerals, enhanced oil recovery, drilling in oil reservoirs, insulation, construction and refining processes such as Vacuum distillation and Delay-Coker reactors. However, foaming and defoaming are not yet understood. Foams trap gas and are not wanted in many applications. Guitian and Joseph (1997) proposed fundamental studies of their observations on foam suppression experiments they carried out in a cold slit bubble reactor. They found that foaming may be strongly suppressed by fluidizing hydrophilic particles in the bubbly mixture below the foam. They suggest that the suppression is achieved by increasing the wetted area of solids surface (walls and particles), by bed expansion and by decreasing the gas hold-up by increasing the effective density of the liquid solid mixture.

Frye and Berg (1989) studied the antifoam action of hydrophobic particles using two different tests (particle-induced film rupture and foam shake test), but they did not use a fluidized bed. Armstrong et at. (1976) observed adhesion of air bubbles to Teflon-coated glass beads fluidized in water. Tsutsumi, Dastidar and Fan (1991) studied the characteristics of water-air-solid fluidization with non-wettable (hydrophobic) particles and classified the flow pattern according to the motion of the particle-bubble aggregates. In this work, we fluidized hydrophobic and hydrophilic versions of two different sands in the same slit bubble reactor Guitian and Joseph (1997) used. We found that the hydrophobic sands suppress the foam substantially better than their hydrophilic counterparts. We also observed that, when foam is not present in the reactor (i.e. at high liquid velocities), the gas hold-up in the bubbly mixture was higher for the hydrophobic version of one sand. This result may be explained in terms of attachment of the particles onto the air bubbles, which increases the residence time of the gas phase, as suggested by Tsutsumi et al. (1991). In the other hand, the gas hold-up in the bubbly mixture for the hydrophobic version of the other sand was smaller. A possible explanation is supported by Armstrong et al. (1976) findings. They suggested that the phenomenon of bubble adhesion to the non-wettable particle leads to a decrease in the apparent density of the particle, which in turn is responsible for a larger bed expansion and smaller gas holdup compared with wettable particle systems. These results suggest that the degree of hydrophobicity matters.

Hydrophobic particles appear to break, and not only to suppress, foam; and they may have a greater application.

••2002••

D.D. Joseph, A. Kamp, R. Bai, 2002.
Foamy oil flow in porous media,
Int. J. Multiphase Flow, 28(10), 1659-1686.

Abstract

Certain heavy oils which foam under severe depressurization give rise to increased recovery factor and an increased rate of production under solution gas drive. These oils not only stabilize foam, but also stabilize dispersion of gas bubbles at lower volume ratios. The way this phenomenon is related to the chemistry of the oil and its viscosity is presently not understood. We present here a mathematical model of reservoir flow of foamy oil which depends only on the velocity through Darcy’s law, the pressure and the dispersed gas fraction. The theory governs only in situations in which the bubbles do not coalesce to produce the percolation of free gas. In this theory the bubbles move with the oil as they evolve. The main empirical content of the theory enters through the derivation of solubility isotherms which can be obtained from PVT data; modeling of nucleation, coalescence, bubble drag laws and transfer functions are avoided. The local pressure difference and dispersed gas fraction are in equilibrium on the solubility isotherm. In a pressure drawdown the time taken for the system to return to equilibrium is described by a rate law characterized by an empirical relaxation time (rate constant). The resulting systems of equations can be reduced to a coupled pair of nonlinear PDE’s for the dispersed gas fraction and pressure difference, which can further be reduced in the equilibrium case to a second order evolution equation for the pressure difference. This system of equations can also be derived from usual theory of two-phase flow in a porous media based on relative permeability under the assumption that the bubbles and oil move in lock step. We propose a reformulation of the conventional theory in which the concept relative permeability of the porous media is replaced with the more familiar concept of an effective phase viscosity. The equations of our relaxation theory are solved numerically, and the mixture viscosity function and relaxation time are selected to match the sandpack experiments of Maini and Sarma [1994].

••2003••

D.D. Joseph, A. Kamp, R. Bai, 2003.
Foamy oil flow in porous media II: Nonlinear Relaxation Time Model of Nucleation,
Int. J. Multiphase Flow, 29(9), 1489-1502.

In a previous communication, here called Part I, we presented a model of the flow of foamy oil in porous media in situations in which the bubbles do not coalesce to produce the percolation of free gas so that the gas moves with the oil as it evolves. A central role in that theory is an equation of state, called the solubility isotherm, which describes an equilibrium between the fraction of dispersed gas and the pressure below the bubble point pressure. A rate equation governing the return to equilibrium was postulated and it requires a value for the relaxation constant multiplying . The theory developed in Part I was applied to experimental data and good agreements were achieved except for sharp transients at early times such as those that occur for sudden drops of pressure at the open end of the closed sand pack. In the present theory we introduce two rates and two relaxation times to describe the dynamics of relaxation of the system to an equilibrium state; one rate for and the other for the pressure as was suggested already in Part I. However, we found that constant relaxation times could not be found to fit all the available data. We interpret this in terms of bubbles nucleating more slowly at initial drawdowns, and more rapidly as gas and vapor is released when the pressure is held below the bubble point. This feature has been more or less successfully addressed by the introduction of two relaxation functions of the gas fraction which allows us to describe the low rates of evolution of when is zero or close to it. The relaxation functions were fit to one rate of depletion in a depletion experiment in which oil is pulled out of a closed sand pack at a constant rate. With this selection of the relaxation function established, the set of governing PDEs is fixed and may be used to predict the results of other experiments. The prediction of the pressure profiles for other greatly different rates of depletion is satisfactory. Moreover, the experimental results processed in Part I, are improved by the new theory with the same fitting.

M.I. Briceño, D.D. Joseph, 2003.
Self-lubricated transport of aqueous foams in horizontal conduits,
Int. J. Multiphase Flow, 29(12), 1817-1831.

The flow characteristics of aqueous foams were studied in a thin flow channel and a round pipe instrumented for pressure gradient and flow rate measurements. The quality of the foam was varied by controlling the volumetric flow rate of liquid and gas, and different flow types were identified and charted. Uniform foams move as a rigid body lubricated by water generated by breaking foam at the wall. A lubrication model leading to a formula for the thickness of the lubricating layer is presented. The formula predicts a layer thickness of 6-8 in the channel and 10-12 in the pipe. The thickness depends weakly on foam quality. An overall correlation for the friction factor as a function of Reynolds number which applies to both channel and pipe is derived. This correlation is consistent with a model in which a rigid core of foam is lubricated by laminar flow of a water layer in the range of measured thickness.

© 2003 Elsevier Ltd. All rights reserved.

Keywords: Foam; Lubrication; Flow pattern; Foam quality; Lubrication foam flow in pipes