J.F. Davidson

Slug flow in fluidised beds

The paper begins by summarising theory and experimental data concerning the rate of rise of a large gas bubble or slug through an inviscid liquid in a vertical tube, or between two flat plates. Experimental data show that the theory can be used to predict the rise of slugs in fluidised beds. Theory is also given to predict the penetration of fluidising fluid from a slug into the particles; this agrees well with experiment, and is important in the design of catalytic reactors operating in the slug flow regime. A tentative theory (due to P.S.B.S.) predicts the transition from the bubble regime to the slug flow regime in a fluidised bed. The result is that slug flow will occur in a tube of diameter D if (U-Uo)/0.35 (gD)12 is greater than about 0.2, where U is the superficial velocity, Uo is the superficial velocity at incipient fluidisation, and g is the acceleration of gravity. This theory does not conflict with published observations by various authors as to the flow regime in given circumstances.

Bubble formation at an orifice in a viscous liquid

Summary A theory of bubble formation based on the motion of a bubble in a viscous liquid has been developed. The theory gives the volume of gas bubbles formed at an orifice in a viscous liquid for both constant gas flow and constant gas pressure. Experiments were carried out with liquids of high viscosity (500-1040 cp). Good agreement with theory was obtained over a large range of gas flow rates (0-50 ml/s).

The prediction of particle cluster properties in the near wall region of a vertical riser (200157)

Abstract Correlations for predicting the properties of clusters of particles travelling near the riser wall are presented. The correlations were developed from experimental data published in the literature on vertical risers ranging from laboratory to industrial scale. Expressions are presented for predicting the size, shape, density, wall film coverage and velocity of particle clusters. These expressions should prove useful in the development of heat transfer and process models for gas–solid riser flow.

The motion of a large gas bubble rising through liquid flowing in a tube

The theory presented here describes the motion of a large gas bubble rising through upward-flowing liquid in a tube. The basis of the theory is that the liquid motion round the bubble is inviscid, with an initial distribution of vorticity which depends on the velocity profile in the liquid above the bubble. Approximate solutions are given for both laminar and turbulent velocity profiles and have the form \begin{equation} U_s = U_c+(gD)^{\frac{1}{2}}\phi(U_c/(gD)^{\frac{1}{2}}), \end{equation} U s being the bubble velocity, U c the liquid velocity at the tube axis, g the acceleration due to gravity, and D the tube diameter; ϕ indicates a functional relationship the form of which depends upon the shape of the velocity profile. With a turbulent velocity profile, a good approximation to (1) which is suitable for many practical purposes is \begin{equation} U_s = U_s + U_{s0}, \end{equation} U s 0 being the bubble velocity in stagnant liquid. Published data for turbulent flow are known to agree with (2), so that in this case the theory supports a well-known empirical result. Our laminar flow experiments confirm the validity of (1) for low liquid velocities.

Regeneration of sintered limestone sorbents for the sequestration of CO2 from combustion and other systems

Abstract The capacity of particles of CaO, produced by calcining limestone, to reactively absorb CO2, degrades with the number of cycles of carbonation and calcination. A novel method of reactivating the stone in humid, ambient air is described. Typically, a calcined limestone has a carrying capacity for CO2 which falls from ∼79% (on the basis of moles of CO2 per mole of CaO) to only about 20–30% after 30 cycles of regeneration and reuse. This new technique enables the carrying capacity to be restored to ∼55%, thereby improving the economics of sequestrating CO2 using a calcium-based sorbent.

The velocity of sound in fluidised beds

Abstract The velocity of sound us in fluidised beds of particles, at or near incipient fluidisation, was measured by two methods: (1) by observing the damped pressure fluctuations immediately after giving the bed a sudden vertical impulse; (2) by cross-correlating the signals from two pressure probes, one above the other in an incipiently fluidised bed, the signals originating from a bubbling section of the bed immediately above the incipiently fluidised section. The measured values of us—of order 10 m/s—agree well with single theory which assumes that the sound wave is transmitted by compressing the interstitial gas isothermally. The sound waves are strongly damped: the theory of damping is inadequate but it appears that damping is due to: (1) inter-particle collisions, and (2) relative motion between the interstitial gas and the particles.

The investigation of a standing wave due to gas blowing upwards over a liquid film; its relation to flooding in wetted-wall columns

A theory is given to predict the shape and amplitude of a standing wave formed on a liquid film running down a vertical surface, and due to an upward flow of gas over the liquid surface. The wave is maintained in position by the pressure gradients induced within the gas stream by acceleration over the windward part of the wave; over the leeward part of the wave, the gas pressure is roughly constant due to breakaway of the gas flow. The wave amplitude is found to be very sensitive to gas velocity so that the theory predicts a critical gas velocity beyond which the wave amplitude becomes very large; this critical velocity is confirmed by experiment, and the experiments confirm the predicted wave shape. The critical gas velocity also agrees reasonably well with published values of the flooding velocity in empty wetted-wall tubes; this velocity is defined as the point at which countercurrent flow of gas and liquid becomes unstable. The phenomenon of flooding, which has puzzled chemical engineers for many years, may thus be due to wave formation on the liquid film. From the theory are derived three dimensionless groups, namely, Weber number

Elutriation from fluidized beds. I: Particle ejection from the dense phase into the freeboard

We \equiv \rho_g U_c^2t_0|T

Particle residence time distributions in circulating fluidised beds

, liquid-film Reynolds number

Gas hold-up and liquid circulation in internal loop reactors containing highly viscous newtonian and non-newtonian liquids

Re \equiv 4\rho_l Q|\mu, and Z \equiv T(\rho_l|\mu g)^{1/3}|\mu