Incipient fluidization

Heterogeneous fluidization Homogeneous fluidization Incipient fluidization Lean phase Minimum fluidization... 

The superficial fluid velocity at which the packed bed becomes a fluidized bed is known as the minimum fluidization velocity, Lfmf- This is also sometimes referred to as the velocity at incipient fluidization (incipient meaning beginning). Umi increases with particle size and particle density and is affected by fluid properties. It is possible to derive an expression for Lfmf by equating the expression for pressure loss in a fluidized bed [Equation (7.2)] with the expression for pressure loss across a packed bed. Thus recalling the Ergun equation [Equation (6.11)] ... 

Fluidization may be described as incipient buoyancy because the particles are still so close as to have essentially no mobility, whereas the usual desire in fluidization is to create bed homogeneity. Such homogeneity can be achieved only by violent mixing. This is brought about by increasing the fluid velocity to the point of blowing "bubbles" or voids into the bed, which mix the bed as they rise. The increased fluid velocity at which bubbles form first is referred to as the incipient (or minimum) bubbling velocity. 

Observations of bubbles emerging through the bed surface show that bubble shape is markedly dependent on liquid velocity. This indicates the existence of a relationship between bed viscosity and liquid velocity. A bed near incipient fluidization is characterized by a high viscosity, and an emerging bubble is of nearly spherical shape, whereas a fluidized bed of high porosity is characterized by a viscosity not very much higher than that of water, so that an emerging bubble is of spherical cap shape. 

Ostergaard (02) measured the wall-to-bed heat-transfer coefficient in a bed of 3-in. diameter. The media were air, water, and glass ballotini of0.5-mm diameter. It was observed that the heat-transfer coefficient for a liquid fluidized bed near the point of incipient fluidization could be approximately... 

The bubbles play the role of the gas phase. The role of the liquid is played by an emulsion phase that consists of solid particles and suspending gas in a configuration similar to that at incipient fluidization. The quasi-phases are in cocurrent flow, with mass transfer between the phases and with a solid-catalyzed reaction occurring only in the emulsion phase. The downward flow of solids that occurs near the walls is not explicitly considered in this simplified model. 

Values for the various parameters in these equations can be estimated from published correlations. See Suggestions for Further Reading. It turns out, however, that bubbling fluidized beds do not perform particularly well as chemical reactors. At or near incipient fluidization, the reactor approximates piston flow. The small catalyst particles give effectiveness factors near 1, and the pressure drop—equal to the weight of the catalyst—is moderate. However, the catalyst particles are essentially quiescent so that heat transfer to the vessel walls is poor. At higher flow rates, the bubbles promote mixing in the emulsion phase and enhance heat transfer, but at the cost of increased axial dispersion. 

The velocity at which gas flows through the dense phase corresponds approximately to the velocity that produces incipient fluidization. The bubbles rise, however, at a rate that is nearly an order of magnitude greater than the minimum fluidization velocity. In effect, then, as a consequence of the movement of solids within the bed and the interchange of fluid between the bubbles and the dense regions of the bed, there are wide disparities in the residence times of various fluid elements within the reactor and in... 

Now the criterion for incipient fluidization is that the force due to the pressure drop must balance the weight of the bed, i.e.,... 

Equation (14-8) gives the (dimensionless) superficial velocity (Fmf) for incipient fluidization. 

The minimum bed porosity at incipient fluidization for nonspherical particles can be estimated from... 

Figure 23.1 Schematic representation of (incipient) particle movement brought about by upward flow of a fluid, leading to fluidization...

AB (- AP) increases with increasing us (slope in Figure 23.4 is about 2), as the bed retains the character of a fixed bed, with g increasing somewhat BC (- AP) is relatively constant, as the bed becomes fluidized B is the point of incipient fluidization at Umf. 

As the fluid velocity is increased the drag on the particles increases and a point is reached where the pressure drop balances the effective weight of bed per unit cross-sectional area. At this point the fluid drag just supports the solid particles. A small increase in the flow rate causes a slight expansion of the bed from its static, packed state. Further increase in the flow rate allows the bed to expand more and the particles become free to move around and the bed is said to be fluidized. The state when the bed just becomes fluidized is known as incipient, or minimum, fluidization. The fluid velocity required to cause incipient fluidization is called the minimum fluidization velocity and is denoted by umf. 

Neglecting the static head component of the pressure drop, a force balance at the point of incipient fluidization can be written as... 

The best method of determining the minimum fluidization velocity umf is experimentally, by measuring the pressure drop across the bed over a range of fluid velocities. The pressure drop increases linearly until fluidization occurs and then increases very slowly indeed up to about twice the minimum fluidization velocity the pressure drop may appear to be constant within experimental error. When a bed is initially fluidized, there is a tendency for the pressure drop across the bed to be rather high and to go through a peak as incipient fluidization occurs. It is possible that this is caused by a need to unstick the particles. If the fluid velocity of an already fluidized bed is reduced, the peak in the pressure drop is not observed and a much clearer transition to the linear pressure drop—flow... 

If it is possible to measure the height of the bed at incipient fluidization, Lmf, then emf can be calculated from equation 9.34 or simply from the ratio of Lmf to the height of the packed bed if the void fraction in the latter is known. 

Consider a bed of particulate solids or powder, say of a size similar to table salt. When a fluid, either a gas or a liquid, is passed upwards through the bed, the bed particles remain stationary or packed at low fluid velocities. This is a packed or fixed bed. If now the velocity of the fluid is increased, fhe particles will begin to separate and move away from one another the bed is said to expand. On increasing the velocity further, a point will be reached at which the drag force exerted by the fluid on a particle is balanced by the net weight of the particle. The particles are now suspended in the upward-moving stream of fluid. This is the point of minimum fluidization, or incipient fluidization, at and beyond which the bed is said to be fluidized. 

At the point of incipient fluidization the drag force exerted on a particle is equal to its net weight. For the whole particle bed the drag force can be equafed fo the product of bed pressure drop AP and bed cross-secfional area A. The nef bed weighf is fhen the product of bed volume, nef densify, fhe fracfion of fhe bed (1 - e) which is occupied by parficles and fhe accelerafion due to gravity Thus, at minimum fluidizing velocity... 

Richardson, J.F., Incipient fluidization and particulate systems, in Davidson, J.F. and Harrison, D., (eds.). Fluidization, Academic Press, London, 1971. 

Assume that the volume of dense phase, the fraction solids in it, and the gas flow through it remain the same at all gas velocities, in which case, the lean phase alone expands and contracts to account for the variation in total volume of fluidized bed with change in gas flow rate. The dense-phase characteristics are given by the conditions at incipient fluidization. 

From Levenspiel, O., Chemical Reaction Engineering/ John Wiley, New York, 1962. As given by conditions of incipient fluidization. 

---