Fluidization, point of incipient

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... 

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. 

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

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... 

Moving-bed operations in which the particles are poised by hydrodynamic drag against gravity to the point of incipient fluidization is represented by Eq. (3.5) when 0 is substituted for e ... 

For the counter-down moving bed, such as shaft furnaces, and shown by the AB segment of the e0 = 0.4 line in Fig. 11, fluid velocity can be assigned any value from zero to the point of incipient fluidization, B. The counter-down moving bed can be operated at fluid velocity less than that specified by Eq. (3.5m), resulting, however, in a pressure gradient less than that for incipient fluidization, L0 Ap(l — e0). This reduced pressure gradient can be prorated in accordance with the theory for idealized fluidization ... 

Group A represents the best powders. They are fine and aeratable, such as cracking catalyst. They fluidize nicely, and expand particulately after reaching the point of incipient fluidization mf, until the first bubbles appear at a higher velocity, the minimum bubbling velocity umb. It is thus evident that the ratio of umJum is always greater than unity, and the greater is this value, the better the powder performs in fluidization. 

Applying Eq. (7-50) to the point of incipient fluidization gives a quadratic equation for the minimum fluidization velocity K)Af-... 

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 complete fluidization, the top of the bed Lc, which is at incipient fluidization, is at fluid velocity uf ... 

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. 

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. 

At the incipient point of fluidization, the pressure drop of the bed will be very close to the weight of the particles divided by the cross-sectional area of the bed (W/A). For the normal gas fluidized bed, the density of the gas is... 

Fluidization of solid particles with these two widely different classes of fluids—liquids and gases—leads to vastly different phenomena of solids behavior, as shown in Fig. 3. For L/S fluidization, as liquid velocity increases beyond the incipient fluidization point, the solids bed continues to expand as if it were an elastic continuum stretching under the dynamic forces of augmented flow, until, near the terminal velocity of the particles, the solid particles can be noted to be suspended sparsely. Throughout this process of liquid-velocity increase, the solid particles are dispersed quite uniformly, fully exhibiting their discrete behavior, essentially independent of one another. Therefore, L/S fluidization was named particulate. ... 

Let us consider a shallow fluidized bed combustor with multiple coal feeders which are used to reduce the lateral concentration gradient of coal (11). For simplicity, let us assume that the bed can be divided into N similar cylinders of radius R, each with a single feed point in the center. The assumption allows us to use the symmetrical properties of a cylindrical coordinate system and thus greatly reduce the difficulty of computation. The model proposed is based on the two phase theory of fluidization. Both diffusion and reaction resistances in combustion are considered, and the particle size distribution of coal is taken into account also. The assumptions of the model are (a) The bed consists of two phases, namely, the bubble and emulsion phases. The voidage of emulsion phase remains constant and is equal to that at incipient fluidization, and the flow of gas through the bed in excess of minimum fluidization passes through the bed in the form of bubbles (12). (b) The emulsion phase is well mixed in the axial... 

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