Theory of fluidization, two phase

A similar application of the concept as a slugging lifter of solids was studied by Singh (1978) based on the two-phase theory of fluidization and the properties of slugs. 

Bubbles, in fluidized beds, 11 805-806 Bubble size control, 11 805 in fluidized beds, 11 819, 821 Bubble size distribution, 12 14 in foams, 12 11 Bubble tear-offs, 20 229 Bubble tray absorbers, 1 27, 29 design, 1 83-86 Bubble-tube reactor, 25 194 Bubble tube viscometer, 21 739 Bubble two-phase theory of fluidization, 11 805-806... 

Two-Phase Theory of Fluidization The two-phase theory of fluidization assumes that all gas in excess of the minimum bubbling velocity passes through the bed as bubbles [Toomey and Johnstone, Chem. Eng. Prog. 48 220 (1952)]. In this view of the fluidized bed, the gas flowing through the emulsion phase in the bed is at the minimum bubbling velocity, while the gas flow above U j, is in the bubble phase. This view of the bed is an approximation, but it is a helpful way... 

In this context we adhere to the two-phase theory of fluidization, which states that almost all the gas in excess of that necessary for minimum fluidization will appear as... 

The distribution of gas flow in the fluidized bed is important for the analysis of the fundamental characteristics of transport properties in the bed. One common method to estimate the gas flow division is based on the two-phase theory of fluidization, which divides the superficial gas flow in the bed into two subflows, i.e., bubble phase flow and emulsion phase flow, as shown in Fig. 9.14. According to the theory, the flow velocity can be generally expressed as... 

The bubbling behavior of a bed is also determined by the fluidizing velocity uQ. According to the two-phase theory of fluidization (29), the excess velocity over that required for minimum fluidization passes through the bed in bubbles, which provides a useful, although oversimplified (30, 31) view of bubble flow. 

The two-phase theory of fluidization has been extensively used to describe fluidization (e.g., see Kunii and Levenspiel, Fluidization Engineering, 2d ed., Wiley, 1990). The fluidized bed is assumed to contain a bubble and an emulsion phase. The bubble phase may be modeled by a plug flow (or dispersion) model, and the emulsion phase is assumed to be well mixed and may be modeled as a CSTR. Correlations for the size of the bubbles and the heat and mass transport from the bubbles to the emulsion phase are available in Sec. 17 of this Handbook and in textbooks on the subject. Davidson and Harrison (Fluidization, 2d ed., Academic Press, 1985), Geldart (Gas Fluidization Technology, Wiley, 1986), Kunii and Levenspiel (Fluidization Engineering, Wiley, 1969), and Zenz (Fluidization and Fluid-Particle Systems, Pemm-Corp Publications, 1989) are good reference books. 

Flow Distribution between Phases. One of the principal assumptions underlying many of the models of fluidized bed reactors is the two-phase theory of fluidization. This theory, really no more than a postulate, holds that the flow beyond that required for minimum fluidization passes through the bed as translating void units. Although not included in what the originators of this postulate (38) appeared to have in mind, the two phase theory is often held to imply, in addition, that the dense phase voidage remains constant and equal to e - for all U > U. ... 

The dynamic and steady-state characteristics of a shallow fluidized bed combustor have been simulated by using a dynamic model in which the lateral solids and gas dispersion are taken into account. The model is based on the two phase theory of fluidization and takes into consideration the effects of the coal particle size distribution, resistance due to diffusion, and reaction. The results of the simulation indicate that concentration gradients exist in the bed on the other hand, the temperature in the bed is quite uniform at any instant in all the cases studied. The results of the simulation also indicate that there exist a critical bubble size and carbon feed rate above which "concentration runaway" occurs, and the bed can never reach the steady state. 

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... 

A first estimate for Qb is given by the two-phase theory of fluidization, proposed by Toomey and Johnstone [130] and developed by Davidson and Harrison [29, 30]. In this theory a bubbling fluidized bed consists of two zones or phases, referred to as the bubble phase consisting of pure gas and the emulsion phase consisting of uniformly distributed particles in a supporting gas steam. The emulsion phase is assumed to be operating at minimum fluidization conditions (7 m/> while the bubble phase carries the remaining gas flow U ... 

Davidson JF, Harrison D, Darton RC, LaNauze RD (1977) The Two-Phase Theory of Fluidization and its Application to Chemical Reactors. In eds Lapidus L, Amundson NR Chemical Reactor Theory, A Review. Prentice-Hall, Englewood Cliffs, New Jersey, pp 583-685... 

A size distribution of particles is always desired rather than a single size in a fluidized bed. The two-phase theory of fluidized-bed operation is suspect when a bed contains appreciable lines, and models based on uniform particles should be used with caution. The dense phase in such cases should really be regarded as consisting of two phases emulsion and clusters of lines (d < 40 pm). Indeed, the results of Yadav et al. (1994) on commercial propylene ammoxidation catalyst clearly show that the lines agglomerate. A critical level of lines (30%) was found in terms of bed expansion, aeratability, and cluster size at which fluid-bed behavior is optimum. They proposed a model that takes the two dense phase components (emulsion and cluster) into account. Adding lines widens the limits of operable gas velocities and minimizes the segregation of particles. 

In most solid-gas systems bubbling occurs when the gas velocity is increased well over the minimum fluidizing velocity. The simplest description of the expansion of a gas-fluidized bed comes from the two-phase theory of fluidization (Rhodes, 1998), originally attributed to Toomey and Johnstone (1952). This theory suggests that the bubbling fluidized bed is composed of two phases the bubbling phase and the particulate phase (also known as the emulsion phase), and that all the gas in excess of that required to fluidize the system will pass through the bed in the form of bubbles. 

A further level of detail is introduced by considering the make-up of the bed - a mixture of bubbles that contain essentially no particles and a dense emulsion phase consisting of solids and gas in intimate contact (from the two phase theory of fluidization - see Chapter 7). The overall bed density is thus a function of the density of the particulate solids, the proportion of sohds and gas in the emulsion phase and the proportion of the bed occupied by bubbles. 

As a first approximation, we will the simple two phase theory of fluidization (see Chapter 7), which means that the average particulate phase voidage will be taken as the voidage at minimum fluidization f and the bubble fraction will be given by Equation (7.28) ... 

Based on extensive studies involving a variety of solid particles and fluids with a wide range of properties, Geldart (1973) classified the fluidization behavior of systems under four categories of particles A, B, C, and D (Figure 9.2). Class B particles conform strictly to the two-phase theory of fluidization described earlier the gas in excess of that needed... 

It is always desirable to have a size distribution of particles rather than a single size in a fluidized bed. The two-phase theory of fluidized-bed... 

Minimum fluidization velocity Two-phase theory of fluidization Geldart s classification... 

The two-phase theory of fluidization was first proposed by Toomey and Johnstone (1952). The model assumed that the aggregative fluidization eonsists of two phases, i.e., the particulate (or emulsion) phase and the bubble phase. The flow rate through the emulsion phase is equal to the flow rate for minimum fluidization, and the voidage is essentially constant at Sn,f. Any flow in excess of that required for minimum fluidization appears as bubbles in the separate bubble phase. Mathematically, the two-phase theory can be expressed as... 

The discouraging result with the previous approach has then led to the development of a sequence of models based on the two-phase theory of fluidization... 

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