Theory two-phase

Conventional filtration theory has been challenged a two-phase theory has been appHed to filtration and used to explain the deviations from paraboHc behavior in the initial stages of the filtration process (10). This new theory incorporates the medium as an integral part of the process and shows that the interaction of the cake particles with the medium controls filterabiHty. It defines a cake-septum permeabiHty which then appears in the slope of the conventional plots instead of the cake resistance. This theory, which merely represents a new way of interpreting test data rather than a new method of siting or scaling filters, is not yet accepted by the engineering community. 

Figure 40. Deviation from two-phase theory for model of bubbling fluidized bed...

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. 

The results of an example calculation for a recirculating fluidized bed coal devolatilizer of 0.51 m in diameter handling coal of average size 1200 pm at 870°C and 1550 kPa are presented in Fig. 11. The calculation is based on operating the fluidized bed above the draft tube at 4 times the minimum fluidization velocity. It is also based on the selection of a distributor plate to maintain the downcomer at the minimum fluidization condition. If the two-phase theory applies, this means that the slip velocity between the gas and the particles in the downcomer must equal to the interstitial minimum fluidizing velocity as shown below. 

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... 

Thus, the bubbling region, which is an important feature of beds operating at gas velocities in excess of the minimum fluidising velocity, is usually characterised by two phases — a continuous emulsion phase with a voidage approximately equal to that of a bed at its minimum fluidising velocity, and a discontinous or bubble phase that accounts for most of the excess flow of gas. This is sometimes referred to as the two-phase theory of fluidisation. 

Essentially aggregative fluidization is a two-phase system there is a dense phase (sometimes reterred to as the emulsion phase), which is continuous, and a discontinuous phase called the lean or bubble phase. The simplitied assumption that all the gas over and above that required tor minimum fluidization flows up through the bed in the form ot bubbles is known as the two-phase theory. It the total volumetric flow ot gas is Q then... 

Two-Phase theory of Davidson According to the two-phase theory, two phases exist in the bubbling fluidized bed (a) the bubbling phase consisting of gas bubbles, and (b) the particulate phase, namely the solids around the bubbles. The particulate phase is alternatively called the emulsion phase. Bubbles stay in the bubble phase and penetrate only a small distance into the emulsion phase. This zone of penetration is called cloud since it envelops the rising bubble. 

Gas in the emulsion phase in plug flow In this case, the following are assumed (a) two-phase theory applies (bubble and particulate phases), (b) plug flow of gas throughout the reactor, i.e. in the bubble and emulsion phase. This model is referred to as the two-phase model with plug emulsion phase (Kelkar and Ng, 2002). 

Ward and his associates355 have also used two phase theories to explain the viscoelastic properties of polymers. 

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... 

Applying the simple two-phase theory to the slugging bed, the average slug velocity in continuous slugging flows can be expressed by [Ormiston et al 1965]... 

Assume that the simple two-phase theory can be applied and the following relationship holds... 

Derive Eqs. (P10.10) and (P10.11) on the basis of the conditions stated. In deriving these equations, consider also the simple two-phase theory (see 9.4.5), which gives the particle velocity above the gas slug as U — Umf. 

Chemical reactor models invariably start from the two-phase theory (12). The interstitial flow is assumed to be in good and continuous contact with solids whilst some by-passing occurs in the bubble phase. There is, however, very little axial or radial mixing of the gas. There may be some exchange between the two phases and Figure 4 depicts this kind of model. 

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. 

Using Porod s two-phase theory of small-angle X-ray scattering Kim140) has analyzed the intensity data for an unoriented molded sample of Kraton 101 and found that the interface between the styrene and butadiene phases is sharp. 

Distribution of flow between phases Two phase theory 2-ct) theory + cloud or U through mr. emulsion Two phase theory Two phase theory... 

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. ... 

Much has been written and said about the two phase theory... 

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... 

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