Multi-phase Flows

A. M. Nazar and T. W. Clyne in T. N. Vezkoglu, ed.. Proceedings Multi-Phase Flow and Heat Transfer Symposium Hemisphere, Washington, D.C., 1980. 

For additional information, see Simpson (Chem. Eng., 75(6), 192-214 [1968]). A critical Fronde number of 0.31 to ensure vented flow is widely cited. Recent results (Thorpe, 3d Jnt. Conf. Multi-phase Flow, The Hague, Netherlands, 18-20 May 1987, paper K2, and 4th Int. Conf. Multi-phase Flow, Nice, France, 19-21 June 1989, paper K4) show hysteresis, with different critical Fronde numbers for flooding and untlooding of drain pipes, and the influence of end effects. Wallis, Crowley, and Hagi (Trans. ASME J. Fluids Eng., 405 13 [June 1977]) examine the conditions for horizontal discharge pipes to run full. 

The effect of physical processes on reactor performance is more complex than for two-phase systems because both gas-liquid and liquid-solid interphase transport effects may be coupled with the intrinsic rate. The most common types of three-phase reactors are the slurry and trickle-bed reactors. These have found wide applications in the petroleum industry. A slurry reactor is a multi-phase flow reactor in which the reactant gas is bubbled through a solution containing solid catalyst particles. The reactor may operate continuously as a steady flow system with respect to both gas and liquid phases. Alternatively, a fixed charge of liquid is initially added to the stirred vessel, and the gas is continuously added such that the reactor is batch with respect to the liquid phase. This method is used in some hydrogenation reactions such as hydrogenation of oils in a slurry of nickel catalyst particles. Figure 4-15 shows a slurry-type reactor used for polymerization of ethylene in a sluiTy of solid catalyst particles in a solvent of cyclohexane. 

Grolmes, M. A., A Simple Approach to Transient Two-Phase Level Swell, Multi-Phase Flow and Heat Transfer III. Part A Fundamentals. Proceedings of the Third Multi-Phase Flow and Heat Transfer Symposium—Workshop, Miami Beach, FL, April 18-20, 1983. 

Fauske, H. K., Turbulent and Laminar Flashing Flow Considerations, Paper Presented at the 4th International Symposium on Multi-phase Flow, Miami Beach, FL, December 15-17, 1986. 

Ismail, 1. et al. (2003) Tomography for multi-phase flow measurement in the oil industry. 4th International Symposium on Measurement Techniques for Multiphase Flows, 2003, Fiangzhou. 

In the above equations, a is a coefficient with the value of 1.0 for single phase flow and 2.0 for multi-phase flow [6], and pis an adjustable coefficient and has a value of 2.1 by fitting the experimental results for the two phase flow. The flow resistant coefficient is determined by the Blasius equation. 

In most cases the only appropriate approach to model multi-phase flows in micro reactors is to compute explicitly the time evolution of the gas/liquid or liquid/ liquid interface. For the motion of, e.g., a gas bubble in a surrounding liquid, this means that the position of the interface has to be determined as a function of time, including such effects as oscillations of the bubble. The corresponding transport phenomena are known as free surface flow and various numerical techniques for the computation of such flows have been developed in the past decades. Free surface flow simulations are computationally challenging and require special solution techniques which go beyond the standard CFD approaches discussed in Section 2.3. For this reason, the most common of these techniques will be briefly introduced in... 

D. Avlonitis, A. Danesh, A. C. Todd, and T. Baxter. The formation of hydrates in oil-water systems. In Proceedings Volume, pages 15-34. 4th Bhran Multi-Phase Flow Int Conf (Nice, France, 6/19-6/21), 1989. 

Pore shape is a characteristic of pore geometry, which is important for fluid flow and especially multi-phase flow. It can be studied by analyzing three-dimensional images of the pore space [2, 3]. Also, long time diffusion coefficient measurements on rocks have been used to argue that the shapes of pores in many rocks are sheetlike and tube-like [16]. It has been shown in a recent study [57] that a combination of DDIF, mercury intrusion porosimetry and a simple analysis of two-dimensional thin-section images provides a characterization of pore shape (described below) from just the geometric properties. 

Yabe, T. Interface Capturing and Universal Solution of Solid, Liquid and Gas by CIP Method . Proceedings of the High-Performance Computing of Multi-Phase Flow, Tokyo, July 18-19, 1997. 

Fauske, H. K., M. A. Grolmes, and J. C. Leung, "Multi-Phase Flow Considerations in Siting Emergency Relief Systems for Runaway Chemical Reactions," Multi-Phase Flow and Heat Transfer III-B, Applications, 899 (1984), Elsevier, Amsterdam, The Netherlands. 

The PDF codes presented in this chapter can be (and have been) extended to include additional random variables. The most obvious extensions are to include the turbulence frequency, the scalar dissipation rate, or velocity acceleration. However, transported PDF methods can also be applied to treat multi-phase flows such as gas-solid turbulent transport. Regardless of the flow under consideration, the numerical issues involved in the accurate treatment of particle convection and coupling with the FV code are essentially identical to those outlined in this chapter. For non-orthogonal grids, the accurate implementation of the particle-convection algorithm is even more critical in determining the success of the PDF simulation. 

Note that the RANS formulation used in (B.44) and (B.45) can easily be extended to the LES, as outlined in Section 5.10. Moreover, by following the same steps as outlined above, DQMOM can be used with the joint velocity, composition PDF transport equation. Finally, the reader can observe that the same methodology is applicable to more general distribution functions than probability density functions. Indeed, DQMOM can be applied to general population balance equations such as those used to describe multi-phase flows. 

El. Edge, R. M., Flatman, A. T., Grant, C. D., and Kalafatoglu, I. E., Symp. Multi-Phase Flow Syst., Inst. Chem. Eng., London Paper C3 (1974). 

The function of a gravity settler is basically to reduce the velocity of a multi-phase flowing system from one which is turbulent and permits entrainment of particles to a velocity which is less turbulent, allowing the suspended particles to collect. Any knockout pot, accumulator, or ex-... 

Department of Chemical Engineering, State Key Laboratory of Multi-Phase Flow in Power Engineering, Xi an Jiaotong University, Xi an 710049, China... 

J. P. K. Seville, A. Ingram, X. Fan, and D. J. Parker, Positron Emission Imaging in Chemical Engineering Fei Wang, Qussai Marashdeh, Liang-Shih Fan, and Richard A. Williams, Electrical Capacitance, Electrical Resistance, and Positron Emission Tomography Techniques and Their Applications in Multi-Phase Flow Systems... 

Electrical Capacitance, Electrical Resistance, and Positron Emission Tomography Techniques and Their Applications in Multi-Phase Flow Systems... 

Various schemes have been applied to solve the forward problem of ECT for the visualization of multi-phase flow components. Forward solutions based on the sensitivity model (Huang et al., 1989 Xie et al., 1992) are the most widely used due to the simplicity and speed of applying this model. The simplest form of the sensitivity model is the single iteration linear forward projection (LFP) which is explained in Equation (4). 

Gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are widely used in the chemical and petrochemical industries for processes such as methanol synthesis, coal liquefaction, Fischer-Tropsch synthesis and separation methods such as solvent extraction and particle/gas flotation. The hydrodynamic behavior of gas-liquid bubble columns and gas-liquid-solid slurry bubble columns are of great importance for the design and scale-up of reactors. Although the hydrodynamics of the bubble and slurry bubble columns has been a subject of intensive research through experiments and computations, the flow structure quantification of complex multi-phase flows are still not well understood, especially in the three-dimensional region. In bubble and slurry bubble columns, the presence of gas bubbles plays an important role to induce appreciable liquid/solids mixing as well as mass transfer. The flows within these systems are divided into two... 

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