Multiphase flows, modeling approaches

The overall gain of the multiphase mixture model approach above is that the two-phase flow is still considered, but the simulations have only to solve pseudo-one-phase equations. Problems can arise if the equations are not averaged correctly. Also, the pseudo-one-phase treatment may not allow for pore-size distribution and mixed wettability effects to be considered. Furthermore, the multiphase mixture model predicts much lower saturations than those of Natarajan and Nguyen - and Weber and Newman even though the limiting current densities are comparable. However, without good experimental data on relative permeabilities and the like, one cannot say which approach is more valid. 

The first approach, which considers a single phase, proposes conventional multiphase flow models, such as ideal flow, dispersion, and residence time distribution models. The second approach, which takes into account two phases as bubble and emulsion, suggests different governing equations for each phase and considers a term for describing mass interchange between the two phases. 

The conclusion from the above is that, with the help of modern powerful computers and modern multiphase flow modeling, it is now feasible to investigate the transport phenomena inside fermenters in great detail. The CFD approach reduces the amount of empiricism substantially, but is not completely free from it. Nevertheless, robust simulations are possible that provide insight and guidance for the design and optimization of fermenters of industrial scale. Commercial software exist that can be used with reasonable confidence, but CFD requires the involvement of a specialist, as many choices during the simulations need to be made. 

In part II of the present report the nature and molecular characteristics of asphaltene and wax deposits from petroleum crudes are discussed. The field experiences with asphaltene and wax deposition and their related problems are discussed in part III. In order to predict the phenomena of asphaltene deposition one has to consider the use of the molecular thermodynamics of fluid phase equilibria and the theory of colloidal suspensions. In part IV of this report predictive approaches of the behavior of reservoir fluids and asphaltene depositions are reviewed from a fundamental point of view. This includes correlation and prediction of the effects of temperature, pressure, composition and flow characteristics of the miscible gas and crude on (i) Onset of asphaltene deposition (ii) Mechanism of asphaltene flocculation. The in situ precipitation and flocculation of asphaltene is expected to be quite different from the controlled laboratory experiments. This is primarily due to the multiphase flow through the reservoir porous media, streaming potential effects in pipes and conduits, and the interactions of the precipitates and the other in situ material presnet. In part V of the present report the conclusions are stated and the requirements for the development of successful predictive models for the asphaltene deposition and flocculation are discussed. 

In eq 51, the first term represents a convection term, and the second comes from a mass flux of water that can be broken down as flow due to capillary phenomena and flow due to interfacial drag between the phases. The velocity of the mixture is basically determined from Darcy s law using the properties of the mixture. The appearance of the mixture velocity is a big difference between this approach and the others, and it could be a reason the permeability is higher for simulations based on the multiphase mixture model. 

Despite its great potential, in the near future CFD will not completely replace experimental work or standard approaches currently used by the chemical engineering community. In this connection it is even not sure that CFD is guaranteed to succeed or even be an approach that will lead to improved results in comparison with standard approaches. For single-phase turbulent flows and especially for multiphase flows, it is imperative that the results of CFD analysis somehow be compared with experimental data in order to assess the validity of the physical models and the computational algorithms. In this connection we should mention that only computational results that possess invariance with respect to spatial and temporal discretization should be confronted with experimental data. A CFD model usually gives very detailed information on the temporal and spatial variation of many key quantities (i.e., velocity components, phase volume fractions, temperatures, species concentrations, turbulence parameters), which leads to in-... 

For multiphase systems a rough distinction can be made between systems with separated flows and those with dispersed flows. This classification is not only important from a physical point of view but also from a computational perspective since for each class different computational approaches are required. For multiphase systems involving multiphase flow both Eulerian, mixed Eulerian-Lagrangian, and two-material free surface methods can be used. An excellent review on models and numerical methods for multiphase flow has been presented by Stewart and Wendroff (1984). A similar review with emphasis on dilute gas-particle flows has been presented by Crowe (1982). 

Turbulence is the most complicated kind of fluid motion. There have been several different attempts to understand turbulence and different approaches taken to develop predictive models for turbulent flows. In this chapter, a brief description of some of the concepts relevant to understand turbulence, and a brief overview of different modeling approaches to simulating turbulent flow processes is given. Turbulence models based on time-averaged Navier-Stokes equations, which are the most relevant for chemical reactor engineers, at least for the foreseeable future, are then discussed in detail. The scope of discussion is restricted to single-phase turbulent flows (of Newtonian fluids) without chemical reactions. Modeling of turbulent multiphase flows and turbulent reactive flows are discussed in Chapters 4 and 5 respectively. 

The subject of the modeling of multiphase flow processes is quite vast and covers a wide range of sub-topics. It is virtually impossible to treat all the relevant issues in a single book, let alone in a single chapter. Here we attempt to provide a brief review of modeling approaches and cite the key references for further details. An attempt is made to provide sufficient information to develop a baseline model. The first section discusses various flow regimes and their key features. Various approaches to... 

It will be useful to discuss here different modeling approaches and some of the key issues in modeling multiphase flow processes. In general, there are three main issues... 

There are three main approaches for modeling multiphase flows ... 

FIGURE 4.1 Modeling approaches for multiphase flows, (a) Volume of fluid approach, (b) Eulerian-Lagrangian approach, (c) Eulerian-Eulerian approach. 

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