Single phase system

Within single-phase systems a further distinction can be made between systems involving (1) laminar flows, (2) turbulent flows, (3) flows with complex rheology, and (4) fast chemical reactions. Of course certain systems exist that fall into several of these classes and therefore also possess their main characteristics. These types of systems are discussed in more detail. 

Further examples of recent applications of the finite element method can be found in Targett et al. (1995) who studied flow through curved rectangular channels of large aspect ratio using the FEM-based FIDAP code. They also compared their computational results with experimental data obtained from visualization experiments and found good agreement between theory and experiment. 

For systems involving turbulent flows accurate modeling is much more complicated in comparison with those involving laminar flow and here it is considered very important to interpret and use the computational results with great care, especially when one deals with turbulent flows in complex geometries. Whenever 

In studies that involve the CFD analysis of turbulent fluid flow, the k-t model is most frequently used because it offers the best compromise between width of application and computational economy (Launder, 1991). Despite its widespread popularity the k-e model, if used to generate an isotropic turbulent viscosity, is inappropriate for simulation of turbulent swirling flows as encountered in process equipment such as cyclones and hydrocyclones (Hargreaves and Silvester, 1990) and more advanced turbulence models such as the ASM or the RSM should be considered. Because these models are computationally much more demanding and involve an increased number of empirical parameters compared to the k-e model, other strategies have been worked out (Boysan et al, 1982 Hargreaves and Silvester, 1990) to avoid the isotropic nature of the classical k-e model. 

The extension of this approach to higher Reynolds numbers and more complex geometries is very important and deserves further attention in the future but depends critically on the future advances in computer hardware and numerical solution methods. As far as LES or partially resolved simulations are concerned, similar limitations exist although these type of simulations can be carried to (much) higher Reynolds numbers. DNS can also be used to obtain insight in turbulence producing mechanisms as shown in the study of Lyons et al. (1989). 

Most of the material balance problems in Chapter 4 could be solved entirely from information given in the problem statements. As you will come to discover, problems in process analysis are rarely so conveniently self-contained before you can carry out a complete material balance on a process, you usually must determine various physical properties of the process materials and use these properties to derive additional relations among the system variables. The following methods can be used to determine a physical property of a process material  

Look It Up. When you need a value for a physical property of a substance—whether it be a density, vapor pressure, solubility, or heat capacity—there is a good chance that someone, somewhere has measured this property and published the result. Since experiments are usually costly and time consuming, a reliable source of physical property data is an invaluable asset in process analysis. Four excellent sources of data are the following  

Perry s Chemical Engineers Handbook, 7th Edition, R. H. Perry and D. W. Green, Eds.. 

CRC Handbook of Chemistry and Physics, 79th Edition, D. Lide, Ed., Chemical Rubber Company, Boca Raton, FL, 1998. 

TRC Databases in Chemistry and Engineering. TRC Thermodynamic Tables Version 1.0. Thermodynamic Research Center, Texas A M University, College Station. Texas, 1994. This is a continuation of the American Petroleum Institute Project 44 Selected Values of the Properties of Hydrocarbons and Related Compounds.  

The observed abnormal grain growth in materials with faceted boundaries can be explained in terms of the variable mobility of a facet which would move by lateral movement of boundary steps (so-called step growth mechanism or 

The mobility of faceted boundaries is also dependent on boundary defects. In the case of BaTi03, 111 twins induced and enhanced abnormal grain growth. On the other hand, dislocations at boundaries in SrTiOs did not enhance the boundary mobility, unlike the enhanced mobility of solid/liquid interfaces by dislocations.In this case, however, the boundary was not fully faceted ( 35% faceted). According to a recent investigation in BaTiOs, it seems that dislocations can also enhance the boundary mobility if the boundary is well faceted. 

---

Funda.menta.1 PropertyRela.tion. For homogeneous, single-phase systems the fundamental property relation (3), is a combination of the first and second laws of thermodynamics that may be written as... 

Protection of a domestic or an industrial single-phase system... 

After having obtained the value of D. value of S.. is determined as discussed above. The reactance of the conductors can then be obtained from the graphs of Figure 28.19(b) drawn for versus X., for varying thicknesses of round conductors, fiere also the btisic graph will represent a single-phase system, having a reactance of 2 X, Refer to Example 28.8. 

Protection of a domestic or an industrial single phase system Ground fault on an LT system Ground fault protection in hazardous areas. Ground leakage in an HT system Core-balanced current transformers (CBCTs). Ground fault (G/F) protection schemes... 

Pathway temperatures must be strictly controlled (especially in single-phase systems) to create a balance between low-temperature oxide dissolution and high-temperature mass transfer limitations. 

Most non-Newtonian fluids are either two-phase systems, or single phase systems in which large molecules are in solution in a liquid which itself may be Newtonian or non-Newtonian, or are in the form of a melt. 

Phase-change cooling systems make do with smaller sizes without necessarily imposing a larger pumping power requirement compared with single-phase systems. 

If the reaction order does not change, reactions with n < 1 wiU go to completion in finite time. This is sometimes observed. Solid rocket propellants or fuses used to detonate explosives can bum at an essentially constant rate (a zero-order reaction) until all reactants are consumed. These are multiphase reactions limited by heat transfer and are discussed in Chapter 11. For single phase systems, a zero-order reaction can be expected to slow and become first or second order in the limit of low concentration. 

Section 1.5 described one basic problem of scaling batch reactors namely, it is impossible to maintain a constant mixing time if the scaleup ratio is large. However, this is a problem for fed-batch reactors and does not pose a limitation if the reactants are premixed. A single-phase, isothermal (or adiabatic) reaction in batch can be scaled indefinitely if the reactants are premixed and preheated before being charged. The restriction to single-phase systems avoids mass... 

Typical scale-up ratios for the incremental approach are shown in Table 5.3-4. It is not surprising that single-phase systems are easier to scale up than multi-phase systems. The reason is that the contact between phases changes with scale. In particular, the presence of solids complicates scale-up. 

If the hydrodynamics of the two-phase systems are understood, and the holdups and phase Reynolds numbers known, the rate of heat transfer can be estimated with about the same confidence as that for single-phase systems. 

For turbulent flow in single-phase systems, the predicted temperature profile is not changed significantly if the Peclet number is assumed to be infinite. Therefore, in turbulent two-phase systems the second-order terms in Eqs. (9) probably do not have a significant effect on the resulting temperature profiles. In view of the uncertainties in the present state of the art for determining the holdups and the heat-transfer coefficients, the inclusion of these second-order terms is probably not justified, and the resulting first-order equations should adequately model the process. 

The motions of the individual fluid parcels may be overlooked in favor of a more global, or Eulerian, description. In the case of single-phase systems, convective transport equations for scalar quantities are widely used for calculating the spatial distributions in species concentrations and/or temperature. Chemical reactions may be taken into account in these scalar transport equations by means of source or sink terms comprising chemical rate expressions. The pertinent transport equations run as... 

The operational interpretation of rA, as opposed to this verbal definition, does depend on the circumstances of the reaction.1 This is considered further in Chapter 2 as a consequence of the application of the conservation of mass to particular situations. Furthermore, rA depends on several parameters, and these are considered in Section 1.4.2. The rate with respect to any other species involved in the reacting system may be related to rA directly through reaction stoichiometry for a simple, single-phase system, or it may require additional kinetics information for a complex system. This aspect is considered in Section 1.4.4, following a preliminary discussion of the measurement of rate of reaction in Section 1.4.3. 

In this chapter, we describe how experimental rate data, obtained as described in Chapter 3, can be developed into a quantitative rate law for a simple, single-phase system. We first recapitulate the form of the rate law, and, as in Chapter 3, we consider only the effects of concentration and temperature we assume that these effects are separable into reaction order and Arrhenius parameters. We point out the choice of units for concentration in gas-phase reactions and some consequences of this choice for the Arrhenius parameters. We then proceed, mainly by examples, to illustrate various reaction orders and compare the consequences of the use of different types of reactors. Finally, we illustrate the determination of Arrhenius parameters for die effect of temperature on rate. 

For a single-phase system, V always refers to the volume of the reacting system, but is not necessarily the volume of the reactor. For example, for a liquid-phase reaction in... 

The purpose of this chapter is to outline the simplest methods of arriving at a description of the distribution of species in mixtures of liquids, gases and solids. Homogeneous equilibrium deals with single phase systems, such as electrolyte solutions (e.g., seawater) or gas mixtures (e.g., a volcanic gas). Heterogeneous equilibrium involves coexisting gaseous, liquid and solid phases. 

As for a single phase system, the rate of the reaction is still dependent on the probability of reactants meeting and therefore on the concentration of the reagents. However, in the biphasic system, the critical concentration of these components is no longer their total concentration in the whole system but the concentration where the reaction takes place. This concentration will be dependent on a number of factors, and the most influential are the rate of diffusion of the reactants to the catalyst and the relative solubility of the reagents in each phase. These two factors are interdependent, and will be considered in turn. 

Electrophoresis is the term given to the migration of charged particles under the influence of a direct electric current. It is a single-phase system and depends upon the relative mobilities of ions under identical electrical conditions. 

---