Phase two-component

Lockhart, R. W., and Martinelli, R. C., Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Plow in Pipes, Chemical Engineering Progress, 45 39 8, 1949. 

For example, for steam (saturated vapor, no liquid) distillation with one organic compound (liquid), there are two phases, two components, and two degrees of freedom. These degrees of freedom that can be set for the system could be (1) temperature and (2) pressure or (1) temperature and/or (2) concentration of the s) stem components, or either (1) pressure and (2) concentration. In steam distillation steam may be developed from water present, so there would be both a liquid water and a vapor phase water (steam) present. For such a case, the degrees of freedom are F = 2 + 2- 3 = l. 

Lockhart RW, Martinelli RC (1949) Proposed correlation of data for isothermal two-phase two-component flow in pipes. Chem Eng Prog 45 39-48 Lowdermilk WH, Lanzo CD, Siegel BL (1958) Investigation of boihng burnout and flow stability for water flowing in tubes, NACA TN 4382. National Advisory Committee for Aeronautics, Washington, DC... 

Lockhart RW, RC Martinelli. Proposed correlation of data for isothermal two-phase, two-component flow in pipes. CEP, 45 (1) 39-48, 1949. 

In the years since 1940, a voluminous literature has appeared on the subject of two-phase cocurrent gas-liquid flow. Most of the work reported has been done in restricted ranges of gas or liquid flow rates, fluid properties, and pipe diameter, and has usually been specific to horizontal or vertical pipe lines. The studies have in most instances been isothermal when two components were being considered nonisothermal cases were almost entirely single-component two-phase situations. Reports of investigations of two-phase two-component cocurrent flow where one component is being transferred across the interphase boundary are nearly nonexistent. 

In the case of the interfacial tension of two pure liquids we have had to deal with the superficial system in equilibrium with a two phase two component system of three dimensions. If we add to this system a third component the problem becomes still more complicated. The simplest case is that in which the added substance is soluble in one phase and completely insoluble in the other, the original liquids being themselves mutually insoluble. The change of interfacial tension should then run parallel to the change of surface tension of the liquid in which the third component dissolves. 

Finally, consider a two-phase, two-component system in which the two phases are separated by an adiabatic membrane that is permeable only to the first component. In this case we know that the temperatures of the two phases are not necessarily the same, and that the chemical potential of the second component is not the same in the two phases. The two Gibbs-Duhem equations for this system are... 

If the overall composition of a two-phase two-component system at a given temperature and pressure is known, the fraction of the system that is liquid or vapor may easily be determined from the enthalpy-concentration chart. 

Richardson, B. L. (1959) Some Problems in Horizontal Two-Phase Two-Component Flow, Ph.D. Thesis, Mechanical Engineering, Purdue University, West Lafayette. 

Calculation Results. The calculations were performed for a two-phase (two-component) medium and the probability function, Y p) [Eq. (243)], was used in the calculations. 

The calculations were made for a two-phase (two-component) inhomogeneous medium assuming that volume strains are elastic, while shear strains are viscoelastic. The ratio of local volume modulii K[ /K 2 was set equal to 10 4. For convenience of calculations, the local shear modulii (phase shear modulii) were written in the form... 

Turpin, J.L. Hungtinton, R.L. Prediction of pressure drop for two-phase, two component co-current flow in packed beds. Am. Inst. Chem. Eng. J. 1967, 6, 1196. 

The single phase, two-component fluid system under consideration contains N molecules of which Nt are of species 1 and Nz are of species 2. The molecules of each species are labeled separately, so that the molecules of species a are numbered 1, 2,. . . Na. For simplicity, we suppose that each molecule contains three degrees of translational freedom and no other degrees of freedom. The positions of the molecules of species a are denoted by the sequence of three vectors R, , . . . , ... 

Let us consider a model two-phase two-component system consisting of a solution of hexyl alcohol (component 2) in water (component 1) at equilibrium with their own vapors. A schematic change in the concentration of water c,(z) and that of hexanol c2(z) across the discontinuity surface is shown in Fig. II-l. In the regions below and above the discontinuity surface the concentrations of both components are constant and equal c, and c2 in the liquid phase, and c" and c2 in the vapor phase, respectively. Furthermore, due to low vapor densities c, c" and c2 c". 

The overall transfer coefficients (related to the overall transfer area) obtained in this three-phase two-component condensation study were about 600 and 1100 Btu/hr/ft /°F for the large and small bubbles, respectively. These compare favorably with the values reported for condensation of steam in water, which are, however, one order of magnitude larger. The difference is reasonable in view of the possibility for mass diffusion at the gas-liquid interface in the two-phase steam-water system, as well as the much higher turbulence encountered, especially in Bankoff s system (B2). 

Up to now two-phase two-component flow under non-isothermal conditions and coupled THM (one-phase flow) have been implemented in this code and validated against different experimental results. For the modelling of water penetration into unsaturated bentonite or clay, a swelling model is available in the code. If the test sample is confined within a constant volume, then a swelling pressure will build up which causes changes to the pore structure and reduces the porosity. A small change in porosity can, however, create a considerable reduction in permeability. 

Of course the equation is not applicable to a mixture of alcohol and water, between which there is no reaction equilibrium. Such a system contains two components and there are two independent chemical potentials. Each of these is a function of composition, as well as of temperature and pressure equation (6 5), on which (6 8) is based, is therefore incomplete and incorrect. From the point of view of the phase rule a two-phase, two-component system is divariant a change in pressure, Ap, is thus not uniquely determined by a temperature change, AT, but depends also on the change in composition of one of the phases. The analogue of equation (6 8) for two component systems will be discussed in 7 2. 

Both phases of a two-phase two-component liquid-vapour system are ideal solutions. The components are 1 and 2 respectively, and when the mole fraction of 2 in the liquid phase is x, that in the vapour phase is y and the total vapour pressure is p. 

---