Compressible Fluid Mixtures

In this section, we consider vapour-liquid equilibrium in binary fluid mixtures. A locus of vapour-liquid critical points may emanate from the critical point of either component. In the simplest case a single continuous locus of vapour-liquid critical points may connect the critical points of the two components. It is important to consider the thermodynamic behaviour of the mixture at constant chemical potential p.2. On comparing eq 10.57 with eq 10.35, we see that, at constant /I21, the scaling fields become identical to those of a one-component fluid. Hence, the thermodynamic behaviour of mixtures at constant fiji can be described by exactly the same equations as for one-component fluids near the vapour-liquid critical point, except that the critical parameters and the system-dependent coefficients will depend parametrically on the hidden field B2 - Use of p,2 as the hidden field is not convenient, since it diverges in the two one-component limits. This problem is avoided by adopting an alternative hidden field proposed by Leung and Griffiths  

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The phenomenon of critical flow is well known for the case of single-phase compressible flow through nozzles or orifices. When the differential pressure over the restriction is increased beyond a certain critical value, the mass flow rate ceases to increase. At that point it has reached its maximum possible value, called the critical flow rate, and the flow is characterized by the attainment of the critical state of the fluid at the throat of the restriction. This state is readily calculable for an isen-tropic expansion from gas dynamics. Since a two-phase gas-liquid mixture is a compressible fluid, a similar phenomenon may be expected to occur for such flows. In fact, two-phase critical flows have been observed, but they are more complicated than single-phase flows because of the liquid flashing as the pressure decreases along the flow path. The phase change may cause the flow pattern transition, and departure from phase equilibrium can be anticipated when the expansion is rapid. Interest in critical two-phase flow arises from the importance of predicting dis-... 

Fluidization The process of suspending powder particles using compressed air, creating a fluid mixture of air and powder. 

In gas separation, a gas mixture at a pressure p0 is applied to the feed side of the membrane, while the permeate gas at a lower pressure (pt) is removed from the downstream side of the membrane. As before, the starting point for the derivation of the gas separation transport equation is to equate the chemical potentials on either side of the gas/membrane interface. This time, however, the chemical potential for the gas phase is given by Equation (2.8) for a compressible fluid, whereas Equation (2.7) for an incompressible medium is applied to the membrane phase. Substitution of these equations into Equation (2.20) at the gas/membrane feed interface yields3... 

If the mass of the two-phase mixture at the valve inlet is 50% liquid or more, a liquid service valve construction must be considered. If the vapour content of the two-phase mixture is greater than 50% (mass), then a valve designed for compressible fluid service is recommended. 

This is not a physical parameter of the fluid mixture but is a convenient parameter that represents the compressibility or expansion of the mixture. It is defined by the formula ... 

Note there is a difference between the Darcy s law for a gas (a compressible fluid) and that for a liquid (an incompressible fluid). Thus, before doing an injection test, it is important to know whether the injected acid gas mixture is in the gas phase or in the liquid phase. 

The third chapter covers convective heat and mass transfer. The derivation of the mass, momentum and energy balance equations for pure fluids and multi-component mixtures are treated first, before the material laws are introduced and the partial differential equations for the velocity, temperature and concentration fields are derived. As typical applications we consider heat and mass transfer in flow over bodies and through channels, in packed and fluidised beds as well as free convection and the superposition of free and forced convection. Finally an introduction to heat transfer in compressible fluids is presented. 

Gas phase viscosity data, iTq, are used in the design of compressible fluid flow and unit operations. For example, the viscosity of a gas is required to determine the maximum permissible flow through a given process pipe size. Alternatively, the pressure loss of a given flowrate can be calculated. Viscosity data are needed for the design of process equipment involving heat, momentum, and mass transfer operations. The gas viscosity of mixtures is obtained from data for the individual components in the mixture. 

The parameter values have been reported in the literature for numerous substances. For 11 hydrocarbon mixtures, the average AAD was 2.3% (ranging from 0.5 to 5.65%). For 12 methane-containing mixtures, the AAD was 3.92% (ranging from 1.32 to 8.16%). The five parameters required for each substance are a drawback to convenient application. The eos is superior in its representation of density of liquid and compressed fluid states—to within 1% up to the highest pressures. 

Glass formation, the other common fate of a compressed fluid, however, gives a much larger viscosity increase. For mixtures and fluids with nonspherical molecules, it is common to produce a metastable glass at some pressure in excess of the equilibrium crystallization point. Methanol is one example. It can be easily superpressed past its crystallization pressure of 3.5 GPa at T = 25°C towards its glass-transition pressure of 11.4 GPa and beyond. Being a... 

The Sanchez and Lacombe LF EoS considers a compressible lattice for the representation of microstates of pure fluids and fluid mixtures. Such a lattice is made of cells, whose volume depends on mixture composition, which can be either empty or occupied by molecular segments of the components considered. The statistical analysis of the possible combinations of molecules in the lattice and the evaluation of the energetic... 

Expression. Both sedimentation and filtration are suitable separation techniques when the mixture of liquid and solids is sufficiently mobile to allow pumping, or similar method of motion, of the fluid to a barrier which retains the solid but not the liquid. If such movement is not possible then separation can be accomplished by compressing the mixture under conditions which permit the liquid to escape while retaining the solid between the compressing surfaces. This technique is called expression. Design of expression equipment is varied. Batch systems usually operate by the application of hydraulic pressure in units such as the box press, pot press, curb press and cage press. Continuous expression utilises equipment such as screw presses, roller mills, and belt presses [23]. 

The main issue here is to achieve the unambiguous separation between solvation and compressibility-driven phenomena, based on the formal splitting of the total correlation functions into their corresponding direct and indirect contributions (Chialvo and Cummings 1994,1995) according to the Omstein-Zemike equation (Hansen and McDonald 1986), and then use the derived rigorous expressions as zeroth-order approximations, for example, reference systems, in the subsequent perturbation expansion of the composition-dependent thermodynamics properties of multicomponent dilute fluid mixtures (vide infra Section 8.3). 

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