Phase equilibria elements

STANJAN The Element Potential Method for Chemical Equilibrium Analysis Implementation in the Interactive Program STANJAN, W.C. Reynolds, Thermosciences Division, Department of Mechanical Engineering, Stanford University, Stanford, CA, 1986. A computer program for IBM PC and compatibles for making chemical equilibrium calculations in an interactive environment. The equilibrium calculations use a version of the method of element potentials in which exact equations for the gas-phase mole fractions are derived in terms of Lagrange multipliers associated with the atomic constraints. The Lagrange multipliers (the element potentials ) and the total number of moles are adjusted to meet the constraints and to render the sum of mole fractions unity. If condensed phases are present, their populations also are adjusted to achieve phase equilibrium. However, the condensed-phase species need not be present in the gas-phase, and this enables the method to deal with problems in which the gas-phase mole fraction of a condensed-phase species is extremely low, as with the formation of carbon particulates. 

Figure 2.14 Electrochemical phase diagram for chalcopyrite with elemental sulphur as metastable phase. Equilibrium lines (solid lines) correspond to dissolved species at 10 mol/L. Plotted points show the upper and lower limit potential of collectorless flotation of chalcopyrite reported from Sun (1990), Feng (1989) and Trahar (1984)...

Figure 2.18 rpH diagram for jamesonite in aqueous solutions with elemental sulphur as metastable phase. Equilibrium lines correspond to dissolved species at 10 moFL... 

Since the chemical potential is an intensive variable, independent of the absolute number of ions present, it can be determined at one point in a system and will be valid for all phases present. This is very useful for geologists in that one need not determine the size of the system for a measurement. However, it is essential to know over what area or distance the chemical potential of an element is constant. The scale of the system must be known in order to use this measurement in an estimate of phase equilibrium. 

In order for a process to be controllable by machine, it must represented by a mathematical model. Ideally, each element of a dynamic process, for example, a reflux drum or an individual tray of a fractionator, is represented by differential equations based on material and energy balances, transfer rates, stage efficiencies, phase equilibrium relations, etc., as well as the parameters of sensing devices, control valves, and control instruments. The process as a whole then is equivalent to a system of ordinary and partial differential equations involving certain independent and dependent variables. When the values of the independent variables are specified or measured, corresponding values of the others are found by computation, and the information is transmitted to the control instruments. For example, if the temperature, composition, and flow rate of the feed to a fractionator are perturbed, the computer will determine the other flows and the heat balance required to maintain constant overhead purity. Economic factors also can be incorporated in process models then the computer can be made to optimize the operation continually. 

Grain boundaries (and boundaries between phases) are elements of the microstructure of crystalline solids, being characterized by their number, shape, and topological arrangement. The microstructure is a non-equilibrium property. In the next section we discuss grain boundaries. 

A. A. Eliseev and G.M. Kuzmichyeva, Phase equilibrium and crystal chemistry in ternary rare earth systems with chalcogenide elements 191... 

As discussed previously, in many propulsion systems the recovery of a large fraction of the dissociation energy in the nozzle expansion through recombination is difficult to achieve. While the assumption of frozen flow with respect to recombination reactions appears necessary for many heat transfer rocket nozzle expansions, it is possible that condensation phenomena are sufficiently rapid to provide near equilibrium flow with respect to phase changes. For this special possibility, phase equilibrium in the presence of frozen dissociation, it has been shown theoretically (48) that the performance in terms of specific impulse of propellants containing light metallic elements can exceed the performance of hydrogen. 

These are described in the next section. Note that when atom balances are used, Dluzniewski and Adler (17) show that "fictitious elements" prevent reaction. Consider a reactor that produces ethylbenzene by reaction of benzene and ethylchloride in the presence of AICI3 catalyst. For calculation of phase equilibrium, downstream of the reactor, fictitious element A replaces a hydrogen atom in benzene (C0H5A) and the moles of each species remain unchanged. 

Therefore, adopting the solution of reactive distillation instead of separate reaction and separation units does not lead automatically to a more efficient process. Matching the conditions of separation and reaction in the same device requires careful design. The element with the highest impact is the chemical reaction. The key condition for an efficient and competitive process by reactive distillation is the availability of a superactive catalyst capable to compensate the loss in the driving force by phase equilibrium, but at the same time ensuring a good selectivity pattern. 

Note that in the equilibrium limit PilPi dX 1 isotopic fractionations vanish but the elemental abundances in the gas will still be fractionated in proportion to their relative saturation vapor pressures. The degree of equilibrium elemental fractionation of the condensed phase will depend on the volume of gas being sufficiently large that a substantial fraction of the elements of interest are in the gas phase. 

The solution to (P12) gives us the optimal separation profile as a function of age within the reactor. However, except in the case of reactive phase equilibrium, the assumption of a continuous separation profile is not really required. Furthermore, a continuous separation profile may not be implementable in practice. To address this, we take advantage of the structure of a discretization procedure for the differential equation system. In this case, we choose orthogonal collocation on finite elements to discretize the above model. This results... 

Once this interpretation has been established, MODEL.LA. (a) generates all the requisite modeling elements and (b) constructs the modeling relationships, such as material balances, energy balance, heat transfer between jacket and reactive mixture, mass transport between the two liquid phases, equilibrium relationships between the two phases, estimation of chemical reaction rate, estimation of chemical equilibrium conditions, estimation of heat generated (or consumed) by the reaction, and estimation of enthalpies of material convective flows. In order to automate the above tasks, MODEL.LA. must possess the following capabilities ... 

The principles and algorithms for calculating fluid-phase equilibria are discussed in many textbooks [36 0]. Here, we focus on methods and data requirements for calculating the component fugacities in a phase as a function of temperature, pressure, and composition this is the key element in all phase-equilibrium calculations. 

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