Esteban Brignole, Selva Pereda, in, 2013 AbstractPhase equilibrium knowledge is required for the design of all sorts of chemical processes that may involve separations, reactions, fluids flow, particle micronization, etc. Indeed, different phase behavior scenarios are required for a rational conceptual process design.
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6 Quasi-Equilibrium Processes. We are often interested in charting thermodynamic processes between states on thermodynamic coordinates. Recall from the end of Section 1.2.3, however, that properties define a state only when a system is in equilibrium. If a process involves finite, unbalanced forces, the system can pass through non. EQUILIBRIUM AND COMPATIBILITY 2-3 Moment stress resultants are the integration of stresses on a surface times a distance from an axis. A point load, which.
The aim of this chapter is to present the possible fluid mixture phase behavior that can be found in binary, ternary, and multicomponent systems. Moreover, representation of phase behavior in terms of phase diagrams is discussed.
Dealing with phase diagrams of complex mixtures is not an easy task for beginners; however, very simple concepts are behind the rules for their construction. Phase diagrams are essential tools for phase equilibrium engineering as they provide valuable hints to understand the process and to assess the feasible and optimum operating regions.
In this chapter, the “phenomenological” meaning of each phase behavior and its relation with molecular properties is discussed. A special attention is given to binary system phase behavior. Even though, in practice we rarely found such simple mixtures, they furnish a great deal of information for the understanding of multicomponent systems. (4.38) T ( 1 ) = T ( 2 ) = ⋯ = T ( p ), P ( 1 ) = P ( 2 ) = ⋯ P ( p ), G ˜ i ( 2 ) = G ˜ i ( 2 ) = ⋯ = G ˜ i ( p ) for all species i.These are general conditions, whether we are dealing with solid, liquid or gas phases.
In the case of vapour-liquid systems which dominate many applications, the liquid and vapour states are often related through such estimations as bubble point and dew point calculations in order to compute the equilibrium concentrations, pressures or temperatures. Certain assumptions need to be made about the ideality of both vapour and liquid phase behaviour.
It is quite common to assume ideal behaviour in both phases, which leads to the following models.Raoult's law model. Domenech, in, 2002 AbstractPhase equilibrium calculations constitute an important problem for designing and optimizing crystallization processes. The Gibbs free energy is generally used as an objective function to find the quantities and the composition of phases at equilibrium. In such problems, the Gibbs free energy is not only complex but can have several local minima. This paper presents a contribution to handle this kind of problems by implementation of a hybrid optimization technique based on the successive use of a Genetic Algorithm (GA) and of a classical Sequential Quadratic Programming (SQP) method: the GA is used to perform a first search in the solution space and to locate the neighborhood of the solution. Then, the SQP method is employed to refine the solution. The basic operations involved in the design of the GA developed in this study (encoding with binary representation of real values, evaluation function, adaptive plan) are presented.
Calcium phosphate precipitation which is of major interest for P-recovery from wastewater has been adopted as an illustration of the implemented algorithm. Wang, in, 2019 AbstractThe Phase Equilibrium Diagram is the road map to the use of two (or more) metals. As the result, there have been numerous efforts to compile the existing (reported) Phase Equilibriums in a book form or electronic form. On the other hand, there is an effort also to theoretically calculate the Phase Diagrams (Society of CALPHAD). However, this effort has not been too successful.
This is because, in order to calculate, one must start from liquid state which we do not yet know how to handle. Here I wish to describe my own effort in this aspect and, in the process, many aspects of Phase Diagrams such as the difference between Congruent Melting Compound versus Incongruent Melting Compound or the shape of liquidus curbs become understandable. I hope this may ultimately lead to a success of the Calculation of Phase Equilibrium Diagrams. Richard Smith. Cor Peters, in, 2013 7.1 OverviewPhase equilibrium of a chemical mixture provides the number and type of phases that are stable with each other subject to thermal, mechanical and chemical driving forces.
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Phase diagrams show the variation of the chemical states of aggregation with changes in temperature, pressure and composition and are typically prepared by holding one condition constant. Phase equilibria of chemical mixtures are used in evaluating new ideas or designing separation strategies in chemical process. For a phase diagram showing vapor–liquid equilibrium (VLE) of a two-component (binary) system, constant temperature (isothermal) conditions allow preparation of a P– x– y diagram ( Figure 7.1), while constant pressure (isobaric) conditions allow the preparation of a T– x– y diagram. A P– x– y diagram is conveniently used for supercritical fluids, because temperature is held constant and pressure is varied. A T– x– y diagram is conveniently used for distillation because pressure is held constant and temperature is varied. Two or more phases are in equilibrium if they have equality of temperature in each phase, equality of pressure in each phase and equality of chemical potential of each component in each phase.
A P– x– y diagram of a binary mixture (1 + 2) that shows the equilibrium states between vapor ( V) and liquid ( L) phases at constant temperature. The liquid phase is the bubble point curve ( P– x 1); the vapor phase is the dew point curve ( P– y 1).
Tie lines are horizontal at constant pressure and they connect equilibrium states of liquid ( x 1) and vapor ( y 1) phase compositions. The critical point ( cp) separates the bubble point and dew point curves. Since T T c1 and T. Esteban Brignole, Selva Pereda, in, 2013 AbstractThis volume on phase equilibrium engineering (PEE) aims to fill the gap between the books on reactors and separation process design and the textbooks on chemical engineering thermodynamics. The goal is to change the focus from the use of thermodynamic relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. In this way, phase equilibrium thermodynamics is put to work.
The main goal of PEE is the design of the system conditions to achieve the desired phase equilibrium scenario that the process at hand requires.In this chapter, the philosophy of phase equilibrium thermodynamic modeling is discussed in the context of process development and chemical plant operation. Typical phase scenarios that are encountered in separation, materials, and chemical process are presented as well as the problem of phase design and the PEE tools. Cleaver, in, 2013 3.2 Non-Ideal Equation of StateThe phase equilibrium and transport properties for CO 2 were partly determined using the Peng-Robinson (1976) equation of state for CO 2.
This is satisfactory for the gas phase, but not for the condensed phase. In addition, it is not accurate for the vapour pressure below the triple point, as it does not consider physical phenomena such as the heat of fusion. Hence, a composite equation of state was constructed whereby the vapour phase was calculated using the Peng-Robinson equation, and the condensed phases and the vapour pressure calculated using Span and Wagner (1996) and the DIPPR tables given in the Knovel library (2011). Calculations were undertaken using the Helmholtz free energy in terms of temperature and molar volume as all other thermodynamic properties can be readily obtained from it. A full description of this non-ideal equation of state with additional formulations to accurately predict solid phase properties including the latent heat of fusion is described in Wareing et al. Woolley, in, 2012 3.2 Non-Ideal Equation of StateThe phase equilibrium and transport properties for CO 2 were partly determined using the Peng-Robinson (1976) equation of state for carbon dioxide.
This is satisfactory for the gas phase, but not for the condensed phase. Furthermore, it is not accurate for the vapour pressure below the triple point and does not account for the discontinuity in properties at that point. In particular, there is no latent heat of fusion. Span and Wagner (1996) is valid for both gas and liquid above the triple point, but does not take account of experimental data below the triple point, nor does it give the properties of the solid. A composite equation of state was therefore used in which the gas phase is computed from Peng-Robinson, the liquid phase from Span and Wagner, and the latent heat of fusion and solid phase from the DIPPR tables ( Knovel library, 2011). Vapour pressures below the triple point are tabulated from Span and Wagner. Calculations were undertaken using the internal energy as all other thermodynamic properties can be readily obtained from it.
The phase equilibrium, phase formation, and phase relations in the Bi 2O 3–ZnO–Nb 2O 5 ternary system were investigated ( H Wang et al., 1998; Kim et al., 2002; Tan et al., 2005; Vanderah et al., 2005). The ceramic samples in a triangular area (see Fig. 17.4) around the cubic pyrochlore phase Bi 1.5ZnNb 1.5O 7 with the compositions of (Bi 3 xZn 2–3 x)(Zn xNb 2– x)O 7 (0 ≤ x ≤ 2/3), (Bi 2– xZn x)(Zn (5– x)/15Nb (10 + x)/15) 2O 7–0.3 x (0 ≤ x ≤ 2), (Bi 2–2 xZn x)(Zn (1– x)/2Nb (2 + x)/3) 2O 7– x (0 ≤ x ≤ 1) and some other compositions around the ‘ideal’ pyrochlore composition Bi 2(Zn 1/3Nb 2/3)O 7 were selected and prepared by conventional powder processing technique ( H Wang et al., 1998). Quenching technology was adopted to keep the high-temperature phase of the samples after they reached the equilibrium.
Based on X-ray diffraction analysis and thermal analysis, the phase formation was studied from 550 °C to 1050 °C with a temperature increment of 50 °C. The isothermal phase diagrams have been obtained. The pure α phase region and β phase region were determined in different temperatures, while the α–β co-existing phase was found to exist between the two single phases region. The phase diagrams of pyrochlores in the Bi 2O 3–ZnO–Sb 2O 5 ( Miles et al., 2006), Bi 2O 3–NiO–Nb 2O 5 ( Valant et al., 2005) and Bi 2O 3–ZnO–Ta 2O 5 ( Khaw et al., 2007) ternary systems have also been elaborated.
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