Phase Rule and Phase Diagrams

2012 ◽  
Keyword(s):  
Phase Diagrams ◽  
Phase Rule

Phase diagrams

2021 ◽  
pp. 19-29
Author(s):  
Adrian P Sutton
Keyword(s):  
Free Energy ◽  
Phase Diagrams ◽  
Binary Systems ◽  
Full Range ◽  
Phase Rule ◽  
Intermediate Phases ◽  
Ordered Alloys ◽  
Regions Of Stability ◽  
Liquid States

Temperature-composition phase diagrams are introduced as maps of the regions of stability of binary systems at constant pressure, usually atmospheric pressure at sea level. Their construction is based on minimisation of the Gibbs free energy as a function of composition at a given temperature. The simple case of miscibility in the solid and liquid states over the full range of composition is discussed first. Eutectic and peritectic phase diagrams result from limited miscibility in the solid state. Intermediate phases, or ordered alloys, usually occur in narrow ranges of composition in phase diagrams, and this is also explained in terms of free energy composition curves. Each phase diagram is shown to obey the phase rule discussed in the previous chapter.

A topological theory of phase diagrams for multiphase reacting mixtures

1990 ◽  
Vol 430 (1880) ◽  
pp. 669-678 ◽  
Keyword(s):  
Phase Equilibrium ◽  
Phase Diagrams ◽  
Topological Invariant ◽  
Global Constraint ◽  
Multicomponent Mixtures ◽  
Phase Rule ◽  
Reacting Mixtures ◽  
Equilibrium Data ◽  
Residue Curve Maps ◽  
Integer Equation

Residue curve maps are an effective way of representing phase equilibria in non-ideal multicomponent mixtures. In this representation the phase equilibrium surfaces are replaced by an equivalent flow of trajectories of a vector field. The flow is characterized by a set of singular points that correspond to the pure components and azeotropes present in the mixture. It is shown that the patterns in these maps for reaction mixtures obey a global constraint arising from a topological invariant for the manifold on which they are defined. This constraint is in the form of an integer equation that phase diagrams must obey in addition to the Gibbs phase rule. The main advantage of the method is that certain global statements can be made about the structure of reactive phase diagrams, independently of the details of phase equilibrium data or models.

The Critical Composition Method A New Convergence Pressure Method

1967 ◽  
Vol 7 (01) ◽  
pp. 54-55 ◽  
Author(s):  
Allen M. Rowe
Keyword(s):  
Phase Diagrams ◽  
Homologous Series ◽  
Phase Rule ◽  
Component System ◽  
Composition Method ◽  
Critical Composition ◽  
Phase Calculation ◽  
K Factor ◽  
Factor Data ◽  
Equilibrium Phases

Abstract A considerable quantity of experimental hydrocarbon K-factor data has been correlated as a function of component identity, temperature, pressure and convergence pressure. To utilize these correlations effectively, convergence pressure must be determined accurately, particularly for volatile mixtures near their critical states. This paper presents phase diagrams that illustrate physically the meaning of convergence pressure. A new method, referred to hereafter as the "critical composition method", will be outlined for calculating convergence pressure. An example calculation has been included to illustrate how to use this new technique. Introduction The principle of hydrocarbon phase composition calculations as applied to such diverse problems as optimizing separator performance or predicting fluid compositions at various stages of reservoir depletion is the same. Usually, temperature, pressure and the numbers of moles of the various components of the fluid contained in a given volume are known. Questions answered by the phase calculation are what fraction of the total mass of fluid exists in each of the equilibrium phases, and what are the mole fractions of die various components in the two phases?To answer these questions the Natural Gasoline Supplymen's Assoc. (NGSMA) has correlated a considerable quantity of K-factor data as a function of temperature, pressure, component identity and convergence pressure. To use these correlations to obtain the best answers possible, one must be able to calculate the convergence pressure. This is particularly true for over-all fluid compositions in the neighborhood of the critical state. STATEMENT OF THEORY Use of convergence pressure as a combating parameter is based on a postulate similar to the law of corresponding states used in correlating PVT data of hydrocarbon gases. This postulate, which proposes convergence pressure as a correlating parameter, has been stated as follows: "The equilibrium vaporization constant for one component in a complex system is the same as the equilibrium constant at the same temperature and pressure for the same number or kind of components, providing only that the convergence pressures of the two systems are exactly the same at the same temperature and that the components are of the same homologous series. This law, as with all laws of physics, cannot be proven theoretically. It can only be justified by experimental data supporting its premises. Arguments have been made that this law violates Gibb's phase rule. For example, consider a four-component system. By Gibb's phase rule, which is thermodynamically rigorous, f = c - P+ 2 = 4, for a four-component, two-phase system. Thus, four independent intensive variables must be specified to establish completely all the intensive variables of the equilibrium phases. On the other hand, according to convergence pressure theory only three variables need be specified for any mixture containing four different components. These variables are temperature, pressure and convergence pressure. Thus, the two laws appear to be in conflict. However, the convergence pressure postulate is more restrictive than Gibb's phase rule. It applies only to mixtures of the same homologous series. Hence, these two concepts are not in disagreement. PHASE DIAGRAMS DESCRIBING CONVERGENCE PRESSURE This paper presents phase diagrams grading from the simple two-component system to the more complex four-component system to illustrate convergence pressure. SPEJ P. 54ˆ

5. Changing the state of matter

2014 ◽  
pp. 70-85
Author(s):  
Peter Atkins
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Chemical Potential ◽  
Solid Phase ◽  
The State ◽  
State Transitions ◽  
Phase Rule ◽  
Freezing Points ◽  
State Of Matter ◽  
Matter Phase

‘Changing the state of matter’ considers the transformations states of matter undergo from one form to another during the processes of freezing, boiling, dissolving, and mixing. All such transformations and the corresponding equilibria that are reached in state transitions can be expressed in terms of the chemical potential and the pushing power it represents. Changes in temperature and pressure can lower or raise boiling and freezing points. Josiah Gibbs' phase rule is concerned with the equilibria between various forms of matter. Phase diagrams help chemists draw conclusions about the compositions of mixtures, minerals, and alloys. Transitions in solutions, including osmosis, and solid-to-solid phase transitions are also discussed.

Phase Rule and Phase Diagrams

2008 ◽  
pp. 539-547
Author(s):  
George R. Blake ◽  
Gary C. Steinhardt ◽  
X. Pontevedra Pombal ◽  
J. C. Nóvoa Muñoz ◽  
A. Martínez Cortizas ◽  
...  
Keyword(s):  
Phase Diagrams ◽  
Phase Rule
Sign in / Sign up

Export Citation Format

Share Document