Page 87 - Handbook of Natural Gas Transmission and Processing Principles and Practices

(2.12)

2.2.5.5. Gibbs Phase Rule
Gibbs phase rule provides an expression for the variance (also called number of degrees of freedom),
denoted dof, of a p-component system, containing k phases in equilibrium:

(2.13)

This dof may be defined as the number of the intensive phase variables of a thermodynamic
system that must be specified to fix the intensive state of each phase (or in other words, to fix all the
other intensive phase variables of the multiphase system).
It is worth noting that intensive global variables (e.g., molar phase proportions, overall
composition …) are not involved in the dof definition.
For a VLE ( ), the Gibbs phase rule leads to:

(2.14)

This result is basically confirmed by the system of Eq. (2.12):

• System of Eq. (2.12) involves equations.
• A number of independent variables are involved in the system of Eq. (2.12):
• Vectors and contain mole fractions each, but only are independent

because of the summation relations such as and .
• Three other independent variables are .
• In total, the system of Eq. (2.12) involves independent
variables.

The number of degrees of freedom is thus given as

(2.15)

2.2.5.6. Calculation Principle of a Phase Envelope
A phase envelope is made up of the loci of the bubble and dew points of a mixture of known overall
composition z .
A bubble point must be understood here as a 2-phase system of known liquid-phase composition;

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