Download presentation

Presentation is loading. Please wait.

Published byRoxana Esarey Modified over 2 years ago

1
Properties of Reservoir Fluids Fugacity and Equilibrium Fall 2010 Shahab Gerami 1

2
Definitions :The specific Gibbs function for a simple compressible substance is: Gibbs Function and Chemical Potential As in a pure substance the specific Gibbs function equals the chemical potential, we can write for a isothermal process: and replacing by the ideal gas EOS we obtain:

3
Chemical Potential and Fugacity From Eq. (3) we can calculate the chemical potential of a pure substance that behaves as an ideal gas. For a real gas we can use an EOS and calculate the chemical potential by integration. This approach is not followed. Instead, a new thermodynamic property is defined such that the form of Eq. (3) still holds for a real gas. This new function is the fugacity,f, defined as: From Eq. (3) we can calculate the chemical potential of a pure substance that behaves as an ideal gas. For a real gas we can use an EOS and calculate the chemical potential by integration. This approach is not followed. Instead, a new thermodynamic property is defined such that the form of Eq. (3) still holds for a real gas. This new function is the fugacity,f, defined as: In addition, as the real gas and the ideal gas behave the same at very low pressure, it is obvious that: Therefore, with the definition of Eq. (4) and with the reference value of f at zero pressure the fugacity is completely defined.

4
Evaluating the Fugacity Using the definition of the isothermal chemical potential, Eq. (2), and the fugacity, Eq. (4) we can write: Eq. (6) in conjunction with an EOS (explicit in the specific volume) can be used to calculate the fugacity. Integrating between two pressures we get:

5
Evaluation of the fugacity from tables or EOS’s is usually done using the fugacity coefficient Φ, defined as: that can be differentiated to obtain: and combining Eq. (15) with Eq. (6) we get: which relates PVT data with the fugacity If we replace the definition of the Z factor in Eq. (17) we obtain:

6
Fugacity & Fugacity Coefficient Fugacity is a thermodynamic property of non-ideal fluids. Physically, It is the tendency of the molecules from one phase to escape into the other. In a mathematical form, the fugacity of a pure component is defined by the following expression: Fugacity Coefficient

7
Soave applied this generalized thermodynamic relationship to equation (5–70) to determine the fugacity coefficient of a pure component, to give

8
In a hydrocarbon multicomponent mixture, the component fugacity in each phase is introduced to develop a criterion for thermodynamic equilibrium. Physically, the fugacity of a component i in one phase with respect to the fugacity of the component in a second phase is a measure of the potential for transfer of the component between phases. The phase with the lower component fugacity accepts the component from the phase with a higher component fugacity. Equal fugacities of a component in the two phases results in a zero net transfer. A zero transfer for all components implies a hydrocarbon system in thermodynamic equilibrium. In a hydrocarbon multicomponent mixture, the component fugacity in each phase is introduced to develop a criterion for thermodynamic equilibrium. Physically, the fugacity of a component i in one phase with respect to the fugacity of the component in a second phase is a measure of the potential for transfer of the component between phases. The phase with the lower component fugacity accepts the component from the phase with a higher component fugacity. Equal fugacities of a component in the two phases results in a zero net transfer. A zero transfer for all components implies a hydrocarbon system in thermodynamic equilibrium. Fugacity and Equilibrium Therefore, the condition of the thermodynamic equilibrium can be expressed mathematically by:

9
The fugacity coefficient of component i in a hydrocarbon liquid mixture or hydrocarbon gas mixture is a function of the system pressure, mole fraction, and fugacity of the component. The fugacity coefficient is defined as: For a component i in the liquid phase For a component i in the gas phase Fugacity Coefficient in a Hydrocarbon Mixture

10
It is clear that, at equilibrium ( f Li = f vi ), the equilibrium ratio, K i, as previously defined by equation (5–1), that is, K i = y i /x i, can be redefined in terms of the fugacity of components as K-Values from EOS Reid, Prausnitz, and Sherwood (1987) defined the fugacity coefficient of component i in a hydrocarbon mixture by the following generalized thermodynamic relationship:

11
By combining the above thermodynamic definition of the fugacity with the SRK EOS (equation 5–70), Soave proposed the following expression for the fugacity coefficient of component i in the liquid phase: Gas phase fugacity coefficient

12
Flow Diagram of Equilibrium Ratio Determination by an EOS

15
Soave (1972) suggests that the van der Waals (vdW), Soave-Redlich- Kwong (SRK), and the Peng-Robinson (PR) equations of state can be written in the following generalized form: Generalized form of 3 Cubic EOS

16
Soave introduced the reduced pressure, p r, and reduced temperature, T r, to these equations, to give

17
In the cubic form and in terms of the Z-factor, the three equations of state can be written as And the pure component fugacity coefficient is given by

Similar presentations

Presentation is loading. Please wait....

OK

5. Equations of State SVNA Chapter 3

5. Equations of State SVNA Chapter 3

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google