Thermodynamic Properties

Introduction

This application calculates the various thermodynamic properties associated with a gas composition, including enthalpy, entropy, the isobaric (constant-pressure) and isochoric (constant-volume) heat capacities, and the Joule-Thomson coefficient. These properties vary with both gas composition and operating conditions and are commonly required as inputs to heat loss and gain calculations, such as gas heater sizing.

All calculation methods require a gas properties file describing the gas composition, or the manual entry of a mole percent for each component. The component mole percentages must sum to 100%. The “real gas” property values reported by the calculator depend on the Compressibility Factor Method that is automatically associated with the selected Calculation Method.

Background

The behavior of thermodynamic properties for a real gas composition deviates from that of an ideal gas. Natural gas mixtures represent a combination of real and ideal gas behavior. Calculating the thermodynamic properties of these mixtures is commonly based on interpolating extensive data sets of experimentally determined values for the individual components, then applying a mixing rule to combine the individual values into a total value representative of the mixture. Several data sources and mixing rules are available.

The values calculated by GASCalc are determined using a user-selected method that combines the data set, in equation form, with appropriate mixing rules to compute the “ideal gas” properties. The method then computes the “real gas” values according to its own definitions. To accurately compute the real gas property values, a suitable Compressibility Factor Method must be used in conjunction with the properties calculation method.

Isentropic Exponent (k value)

The ratio of the constant-pressure specific heat capacity (C_p) to the constant-volume specific heat capacity (C_v) is often referred to as the isentropic exponent, or “k” value, and GASCalc uses this definition in some of its calculations. The true isentropic exponent is related to this ratio and is often approximated by it; however, the two are not equal. The C_p to C_v ratio is reported in the thermodynamic property results for some calculated values, but the true isentropic exponent is only reported in the Sonic Velocity calculation when using the AGA 10 – 2003 or either of the AGA 8 calculation methods.

Joule-Thomson Cooling

In most cases, in the absence of an outside heat source, when the pressure of a real gas is reduced the temperature of the gas is also reduced. This is known as Joule-Thomson cooling and is the principle behind many refrigeration cycles. The effect is especially prevalent when gas pressure is suddenly reduced, such as when gas flows through a regulator, relief valve, or a partially open (throttled) valve, so the outlet temperature of a regulator is nearly always lower than the inlet temperature.

This phenomenon also occurs in pipe flow; however, the pressure drop there usually occurs in small, gradual increments, and the heat gain from the environment surrounding the pipe is generally greater than the cooling effect of the pressure drop. As a result, the downstream temperature of a pipe segment is often nearly equal to the upstream temperature, regardless of the pressure drop across the segment. The Joule-Thomson coefficient can be used to estimate the downstream gas temperature when the inlet temperature and pressure drop are known; it is expressed in terms of temperature difference per pressure difference.

Equations

The calculator includes three methods for the thermodynamic properties. The full details of each method are extensive, and we encourage users to refer to the cited references for the complete calculation procedures and parameter definitions.

American Gas Association Report No. 10 – 2003

Except for the Joule-Thomson coefficient, the thermodynamic property calculations are performed using the procedures outlined in AGA Report No. 10, “Speed of Sound In Natural Gas and Other Related Hydrocarbon Gases,” 2003 (Reference 1). This is the only method that reports the “Real Gas” specific heat, enthalpy, and entropy items, and it is required for the Joule-Thomson coefficient equation below.

Joule-Thomson Coefficient

Note: The equation below only applies when using the American Gas Association Report No. 10 – 2003 calculation method.

As implemented in the calculator, the Joule-Thomson coefficient is calculated using the method described by Maric and Ivek (Reference 2), using various equation-of-state values defined by AGA Report No. 8, 1992 (Reference 3), and using the following equation:

\mu_{JT} = \frac{R T^2}{P\, C_P} \left(\frac{\partial Z}{\partial T}\right)_P

\mu_{JT} = \frac{R T^2}{P\, C_P} \left(\frac{\partial Z}{\partial T}\right)_P

Where:
μ_JT − Joule-Thomson Coefficient, equal to ΔT / ΔP (°R/psi)
C_P − Constant Pressure Specific Heat
P − Gas Pressure (psia)
R − Universal Gas Constant
T − Gas Temperature (°R)
ΔP − Pressure Drop (Difference) (psi)
ΔT − Temperature Drop (Difference) (°R)
(∂Z / ∂T)_P − Partial derivative of compressibility with respect to temperature at constant pressure

American Gas Association Report No. 8 – 2017 (Detail)

The thermodynamic property calculations are performed using the procedures outlined in AGA Report No. 8, “Thermodynamic Properties of Natural Gas and Related Gases,” Parts 1 & 2, 2017 (References 4 and 5), using the DETAIL equation of state.

American Gas Association Report No. 8 – 2017 (GERG-2008)

The thermodynamic property calculations are performed using the procedures outlined in AGA Report No. 8, “Thermodynamic Properties of Natural Gas and Related Gases,” Parts 1 & 2, 2017 (References 4 and 5), using the GERG-2008 equation of state.

Case Guide

Part 1: Create Case

Input Parameters

Part 2: Outputs/Reports

Results

Note: The AGA Report No. 10 – 2003 method uses an iterative solution algorithm, so its results are not instantaneous unlike most other calculation routines. The number of decimal places shown for any calculated item can be set under File > Preferences > Decimals.

References

• American Gas Association, AGA Report No. 10, Speed of Sound In Natural Gas and Other Related Hydrocarbon Gases, 2003.
• InTech, Natural Gas, Natural Gas Properties and Flow Computation, Ivan Maric and Ivan Ivek, 2010.
• American Gas Association, AGA Report No. 8, Compressibility of Natural Gas and Other Related Hydrocarbon Gases, 1992, 1994 Printing.
• American Gas Association, AGA Report No. 8 Part 1, Thermodynamic Properties of Natural Gas and Related Gases, DETAIL and GROSS Equations of State, 3rd Ed., 2017.
• American Gas Association, AGA Report No. 8 Part 2, Thermodynamic Properties of Natural Gas and Related Gases, GERG-2008 Equation of State, 1st Ed., 2017.

FAQ