Ideal Gas Law

The ideal gas law is a simple equation of state model that describes various gases at ideal or stock tank conditions. The condition range for the ideal gas law is bounded by low pressures and high temperatures near 14.7 psia (1 atm) and 60\(^\circ\)F (15\(^\circ\)C). The ideal gas law is a combination of relationships discovered before the 1800's for ideal gas behavior. The equation for the ideal gas law is given by

$$\begin{equation}\label{IGL} pV = nRT \end{equation}$$

By keeping two of the state-variables constant (pressure, volume, temperature and molar amount), you get the following experimental relationships.

Boyle's Law

In Boyle's law, the system is assumed to have a constant molar amount and temperature. The resulting simplification of the ideal gas law then becomes

$$\begin{equation}\label{eq:Boyle} p_1V_1 = p_2V_2 \end{equation}$$

Charles' Law

In Charles' law, the system is assumed to have a constant molar amount and pressure. The resulting simplification of the ideal gas law then becomes

$$\begin{equation}\label{eq:Charles} \frac{V_1}{T_1} = \frac{V_2}{T_2} \end{equation}$$

Avogadro's Law

In Avogadro's law, the system is assumed to have a temperature and pressure. The resulting simplification of the ideal gas law then becomes

$$\begin{equation}\label{eq:Avogadro} \frac{V_1}{n_1} = \frac{V_2}{n_2} \end{equation}$$

Gay-Lussac's Law

In Gay-Lussac's law, the system is assumed to have a molar amount and volume. The resulting simplification of the ideal gas law then becomes

$$\begin{equation}\label{eq:Gay-Lussac} \frac{P_1}{T_1} = \frac{P_2}{T_2} \end{equation}$$

Non-Ideal Gases

Modification for the ideal gas law must be applied to the ideal gas law for non-ideal conditions as well as chemically reacting gas mixtures. For most petroleum systems, any chemical reactions can be assumed to be negligible, however the pressure and temperature conditions of typical reservoirs are far beyond the range of validity of the ideal gas law. Modifications have therefore been introduced to describe both real gases through the real gas law and for multi-phase systems though cubic equations of state.

The general approach to enhance the predictions of the ideal gas law has been to introduce a generalized EOS model on the form

$$\begin{equation}\label{eq:eos} Z = \frac{pv}{RT} \end{equation}$$

where \(v\) is the molar volume (\(v=V/n\)) and \(Z\) is the Z-factor.

Applying the generalized EOS model in equation \eqref{eq:eos} results in the ideal gas being a special case when the Z-factor is equal to 1.