Multicomponent Vapor-Liquid Equilibrium

So-called white oil is pressurized and cooled gas well vapors. In Texas awhile back, independent producers operated refrigeration units (to as low as −20°F) at their wells, exploiting a 1977 letter from the legal counsel of the Texas Railroad Commission (the agency that governed oil and gas production) that said “white oil” could be deemed oil rather than gas. There were advantages to having a well classified as an oil well; namely, one oil well could be drilled on 10 acres, but a gas well required 640 acres, and at that time, white oil could be sold for six times the price of natural gas (which was under price control). In 1984, after years of contention, Judge Clark overruled the Railroad Commission. As a result, it issued a new order that said for a liquid to be counted as crude oil, it must be liquid in the reservoir, liquid in the well bore, and liquid at the surface. Over $27 billion of gas reserves were involved in this controversy. You can see that determining the true state and composition of petroleum products can be a serious matter.

Multicomponent vapor-liquid equilibrium pertains to systems that contain three or more components in the vapor or liquid phases. Vapor-liquid equilibrium calculations for multicomponent systems are performed in a manner analogous to the ones for binary systems. For bubble point calculations, Σiyi=1; therefore, the bubble point equation can be written in terms of the known liquid compositions (x_i) and the component K-values (K_i):ΣinxiKi=1

For dew point calculations, Σixi=1; therefore, the dew point equation can be written in terms of the known vapor composition (y_i) and the component K-values (K_i):ΣinyiKi=1

Note that both the bubble point and dew point equations are, in general, nonlinear equations with temperature as the only unknown.

To calculate the bubble point or the dew point using these equations, you will need the K-values for each component in the system. Bubble point and dew point calculations are used by commercial process simulators to model distillation columns and other separation processes. Equations of state are used by commercial process simulators to calculate component K-values for bubble and dew point calculations. For example, the SRK method is routinely used to calculate the K-values for nonpolar systems (e.g., hydrocarbons), and the UNIQUAC equation of state is used to calculate the K-values for a wide range of polar systems (i.e., systems with strong intermolecular interactions, such as hydrogen bonding).