### The Spitzglass Equation for Sizing Gas Pipelines

Originally published in 1912, the Spitzglass Equation is used for sizing fuel gas pipes (although now it is superseded by better correlations).  Two versions of the equation exist;  one for low pressures (below 1 psi or 6.9 kPa) and another for medium pressures (above 1 psi or 6.9 kPa). However, both equations are typically used at near-atmospheric conditions, with pipe diameters below 10 inches (otherwise the friction factor is not accurately modeled).

This Excel spreadsheet solves both versions of the Spitzglass equations, with full units support.

The equations implemented are as follows

Spitzglass Low Pressure (<1 psi)

Spitzglass Medium Pressure (>1 psi)

The notation is given here.  These equations differ slightly to those versions typically presented in the literature because they include the effect of gas compressibility, and vertical pipe travel (i.e. potential energy).

I've also implemented other equations for sizing gas pipelines, including the Weymouth Equation, Panhandle Equation and the IGT Distribution Equation.

### Multicomponent Equilibrium Flash Calculation

When a multicomponent liquid stream undergoes a sudden decrease in pressure (by, for example, flowing through a valve), part of the feed vaporizes.  The vapor product is richer in the more volatile components (i.e. those with a higher equilibrium constant) than the liquid product. This is known as an equilibrium flash, and is the basis of many unit operations in the process industries, including distillation.

This Excel spreadsheet implements an isothermal multicomponent equilibrium flash calculation. The spreadsheet includes a set of chemical components as the input feed (i.e. the molar amount in the feed stream, together with their K-values), but these can be easily modified.

We then use the Rachford-Rice equation to calculate the fraction of each component in the product streams. The equation is

where zi is the mole fraction of component i in the liquid feed, Ki is the equilibrium constant (at the appropriate temperature and pressure) and β is the fraction of feed that is vaporised. Obviously, β is between 0 and 1.

We then solve the Rachford-Rice equation iteratively. All you need to do is find the value of β that makes the Rachford-Rice equation equal to zero using Excel's Solver function.  See the screengrab below for specific instructions.

The principles demonstrated in the spreadsheet are the basis of many other calculations that involve vapor-liquid equilibria, and are used in petroleum refineries, chemical plants and natural gas plants,