A Gas System

Although gas systems are modelled using the same continuity equations as other systems (mass, moles, energy, momentum), the big difference is that they deal with compressible fluids. This means that the relationships between the various ‘state' variables (e.g. temperature and pressure) need to be described by thermodynamic state equations. In models of gas systems, energy balances almost always need to be included too.

In this simple example we'll look at how a model for a gas system can be set up. The system we will model is a simple gas surge vessel, where the gas enters at flowrate Fin and leaves at flowrate Fout. The internal conditions of the vessel are: volume V cubic metres; pressure P N.m^-2, temperature T Kelvin, number of moles n kg.moles. To simplify things we'll assume isothermal operation.

In balances with gas systems it makes sense to use mole balances rather than mass balances. Have a go at forming a mole balance for the example:

If we assume that the ideal gas law applies we can convert the mole balance into a balance that shows how the pressure in the vessel changes (remember that we are assuming isothermal operation). Have a go at converting the mole balance:

It is often necessary to convert the mole balance in this way - usually the inflow and the outflow from the vessel will be dependant on the square-root of the pressure driving force, e.g.(Cin and Cout are discharge coefficients):