Analogy to the dimensionless phase equilibrium

We can express phase equilibrium calculations in a dimensionless form by introducing a variable substitution for the vapor fraction.

We assume the following component and overall mole balance around a two-phase equilibrium:

By applying the substitution of and inserting the equation for the overall mole balance into the equation for the component mole balance, we get the well-known dimensionless flash equation:

In practice, we must solve the phase equilibrium and the reaction equilibrium in parallel since both processes happen at the same time. For modelling convenience, we can separate these phenomena into two parts. Consider the following calculation schematic:

Figure: Simultaneous reaction and phase equilibrium

The reaction equilibrium relates zin to zout and the phase equilibrium relates zout to the vapor composition (y) and the liquid composition (x). As the reaction equilibrium itself depends on x and y (depending on the phases in which the reaction takes place), we must solve the equations iteratively. Both equilibrium calculations are independent of the actual flow in the balanced system and only depend on the feed conditions (T, P, and zin).