One possible response is to teach only methods that can be computed by hand. This certainly forces a more fundamental understanding of the equations, but it limits the types of models that can be considered and it can be tedious, especially for a test question.
On the other hand, modern engineering rarely involves that kind of hand calculation and the models are much more sophisticated. Process simulators or thermodynamics packages present the workings of the model equations as black boxes, with little insight as to what is happening within the box. The pitfall is that the students cannot understand what is wrong when something goes awry, or even recognize that something might be wrong.
These observations suggest the need for some kind of middle ground. We illustrate this middle ground with the Peng-Robinson (PR) equation for mixtures as applied to fluid phase equilibria. The PR model is sufficiently sophisticated for most modern process simulators. The analytical solution of this cubic equation circumvents the need for calling the Excel Solver. The PR model and its multiple roots are familiar to students from their prior study of pure fluids. The expressions for the fugacity coefficient have been derived in class and similar derivations are familiar from homework covering other equations of state. In this context, providing a spreadsheet to students comes very close to simply saving them some tedious typing. It is up to the students to assemble the fugacity coefficients to solve practical problems.
The spreadsheet to be illustrated in this presentation provides the capability for students to solve flash problems by selecting the correct assembly of fugacity coefficients based on the appropriate roots. But beware of oversimplifying by simply calling the Excel Solver or applying Excel's iteration feature! Those tricks may work at low pressure if your initial guess is very good, but mixing gaseous components and raising the pressure causes the solution to vary from the three-root region to the one-root region, forcing the student to guide the convergence with intelligence. In this way, the students can appreciate the difficulty of some types of convergence and have an alternative to simply stating “stupid computer” when the black box goes awry. Assessing the students' capability to learn and apply this methodology is demonstrated with ConcepTests, a project that simulates a distillation train, and exam performance.