Accurate candidate regions

This example uses a subroutine MODEL that computes only the values fu e) of the expectation function in Eq. (C.6-1). Input values DEL(i)=-lD-2 are used, with IDIF=1 so that GREGPLUS uses forward-difference approximations of the derivatives dfu 0)/d0j. To make these approximations accurate, the elements DEL(I) are refined by GREGPLUS in each iteration, using Eq, (6.B-7). Abbreviated output is requested by using LISTS = 1. Finally, an additional event condition is selected from five candidates, to minimize the volume of the three-parameter HPD region. Details of the implementation of this example in Athena Visual Studio can be found by running the software and selecting Book Examples under the Help menu item. 

Equation-of-state methods appear to be the most likely candidates for reliable accurate data. They are capable of predicting enthalpy, entropy, density, fugacity, vapor-liquid, and liquid-liquid data from one equation in regions where both low and high densities are encountered. Rapid computation requires that the equation be simple yet accurate without computational difficulties in areas surrounding the critical point. 

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