Implementing an Equation of State without Derivatives: teqp

This work uses advanced numerical techniques(complex differentiation and automatic differentiation) to efficientlyand accurately compute all the required thermodynamic properties ofan equation of state without any analytical derivatives???particularlywithout any handwritten derivatives. It avoids the tedious and error-prone process of symbolic differentiation, thus allowing for morerapid development of new thermodynamic models. The techniquepresented here was tested with several equations of state (van derWaals, Peng-Robinson, Soave-Redlich-Kwong, PC-SAFT, andcubic-plus-association) and high-accuracy multifluid models. Aminimal set of algorithms (critical locus tracing and vapor-liquidequilibrium tracing) were implemented in an extensible and conciseopen-source C++ library: teqp (for Templated EQuation of statePackage). This work demonstrates that highly complicated equations of state can be implemented faster yet with minimalcomputational overhead and negligible loss in numerical precision compared with the traditional approach that relies on analyticalderivatives. We believe that the approach outlined in this work has the potential to establish a new computational standard whenimplementing computer codes for thermodynamic models.