Free-Form Parametric Fitting of Van der Waals Binodal and Spinodal Curves with Bat Algorithm

This paper concerns the Van der Waals (VdW) equation of state, originally conceived to be a generalization of the ideal gas law. For practical use, it is often necessary to compute two characteristic curves of VdW, called binodal and spinodal curves. They are usually constructed through polynomial fitting from a collection of 2D points in the pressure-volume plane by using standard numerical procedures. However, the resulting models are still limited and can be further enhanced. In this paper, we carry out this task through least-squares approximation of sets of 2D points using free-form Bézier curves. This requires to perform data parameterization in addition to computing the poles of the curves. To this aim, we apply a powerful nature-inspired swarm intelligence method for continuous optimization called the bat algorithm. To test the performance of this new approach, it has been applied to real data of a gas. Our experimental results show that the method can reconstruct the characteristic curves with very good accuracy. In addition, the computing times are also very good, given the complexity of this problem. These remarkable features make this approach very promising in the field. Furthermore, it is actually ready to be applied to real-world instances of chemical components and mixtures.