Surrogate Modeling of Fugacity Coefficients Using Adaptive Sampling

Abstract

Complex thermodynamic models such as the perturbed chain statistical associating fluid theory (PC-SAFT) model describe the phase equilibria in a chemical process in a very precise way; however, because of their implicit and complex nature, the application of such models in process simulation and optimization can lead to a high computational effort, which may prevent the direct application of such models in process simulation and optimization. In this contribution, we replace the iterative calculation of the fugacity coefficient using PC-SAFT with explicit surrogate models that are trained using a novel adaptive sampling method.

Hybrid Semi‐parametric Modeling in Separation Processes: A Review

“…Recent studies have shown that, by employing GP and ANN trained on data obtained from the PC‐SAFT in an LLE system, accurate predictions of phase equilibrium can be obtained around 36 times faster than by using the original PC‐SAFT . This surrogate model was later augmented by introducing an SVM that classifies the validity of the operating conditions (ensuring only operating conditions within the two‐phase region are considered) .…”

Surrogate Modeling of Thermodynamic Equilibria: Applications, Sampling and Optimization

“…Towards this goal, the so-called jackknife variance is employed, as it showed promising results in previous work [5]. The bootstrap method can also be used as the variance estimation method, Nentwich et al [6] report similar results compared to the jackknife variance.…”

“…As an alternative, one can implement the calculation of the equilibrium in the process model and provide thermodynamic information via auxiliary quantities, e.g., the fugacity coefficients. This is called the indirect method, see [6]. In this case, the process model into which the surrogate is embedded has to include the isofugacity constraints explicitly.…”

The Potential of Hybrid Mechanistic/Data‐Driven Approaches for Reduced Dynamic Modeling: Application to Distillation Columns

“…Here, the surrogate models of choice are typically artificial neural networks (ANNs) and Gaussian processes (GP, also referred to as Kriging). For instance, Nentwich et al [42] apply both ANNs and GPs as explicit surrogate models for calculating fugacity coefficients in a hydroformylation process replacing an iterative procedure from the PC-SAFT property model. Likewise, we replace implicit thermodynamic functions from the Helmholtz equation of state for working fluid properties in an organic Rankine cycle by ANNs that allow for calculating any property in an explicit way, thereby speeding up deterministic global optimization of the process [43,44].…”

“…However, as the ANNs only replace well‐defined stationary (algebraic) equations, training data can be obtained easily by solving these equations offline. Here, a suitable coverage of the relevant input space can be achieved by using advanced sampling methods (e.g., 42, 54, 55). Assuming maximum internal column flows to be known and considering that compositions are inherently bounded between zero and one, the risk for extrapolation of the ANNs could, thus, in principle be entirely circumvented.…”