An Extended Equation of State Modeling Method I. Pure Fluids

Abstract

A new technique is proposed here to represent the thermodynamic surface of a pure fluid in the fundamental Helmholtz energy form. The peculiarity of the present method is the extension of a generic equation of state for the target fluid, which is assumed as the basic equation, through the distortion of its independent variables by individual shape functions, which are represented by a neural network used as function approximator. The basic equation of state for the target fluid can have the simple functional form of a cubic equation, as, for instance, the Soave-Redlich-Kwong equation assumed in the present study. A set of nine fluids including hydrocarbons, haloalkane refrigerants, and strongly polar substances has been considered. For each of them the model has been regressed and then validated against volumetric and caloric properties generated in the vapor, liquid, and supercritical regions from highly accurate dedicated equations of state. In comparison with the underlying cubic equation of state, the prediction accuracy is improved by a factor between 10 and 100, depending on the property and on the region. It has been verified that about 100 density experimental points, together with from 10 to 20 coexistence data, are sufficient to guarantee high prediction accuracy for different thermodynamic properties. The method is a promising modeling technique for the heuristic development of multiparameter dedicated equations of state from experimental data. KEY WORDS: cubic equation of state; extended equation of state; feed forward neural network; fundamental equation of state; Helmholtz energy equation; pure fluids; thermodynamic properties.

An Assessment of Research Needs Related to Improving Primary Cement Isolation of Formations in Deep Offshore Wells

“…High accuracy for predictions on the thermodynamic properties of fluids can be obtained with the empirical multiparameter equations of state [36,37,38]. These equations of state are fluid specific and commonly expressed in terms of the reduced Helmholtz energy.…”

An Extended Equation of State Modeling Method II. Mixtures

“…In a former paper [18], the EEoS-NN framework for pure fluids was fully discussed and reference is made to that work for further modeling details, while the ECS method and its enhancements were dealt with in Refs. 16 and 17. The background of the proposed technique is constituted by the ECS method, which states that for two conformal fluids, denoted with the subscripts 0 and j , the fundamental equation holds:…”

“…In order to overcome the basic requirements of the ECS method, which are the conformality between target and reference fluids and the availability of a fundamental DEoS for the reference fluid, an EEoS model has been proposed [18] avoiding these constraints. Instead of a "reference fluid," only a "reference equation" for the target fluid itself is needed for the application of the technique.…”

“…In the proposed method [18], the analytical form of the shape functions θ j (T j , ρ j ) and φ j (T j , ρ j ) is expressed through a multi-layer feedforward neural network (MLFN), that is, a universal function approximator [21]. The values of the coefficients of the neural network are obtained through a regression procedure, indicated as "training," which forces the model to represent known values of experimentally accessible thermodynamic quantities for the target fluid, aimed at obtaining a precise multiproperty representation of the fluid itself.…”

“…18, in which a preliminary EoS for the target fluid itself is assumed as a reference instead of the equation for the reference fluid; in this way, the reference fluid becomes obsolete. The starting EoS, that can be, for instance, a simple cubic equation, is then improved and extended through the application of scale factors that correct the discrepancies between the initial model and experimental data by distorting the independent variables of the equation.…”