Interaction Parameters For Equations Research Articles

Shape factors and interaction parameters in equations of state Part I. Repulsion phenomena in rigid particle systems

An equation of state for the fluid phase of nonattracting rigid particles of arbitrary shape is presented. A particle shape factor is defined and its dependence on the packing fraction is evaluated from Monte Carlo and molecular dynamics simulation results for a variety of nonattracting asymmetric rigid particles, e.g., rigid-sphere polymers, ellipsoids, star particles, spherocylinders.

A systematic approach for the efficient estimation of interaction parameters in equations of state using binary vle data

AbstractA systematic and computationally efficient approach for the estimation of the interaction parameters in equations of state using binary vapor liquid equilibrium (VLE) data is presented. Initially, the best set of interaction parameters is estimated by implicit least squares. Subsequently, the VLE calculations are performed using these parameters. Based on the quality of the fit it is decided whether these estimates suffice or implicit maximum likelihood estimation should be performed to obtain the statistically best values. Estimation subject to the liquid phase stability constraint is performed when erroneous phase behavior is computed. The approach is illustrated with typical examples.

Constrained least squares estimation of binary interaction parameters in equations of state

Regression of binary vapor—liquid equilibrium (VLE) data is used routinely for the estimation of binary interaction parameters in equations of state. In most cases, least squares or maximum likelihood estimation yields satisfactory results. However, it has been observed that the thermodynamic model may predict erroneous phase separation. Instead of modifying the model, it is often preferable to estimate values for the interaction parameters that ensure prediction of the correct phase behavior. In this paper, the constrained least squares estimation method of Englezos et al. ( Fluid Phase Equil. 53, 81–88, 1989) has been improved to overcome the limitations caused by the lack of adequate and well distributed experimental VLE data. The liquid phase stability criterion is evaluated throughout a user-specified portion of the experimental equilibrium T- P- x surface. The method is illustrated with the estimation of the binary interaction parameters of the diethylamine—water system.

Simultaneous regression of binary VLE and VLLE data

A computational methodology for the simultaneous regression of binary vapor—liquid and vapor—liquid—liquid equilibrium data is presented. It is used for the estimation of the interaction parameters in equations of state. An implicit least-squares estimation procedure has been developed which yields the best set of parameter estimates for the equation of state. Subsequently, if the thermodynamic model is capable of representing the data without any systematic deviation, the statistically optimal parameters can be obtained by a proposed implicit maximum likelihood estimation procedure. The key advantage of both the estimation procedures is the absence of any iterative phase equilibrium computations. As a result, the methodology is easily implemented and is computationally very efficient. The application of the method is illustrated with a typical example (hydrogen sulfide—water).

Estimation of multiple binary interaction parameters in equations of state using VLE data. application to the Trebble-Bishnoi equation of state

A systematic approach for the estimation of binary interaction parameters for equations of state is presented. A least-squares procedure which is computationally very efficient is advocated for the calculation of the binary interaction parameters. Subsequently, if the calculated phase behavior represents the experimental data without a gross bias, the statistically best parameters can be obtained by maximum likelihood (ML) estimation. For these cases, the use is advocated of an implicit ML estimation procedure which is computationally significantly more efficient than the “error in variables” method. The proposed approach is particularly suitable for equations of state which have more than one interaction parameter. In such cases, the best parameter set is chosen from among several combinations of interaction parameters present in the equation of state.