LORETA With Cortical Constraint: Choosing an Adequate Surface Laplacian Operator

Low resolution electromagnetic tomography (LORETA) is a well-known method for the solution of the l2-based minimization problem for EEG/MEG source reconstruction. LORETA with a volume-based source space is widely used and much effort has been invested in the theory and the application of the method in an experimental context. However, it is especially interesting to use anatomical prior knowledge and constrain the LORETA's solution to the cortical surface. This strongly reduces the number of unknowns in the inverse approach. Unlike the Laplace operator in the volume case with a rectangular and regular grid, the mesh is triangulated and highly irregular in the surface case. Thus, it is not trivial to choose or construct a Laplace operator (termed Laplace-Beltrami operator when applied to surfaces) that has the desired properties and takes into account the geometry of the mesh. In this paper, the basic methodology behind cortical LORETA is discussed and the method is applied for source reconstruction of simulated data using different Laplace-Beltrami operators in the smoothing term. The results achieved with the different operators are compared with respect to their accuracy using various measures. Conclusions about the choice of an appropriate operator are deduced from the results

Prediction of Molecular Weight of Petroleum Fluids by Empirical Correlations and Artificial Neuron Networks

The exactitude of petroleum fluid molecular weight correlations affects significantly the precision of petroleum engineering calculations and can make process design and trouble-shooting inaccurate. Some of the methods in the literature to predict petroleum fluid molecular weight are used in commercial software process simulators. According to statements made in the literature, the correlations of Lee–Kesler and Twu are the most used in petroleum engineering, and the other methods do not exhibit any significant advantages over the Lee–Kesler and Twu correlations. In order to verify which of the proposed in the literature correlations are the most appropriate for petroleum fluids with molecular weight variation between 70 and 1685 g/mol, 430 data points for boiling point, specific gravity, and molecular weight of petroleum fluids and individual hydrocarbons were extracted from 17 literature sources. Besides the existing correlations in the literature, two different techniques, nonlinear regression and artificial neural network (ANN), were employed to model the molecular weight of the 430 petroleum fluid samples. It was found that the ANN model demonstrated the best accuracy of prediction with a relative standard error (RSE) of 7.2%, followed by the newly developed nonlinear regression correlation with an RSE of 10.9%. The best available molecular weight correlations in the literature were those of API (RSE = 12.4%), Goosens (RSE = 13.9%); and Riazi and Daubert (RSE = 15.2%). The well known molecular weight correlations of Lee–Kesler, and Twu, for the data set of 430 data points, exhibited RSEs of 26.5, and 30.3% respectively

Prediction of Molecular Weight of Petroleum Fluids by Empirical Correlations and Artificial Neuron Networks

The exactitude of petroleum fluid molecular weight correlations affects significantly the precision of petroleum engineering calculations and can make process design and trouble-shooting inaccurate. Some of the methods in the literature to predict petroleum fluid molecular weight are used in commercial software process simulators. According to statements made in the literature, the correlations of Lee–Kesler and Twu are the most used in petroleum engineering, and the other methods do not exhibit any significant advantages over the Lee–Kesler and Twu correlations. In order to verify which of the proposed in the literature correlations are the most appropriate for petroleum fluids with molecular weight variation between 70 and 1685 g/mol, 430 data points for boiling point, specific gravity, and molecular weight of petroleum fluids and individual hydrocarbons were extracted from 17 literature sources. Besides the existing correlations in the literature, two different techniques, nonlinear regression and artificial neural network (ANN), were employed to model the molecular weight of the 430 petroleum fluid samples. It was found that the ANN model demonstrated the best accuracy of prediction with a relative standard error (RSE) of 7.2%, followed by the newly developed nonlinear regression correlation with an RSE of 10.9%. The best available molecular weight correlations in the literature were those of API (RSE = 12.4%), Goosens (RSE = 13.9%); and Riazi and Daubert (RSE = 15.2%). The well known molecular weight correlations of Lee–Kesler, and Twu, for the data set of 430 data points, exhibited RSEs of 26.5, and 30.3% respectively