Nonlinear Least-squares Fitting Method Research Articles

Non-linear least-square fitting method for characterization of forward osmosis membrane

We assess three forward osmosis (FO) performance data collection protocols, namely multiple-filtration, multi-stage and single-stage using non-linear least-square fitting method to simultaneously characterize water permeability coefficient (A), solute permeability coefficient (B) and structural parameter (S) of FO membranes. They differ only on the procedure to acquire water and reverse salt flux data. Both set of fluxes data were later used as inputs in non-linear least-square fitting optimization to obtain the A, B and S parameters. The method were evaluated using two commercial FO membranes. We employed the mass-transport models that counting for internal and external concentration polarizations in the feed and the draw sides. We also demonstrated the use of the single-stage protocol to characterize fouled FO membranes. Overall results showed that all protocols are equally effective for characterizing FO membranes, demonstrating generality of the least-square fitting method. Furthermore, the single-stage protocol can be used for characterizing fouled FO membrane in situly. As expected, fouling was more severe for the active layer facing draw solution (ALDS) than the active layer facing feed solution (ALFS) mode, as was also reflected by larger changes of their properties relative to their pristine conditions. The ability to characterize fouled membrane using the single-stage protocol could help to unravel mechanisms of fouling in FO. For instance, as demonstrated in this study, fouling in ALDS mode occurred internally by penetrating support layer.

Electric circuit modeling of fuel cell system including compressor effect and current ripples

This study aims to investigate the development of an Electrical Circuit Model (ECM) that represents the behavior of a PEM fuel cell system. The ECM parameters are identified based on sets of impedance data obtained by using a characterization process known as Electrochemical Impedance Spectroscopy (EIS). In this process, a small magnitude of alternating current sweeping a broad spectrum of frequencies is superimposed on a DC current drawn from the fuel cell while measuring the resulting voltage response. The measured impedance is fitted to an ECM using a nonlinear least-square fitting method. The proposed ECM is able to reflect the voltage response of the system to current ripples and represent the effect of the compressor. The proposed model is validated using a commercial fuel cell power module. In general, such model representation is useful for analyzing the effects of the operating conditions on the fuel cell performance, efficiency and durability. It also helps in comprehending the effects of current ripple on the fuel cell while operating with power-conditioning units

Supercritical water gasification of glycerol: Intermediates and kinetics

In this paper, the liquid products from supercritical water gasification (SCWG) of glycerol were analyzed and some intermediates were identified. A simplified reaction pathway for gases production from SCWG of glycerol was proposed. The first quantitative kinetics model for describing the gaseous products (H2, CO, CH4 and CO2) of SCWG of glycerol was developed. The model comprises seven reactions to describe the typical reactions in SCWG, and the reaction rate constant of each reaction was obtained by using the nonlinear least-square fitting method. The reaction rate analysis showed that the main sources of hydrogen yield were glycerol pyrolysis and steam reforming of intermediates, while the hydrogen yield from water–gas shift reaction (WGSR) was very small. The temperature estimated by the kinetics model for completely SCWG of glycerol solution was given. In addition, the sensitivity analysis of rate constant of WGSR was done based on the model.

Experimental study of gas–liquid mass transfer coupled with chemical reactions by digital holographic interferometry

This work deals with the development of a new experimental tool and an original procedure to study the gas–liquid absorption process coupled with chemical reactions in the liquid phase. This absorption is realized inside a Hele-Shaw cell and digital holographic interferometry is used to visualize the formation and the development of the diffusion layer during the mass transport in the liquid phase in the vicinity of the gas–liquid interface. An image processing code is developed to extract quantitative information from the raw experimental results. The experimental results are compared to a mass transfer model in the liquid phase of the Hele-Shaw cell and some physico-chemical parameters of this model are estimated from this comparison using on a non-linear least-square fitting method. The developed procedure is used to study the gaseous CO 2 absorption in NaHCO 3–Na 2CO 3 aqueous solution. Calibration curves are determined and experiments are realized for several couples of NaHCO 3–Na 2CO 3 initial concentrations. The estimated values of the physico-chemical parameters for each experiment are presented and they are compared to the values calculated from correlations found in the literature. A reasonable agreement is observed, which tends to show that the methodology is promising and could be applicable to other systems.

Extended electron energy loss fine structure simulation of the local boron environment in sodium aluminoborosilicate glasses containing gadolinium

Electron energy loss boron K-edge spectra of gadolinium-bearing sodium aluminoborosilicate glasses were acquired. Extended electron energy loss fine structure studies were performed in both extended and near edge region. Using Gd-metaborate, GdB 3O 6, as a model, we fitted the experimental B K-edge spectra of the glasses containing 30 and 47 mass% Gd 2O 3 in r-space with a non-linear least-square fitting method. Based on the results obtained from the current study, the majority of borate units appear to react with Gd cations and the local environment of Gd cations resembles that of the Gd-metaborate structure. Therefore, a distorted Gd-metaborate-like local atomic structure is proposed, in which each Gd cation is stabilized by one tetragonal BO 4 unit and two trigonal BO 3 units. The similarity of the chemical environment between the two high Gd-bearing glasses implies that the local Gd-metal borate environment, 1BO 4:Gd:2BO 3, is stable. When the Gd to B ratio in the glasses exceeded 1 to 3 ratio, according to the model, excess Gd cations should form bonds with silicate units. The modeling results are further supported by the energy loss near edge spectra data and previously results obtained from Raman and laser fluorescence deduced phonon side band studies.

On the Determination of Velocities of Radar Meteors

AbstractThe results of testing the classical method of velocity determination based on the positions of the extrema of Fresnel diffraction patterns (FDP) in radio echo amplitude, is presented. This technique is compared to the method of nonlinear least squares fitting (NLSF) of the theoretical patterns to the observed those. It is shown that while the classical method can fail in yielding correct values for the velocity of radar meteors, the NLSF method always yields good results.

Mechanism of H 2D 2 equilibration on potassium-graphite intercalation compounds

H 2D 2 equilibration reaction was investigated on the lamellar graphite intercalation compounds, C 8K and C 24K. The catalytic activity of these compounds did not depend on the stage number which was a measure of the extent of potassium intercalation, but was concerned with the area of the surface parallel to the c axis of the host graphite crystallites. A computer analysis of the reaction-time course by the nonlinear least-square fitting method revealed that the reactions proceeded via the exchange between chemisorbed atoms and gaseous (or physisorbed) molecules. By combining these findings with the data of catalyst deactivation by O 2 or CO, the structure of active site and the catalytic behavior like that of electron donor-acceptor complexes were discussed.