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A new approach in regression analysis for modeling adsorption isotherms.

ABSTRACT: Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

SUBMITTER: Markovic DD

PROVIDER: S-EPMC3929603 | biostudies-literature | 2014

REPOSITORIES: biostudies-literature

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A new approach in regression analysis for modeling adsorption isotherms.

Marković Dana D DD Lekić Branislava M BM Rajaković-Ognjanović Vladana N VN Onjia Antonije E AE Rajaković Ljubinka V LV

TheScientificWorldJournal 20140130

Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for in ...[more]

PMID: 24672394

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Project description:The presence of kerogen in source rocks gives rise to a plethora of potential gas storage mechanisms. Proper estimation of the gas reserve requires knowledge of the quantities of free and adsorbed gas in rock pores and kerogen. Traditional methods of reserve estimation such as the volumetric and material balance approaches are insufficient because they do not consider both the free and adsorbed gas compartments present in kerogens. Modified versions of these equations are based on adding terms to account for hydrocarbons stored in kerogen. None of the existing models considered the effect of kerogen maturing on methane gas adsorption. In this work, a molecular modeling was employed to explore how thermal maturity impacts gas adsorption in kerogen. Four different macromolecules of kerogen were included to mimic kerogens of different maturity levels; these were folded to more closely resemble the nanoporous kerogen structures of source rocks. These structures form the basis of the modeling necessary to assess the adsorption capacity as a function of the structure. The number of double bonds plus the number and type of heteroatoms (O, S, and N) were found to influence the final configuration of the kerogen structures, and hence their capacity to host methane molecules. The degree of aromaticity increased with the maturity level within the same kerogen type. The fraction of aromaticity gives rise to the polarity. We present an empirical mathematical relationship that makes possible the estimation of the adsorption capacity of kerogen based on the degree of polarity. Variations in kerogen adsorption capacity have significant implications on the reservoir scale. The general trend obtained from the molecular modeling was found to be consistent with experimental measurements done on actual kerogen samples. Shale samples with different kerogen content and with different maturity showed that shales with immature kerogen have small methane adsorption capacity compared to shales with mature kerogen. In this study, it is shown for the first time that the key factor to control natural gas adsorption is the kerogen maturity not the kerogen content.

Dataset Information

A new approach in regression analysis for modeling adsorption isotherms.

Publications

A new approach in regression analysis for modeling adsorption isotherms.

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