Use of optimization to develop a correlation model for predicting residual NAPL saturation

Abstract

Predicting the residual saturation of a trapped non-aqueous phase liquid contaminant is critical to estimating the region of contamination, the design of remediation strategies, and risk assessment. Models were developed to predict residual NAPL saturation utilizing optimization and non-linear error functions, consequently allowing for a broader mathematical approach to model development. The input parameters evaluated represent soil and fluid properties: the uniformity coefficient (C u ), the coefficient of gradation (C c ), the capillary number (Nc), the bond number (Nb) and the total trapping number (Nt). Overall, the model that performed best was based on a second-order equation with the independent variables C u and Nt 1 using the sum of the squares of the errors. The nonlinear error function based on a derivative of Marquardt's Percent Standard Deviation performed best for three other cases.

Isotherms for the adsorption of Cu(II) onto lignin: Comparison of linear and non-linear methods

“…However, transformations of non-linear isotherm equations to linear forms implicitly alter their error structure and may also violate the error variance and normality assumptions of standard least squares. In recent years, several error analysis methods, such as the coefficient of determination, the sum of the errors squared, a hybrid error function, Marquardt's percent standard deviation, the average relative error and the sum of absolute errors, have been used to determine the best-fitting isotherm [7][8][9][10].…”

An effective response surface-based optimisation approach for soil vapour extraction system design

“…It is generally termed the response surface (RS)-based modelling technique or the so-called simulation/regression (S/R) modelling, and has been successfully applied in water resources research (Alley 1986, Lefkoff and Gorelick 1990, Cooper et al 1998, Aly and Peralta 1999, Zheng and Wang 2002, Mugunthan et al 2005, Chevalier 2006, Kisi and Cigizoglu 2007) and also in other research fields, such as structural, solid and thermal mechanic designs (see, for example, Alvarez et al 1988, Schoofs et al 1997, Variyam and Sitaraman 1999, Wang 2003, Cheng et al 2004. In those studies, it was claimed that the RS-based modelling approach can greatly simplify the associated simulations and thus improve computational efficiency.…”