Zero‐Order Kinetics Model for the Christensen‐Larsen Method for Fugitive Fuel Age Estimates

Abstract

Estimating time of a middle distillate fuel release in soil can be performed under certain restricting environmental conditions using the Christensen‐Larsen method (CLM). This method is based on the linear correlation between the time since a diesel fuel release and the corresponding value of n‐heptadecane to pristane ratio (n‐C17/Pr) but requires knowledge of the initial ratio value. The empirical nature of this method does not, however, allow accounting for variance in the initial fuel value used by CLM. Based on the zero‐order approximation of the Monod model, we have deduced a generalized equation that can be used for estimating release ages of middle distillate fuels with different initial values. When combined with other site‐specific factors, this equation provides a useful tool for the time of release estimates.

Age Dating Heating-Oil Releases, Part 1. Heating-Oil Composition and Subsurface Weathering

“…However, several recent studies conclude that the method is viable, although with limitations; for example, more than one sample is recommended and knowledge of the original n-C 17 /pr ratio is needed (Wade, 2001;Hurst, 2003;Hurst and Schmidt, 2005;Oudijk et al, 2006;Hurst and Schmidt, 2007;Oudijk, 2007;Hurst and Schmidt, 2008). Galperin and Kaplan (2008d) recently provided a model based on different initial n-C 17 /pr values.…”

On Age-Dating Distillate Fuels: A Commentary on the Methods of Hurst & Schmidt (2005) and Galperin & Kaplan (2008)

“…Recent commentaries on these works have gone back and forth in a lively discussion of the issue (Oudijk, 2007;Hurst & Schmidt, 2007, 2008Galperin & Kaplan, 2008b). Galperin and Kaplan (2008a) deserve credit for moving us (finally) from the empirical relationship of Christensen and Larsen (1993) to a similar relationship derived from fundamental first principles, dispelling some of the more speculative aspects of Hurst and Schmidt (2005) on timing of hydrocarbon degradation. However, let it be said that the efforts of Hurst and Schmidt have definitely moved the discussion of age-dating petroleum releases forward.…”

“…The C&L approach, however modified, may only need to be considered semi-quantitative. As stated previously, forensic investigators should consider the methods of Hurst and Schmidt (2005) and Galperin and Kaplan (2008a), in addition to the Christensen and Larsen (1993) technique, but no single work should be relied upon as having the final say, even the ones written and advocated by us. It is incumbent upon each and every one of us to guard against the let it fly approach, adhere to a rigorous scientific method to evaluate the problem of age-dating of distillate fuels on a case-by-case site-specific basis, and always maintain an understanding of the problems associated with any single age-dating approach.…”

“…Hurst and Schmidt (2005) and Galperin and Kaplan (2008a) both provided methodologies to estimate the timing of a diesel-fuel release (or a release of no. 2 fuel oil) to subsurface soils.…”

“…The methods offered by Hurst and Schmidt (2005) and Galperin and Kaplan (2008a), in general, use the rate of petroleum weathering in the soil as a proxy for age. The basis for these two methods cited considers only the petroleum composition, at time t = 0 and then at time t = x.…”