Refinement of the gradient method for the estimation of natural source zone depletion at petroleum contaminated sites

https://doi.org/10.1016/j.jconhyd.2021.103807Get rights and content

Highlights

  • The accuracy of the traditional gradient method to estimate NSZD rates is examined.

  • The traditional gradient method can underestimate the flux up to a 10-fold factor.

  • New methods for the estimation of oxygen and carbon dioxide flux are presented.

  • The developed analytical solutions are in good agreement with field data.

Abstract

Rates of natural source zone depletion (NSZD) are increasingly being used to aid remedial decision making and light non-aqueous phase liquid (LNAPL) longevity estimates at petroleum release sites. Current NSZD estimate methods, based on analyses of carbon dioxide (CO2) and oxygen (O2) soil-gas concentration gradients (“gradient method”) assume linear concentration profiles with depth. This assumption can underestimate the concentration gradients especially above LNAPL sources that are typically characterized by curvilinear or semi-curvilinear O2 and CO2 concentration profiles. In this work, we proposed a new method that relies on calculating the O2 and CO2 concentration gradient using a first-order reaction model. The method requires an estimate of the diffusive reaction length that can be easily derived from soil-gas concentration data. A simple step-by-step guide for applying the new method is provided. Nomographs were also developed to facilitate method application. Application of the nomographs using field data from published literature showed that NSZD rates could be underestimated by nearly an order of magnitude if reactivity in the vadose zone is not accounted for. The new method helps refine NSZD rates estimation and improve risk-based decision making at certain petroleum contaminated sites.

Introduction

Petroleum hydrocarbons released in the subsurface tend to form light non-aqueous phase liquids (LNAPL) that migrate downward in the vadose zone under the force of gravity (Rivett et al., 2011). During the vertical percolation, the LNAPL is partially entrapped in the pores of the soil as an immobile residual phase due to the establishment of capillary forces (ITRC, 2009). If the quantity of the release is significant, LNAPLs can reach the capillary fringe and partially penetrate the saturated zone (U.S. EPA, 1995).

LNAPL constituents in the smear zone undergo a series of naturally occurring processes that can lead to a progressive reduction of the source mass (Lari et al., 2019). In the late 90's the main mechanism attributed to the natural attenuation of LNAPL was the dissolution of the soluble constituents in groundwater and the subsequent aqueous phase biodegradation occurring through various terminal electron acceptor processes (Newell et al., 2002). The term used to describe the attenuation of concentration of dissolved constituents in groundwater was monitored natural attenuation or MNA (U.S. EPA, 1999). Later, it was found that within the LNAPL body and overlying capillary fringe, methanogenic biodegradation of hydrocarbons occurs and generates CH4 and CO2 (Amos and Mayer, 2006). The methane and petroleum hydrocarbons volatilized from the saturated zone are then aerobically biodegraded in the vadose zone leading to a consumption of O2 from the soil-gas and a generation of CO2 and heat (ITRC, 2018). These processes were found to be the main drivers of the progressive depletion of LNAPL sources (Garg et al., 2017). The combination of the attenuation processes occurring in the saturated and in the vadose zone is commonly termed natural source zone depletion or NSZD (API, 2017; ITRC, 2018). An increasing number of studies have demonstrated that NSZD occurs in most sites impacted by petroleum hydrocarbons with measured depletion rates ranging from thousands to tens of thousands of liters per hectare per year (e.g. see Amos et al., 2005; Johnson et al., 2006; Lundegard and Johnson, 2006; Sihota et al., 2011; McCoy et al., 2014; Sihota and Mayer, 2015; Eichert et al., 2017; Garg et al., 2017; Verginelli et al., 2018; Sihota et al., 2018; Kulkarni et al., 2020; McHugh et al., 2020; DeVaull et al., 2020).

As described in detail in the recent guidelines issued by API (2017), ITRC (2018) and CRC CARE (2018), over the last decades several approaches were successfully applied to quantify the NSZD rates. The most widely used methods involve mass-flux estimates of bulk hydrocarbon attenuation based on measuring rates of CO2 production with dynamic closed chambers (DCC, Sihota et al., 2011) or passive flux traps (McCoy et al., 2014) and assumptions of biodegradation reaction stoichiometry (ITRC, 2018). NSZD rates can also be estimated by calibrating reactive transport models to O2, CO2, or petroleum hydrocarbon soil-gas concentration data (Lahvis and Baehr, 1996; Lahvis et al., 1999). Some sites with significant methane production may require the application of relatively sophisticated numerical modeling (Sihota and Mayer, 2012) such as the MIN3P-DUSTY model (Molins and Mayer, 2007).

In the so-called “gradient method”, the difference in O2 or CO2 concentration between the upper and lower boundary control points of measurement, divided by the vertical distance between the control points, gives an estimate of the vertical concentration gradient which is used to calculate the diffusive flux using the Fick's law (Johnson et al., 2006; Lundegard and Johnson, 2006). The O2 and CO2 fluxes are then stoichiometrically converted into a NSZD rate. A critical step for the application of the gradient method is the selection of the upper and lower boundary control points of O2 and CO2 data needed for the linearization of the concentration profile. The API (2017) guidance provides some indication on the selection of these locations above the hydrocarbon reaction zone and based on geologic and gas profile shape considerations. However, depending on the type of hydrocarbons source and on the number of vertical soil-gas sampling points, this linear approximation can lead to inaccurate estimates of the concentration gradient especially in LNAPL source areas where NSZD rates are typically estimated. Specifically, the linear approximation of the concentration gradient is expected to work well for dissolved-phase sources. In such scenario the aerobic reaction zone is usually developed in relatively close proximity to the water table above the source (Lahvis et al., 2013) and the reaction zone is relatively short as the reaction can be considered almost instantaneous with respect to the diffusion of vapors in the vadose zone (Davis et al., 2009). Similarly, in areas not impacted by hydrocarbons that typically show little O2 consumption and CO2 production because of baseline soil respiration within the vadose zone (DeVaull, 2007) an associated flat rate of change in concentration over depth can be expected (CRC CARE, 2018). Above LNAPL sources, the position of the aerobic reaction is instead expected at some distance above the source zone because of higher hydrocarbon vapor mass flux (Abreu et al., 2009) with thicker reaction zone compared to the one expected above dissolved-phase sources (Davis et al., 2005). Fig. 1 depicts the potential O2 and CO2 profiles expected for the different scenarios discussed above. Note that these behaviors are analogous to the ones previously identified by Roggemans et al. (2001) and by Davis et al. (2005) for O2 and hydrocarbons. Thus, in the presence of LNAPL sources, curvilinear or semi-curvilinear O2 and CO2 profiles are expected and, in such cases, the linear approximation underlying the traditional gradient method can fail to accurately predict the fluxes needed for the estimation of the natural attenuation rates. To address this issue, we propose a new approach for the gradient method that relies on simplified analytical solutions accounting for diffusive reactive transport. The method is applied in a step-wise fashion to estimate NSZD rates based on data reported in published field studies. The value of the method is illustrated through a comparative assessment of NSZD rates determined using the new and traditional gradient methods.

Section snippets

Analytical solutions

The 1-D steady state analytical solutions were obtained assuming a homogenous soil with a constant diffusion coefficient. As schematically illustrated in Fig. 2, fixed O2 and CO2 concentrations at the ground surface and at the top of the anaerobic zone were set as boundary conditions for the derivation of the differential equations. The exact analytical solutions obtained using these boundary conditions are reported in the supplementary material section. Here below are reported some simplified

Nomographs to estimate NSZD rates

Nomographs were developed from the various analytical solutions to simplify the estimation of site-specific NSZD rates (Fig. 4). The nomographs require estimates of reaction length, the maximum concentrations of O2 and CO2, and the O2 or CO2 concentration gradient across the vadose zone region of interest as input. Fig. 4a and b depicts the O2 and CO2 fluxes calculated as a function of the reaction length (LR) for different maximum concentrations observed in the field (5–21%). The reaction

Conclusions

The results shown in this work highlighted that for LNAPL sites exhibiting non-linear concentration profiles of O2 and CO2, the traditional gradient method can underestimate the fluxes and associated NSZD rates up to almost one order of magnitude. In such cases, the method based on reactive transport proposed in this work may be better suited. The refinement of NSZD rates is indeed important given that the experience gained in the last years shows that most all sites fall within a factor of 10 (

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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