Skip to main content
NCBI home page
NIHPA Author Manuscripts logoLink to NIHPA Author Manuscripts
. Author manuscript; available in PMC: 2021 Nov 1.
Published in final edited form as: J Contam Hydrol. 2020 Sep 17;235:103716. doi: 10.1016/j.jconhyd.2020.103716

MATHEMATICAL MODELING OF ORGANIC LIQUID DISSOLUTION IN HETEROGENEOUS SOURCE ZONES

Zhilin Guo 1,*, Ann E Russo 2, Erica L DiFilippo 3, Zhihui Zhang 2, Chunmiao Zheng 1, Mark L Brusseau 2,3,*
PMCID: PMC7704655  NIHMSID: NIHMS1629625  PMID: 32977295

Abstract

A simple one-dimensional heterogeneous-source model was used to simulate dissolution of organic liquid that was non-uniformly distributed in physically heterogeneous porous media. The permeability field was depicted as a pseudo-homogeneous medium. The source zone was discretized into multiple domains representing different organic-liquid configurations and hydraulic accessibilities, each with a different representative upscaled mass transfer rate coefficient that is temporally variable. This simplified approach represents a system where minimal information is available regarding system heterogeneities. All factors that influence dissolution were incorporated into the calibrated mass transfer terms. The mass transfer terms were calibrated for each zone separately. The one-dimensional, heterogeneous-source model adequately simulated the multi-stage dissolution behavior observed for column-scale systems that were packed with different natural soils, as well as for flow-cell systems wherein the source zone consisted of both a residual zone and pool. The results indicate that the model adequately simulated the presence of multiple organic-liquid zones in porous media with different configurations and hydraulic accessibilities, which accounts for the non-ideal dissolution behavior observed. The calibrated mass transfer terms for each source type were consistent with those obtained for systems that contained only one of either source type.

Keywords: NAPL dissolution, Multi-stage mass discharge, Upscaled models, Heterogeneous-source model

1. Introduction

One of the most critical issues associated with hazardous waste sites is the presence of non-aqueous phase liquids (NAPL), such as fuels, creosote, coal tars and chlorinated solvents, in the subsurface (NRC, 1994; 2000; 2005; 2013). Once released, these organic liquids can migrate downward into the aquifer and serve as long-term sources of contamination. A great amount of research has been conducted on NAPL source-zone behavior over the past several decades. It is now well established that the mass discharge associated with such source zones depends upon the distribution and configuration of the organic liquid (e.g., pool or ganglia), as well as the structure of the flow field.

Numerous mathematical models and functions have been developed to simulate NAPL dissolution and mass discharge from NAPL source zones. Most simplified models produce singular mass discharge (dissolution) profiles comprising monotonic decreases in concentration. However, so-called multi-stage mass discharge, due to the variability of NAPL distribution and configuration in the source zone, has been observed in field measurements (e.g., Brusseau et al., 2007; DiFilippo and Brusseau, 2008; Brusseau et al., 2013; Brusseau and Guo, 2014; Teramoto and Chang, 2017), laboratory experiments (e.g., Zhang et al., 2008; Russo et al., 2009; DiFilippo et al., 2010; Mateas et al.,2017; Karaoglu et al., 2019), and numerical simulations (e.g., Lemke et al., 2004; Soga et al., 2004; Christ et al., 2010; Yang et al., 2018). This multi-stage behavior typically exhibits alternating periods of pseudo steady-state dissolution and relatively rapid declines in concentration, as shown in Figure 1. The abrupt change in concentration is typically caused by a transition of the particular source-zone domain or configuration predominantly contributing to mass discharge, i.e., between regions of NAPL contamination that have significantly different hydraulic accessibilities. A simple extreme example would be the transition from a ganglia-dominated system to a pool-dominated system (e.g., Lemke et al., 2004; Parker and Park, 2004; Christ et al., 2010; Rivett et al., 2014; DiFilippo et al., 2010; DiFilippo and Brusseau, 2011a).

Figure 1.

Figure 1.

Open in a new tab

Conceptual NAPL dissolution behavior during a mass removal process. The solid line represents multi-stage dissolution behavior, and the dash line represents singular behavior. The conceptualization is based on laboratory and field experiment observations in prior research (e.g., DiFilippo and Brusseau, 2008; Russo et al., 2009; DiFilippo et al., 2010; Brusseau et al., 2013; Brusseau and Guo, 2014).

A number of approaches have been used for simulating multi-stage dissolution of organic liquid and mass discharge from source zones. Multi-process mathematical models can be applied to represent dissolution in complex, heterogeneous systems (e.g., Zhang and Brusseau, 1999; Christ et al., 2006; Karaoglu et al., 2019). However, these models require detailed characterization of system heterogeneities and source-zone architecture and the information is often unavailable. In addition, the complexity and cost of computing remains high even with current computational capacity. Consequently, there is great interest in using simpler, upscaled models to simulate source dissolution.

In the past two decades, several different types of simple, upscaled models have been developed and tested, such as equilibrium streamtube methods, power law relationships between concentration and mass, dual-domain models, and other methods with upscaled effective mass transfer rate coefficients (Parker and Park, 2004; Jawitz et al., 2005; Basu et al., 2008; Marble et al., 2008; Christ et al., 2010; DiFilippo and Brusseau, 2011a; Boroumand and Abriola, 2015). However, most of these models (e.g., Parker and Park, 2004; Jawitz et al. 2005; Basu et al., 2008; Marble et al., 2008; Luciano et al., 2018) produce smooth singular dissolution profiles and thus are not able to capture non-singular dissolution behavior caused by the complexity of the source zone architectures.

Two general approaches have been taken to attempt to simulate multi-stage dissolution behavior. One is based on the dual-domain conceptualization. Such models have been used successfully to simulate solute transport in heterogeneous NAPL-contaminated systems (e.g., Brusseau, 1992; Powers et al., 1998; Falta, 2003; Konikow, 2011; Vasudevan et al. 2016; Guo et al., 2019). Christ et al. (2010) presented an upscaled two-domain mass-transfer model to reproduce dissolution behavior in pool-dominated scenarios, which divided the source zone into two domains, ganglia- and pool-dominated regions. The dissolution process was described by simple mass-removal functions. The model successfully simulated the two-stage NAPL dissolution process. However, it requires prior knowledge of the source structures, i.e. the fractions of NAPL mass located in ganglia and pools, which is not always available for field systems. Moreover, the model cannot capture the complex dissolution behavior evident when more than two effective domains exist.

The second approach is based on using macroscopic system-indicator parameters that are allowed to change with time to account for the temporal evolution of the source zone (e.g., DiFilippo and Brusseau, 2011a; Kokkinaki et al., 2014). DiFilippo and Brusseau developed a model that incorporated macroscopic parameters accounting for the source zone cross-sectional area and length as well as changes in relative permeability. These parameters varied as a function of mass removal with time (as the organic-liquid distribution and relative permeability change). The model was successful in simulating multi-stage dissolution behavior observed for flow-cell experiments. Kokkinaki et al. (2014) used an approach similar to that of DiFilippo and Brusseau, explicitly considering the temporal evolution of parameters representing the local DNAPL saturation, the source zone projected area, and the relative permeability. The model was evaluated by simulating data obtained from both real and hypothetical source zones and demonstrated the capability to describe the multi-stage dissolution behavior. These two studies demonstrated the effectiveness of the temporally variable system-indicator approach for simulating multi-stage dissolution behavior. However, measurements of these indicator parameters multiple times during mass-removal is likely to be difficult and expensive for many field applications. Therefore, a method that can be readily applied to complex NAPL source zones to reproduce the multi-stage dissolution process is still a focus of research.

The purpose of this study is to investigate the use of a one-dimensional, heterogeneous-source model to simulate organic-liquid dissolution from a source zone consisting of multiple NAPL configurations and hydraulic accessibilities. The model assumes uniform flow and transport but treats the organic-liquid source zone as comprising multiple domains with different upscaled mass transfer rate coefficients. The dissolution process was explicitly described, and incorporates the impact of temporal evolution of the source zone on mass transfer rate coefficients. The model is applied to data sets generated from column experiments comprising different soils and flow cell experiments with different domain configurations.

2. Materials and Methods

2.1. Systems investigated

As noted above, the objective of this study was to evaluate the use of a one-dimensional, heterogeneous-source model for simulating organic-liquid dissolution from systems with complex source types (i.e., containing organic liquid in both residual zones and pools). Data obtained from a series of column experiments and flow-cell experiments were used to evaluate the model. The systems were designed to reflect a variety of organic-liquid distributions and flow-field heterogeneities.

2.1.1. Column experiments

Data were generated in previously published studies (Russo et al., 2009a; Mahal et al., 2010). A brief overview is discussed herein. Experiments were conducted with 7-cm long and 2.1-cm ID stainless steel columns (Alltech). Trichloroethene (TCE) (Aldrich Chemical Co., Inc, Milwaukee, WI) was used as the model organic liquid. Pentaflourobenzoic Acid (PFBA) (Aldrich Chemical Co., Inc.) was used as a conservative tracer to determine the hydrodynamic properties of the packed column. The porous media used were Eustis soil, Borden soil, Hayhook soil and Mt. Lemmon soil as well as a mixed sand. The media encompass a wide range of particle size distributions (reflected in the uniformity coefficients) (Table 1).

Table 1.

Properties of Porous Media in Column Experiments

Porous
Media		 Sand
%		 Silt
%		 Clay
%		 Bulk
Density
(g/cm3)		 Porosity Median
Grain
Diameter
d50
(mm)		 Organic
Content
(OC)		 Uniformity
Coefficient
(UC)		 R
Borden soil 96.2 2 1.8 1.74 0.34 0.21 0.03 1.92 1.54
Eustis soil 95.9 1 4.4 1.69 0.36 0.27 0.38 2.3 2.43
Hayhook soil 85.5 4.3 10.2 1.64 0.38 0.26 0.08 16 1.34
Mixed sand* 1.87 0.29 0.34 3.45 1.58
Open in a new tab
*

mixed sand – accusand and granusil Michele mahal, bulk density avg of organic liquid exps

Dissolution began by flushing the column with CaCl2 solution and collecting aqueous samples at a flowrate of 0.7 ml/min. Electrolyte solution was pumped into the column from the bottom (the same direction as injection) using a HPLC pump. Samples were collected in 2 ml or 5 ml glass syringes (Popper & Sons, Inc, New Hyde Park, N.Y.), and were diluted as needed. PFBA samples were analyzed using a UV-vis spectrophotometer (SPD-10A Shimadzu) at a wavelength of 262 nm. Aqueous TCE samples, ranging in concentrations from saturation (1200-1500 mg/L) to approximately 10 mg/L were analyzed using a UV-vis at a wavelength of 232 nm. A GC-ECD (Electron Capture Detector) was used to analyze samples below 10 mg/L. The detection limit on this instrument is approximately 0.2 μg/L.

2.1.2. Flow cell experiments

The flow cell data were published in DiFilippo et al. (2010); a brief description is presented below. Three natural sand media with different median particle diameters were used in these experiments, 713 μm (20/30 mesh), 359 μm (40/50 mesh), and 172 μm (70/100 mesh) (Unimin Corp.). Representative hydraulic conductivities for the three media are 15, 4, and 0.1 cm/min, respectively (Schroth et al., 1996). Trichloroethene (TCE), ACS grade (Aldrich), was used as the organic liquid. The organic liquid was dyed with Sudan IV (Aldrich) at a concentration of 100 mg/L, which has been shown to have minimal impact on fluid properties and behavior (Schwille, 1988; Kennedy and Lennox, 1997).

A total of three experiments were conducted for the study (Table 2). The Control experiment consisted of a homogeneous pack of 40/50 sand. A residual saturation of TCE was emplaced in the middle of the flow cell by manually mixing and packing the source zone with organic liquid using standard procedures (Brusseau et al., 2000; Brusseau et al., 2002; Brusseau et al., 2008). This method developed a source zone wherein organic liquid was present at residual saturation in a small portion (10%) of the total flow field. The Mixed-Source experiment consisted of a uniform pack of 40/50 sand with a 2 cm thick capillary barrier (70/100 sand) located along the bottom. The Heterogeneous experiment consisted of a matrix of 40/50 sand with lenticular zones of coarser (20/30) and finer (70/100) sand. Organic liquid distribution was spatially nonuniform for both of these experiments and encompassed a range of saturations (Figure 1). For the Mixed-Source and Heterogeneous experiments, the distribution of organic liquid was characterized using a Light Reflection Visualization (LRV) method (Kechavarzi et al., 2000; DiFilippo and Brusseau, 2011b).

Table 2.

Summary of system parameters and modeling calibrated parameters for the one-dimensional, one-source model

Experiment Q (ml/min) PV (ml) q (cm/hr) v (cm/hr) kLa β4
Control 2.65 185.4 3.28 9.42 0.4 0.5
Mixed Source 3.27 913.3 3.18 9.13 0.16 1.2
Heterogeneous 3.33 812.9 3.36 9.66 0.05 0.8
Open in a new tab

2.2. Conceptualization

In this work, a simple one-dimensional dissolution and solute transport model is used to simulate dissolution from a non-uniformly distributed source zone. The porous medium and water flow were assumed to be uniform. Two sets of simulations were used to predict dissolution from these systems. The first set of simulations (one-dimensional, one-domain) treated the organic-liquid as one source, uniformly distributed across the entire length and cross-section of the system. The second set of simulations (one-dimensional, heterogeneous-source) divided the organic liquid source into multiple sources representing the residual portions and pool portions with different mass transfer rate coefficients in the source zone. Mass-transfer coefficients were calibrated for each domain separately.

2.3. One-Dimensional, Heterogeneous-Source Model

The governing equation for solute transport in the flow cells with dissolution of organic liquid is described by:

θa∂C∂t+ρN∂θN∂t=∂∂xi(θaDij∂C∂xj)−qi∂C∂xi (1)

where C is the aqueous concentration of solute; θa is the fractional volumetric water content; θN is the fractional volumetric content of the organic liquid; θN is density of the organic liquid; qi is Darcy velocity; Dij is the dispersion coefficient tensor; xi is cartesian coordinates; i, j = 1, 2, 3 and conforms to the summation convention; and t is time. Sorption of the organic compounds by the media used in these experiments is minimal, and is therefore ignored.

The model allowed for discretization of organic liquid into multiple domains. Organic liquid in each domain was assumed to be uniformly distributed across the entire length and cross-sectional area of the system. With this approach, larger scale factors influencing dissolution and transport are not explicitly represented in the model. Their impacts are incorporated into calibrated dissolution rate coefficients. The importance of each domain to the overall dissolution behaviour was controlled by the ratio of the cross-sectional area of each source type to the cross-sectional area of the entire source zone. Organic-liquid dissolution in each domain is described with the widely used first-order mass transfer equation:

ρN∂θN∂t=kLa(C−Cs) (2)

where kLa is a lumped mass transfer coefficient for dissolution, and Cs is the aqueous solubility of the organic liquid. The time dependency of kLa is represented by:

kLa(t)=kLa0[Re(t)Re0]β1[θN(t)θN0]β4 (3)

where kLa0 and Re0 are the initial local (nodal) values; Re is the Reynolds number; β1 and β4 are coefficients. The organic dissolution can be described as:

ρN∂θNi∂t=kLai0[Rei(t)Rei0]β1[θNi(t)θNi0]β4(C−Cs)

where i=1,2,…m; and m is the total number of discrete dissolution domains. As described in Zhang and Brusseau (2004), values of β1 were provided by Powers et al. (1994) based on analysis of dissolution data. β4 is solely associated with the temporal variability of kLa. Therefore, two parameters were calibrated, kLa and β4 in this study. The simulations were very sensitive to the magnitude of the calibrated terms, with coefficient of variations of less than approximately 5%. A single region approach was also used to model the observed data. It assumes that the dissolution of the organic liquid in the system is controlled by a single rate coefficient and one effective organic liquid configuration or interfacial area.

3. Results and Discussion

3.1. Experiments results

3.1.1. Column experiments

As discussed previously, column experiments were conducted with various natural porous media (Borden, Eustis, Hayhook and Mt. Lemmon soils) as well as a mixed sand. Borden and Eustis dissolution experiments had a residual saturation of 11.4 and 14.7%, respectively. Mt. Lemmon soil and the mixed sand had residual saturations of 8.1 and 8.2%, respectively. Hayhook soil experiments had higher residual saturations of approximately 20% saturation.Observed dissolution behavior was characterized by an initial steady state stage followed by a transient region. In addition, a secondary step in the dissolution process was observed at approximately one log below solubility (Figure 2), in which concentrations decreased gradually for a significant number of pore volumes.

Figure 2.

Figure 2.

Open in a new tab

Organic-liquid distribution for the (a) Mixed Source and (b) Heterogeneous experiments. Organic-liquid saturation was determined using imaging as described in the text. The matrix of the Mixed-Source experiment was composed of 40/50 sand and the gray zone was composed of 70/100 sand. The matrix of the Heterogeneous experiment was composed of 40/50 sand. The black-outlined zones were composed of 20/30 sand and gray zones were composed of 70/100 sand. The organic-liquid saturation is defined using the color scale, where warm colors indicate high organic-liquid saturation and cool colors represent low saturation. The spatial resolution for each image was 0.02 mm2.

The secondary region extends for approximately 50 pore volumes for both Eustis and Borden dissolution experiments. For Hayhook soil, the secondary region begins at less than one log below solubility and extends for approximately 100-150 pore volumes (Figure 3). Similar behavior was also observed for the mixed sand experiments, where secondary stages are observed at less than one log below solubility and extend for approximately 100-200 pore volumes (Figure 4). For Mt. Lemmon soil dissolution, the secondary region is observed at approximately three logs below solubility and extends for approximately 700 pore volumes. The high organic carbon content associated with Mt. Lemmon soil may have an impact on TCE configuration and thus the observed dissolution behavior.

Figure 3.

Figure 3.

Open in a new tab

Mathematical simulations and experiment data for dissolution experiments with Eustis and Borden soil in column experiments.

Figure 4.

Figure 4.

Figure 4.

Open in a new tab

Elution curve for dissolution experiments with Hayhook soil (a) and Mt. Lemmon soil (b) in column experiments.

3.1.2. Flow cell experiments

The contaminant elution curves for the control and flow-cell experiments are presented in Figure 6. The effluent concentrations for the control experiment initially remained steady and after 40% of the total organic-liquid mass was removed, the concentration dropped quickly to three orders of magnitude lower. The elution curves for the Mixed Source and Heterogeneous experiments exhibited relatively extensively asymptotic periods after the concentrations gradually decreased approximately one order of magnitude, and then declined rapidly to lower concentration. The multi-stage behaviors are due to the source distributions, which also reflects the impacts of mass-removal constraints. And the steady state period represents the transition of dissolution of pool source to ganglia source.

Figure 6.

Figure 6.

Open in a new tab

Measured effluent concentrations and model simulations using the one-dimensional, one-source model for the control and flow-cell experiments.

3.2. Mathematical Modeling

3.2.1. Single region model

Mathematical modeling was conducted to simulate the observed organic immiscible liquid dissolution behavior. Initially, attempts were made to describe observed dissolution behavior with a single-region model. The single-region model was not able to reproduce the multi-stage dissolution behavior observed in the column experiments (results not shown).

For the flow cell experiments, the one-dimensional, one-source simulations of the measured data are presented in Figure 6. The calibrated values for kLa and β4 are presented in Table 2. Inspection of Figure 6 shows that the predicted simulations provide a good match to the Control experiment, as well as the early elution behavior for both the Mixed Source and Heterogeneous experiments. The early stage elution behavior for the Mixed Source and Heterogeneous experiments is controlled by dissolution of organic-liquid mass from the residual saturation regions of the source zone, which had initial saturations of 0.11 and 0.14 for the Mixed Source and Heterogeneous experiments, respectively (DiFilippo et al., 2010). The calibrated kLa and β4 values for the Mixed Source and Heterogeneous experiments are consistent with simulations of systems with a similar initial residual saturation source zone (Sn = 0.06) that is hydraulically accessible (Marble et al., 2008). The one-source model, however, does not adequately simulate the late stage elution behavior for either the Mixed Source or Heterogeneous experiments. The late stage elution behavior for these experiments is controlled by dissolution from the hydraulically-poorly accessible organic-liquid pools, which had initial saturations of 0.18 and 0.20 for the Mixed Source and Heterogeneous experiments, respectively (DiFilippo et al., 2010).

3.2.2. Heterogeneous-source model

For the column experiment results, a multiple region model with three zones was used for the majority of the experiments, although in some cases, two zones were sufficient to describe the behavior. The multi-region model is based on the assumption that more than one organic liquid configuration is present in the column, with one organic liquid configuration contributing to the steady state region and another organic liquid configuration contributing to the observed dissolution behavior for the secondary region. Results of the mathematical modeling are shown in Table 3. Zone fractions are shown in the table, representing the different fractions of organic liquid volumes in each section of the model required to support the observed dissolution behavior.

Table 3.

Dissolution Experiments and Modeling Parameters for Column Experiments

Porous Media Initial Saturation % Zone fractions* Kla (h−1)
Borden soil Exp 1 11.4 0.7, 0.27, 0.08 25.7, 23.7, 4.5
Eustis soil Exp 2 14.7 0.67, 0.31, 0.08 30.4, 24.9, 4.3
Hayhook soil Exp 1 24.5 0.52, 0.24, 0.24 51.5, 21.3, 2.9
Hayhook soil Exp 2 21.1 0.54, 0.25, 0.26 49.2, 21.4, 3.2
Mixed sand Exp 1 23.7 0.77, 0.22 32.3, 5.0
Mixed sand Exp 2 21.9 0.5, 0.4995. 0.005 7.0, 5.0, 9.0
Mt. Lemmon soil Exp 1 8.14 1.05, 0.29 21.0, 0.07
Open in a new tab
*

Zone fractions refer to number of zones used for simulation

The majority of the organic liquid is observed in the first and second zone with only a very small amount of organic liquid present in the last zone. This distribution intuitively makes sense, because in the third zone, the accessible residual organic liquid in the system has been removed, leaving a small amount of organic liquid wherein mass removal is transitioning to the sorption/desorption phase of the removal process. Although the sorption/desorption tail can exist for a long time, the mass that is being removed during this time is relatively small, with approximately 99% of the mass being previously removed during the dissolution process (Johnson et al., 2003).

The lumped mass transfer coefficient (kLa), which includes the organic-liquid/water interfacial area, is also compared in Table 3. The interfacial area decreases during dissolution, which in turn decreases the mass transfer rate which is reflected in the lumped mass transfer rate coefficient. The lumped mass transfer rate coefficient is larger for the Hayhook experiments in the first zone than for the Eustis and Borden experiments. However, the mass transfer coefficient for the 2nd zone in all the experiments remains similar. From these results we can see that different rates of mass transfer are present during the dissolution process. This is further evidence that several effective organic liquid configurations could be present in the system, leading to the observed non-ideal behavior.

In a previous study (Russo et al., 2009b), X-ray Synchrotron microtomography imaging was conducted to observed dissolution behavior of TCE in Hayhook soil at the pore scale. Dissolution was observed to be non-ideal, in which TCE mass was removed from the entire length of the column during each step of dissolution. This is in contrast to the expected dissolution behavior, in which removal of organic liquid first occurs nearest the inlet end of the column. The dissolution front would then migrate downgradient through the column once all of the organic liquid nearest the inlet has been removed. This stepwise organic liquid removal was not observed in imaging.

The type of pore-scale behavior observed from imaging can be related to the column scale behavior observed in which secondary regions were present before large decreases in concentration occurred. We can hypothesize that the initial steady-state region is supported by dissolution of a particular set of organic liquid blobs and ganglia, while the second observed region is supported by a different set with a different distribution or configuration at the pore scale. The modeling results (Figure 3 and 4) presented in this study further support this hypothesis. The lumped mass transfer coefficient, kLa, includes the organic-liquid/water interfacial area which decreases during dissolution, which in turn should decrease the kLa. From Table 3, we observe that lumped mass transfer coefficient values for the first and second zones in most experiments are relatively similar. This indicates that small changes have occurred to alter the organic-liquid/water interfacial areas, which would occur if only a small portion of the immiscible liquid present in the system was being affected by the initial dissolution process.

For the flow cell experiments, a one-dimensional, two-source model was used to simulate the measured data. The calibrated kLa and β4 values for each zone are presented in Table 4. The organic-liquid dissolution area (A) for each zone was calculated as the ratio of the cross-sectional area of each zone to the total cross-sectional area of the source zone (Table 4). Inspection of Figure 7 shows that predicted simulations using the two-source model provide a good overall fit to both the early and late stage observed elution behavior. The late stage increases in concentration observed in the heterogeneous experiment is not captured by the model. This increase in concentration is due to changes in the relative permeability of this zone as organic-liquid was removed through dissolution (DiFilippo et al., 2010) which was not explicitly defined in the model. The model does, however, capture the general elution behavior in this region. The calibrated kLa and β4 values for zone 2 are consistent with simulations for systems with organic liquid pools with a similar initial saturation (Sn = 0.2) (Marble et al., 2008).

Table 4.

Summary of system parameters and modeling calibrated parameters for the one-dimensional, dual-source model

Experiment Zone 1 Zone 2
kLa β4 A kLa β4 A
Control 0.4 0.5 1.0 - - -
Mixed Source 0.16 1.2 0.9 0.03 0.09 0.2
Heterogeneous 0.05 0.8 1.0 0.03 0.06 0.2
Open in a new tab
Figure 7.

Figure 7.

Open in a new tab

Measured effluent concentrations and model simulations using the one-dimensional, dual-source model for the flow-cell experiments.

4. Summary and Conclusions

A simple one-dimensional, heterogeneous-source model was used to simulate the multistage dissolution behavior observed for column experiments comprising different natural soils, as well as for flow-cell systems wherein the source zone consisted of both a residual zone and pool. This highly simplified approach represents a system where minimal information is available regarding system heterogeneities. All factors that influence dissolution were incorporated into the calibrated mass transfer coefficients. The mass transfer coefficients are different for each zone with different source type, which is also varied temporally with evolution of source zone.

Mathematical modeling of dissolution experiments supports the hypothesis that different organic-liquid configurations are present that have different hydraulic accessibilities and therefore different rates of dissolution. The different organic-liquid configurations contribute to the occurrence and magnitude of the secondary regions. The one-source model was not able to simulate the multi-stage dissolution behavior observed in both column and flow cell experiments. Conversely, the heterogeneous-source model (three sources used for column experimental results and two sources used for flow-cell experimental results) successfully reproduced the observed data. The mass transfer rate terms were calibrated for each zone separately. The calibrated mass transfer rate terms for each source type (residual or pool) were consistent with similar systems which contained only one source type. Based on this, it provides a possibility of applying the method to a system without calibrating the parameters, where the initial saturation for each zone, pool or residual, is acquired by some independent means. The mass transfer rate coefficients determined for prior sites with similar saturation for each source type can be applied. In contrast to other methods that require prior knowledge of the source structures (Christ et al., 2010) or parameters such as source zone projected area, the averages of local DNAPL saturations and water relative permeabilities (Kokkinaki et al., 2014) or permeability indicator (DiFilippo and Brusseau, 2011a), the method developed in this study offers a relatively simple and feasible way to model the multi-stage behavior. However, when applying the parameter values that are calibrated from small scale, such as column experiments, to field scale, the dilution effect needs to be considered as illustrated in Mable et al. (2008).

In addition, Boroumand and Abriola (2015) showed the correlation between mass transfer and source zone and indicated that the mass transfer rates are changing with source depletion during the mass removal, and also the potential flow field change (Guo et al., 2020). However, while most previous studies have focused on reproducing changing mass flux due to properties associated with site or source conditions, studies on the temporal change in mass transfer are rare. Therefore, incorporating the temporal change in mass transfer due to evolution of source zone or flow field is important for accurately modeling the dissolution during site remediation. Exploring a robust method that can predict the multi-stage dissolution behaviors remains challenge and very important for sites with complex source structure and high heterogeneity during the remediation. By combining the heterogeneous-source system with temporally varied mass transfer rate coefficients for each zone, this work provides insight on development of a more cost-effectively and robust way modeling the dissolution process in large complex systems.

Figure 5.

Figure 5.

Open in a new tab

Elution curve for dissolution experiments with Mixed sand in the column experiment.

Highlights:

  • NAPL dissolution in heterogeneous media was simulated by a ID heterogeneous-source model.

  • The model simulated the presence of multiple organic-liquid domains in porous media.

  • The model adequately simulated the multi-stage dissolution behavior.

  • Incorporating the temporal change in mass transfer is important to simulate dissolution.

Acknowledgements

This research was supported by the National Institute of Environmental Health Sciences Superfund Basic Research Program (Grant Number ES04940) and the National Natural Science Foundation of China (Grant Number 41931292).

Footnotes

Conflict of Interest

The authors declare no competing financial interest.

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

References

  1. Bahar T, Golfier F, Oltéan C, Lefevre E, & Lorgeoux C, 2018. Comparison of theory and experiment for NAPL dissolution in porous media. Journal of contaminant hydrology, 211, 49–64. [DOI] [PubMed] [Google Scholar]
  2. Basu NB, Fure AD and Jawitz JW, 2008. Simplified contaminant source depletion models as analogs of multiphase simulators. Journal of Contaminant Hydrology, 97(3-4): 87–99. [DOI] [PubMed] [Google Scholar]
  3. Boroumand A and Abriola LM, 2015. On the upscaling of mass transfer rate expressions for interpretation of source zone partitioning tracer tests. Water Resources Research, 51(2), 832–847. [Google Scholar]
  4. Brusseau ML, 1992. Rate-Limited Mass-Transfer and Transport of Organic Solutes in Porous-Media That Contain Immobile Immiscible Organic Liquid. Water Resources Research, 28(1): 33–45. [Google Scholar]
  5. Brusseau ML, Nelson NT, Oostrom M, Zhang Z, Johnson GR and Wietsma TW, 2000. Influence of heterogeneity and sampling method on aqueous concentrations associated with NAPL dissolution. Environmental Science & Technology, 34: 3657–3664. [Google Scholar]
  6. Brusseau ML, Zhang ZH, Nelson NT, Cain RB, Tick GR and Oostrom M, 2002. Dissolution of nonuniformly distributed immiscible liquid: Intermediate-scale experiments and mathematical modeling. Environmental Science & Technology, 36(5): 1033–1041. [DOI] [PubMed] [Google Scholar]
  7. Brusseau ML, DiFilippo EL, Marble JC and Oostrom M, 2008. Mass-removal and mass-flux-reduction behavior for idealized source zones with hydraulically-poorly-accessible immiscible liquid. Chemosphere, 71: 1511–1521. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Brusseau ML, Matthieu III DE, Carroll KC, Mainhagu J, Morrison C, McMillan A, Russo AE and Plaschke M, 2013. Characterizing long-term contaminant mass discharge and the relationship between reductions in discharge and reductions in mass for DNAPL source areas. Journal of contaminant hydrology, 149, 1–12. [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Brusseau ML and Guo Z, 2014. Assessing contaminant-removal conditions and plume persistence through analysis of data from long-term pump-and-treat operations. Journal of contaminant hydrology, 164, 16–24. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Christ JA, Ramsburg CA, Pennell KD and Abriola LM, 2006. Estimating mass discharge from dense nonaqueous phase liquid source zones using upscaled mass transfer coefficients: An evaluation using multiphase numerical simulations. Water Resources Research, 42(11). [Google Scholar]
  11. Christ JA, Ramsburg CA, Pennell KD and Abriola LM, 2010. Predicting DNAPL mass discharge from pool-dominated source zones. Journal of Contaminant Hydrology, 114(1-4), 18–34. [DOI] [PubMed] [Google Scholar]
  12. DiFilippo EL, Carroll KC, and Brusseau ML, 2010. Impact of organic-liquid distribution and flow field heterogeneity on reductions in mass flux, Journal of Contaminant Hydrology, 115, 14–25 [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. DiFilippo EL, and Brusseau ML, 2011a. Assessment of a simple function to evaluate the relationship between mass flux reduction and mass removal for organic-liquid contaminated source zones, Journal of Contaminant Hydrology, 123(3), 104–113. [DOI] [PMC free article] [PubMed] [Google Scholar]
  14. DiFilippo EL, and Brusseau ML, 2011b. Application of light reflection visualization for measuring organic-liquid saturation for two-phase systems in two-dimensional flow cells, Environmental Engineering Science, 28, 803–809. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Falta RW, 2003. Modeling sub-grid-block-scale dense nonaqueous phase liquid (DNAPL) pool dissolution using a dual-domain approach. Water Resources Research, 39(12). [Google Scholar]
  16. Grant GP and Gerhard JI, 2007. Simulating the dissolution of a complex dense nonaqueous phase liquid source zone: 1. Model to predict interfacial area. Water Resources Research, 43(12). [Google Scholar]
  17. Guo Z, Fogg GE and Henri CV, 2019. Upscaling of Regional Scale Transport Under Transient Conditions: Evaluation of the Multirate Mass Transfer Model. Water Resources Research, 55(7), 5301–5320. [Google Scholar]
  18. Guo Z, Henri CV, Fogg GE, Zhang Y, and Zheng C, 2020. Adaptive Multirate Mass Transfer (aMMT) Model: A New Approach to Upscale Regional - Scale Transport Under Transient Flow Conditions. Water Resources Research, 56(2), e2019WR026000. [Google Scholar]
  19. Jawitz JW, Fure AD, Demmy GG, Berglund S and Rao PSC, 2005. Groundwater contaminant flux reduction resulting from nonaqueous phase liquid mass reduction. Water Resources Research, 41(10). [Google Scholar]
  20. Johnson GR, Zhang Z, and Brusseau ML, 2003. Characterizing and quantifying the impact of immiscible-liquid dissolution and nonlinear, rate-limited sorption/desorption on low-concentration elution tailing, 39 (5), 1120. [Google Scholar]
  21. Karaoglu AG, Copty NK, Akyol NH, Kilavuz SA and Babaei M, 2019. Experiments and sensitivity coefficients analysis for multiphase flow model calibration of enhanced DNAPL dissolution. Journal of contaminant hydrology, 225, 103515. [DOI] [PubMed] [Google Scholar]
  22. Kaye AJ, Cho J, Basu NB, Chen XS, Annable MD, Jawitz JW, 2008. Laboratory investigation of flux reduction from dense non-aqueous phase liquid (DNAPL) partial source zone remediation by enhanced dissolution. Journal of Contaminant Hydrology, 102 (1–2), 17–28. [DOI] [PubMed] [Google Scholar]
  23. Kennedy CA and Lennox WC, 1997. A pore-scale investigation of mass transport from dissolving DNAPL droplets. Journal of Contaminant Hydrology, 24(3-4): 221–246. [Google Scholar]
  24. Kokkinaki A, O'Carroll DM, Werth CJ and Sleep BE, 2013. Coupled simulation of DNAPL infiltration and dissolution in three-dimensional heterogeneous domains: Process model validation. Water Resources Research, 49(10), 7023–7036. [Google Scholar]
  25. Kokkinaki A, Werth CJ and Sleep BE, 2014. Comparison of upscaled models for multistage mass discharge from DNAPL source zones. Water Resources Research, 50(4), 3187–3205. [Google Scholar]
  26. Konikow LF, 2011. The secret to successful solute-transport modeling. Groundwater, 49(2), 144–159. [DOI] [PubMed] [Google Scholar]
  27. Lemke LD, Abriola LM and Goovaerts P, 2004. DNAPL source zone characterization: Influence of hydraulic property correlation on predictions of DNAPL infiltration and entrapment, Water Resour. Res, 40, W01511, [Google Scholar]
  28. Luciano A, Mancini G, Torretta V and Viotti P, 2018. An empirical model for the evaluation of the dissolution rate from a DNAPL-contaminated area. Environ Sci Pollut Res 25, 33992–34004. [DOI] [PubMed] [Google Scholar]
  29. Mahal MK, Murao A, Johnson GR Russo AE, and Brusseau ML, 2010. Non-ideal Behavior During Complete Dissolution of Organic Immiscible Liquid: 2. Ideal Porous Media, Water Air Soil Pollut., 213, 191–197. [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Marble JC, DiFilippo EL, Zhang Z, Tick GR and Brusseau ML, 2008. Application of a lumped-process mathematical model to dissolution of non-uniformly distributed immiscible liquid in heterogeneous porous media. Journal of Contaminant Hydrology, 100(1-2): 1–10. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Mateas DJ, Tick GR, Carroll KC, 2017. In situ stabilization of NAPL contaminant source-zones as a remediation technique to reduce mass discharge and flux to groundwater, Journal of Contaminant Hydrology, 204, 40–56. [DOI] [PubMed] [Google Scholar]
  32. Nambi IM, and Powers SE, 2000. NAPL dissolution in heterogeneous systems: An experimental Study in a simplified heterogeneous system, Journal of Contaminant Hydrology, 44(2), 161–184. [Google Scholar]
  33. NRC, National Research Council, 1994. Alternatives for Ground Water Cleanup. National Academy Press, Wachington, D.C. [Google Scholar]
  34. NRC, National Research Council, 2000. Research Needs in Subsurface Science. National Academy Press, Washington, D.C. [Google Scholar]
  35. NRC, National Research Council, 2005. Contaminants in the Subsurface: Source Zone Assessment and Remediation. National Academy Press, Washington, D.C. [Google Scholar]
  36. NRC, National Research Council, 2013. Alternatives for managing the nation's complex contaminated groundwater sites. National Academies Press, Washington, D.C. [Google Scholar]
  37. Parker JC and Park E, 2004. Modeling field-scale dense nonaqueous phase liquid dissolution kinetics in heterogeneous aquifers. Water Resources Research, 40(5). [Google Scholar]
  38. Powers SE, Abriola LM and Weber WJ, 1994. An Experimental Investigation of Nonaqueous Phase Liquid Dissolution in Saturated Subsurface Systems - Transient Mass-Transfer Rates. Water Resources Research, 30(2): 321–332. [Google Scholar]
  39. Powers SE, Nambi IM and Curry GW Jr., 1998. Non-aqueous phase liquid dissolution in heterogeneous systems: Mechanisms and a local equilibrium modeling approach. Water Resources Research, 34(12): 3293–3302. [Google Scholar]
  40. Rivett MO, Dearden RA, and Wealthall GP, 2014. Architecture, persistence and dissolution of a 20 to 45 year old trichloroethene DNAPL source zone. Journal of contaminant hydrology, 170, 95–115. [DOI] [PubMed] [Google Scholar]
  41. Russo AE, Mahal MK, and Brusseau ML, 2009a. Nonideal behavior during complete dissolution of organic immiscible liquid. Journal of Hazardous Materials, 172(1), 208–213. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Russo AE, Narter M, Brusseau ML, 2009b. Characterizing pore-scale dissolution of organic immiscible liquid in a poorly-sorted natural porous medium, Environ. Sci. Technol, 43, 5671–5678. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Schroth MH, Ahearn SJ, Selker JS and Istok JD, 1996. Characterization of miller-similar silica sands for laboratory hydrologic studies. Soil Science Society of America Journal, 60(5): 1331–1339. [Google Scholar]
  44. Schwille F, 1988. Dense chlorinated solvents in porous and fractured media (translated by Pankow JF). Lewis Publications, Chelsea, MI, 144 pp. [Google Scholar]
  45. Soga K, Page JWE, and Illangasekare TH, 2004. A review of NAPL source zone remediation efficiency and the mass flux approach. Journal of Hazardous Materials, 110(1-3), 13–27. [DOI] [PubMed] [Google Scholar]
  46. Teramoto EH and Chang HK, 2017. Field data and numerical simulation of btex concentration trends under water table fluctuations: example of a jet fuel-contaminated site in Brazil. Journal of contaminant hydrology, 198, 37–47. [DOI] [PubMed] [Google Scholar]
  47. Vasudevan M, Suresh Kumar G and Nambi IM, 2016. Numerical modelling on rate-limited dissolution mass transfer of entrapped petroleum hydrocarbons in a saturated sub-surface system. ISH Journal of Hydraulic Engineering, 22(1), 3–15. [Google Scholar]
  48. Yang L, Wang X, Mendoza-Sanchez I and Abriola LM, 2018. Modeling the influence of coupled mass transfer processes on mass flux downgradient of heterogeneous DNAPL source zones. Journal of contaminant hydrology, 211, 1–14. [DOI] [PubMed] [Google Scholar]
  49. Zhang CY, Yoon H, Werth CJ, Valocchi AJ, Basu NB and Jawitz JW, 2008. Evaluation of simplified mass transfer models to simulate the impacts of source zone architecture on nonaqueous phase liquid dissolution in heterogeneous porous media. Journal of Contaminant Hydrology, 102(1-2): 49–60. [DOI] [PubMed] [Google Scholar]
  50. Zhang Z and Brusseau ML, 2004. Nonideal transport of reactive contaminants in heterogeneous porous media: 7. distributed-domain model incorporating immiscible-liquid dissolution and rate-limited sorption/desorption. Journal of contaminant hydrology, 74(1-4), 83–103. [DOI] [PubMed] [Google Scholar]

RESOURCES