Conceptual Model for Landfill Hydrologic Transport Developed Using Chloride Tracer Data and Dual-Domain Modeling

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Conceptual Model for Landfill Hydrologic Transport Developed Using Chloride Tracer Data and Dual-Domain Modeling RICHARD A. STATOM P.O. Box 5218, Department of Physics and Earth Science, University of North Alabama, Florence, AL 35631

JOHN E. McCRAY Division of Environmental Science and Engineering, Colorado School of Mines, Golden, CO 80401-1887

GEOFFREY D. THYNE Department of Geology and Geological Engineering, Colorado School of Mines, Golden, CO 80401-1887

Key Terms: Environmental Geology, Pollution Modeling, Hydrogeology, Geochemistry, Infiltration

Although the model performance was not as sensitive to the values of the dual-domain parameters, inclusion of these parameters was required to accurately simulate the long-term temporal trend.

ABSTRACT Waste-derived chloride present in a landfill cell was used as a hydrologic tracer in conjunction with a mathematical model to better elucidate landfill hydrologic dynamics for a municipal solid-waste landfill in which the cover material is significantly more permeable than the waste material. Long-term temporal chloride data from a lined landfill cell in Florida were used to calibrate a variably saturated dual-domain model (originally developed for soilscience research) to landfill hydrology and solute transport. The model successfully simulated the chloride temporal trend. The dual-domain processes were needed to simulate the long-term decline in conservative chloride concentrations. However, the temporal variations about the general trend could only be simulated accurately by considering the variations in landfill recharge. The fitted value of Darcy flux (0.274 cm/day) was less than literature values, and the dispersion coefficient (900 cm2/day) was higher than simple estimates based on heterogeneous aquifers. The other fitted parameters, firstorder mass transfer coefficient (0.0018/day) and fraction of mobile water (0.22), were within the range of values reported in the literature. Model sensitivity studies were conducted to assess the relative importance of each parameter. The most sensitive parameter was recharge rate to the landfill, a factor that can be measured with the proper instrumentation.

INTRODUCTION Modeling of flow and chemical concentrations in municipal solid waste (MSW) leachate has been the subject of several studies in the past 25 years (e.g., Straub and Lynch, 1982; Demetracopoulos et al., 1986; Rosqvist and Destouni, 2000; and Suk et al., 2000). In general, these investigations have been based on theoretical concepts or small-scale experimental data in which the conditions were highly controlled. Modeling of data from full-scale operating landfills has been sparse, largely because of the lack of large sets of temporal data (El-Fadel et al., 1997). In a recent study at a lined MSW landfill cell located in southeast Florida, temporal changes that have occurred in leachate concentration over a 12½-year period were evaluated (Statom et al., 2004). It was noted in that study that many of the parameters had decreasing trends in solute concentrations as the landfill aged. Although short-term concentration variations were observed, most parameters had a significant degree of covariance and almost all had similar declining trends. The covariance and slope similarity suggest that the mechanism for release of these contaminants from the waste to the leachate once they are solubilized is a physical phenomenon, as opposed to biological and chemical processes. Although it is understood that microbial and chemical degradation of the waste is an essential component for solubilization of many of the contaminants, once that process is complete the abiotic physical pro-

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cesses of dilution, dispersion, diffusion, and advection may produce the observed temporal concentration profiles. Chian and DeWalle (1976) suggested that many of the cations released from landfills originated from flushing of the waste. The covariance and slope similarities of many of the inorganic components evaluated by Statom et al. (2004) tend to suggest that physical mechanisms may be responsible for other chemical components as well. At the scale of a landfill, it is reasonable that chemical transport is controlled by large-scale physical nonequilibrium processes (i.e., diffusion from compacted waste materials into the ‘‘fast-flow’’ domains), not by local mass-transfer kinetics. If the release of soluble inorganic chemical components from the waste after microbial and chemical action is indeed controlled by physical attributes, then the hydraulic properties of the landfill become very important constraints on the chemical composition of the leachate. It has been demonstrated in laboratory and small-scale landfill experiments that landfills cannot be modeled as homogeneous material with flow occurring in all areas uniformly, but that preferential pathways for leachate flow develop in the waste (Zeiss and Major, 1993; Zeiss and Uguccioni, 1995; and Rosqvist and Destouni, 2000), and in the cover material, if it is more hydraulically conductive than the waste (Blight et al., 1992). Zeiss and Major (1993) reported that these pathways constituted approximately 28 percent of the total waste cross-sectional area, and Rosqvist and Destouni (2000) noted that the majority of fluids (55–90 percent) flows through 5–47 percent of the total water content. Several researchers (Zeiss and Major, 1993; Rosqvist and Bendz, 1999; and Rosqvist and Destouni, 2000) have suggested that the majority of the leaching of chemical components from the waste occurs in proximity to these flow paths, and that the waste not adjacent to these pathways has less influence on the chemical nature of the resultant leachate. It has been suggested that diffusion and slow advection are the major mechanisms controlling the flow of chemical components from waste that is not adjacent to the more active flow paths, causing a slow release over time (Rosqvist and Destouni, 2000). This variable release of contaminants from the waste can account for the rapid increase of parameters in the leachate in the early stages of a landfill and the slow decrease as the landfill ages, as noted by Statom et al. (2004) and earlier studies (Qasim and Burchinal, 1970; Pohland and Englebrecht, 1976; Lu et al., 1985; and Rosqvist and Destouni, 2000). The presence of preferential pathways in the refuse and other areas of the landfill is sometimes referred to as a dual-domain system (Bendz et al. 1998), and is analogous to phenomena found in structured soils (Brusseau et al., 1989; van Genuchten and Wagenet, 1989; Gerke


and van Genuchten, 1993; and Neville et al., 2000). In such systems, the movement of relatively clean water through contaminated soil results in the rapid release of contaminants near major pathways of flow, and a slow release from areas where small pore sizes between the soil grains restrict flow. Movement of contaminants in the flow paths is caused by advection, and movement in the small pores is by diffusion and slow advection (van Genuchten and Wagenet, 1989). However, Griffioen and others (1998) concluded that the mass transfer between immobile and mobile regions is controlled by mobilephase velocity rather than diffusion. The resultant breakthrough curves in these dual-domain systems generally show a rapid increase in solute concentration to a peak and then a decrease with tailing (Brusseau et al., 1989; Destouni et al., 1994). The similarity of soil systems to the temporal trends in MSW landfill leachate concentration suggests that computer codes developed for modeling solute transport in soils could be applied to landfills. In this study, a variably saturated dual-domain model developed for soils in the vadose zone is used to simulate the overall trend in chloride concentration from a closed landfill cell. SITE DESCRIPTION The chloride data used in this study are from the Dyer Boulevard Landfill, located in Palm Beach County, Florida, USA. Palm Beach County is situated in the southeastern portion of the state and is characterized by a semi-tropical climate. It receives an average of 152.4 cm (60 in.) per year, with more than 70 percent of the rainfall occurring between May and October (Land et al., 1973). The landfill is a 164-hectare (405-acre) site that was operated from 1968–1992. The facility contains several landfills, which range in design from an open dump to a lined sanitary landfill with a leachate collection system. The leachate data from a lined MSW landfill cell that operated from 1984–1990 are used in this study. This cell contains the oldest waste in the lined landfill, and gives the best account of the long-term changes that occurred in leachate concentration at the landfill. The cell is approximately 4.7 hectares (11.5 acres) in area and contains approximately 327,000 metric tons (360,000 tons) of waste. The waste is composed primarily of municipal solid waste, 72.4 percent of which is paper, organic material, and plastic (Beck & Associates, 1995). The sampling program started in December 1988 and continued until May 2001. (Note: landfill behavior from the first four years of waste deposition in the cell is not accounted for in the data set.) During landfilling operations, approximately 15 cm (6 in.) of local soil or sand was emplaced at the end of each day over the waste to control odors and disease vectors, and this resulted in relatively low-permeability

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Conceptual Model for Landfill Hydrologic Transport

waste encased by high-permeability cover material. Closure was completed in December 1992 and involved installing a 20-mil PVC liner over the top of the landfill and covering it and the side slopes with approximately 61 cm (18 in.) of sand and 15 cm (6 in.) of local soils. This closure procedure restricted infiltration of rainfall but did not stop all moisture from entering the waste. This is reflected by the short-term variability in the data attributed to rainfall (Statom et al., 2004).

 Dispersion is longitudinal, Fickian, and constant without a transverse component.  Initial concentrations are uniform within the domain. Although no landfill, nor any geological system, strictly adheres to these assumptions, we find that the model is still very useful in elucidating rarely-studied flow processes within landfills. The governing equations for the model are presented below.

METHODOLOGY Mobile region: This study focuses on long-term temporal trends in leachate concentration, because those are more relevant for practical landfill operations that deal with 10–30 year time periods. However, it also addresses the extreme short-term variability in leachate concentration reported in the literature (Chian and DeWalle, 1976; Lu et al., 1985; and Statom et al., 2004), and reports of the influence of rainfall on individual analyses (Chu et al. ˚ kesson and Nilsson, 1997). Temporal trends are 1994; A modeled in order to simulate the major components controlling leachate generation and minimize the variability and external influences. Chloride (Cl) was chosen as the parameter to be modeled because of its generally non-reactive nature. Chloride is typically found in MSW landfill leachate, the source of which is probably various materials in the landfill containing sodium chloride (salt), such as processed food waste, preserved food waste, and household and industrial cleaners. With the use of a non-reactive tracer common in landfill leachate, it is anticipated that the hydraulic characteristics of the landfill that are important in controlling the chemical composition of leachate can be identified and studied. MODELING The computer code used is a semi-analytical solution for a one-dimensional solute transport model with multiprocess non-equilibrium (MPNE1-D, version 3.2) developed by Neville and others (2000), and based on a theory presented by Brusseau and others (1989). The solution is based on several assumptions, including the following (Neville, 2003):  The domain is a dual-porosity continuum (immobile and mobile porosity regions exist).  Mass transfer is first-order between the immobile and mobile regions.  Material properties are spatially uniform and temporally constant within the regions.  The Darcy flux is steady, one-dimensional, and spatially uniform.

@Cm @Cm @ 2 Cm ¼ q þ hm D  aðCm  Cim Þ @t @x @x2 @Cim Immobile region: him ¼ aðCm  Cim Þ @t hm

ð1Þ ð2Þ

The initial and boundary conditions are: Cm ðx; 0Þ ¼ C0 Cim ðx; 0Þ ¼ C0 @Cm qCm ð0; tÞ  hm D ð0; tÞ ¼ 0 @x Cmð‘; tÞ ¼ 0

ð3Þ ð4Þ ð5Þ ð6Þ

where Cm ¼ solute concentration in mobile-region dissolved phase [ML3] Cim ¼ solute concentration in the immobile-region dissolved phase [ML3] hm ¼ mobile water content [](hm ¼ /h) him ¼ immobile water content [](him ¼ (1  /)h) x ¼ distance from inflow boundary [L] t ¼ time elapsed since beginning of solute release [T] D ¼ hydrodynamic dispersion coefficent [L2T1] q ¼ Darcy flux [LT1] a ¼ first-order mass transfer coefficient / ¼ fraction of pore water that is mobile (/ ¼ hm/h) h ¼ total water content [] ¼ him þ hm

CONCEPTUAL MODEL The conceptual model for this study is that a landfill is essentially a reservoir of potential solutes that are depleted over time through flushing of relatively clean water through the waste. Flow of water through the landfill is controlled by advection and dispersion through preferential pathways in the waste and diffusion with slow advection through the less permeable portions. In

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important step in understanding the major factors in controlling leachate concentration over time. MODEL PARAMETERS

Figure 1. Graphical representation of dual-domain system in the Dyer Boulevard Landfill. The mobile regions are composed of daily cover (sand), waste near the cover, and preferential pathways through the waste. The interior portions of the waste represent immobile regions.

this particular landfill, preferential pathways in the waste are enhanced by the daily cover material, which is composed mostly of clean sand from a local dredging operation. This system provides a dual domain of immobile and mobile regions that contribute solutes to the leachate at different rates over time (Figure 1). In MPNE1-D, the landfill is simulated as a onedimensional column filled with porous media that are unsaturated and have an initial relative solute concentration of 1.0 that is uniformly distributed throughout the column in the immobile regions (Cim(x,0) ¼ C0). The mobile domain is free of any solute (Cm(x,0) ¼ 0). The initial value of 1.0 is used because the actual value of the mass of chloride in the landfill is unknown, and by using a relative scale the model output can be compared to actual leachate concentrations normalized as C/Cmax. The solute-free mobile region is used to simulate the clean sand used for cover material in the landfill and channels through the waste. Relatively clean water is flushed through the column at a constant rate, and the solute moves from the immobile to the mobile domain at a rate defined by the first-order mass-transfer coefficient. The mobile domain solute concentration is measured at the outflow point at the end of the column. This model is analogous to a landfill that has reached its final design volume without reaching field capacity (the moisture content at which liquids begin to be discharged from the waste) and is then subjected to a constant influx of rainfall or irrigation. In reality, most landfills are subjected to rainfall and begin discharging leachate during disposal operations, so this model is somewhat simplistic and lacks several constraints found in full-scale landfills. However, if a semi-analytical solution can effectively simulate the actual data from a landfill cell, then it is an


The hydrologic parameters used in MPNE1-D for this study are the total water content (h), the fraction of mobile pore water (/), Darcy flux (q), hydrodynamic dispersion coefficient (D), first-order mass-transfer coefficient between the immobile and mobile domains (a), landfill height (L), bulk density (qB), and time (t). Because a non-reactive tracer is being used in this study, neither sorption nor decay is considered. Of these parameters, the Darcy flux, mass-transfer coefficient, dispersion coefficient, and proportion of mobile water were fitted to the temporal chloride data. The other parameters were fixed, based on data from previous studies of the Dyer Boulevard Landfill or from the literature. A sensitivity study is presented that confirms the value of this approach. A compilation of landfill hydrologic data from the literature is shown in Table 1 and the initial and final parameters used in the model are in Table 2. The parameters to be adjusted in the calibration process are interrelated to some extent, so unique values are not expected. To minimize the correlation-related effects, the parameters that were expected to have the most effect on the simulations were adjusted first, and then minor adjustments were made with the parameters that were expected to have a lesser effect. Infiltrating precipitation is represented in the model by the Darcy flux. Because the chloride concentrations from the Dyer Boulevard Landfill show a correlation with precipitation totals (Statom et al, 2004), this parameter is expected to have a significant effect on the simulation and was therefore adjusted first. The proportion of mobile domain is expected to have an effect on concentrations by controlling the volume of preferential flow paths that transport the chemical components through the landfill. Because this aspect of the landfill architecture can affect Darcy flux, it was adjusted next. The mass transfer rate, which controls the mass flux from the immobile domain, was expected to have a significant effect on the concentration reported in the model and was thus adjusted next. The dispersion coefficient, which is closely correlated to Darcy flux because of the inclusion of pore water velocity in its calculation, was adjusted last. No direct measurements of the moisture content at the Dyer Boulevard Landfill are available. In order to estimate the moisture content, the literature was reviewed and a number of values were compiled (Table 1). These values, which cover a considerable range (10–70 percent), include a study by Ham and others (1997) in which the moisture content of selected waste materials in the Dyer Boulevard Landfill was measured. The study

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Conceptual Model for Landfill Hydrologic Transport Table 1. Hydrologic parameters from the literature.


Moisture Content (vol/vol)

Qasim and Burchinal (1970) Korfiatis et al. (1984)

0.499–0.428 (grav.) 0.2727

Demetracopolous et al. (1986) Oweis et al. (1990)

0.35 0.10–0.20

Ahmed et al. (1992) Zeiss and Major (1993)

Ksat (cm/second)

Kunsat (cm/second)

Darcy Flux (cm/second)

Bendz and Bengtsson (1996) Bendz et al. (1998) Rosqvist and Bendz (1999) McCreanor and Reinhart (2000) Rosqvist & Destouni (2000) Suk et al. (2000) Yuen et al. (2001)

Proportion of Mobile Water

3.23 3 102


1.3 3 102 –8 3 103 2.12 3 105 1.1 3 103 –1.5 3 104 2 3 102 1.74 3 102 –1.22 3 103

Ham et al. (1997) (Dyer Blvd. Landfill) (Selected material) Zeiss and Uguccioni (1995)

Average Linear Velocity (cm/second)

0.686–0.714 (grav.) 6.14 3 105 –6.08 3 106 0.3 0.46–0.43

4.0 3 103

9.8 3 104 1.6 3 103 –9.8 3 104


105–4.3 3 103


102–107 0.27–0.46 0.462 0.55 (grav.)

1.84 3 102

reported that the moisture content (by weight) of newspaper and food products averaged 70 percent. As noted above, the composition of the waste in the Dyer Boulevard Landfill is largely paper, plastic, and organic matter. Therefore, even though a complete sample of the waste was not analyzed, the analyses do indicate that the Dyer Boulevard Landfill moisture content would be at the high end of the values generally reported in the literature. The high rainfall and semi-tropical environment of southeastern Florida are assumed to be responsible for the high moisture content in the Dyer Boulevard Landfill. The MPNE1-D code utilizes the total moisture content (which is composed of both the immobile and the mobile domains), so moisture values for the waste and the sandcover material were needed. Using a moisture content of 50 percent for the waste and 20 percent for a sandy loam soil at field capacity (Fetter, 2001), a value of 70 percent was obtained. The fraction of mobile water was estimated from the volume of sandy cover material in the landfill and from literature values of the mobile domain in other landfill waste. The average daily waste disposal volume (lift) at the Dyer Boulevard Landfill was approximately 6 m 3 6 m 3 31 m (20 ft 3 20 ft 3 100 ft), with a daily cover of 0.15 m (6 in.) (Kinley, 2002). The sand cover is shared equally with the surrounding lifts, so the volume of cover encapsulating the waste is about one-half of the daily cover volume and represents approximately 5.5 percent of

the total volume of material deposited in the landfill. Studies from other landfills, such as that by Zeiss and Major (1993), reported that in a column of compacted waste, water flowed in narrow channels comprising 28 percent of the cross-sectional area. Rosqvist and Destouni (2000) reported that the mobile domain of old, compacted, undisturbed waste was 5–16 percent of the total waste volume, versus 55–70 percent for fresh, coarse waste. Data from the Dyer Boulevard Landfill covered a period of 12½ years, so an average value representing older waste plus the daily cover were used as a basis for the initial value for the mobile domain (mobile water) of 0.11. Literature values for Darcy flux in landfill samples are varied. Bendz and others (1998) reported a flow of 9.8 3 104cm/second for laboratory studies of well-degraded waste from an experimental landfill. Rosqvist and Table 2. Initial and final parameter values used in this study. FirstOrder Total Hydrodynamic Mass Bulk Moisture Darcy Dispersion Density Content Flux Proportion Transfer (hT) (q) of Mobile Coefficient Coefficient Time (qB) 3 3 3 (g/cm ) (cm /cm ) (cm/d) Water (/) (a) (1/day) (D) (cm2/day) (days) Initial 1.222 Final 1.222

0.7 0.7

1.46 0.274*

0.11 0.22*

0.002 0.0018*

287 900*

7,000 7,000

*Fitted parameter.

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Figure 2. Temporal chloride data used in this study. The linear regression line defines the overall decreasing trend.

Figure 3. Results of the MPNE1-D model plotted with chloride data and the linear regression line.

Destouni (2000) found that the Darcy flux ranged from 105 to 4.3 3 103 cm/second, depending on the age and decomposition level of the waste and the water application methods. However, unsaturated hydraulic conductivity (Kunsat) in MSW landfills has been reported to range from 1.74 3 102 to 1.22 3 103 cm/s (Zeiss and Major, 1993) and from 6.14 3 105 to 6.08 3 106 cm/s (Zeiss and Uguccioni, 1995). The flow in a field-scale landfill cell would be expected to be less than Kunsat. Thus, a value equal to one half of the average of the lower range Kunsat values (1.69 3 105 cm/second [1.46 cm/ day]) was chosen as the initial Darcy flux value. Literature values for the hydrodynamic dispersion coefficient in a landfill are rare. Hydrodynamic dispersion (Fickian) is defined as DL ¼ aLvx þ D*. In this study the diffusion term (D*) in the mobile domain is considered much smaller than the first term, so only estimates for dispersivity (a) and the average pore water velocity (v) were needed. Gelhar and others (1992), in their review of field-scale dispersion in aquifers, reported that longitudinal dispersivity is scale dependent and ranges from 102 to 104 m for scales ranging from 101 to 105 m. Xu and Eckstein (1995) used the equation aL ¼ 0.83(LogL)2.414 in their analysis of the relationship between flow length and longitudinal dispersivity. Using this equation and the height of the landfill (2,134 cm), a value of 15.135 cm was calculated. According to Brusseau and others (1989), advective-dispersive mass transport is restricted to the mobile domain and v ¼ q/h is the average pore water velocity for the MPNE model. Using the mobile domain water content (hm ¼ /h) as the water content and the initial Darcy flux of 1.46 cm/day for the velocity calculation, a pore water velocity of 18.97 cm/day for the mobile domain was calculated. Multiplying the estimated dispersivity by the pore water velocity produces an initial dispersion coefficient of 287 cm2/day. First–order mass-transfer coefficients between the immobile and mobile domains for solid wastes were

not found in the literature reviewed for this study; however, values for soils are available. Destouni and others (1994) reported a calibrated chloride masstransfer coefficient in unsaturated heterogeneous soils of 0.0048/day (0.0002/hour). Feehley and others (2000) used values of 0.001–0.0005/day at the Macro Dispersion Experiment site in Columbus, Mississippi, and Neville and others (2000) used values of 0.03–0.075/day in the verification of the semi-analytical solution that is the basis of the code used in this study. The initial value used in this study is 0.002/day, which is within the range of values in the literature reviewed. Bulk density (qB) values for solid waste are rare in the literature. Yuen and others (2001) calculated an in situ bulk density of 0.83 ton/m3 (0.83 g/cm3) for waste in a capped landfill (including cover material). However, the cover (a clayey sandy silt) was stripped before applications of additional lifts were emplaced in an attempt to reduce barrier effects of the cover on circulation of leachate. We chose the value of 1.222 g/cm3 used by Brusseau and others (1989) and Neville and others (2000), which is consistent with values for coarse-grained soils. Several model simulations were conducted using both values, and no differences were found in the results.


MODEL RESULTS AND DISCUSSION Chloride data from the temporal trends study are shown in Figure 2. Chloride concentrations vary from a high of 1,580 mg/l to a low of 63 mg/l. To facilitate model interpretation, the data have been plotted on a relative scale of C/Cmax, where Cmax is the highest concentration of the subject parameter. The linear regression line shows an overall decreasing trend. By fitting q, a, D, and / to the linear regression line following the sequence previously described, MPNE1-D produced a reasonable fit, as shown in Figure 3. The final values calibrated to the regression line are shown in Table

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2. The model shows an early rapid increase in concentration to a maximum value and then a gradual decreasing trend. This type of curve is similar to those found in laboratory and pilot-scale landfill experiments (Qasim and Burchinal, 1970; Rosqvist and Bendz, 1999; and Rosqvist and Destouni, 2000). The basic shape of the curve and the slope of the decreasing tail were most affected by changes in q. The a value also had a significant effect on curve shape, especially the maximum concentration predicted by the model and the slope of the trend of early-time data. Changes in / did not affect the shape of the curve significantly, but did affect the maximum concentration the curve achieves. Changes in D had a minor effect on the shape of the curve, mainly controlling the linearity of the decreasing trend. The fitted q value of 0.274 cm/day (3.17 3 106 cm/s) is smaller than the lowest values reported by Bendz and others (1998), Rosqvist and Bendz (1999), and Rosqvist and Destouni (2000) (Table 1). It is also lower than values for unsaturated hydraulic conductivity reported by Zeiss and Major (1993) and Zeiss and Uguccioni (1995). The smaller values for q in the landfill are not surprising, because the model is fitted to data from a full-scale 21.34-m- (70-ft-) high landfill with a complex internal architecture as compared to the laboratory and pilot-scale experiments from the literature. Also, it should be noted that the high-permeability cover material in the landfill additionally complicates the flow path as compared to laboratory experiments. Blight and others (1992) observed that leachate movement in a landfill could be influenced by the geometry of high-permeability cover layers. Bendz and others (1998) noted that a significant proportion of leachate flow can occur in the horizontal direction because of disposal procedures. This horizontal flow could effectively reduce vertical Darcy flux in the landfill to values less than those reported for the laboratory and pilot-scale experiments. The proportion of mobile water (or mobile domain) from the calibrated model (/ ¼ 0.22) is twice the initial value (/ ¼ 0.11), but within the range of values reported in the literature. The increase over the initial value can be accounted for by noting that when the initial value was determined, the lowest values in the literature for the mobile domain in refuse were used in conjunction with estimates of total cover material in the landfill. The increased fitted value suggests that the waste in the Dyer Boulevard Landfill could have a volume of permeable areas closer to the mid-range of values found in the literature. The calibrated a value of 0.0018/day is smaller than the initial value (0.002/day), but well within the range of values reported in the literature. This suggests that values of mass transfer between the immobile and mobile regions determined for soils may be applicable for solid waste.

Figure 4. Variation in predicted solute concentration with time for an order of magnitude variation of the Darcy flux from the fitted value.

The fitted D value of 900 cm2/day was significantly higher than the initial value (285 cm2/day) used in the model. This is expected when using a one-dimensional model to fit three-dimensional flow. Like the Darcy flux, dispersion of solutes in the vertical direction is influenced by the three-dimensional geometry of the channels in the landfill created by the permeable cover material and the preferential flow paths in the waste. Also, the initial value was estimated using equations developed for heterogeneous aquifers. It is not surprising that the apparent dispersion in this landfill is greater than calculated for heterogeneous aquifers. SENSITIVITY ANALYSIS Once the model was calibrated to the temporal chloride data from the landfill, a series of simulations was conducted to determine the sensitivity of the model results to changes in model-input parameters. Sensitivity analysis enables a better understanding of the relative influence of various physical parameters on chemical transport in the landfill, and provides insight into how the uncertainty of model-input values influences performance of the model. The Darcy flux was varied by an order of magnitude above and below the fitted value and, as seen in Figure 4, the change was significant. Increasing the flow caused a rapid reduction in concentration after it had reached a maximum, and decreased flow caused an insignificant decrease in concentration after reaching a maximum. The increased flow simulation suggests that in a dual-domain system, if the Darcy flux is of sufficient magnitude, the reservoir of solutes can be effectively depleted in a comparatively short amount of time, provided that the solutes can migrate into the flowing water quickly enough. As noted above, several researchers have suggested that the majority of leaching of chemicals

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Figure 5. Variation in predicted solute concentration with time for orders of magnitude variation in the first-order mass-transfer coefficient.

Figure 6. Variation in predicted solute concentration with time for a reasonable range of mobile water (11–44 percent).

from waste occurs in proximity to flow paths and that the waste not adjacent to these pathways has less influence on the chemical nature of the resultant leachate (Zeiss and Major, 1993; Rosqvist and Bendz, 1999; and Rosqvist and Destouni, 2000). The increased flow simulation also suggests that if flows of this magnitude continued along preferential flow paths for extended periods of time, the solute reservoirs in the waste adjacent to the flow paths could be depleted to very low levels as compared to other areas of the landfill. This would be reflected in low solute concentrations in the leachate even though the landfill as a whole has untapped reservoirs of solutes. The low flow simulation, however, indicates that if q is low enough, the overall transfer of mass from the waste to the leachate will be close to steady-state conditions and a constant (or very slowly declining) solute concentration will result. The results of the sensitivity analysis for q clearly point to the need for accurate measurements of infiltration rates into the landfill to simulate landfill-pollutant data. Of course, the impact of velocity is interdependent with the mass-transfer characteristics of the waste and cover material. A sensitivity analysis on the mass-transfer parameter is discussed below. The first-order mass-transfer coefficient was varied by orders of magnitude, and the results are shown in Figure 5. Mass-transfer coefficients have a direct relation with the maximum solute concentration, with smaller masstransfer coefficients resulting in lower concentrations of solutes in the leachate. The mass transfer rate was decreased over three orders of magnitude, with the result that the curve shows increasingly lower solute concentrations to the point that very little solute is transferred at all. However, an increase of one order of magnitude over the fitted value has little effect on the curve, and an increase of two orders of magnitude shows no additional change, suggesting that the mass transfer of chloride has a maximum value that can be achieved, given the

constraints imposed by the other parameters. This limit to mass transfer of solutes from the waste to the leachate implies that the solute concentration in the leachate would decrease during large infiltration events. Mass-transfer coefficients would be smaller, for example, with more compacted waste or less permeable mobile domains. Mass-transfer coefficients would be difficult to measure. Likely, only model calibration could be used to estimate this parameter at the landfill scale. However, reducing uncertainty associated with other parameters that are more easily measured would make model estimation of the mass-transfer coefficient more reliable. The changes in the proportion of mobile water (mobile domain) seen in Figure 6 are on the orders of two times and one-half times the fitted value. These changes affect the maximum concentration the curve achieves, but the overall shapes of the curves are very similar and appear to converge at later times. The increased fraction of mobile water results in lower initial concentrations for the same flow velocity and mass-transfer coefficient, and less of a declining trend. Conversely, the lower fraction of mobile water has a higher initial concentration and more of a declining trend. This implies that with larger fractions of mobile domain (cover material and preferential flow paths in the waste), the relative amount of immobile domain (waste material) adjacent to the flow paths is reduced, and thus lower amounts of solutes are transferred from the waste and transported. This results in lower overall concentrations, and a slower rate of depletion of solutes from the waste will be reflected in the increased tailing of the temporal trend. Smaller fractions of mobile domain (and therefore more immobile domain) increase the relative amount of waste available for mass transfer, and thus increased solute concentrations are found in the leachate. The temporal trend for a lower fraction of mobile domain shows more of a negative slope than the other plots, suggesting that the


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Conceptual Model for Landfill Hydrologic Transport

Figure 7. Variation in predicted solute concentration with time for an order of magnitude variation in the hydrodynamic dispersion coefficient from the fitted values.

Figure 8. Variation in predicted solute concentration with time for a range of total water content between 0.5 and 0.86.

rate of depletion of solutes from the waste is greater. Because this analysis assumes a constant total porosity, the important effect of changing the mobile/immobile fraction is primarily to introduce a lower mass of chemical into the system, because the initial (and total) reservoir of solutes is assumed to exist only in the immobile domain (i.e., the waste material). The mobile/immobile parameter is relatively important. A first estimate of the mobile/immobile fraction is the ratio of cover material to waste, which can be estimated by the landfill operator if adequate records are available. Of course, the mobile domain will be somewhat larger than this first estimate because of actual preferential flow paths in the waste. Furthermore, it is useful to note that for some landfills, the cover material may be less permeable than the waste (e.g., a cover material of clay or fine silt), and therefore would not a part of the mobile domain. Figure 7 shows the effect of a change of several orders of magnitude in hydrodynamic dispersion. This variation slightly changes the shape of the curve, but does not dramatically affect the trend of the concentration. This is not surprising, because dispersion is really a lumped parameter that accounts for flow-field heterogeneities in the mobile domain (Fetter, 2001). The model used for this study inherently accounts for heterogeneities by the dualdomain formulation. Thus, the additional effect of increased dispersion in the mobile domain is relatively insignificant compared to the more important processes associated with solute transfer between the immobile domain and the mobile (advection-dominated) domain that carries solutes to the outlet of the landfill. Increased dispersion in the mobile domain will effectively reduce the concentration driving force for mass transfer from the low-permeability waste material at the advective front in the mobile domain. This will reduce mass transfer at the front and result in slower depletion of solutes from the

immobile domain, and less of a declining temporal trend. Conversely, a smaller dispersion coefficient will tend to cause a faster depletion of solute reserves adjacent to the preferential flow paths, and cause a more rapid decrease in overall solute concentration. The lack of significant change in the curves with orders-of-magnitude difference in the dispersion coefficient suggests that the model is not very sensitive to changes in dispersion, which is advantageous because it is difficult to measure. Figure 8 shows the variation in the predicted solute concentration with time caused by changing the total water content of the landfill from 50 to 86 percent. This variation primarily affects the slope of the curve after achieving a maximum concentration. The smaller water content (50 percent) shows a more rapid decrease in concentration over time compared to the model value (70 percent); however, the curve flattens out somewhat, which suggests that the rate of solute depletion of the waste may become more stable as the landfill ages. The curve of the 86 percent water content (the maximum water content the model will simulate) has a less negative slope than the fitted value, which suggests that larger concentrations over time can be expected. These curves imply that with greater water content in the landfill as a whole, more solutes are present in the system, and thus a longer time is required to flush solutes from the system. Conversely, lower water content decreases the mass loading from the waste, which is reflected in lower concentrations in the leachate. The sensitivity analyses suggest that changes in q have the greatest effect on solute concentration, as reflected in the shape of the curves in Figure 4. Previous research˚ kesson and Nilsson, 1997) have ers (Chu et al., 1994; A noted that rainfall amounts have a significant effect on leachate concentration, with higher amounts causing lower leachate concentrations. Variations in rainfall have also been cited as a possible reason for the short-term

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Statom, McCray, and Thyne

Figure 9. Predicted versus actual values using fitted Darcy flux to reproduce short-term variations in chloride concentrations. Note: at extremely high concentrations (C/Cmax . 0.79), the model failed and did not provide values.

variations in chloride concentrations in the Dyer Boulevard Landfill (Statom et al., 2004). SIMULATION OF CHLORIDE CONCENTRATIONS Using changes in q alone (all other parameters were maintained at the calibrated values), the short-term variations in chloride concentrations were simulated using the MPNE1-D model. The results of these simulations are presented in Figure 9, which shows that the majority of data points were successfully simulated by the model. It should be noted that at extremely high concentrations (C/Cmax . 0.79), the model did not provide accurate values. This is probably caused by the low water flux (and thus advection) being overpowered by dispersion, thus causing the model to fail. To further support the premise that rainfall controls the short-term variations in the data, rainfall amounts averaged for 30 days prior to sampling were plotted against the fitted q values (Figure 10). This plot shows that, as a general rule, increases in rainfall amounts coincide with increases in q, especially after closure, when the amounts of waste in the landfill become fixed. The plot also shows that, as a general rule, infiltration is less than precipitation (a required condition caused by the effects of evapotranspiration and surface-water runoff), which points to the reasonableness of the model results. This simulation also supports the conceptual model of this study that landfills can be treated as reservoirs of solutes that are depleted over time by flushing relatively clean water through the waste. IMPLICATIONS FOR LANDFILL CONSTRUCTION AND OPERATION The results of the model show that the way a landfill is constructed and operated can have an influence on the


Figure 10. Comparison of 30-day precipitation totals in cm/day and Darcy flux value required to match the concentration data.

solute load of the leachate. The Darcy flux and the relative proportion of mobile to immobile domains are the two factors that have the greatest potential to be influenced by landfill designers and operators. The model was the most sensitive to changes in q, which appears to be a proxy for rainfall, at least in this semi-tropical location. Solute concentrations are inversely proportional to flux, with high rainfall producing lower solute loads. Thus, designing landfill operational topography to promote runoff and lining the top and side slopes with low-permeability material should reduce the total volume of leachate produced, but the solute concentration may be initially higher and extend the time until solutes are depleted. The composition and thickness of fill used for daily and intermediate cover can affect the mobile/immobile ratio. An increase in the amount of high-permeability fill used for cover will lower the maximum solute concentration, but the amount of time to remove all the solutes will be longer (tailing). In addition, if low-permeability fill were used, then the hydrologic transport would likely be different than that observed for this study because the differences between the immobile (diffusion-limited) domain and the mobile (fast-flow) domain would be less drastic. CONCLUSIONS This research demonstrates that a semi-analytical solution for a multi-process non-equilibrium (dual-domain) model designed for solute transport in unsaturated soils can be used to simulate long-term chloride temporal trends from a field-scale landfill cell. This suggests that a dualdomain conceptual model can describe the physical solutetransport processes in the Dyer Boulevard Landfill and provide insights into the major factors or processes that influence leachate concentration.

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Conceptual Model for Landfill Hydrologic Transport

The calibrated model demonstrates that the fitted parameters / and a are within the range of values in the literature. The fitted value for q is less than values reported from laboratory and pilot scale landfill experiments in the literature; however, the Darcy flux from a full-scale landfill would be expected to be less, because of the size and complexity of the landfill internal architecture. Literature values of D for landfills are rare, so a value estimated from equations developed for heterogeneous aquifers was used as an initial value in the model. The fitted value for dispersion in the landfill cell was considerably larger than the aquifer value, but the presence of permeable daily-cover material in the landfill could promote horizontal flow, which would increase apparent dispersion in the vertical direction. Additionally, increased apparent dispersion would be expected when using a one-dimensional model to simulate three-dimensional flow. Sensitivity analysis of the fitted parameters shows that changes in q caused the most significant change in the solute concentration and temporal trends of all the parameters evaluated. This suggests that the flow of moisture through the landfill is perhaps the most important factor controlling leachate concentration after microbial and chemical processes have generated the solutes in the waste. In order to test this assumption, the model was used to simulate the individual chloride analyses from the cell in addition to the overall trend (as defined by the regression line of concentration versus time), using changes in q exclusively. The results were generally positive, and only a few high concentration points could not be successfully simulated. In summary, dual-domain processes were required to simulate the long-term decline in conservative chloride concentrations. However, the temporal variations about the general trend could only be simulated accurately by considering the variations in landfill recharge. Model sensitivity studies indicate that the most sensitive parameter was recharge rate to the landfill, a factor that can be measured with the proper instrumentation. The model was not as sensitive to changes in dual-domain parameters, but they were required to accurately simulate the long-term temporal trend. The model’s lack of sensitivity with respect to the dual-domain parameters is fortuitous because these parameters are difficult to measure. Acceptable ranges for these parameter values would therefore be readily obtained from model calibration. The application of the modeling results to actual landfilling operations suggests that by controlling the amount of precipitation infiltrating the landfill and the volume and type of fill material used for daily and intermediate cover, the leachate concentration can be influenced. Finally, it is useful to note a few points. First, landfills that contain cover material that is less permeable than (or near the same permeability as) the waste would likely not

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