Abstract
In the assessment of the risks to groundwater posed by most landfills, the production and transport of ammonium is the key factor. Although a long list of toxic and dangerous substances can appear in the leachate from a landfill, the chemical component with the greatest impact both on the ecology and on groundwater abstractions is usually ammonium. It is therefore vital that information on the behaviour of ammonium in groundwater is compiled in order to reduce the uncertainties associated with predictions of groundwater impact.
The transport of ammonium is attenuated by two main processes: cation exchange and oxidation (often biologically enhanced). The effect of these can probably be approximated by a combination of linear retardation and exponential degradation. In principle, comparison of the breakthrough curves of ammonium and chloride at monitoring points should allow quantification of the contributions of these two processes in terms of retardation factors and decay rates.
Three case studies at different scales are compared. The results indicate that retardation factors are not higher than 3, and that degradation does contribute to reduction in concentration. While only three studies have been examined, the results seem to contrast with the typical assumptions made in risk assessments.
Introduction
In the assessment of the risks to groundwater posed by most landfills, the production and transport of ammonium is the key component. Although a long list of toxic and dangerous substances can appear in the leachate from a landfill, the chemical component with the greatest impact both on the ecology and on groundwater abstractions is usually ammonium. It is therefore vital that information on the behaviour of ammonium in groundwater is compiled in order to reduce the uncertainties associated with predictions.
One of the commonly used databases for transport parameters is provided by the User Manual to the risk assessment program LandSim (⇓Golder 1996). This program was commissioned by the UK Environment Agency to standardize the approach to the calculation of landfill impact on groundwater in the UK. In the User Manual (and in the default settings in the program), the distribution coefficient for ammonium is given a mean value of 25 l/kg which implies that, in the average soil or rock, contaminants will be slowed down by a factor of about 240. Is ammonium really retarded this much?
There are very few measurements of ammonium distribution coefficients available in the literature, but data presented in ⇓Thornton et al. (in press) for UK sandstone suggest values ranging from 0.08 l/kg to 0.4 l/kg. The maximum figure is nearly two orders of magnitude less than the LandSim default value quoted above.
In this paper, the details of the mechanisms specific to ammonium transport in groundwater will be considered. Field and laboratory data are examined in order to assess the retardation and consider whether an element of degradation may be present in the observed behaviour. Although only three case studies are presented in this paper, it is hoped that by collating this information the uncertainty about ammonium transport may be reduced and the prediction of impact may be improved.
Landfill leachate
The composition of landfill leachate in the UK has been analysed in some detail, particularly by ⇓Aspinwall & Co (1995). ⇓Table 1 compares the UK Drinking Water standards (as given in the Water Supply (Water Quality) Regulations 1989, SI 1147) with the concentrations typically found in leachate from landfills taking predominantly domestic and commercial waste. Red List substances (as defined under the Trade Effluents (Prescribed Processes and Substances) Regulations 1989, SI1156) are only included if they were detected in over 40% of leachate samples and a drinking water standard is defined. Lists I and II are as defined in the Groundwater Directive 80/68/EEC, which has been implemented in UK Law by Regulation 15 of the Waste Management Licensing Regulations, 1994, SI 1056 and, more recently, by the Groundwater Regulations, 1998, SI 2746.
Many substances occur in leachate at higher concentrations than ammonium but these are generally major ions with high acceptability levels. Ammonium is the only species which occurs at high concentrations in leachate (i.e. hundreds of mg per litre) and is also on List I or List II, the EU‐defined lists of dangerous substances. There are, of course, many more toxic substances released, but these tend to be at much lower concentrations and unique to individual landfills. In general, the dangerous organic species are at low concentrations and subject to degradation and sorption. Toxic inorganics (such as heavy metals) also occur at lower concentrations.
From ⇑Table 1, it is apparent that the contaminants of most concern are likely to be iron, ammonium, manganese and possibly potassium. Most other contaminants, including the organics, will be adequately diluted by the natural groundwater flow beneath the landfill which usually dilutes by at least a factor of 10 (even without a liner). Only ammonium of these four is on List I or List II. This paper will focus on a more detailed consideration of the transport of ammonium.
Transport of dissolved contaminants in groundwater
For conservative contaminants dissolved in groundwater, the one‐dimensional transport equation including advection and dispersion for a constant concentration source of contaminant was solved by ⇓Ogata & Banks (1961). ⇓Sauty (1980) solved a slight variation on this problem which assumed a constant injection rate at the origin. Both of these solutions have rather complicated second terms, which are equal and opposite in sign so that the average of the two solutions (now known as the Sauty approximation) is much simpler. The Sauty approximation, neglecting molecular diffusion, is: where C is the concentration of the contaminant in the groundwater at distance x from the source and time t (mg/l), C_{0} is the source concentration (mg/l), x is distance (m), t is time (d), v is the average linear groundwater velocity (m/d) and α is the longitudinal dispersivity (m). This equation can easily be expanded to a version including a retardation factor and an exponential degradation term for non‐conservative contaminants such as ammonium (see ⇓Bear (1972) for instance). The process of retardation acts simply to slow the velocity of the contaminant by a constant factor and can be used to approximately represent adsorption (see ion exchange section). Degradation causes the amount of contaminant to reduce exponentially as time passes. with where R is the retardation factor as defined by equation (3), λ is the exponential decay (d^{−1}) and λ = ln(2)/H where H is the half‐life (d). There are seven variables in this equation (C_{0}, x, α, t, v, λ and R). In the context of a landfill, two of these (x and t) will be constrained by the location of the monitoring point relative to the landfill and by the time since the landfill commenced filling. There are complications such as the exact distance for a large landfill and the time allowance for waste absorption and travel times through the liner and unsaturated zone but these are estimable. Three more of the parameters are partially constrained (C_{0}, α, v). Measurements of permeability and porosity are required to estimate dilution and velocity, and dispersivity may be best estimated by calibrating to the breakthrough curve.
The chloride breakthrough curve can then be used to calibrate these five variables using equation (1). The assumption may then be made that the same values of α, v, x, and t are appropriate to ammonium transport. C_{0} for ammonium can usually be estimated from an analysis of the leachate and the dilution ratio observed for chloride. This leaves only two unknowns for the ammonium equation (2): λ and R. Hence curve‐fitting with a reasonable amount of data should allow relatively confident parameter estimation. However the validity of this equation is first discussed.
Applicability of solution to ammonium
Ammonium is not a conservative contaminant. It is retarded by two main processes: ion exchange and oxidation. These processes are discussed below.
Ion exchange
Ion exchange is an adsorption process whereby positive ions are attracted to negatively charged clay‐mineral surfaces and held there. Ammonium in solution (as NH_{4}^{+}) will occupy these sites before any of the other common monovalent metals. The selectivity sequence is not established with certainty (and there are different versions) but most are similar to the following one derived from ⇓Appelo & Postma (1993): There are two main approaches to the quantitative treatment of ion exchange. A mathematical description can be derived fairly easily if one major assumption is made. The assumption is that ammonium is adsorbed according to a linear isotherm i.e. the amount of solute sorbed by the soil is proportional to the concentration of solute in the groundwater. The constant of proportionality is called the distribution coefficient K_{d} (l/kg).
This formulation implies reversibility (i.e. when the contaminant has passed through all the sorbed material is dropped back into the groundwater) whereas there is evidence that ion exchange is not reversible by simple flushing (see for example ⇓Fig. 1). Processes that may release the ammonium ions are oxidation to nitrate in‐situ and displacement by more reactive ions.
The linear isotherm assumption has two other major weaknesses:
(1) it allows the soil to adsorb indefinitely which is not realistic. There must come a time when all the sites are used up. However, in the context of contaminant modelling, if the linear relationship is still valid at maximum (source) concentration, then this formulation is probably reasonable.
(2) there is not much experimental evidence that the relation between solute sorbed and solute in solution is linear. There are many alternative theories including the Freundlich and Langmuir isotherms and these are described in the literature (e.g. ⇓Fetter 1993). The Langmuir isotherm attempts to address the issue of an upper bound on the amount of solute that can be adsorbed. ⇓Fetter (1993) provides an example of how this assumption can bring arrival times forward by about 10% from the linear isotherm retardation.
The convenience of the linear isotherm assumption is that by including it in the transport equation, it turns out that this cation exchange has no other effect than to slow the contaminant down by a constant factor. Instead of the governing equation with the speed of the groundwater, v, the contaminant follows the same mathematical equation but with the speed changed to v/R, where R is the retardation factor defined as: where ρ is bulk density (kg/l), n is porosity and K_{d} is distribution coefficient (l/kg).
Plug flow approach to ion exchange
There is another approach to calculation of the delay imposed by ion exchange. If the contaminant movement is thought of as plug flow, then no ammonium will reach the target until all the sites have been used up. The linear isotherm theory is abandoned in favour of the assumption of total absorption until all sites are occupied resulting in a sharp contaminant front.
The Cation Exchange Capacity (CEC) of a material is a measure of how many sites there are per kilogramme of soil. Tables of estimated values for the common clays are given both in ⇓Lloyd & Heathcote (1985) and ⇓Yong (1985) (reproduced in ⇓Domenico & Schwarz 1990). For illite clay, for example, the values given for CEC are 100 to 400 eq/kg (⇓Lloyd & Heathcote 1985) and 250 meq/kg (⇓Yong 1985).
The delay imposed on the ammonium transport, T (days), may be calculated by where Q is groundwater flow rate (m^{3}/d), R_{e} is reaction efficiency, V is volume of soil (m^{3}), CEC is cation exchange capacity (meq/kg), 14 mg/meq is the atomic weight of the nitrogen (assuming ammonium concentration is recorded in mg/l as N). The Reaction Efficiency is introduced to allow for the fact that only a proportion of the available CEC sites can be occupied. It is interesting to compare this with the time delay introduced using the retardation approach, which is The implication of combining equations (4) and (5) (and using the fact that v=Qx/Vn) is that: This seems consistent with the definition of the distribution coefficient as the ratio of adsorbed ions to dissolved ions since the fluid generally contains concentration C_{0}. The dependence on the concentration illustrates the fundamental difference between the two approaches. The retardation approach assumes adsorption depends on concentration whereas the plug flow approach assumes it is a constant amount. The two approaches will only produce the same time delay if equation (6) is satisfied.
The laboratory experiments carried out by ⇓Thornton et al. (1995) favour the retardation calculation over the plug flow. If ammonium concentration is increased, the plug flow time delay is reduced (since the capacity is used up more rapidly) where as the time delay implied by retardation remains the same. Thornton’s results with a stronger leachate (‘M‐phase’) appear to be delayed slightly more than the weaker A‐phase leachate, although there may be other more complex chemical reactions at work.
Given that the CEC is easily measurable and K_{d} is less well known, this provides a method of estimating the equivalent distribution coefficient for ammonium. Assuming a source concentration after dilution of 50 mg/l, the distribution coefficient is calculated as 14 l/kg in clay assuming typical CEC of 250 meq/kg and R_{e} of 20%. In a typical sand aquifer (using density and porosity of 1.9 kg/l and 0.3 respectively), with say 10% clay, the distribution coefficient would be 1.4 l/kg and the retardation factor about 10.
In the computer program LandSim (⇓Golder 1996), the default distribution coefficient for ammonium is ascribed a uniform probability distribution between 0 and 50 l/kg. LandSim applies Monte Carlo uncertainty analysis to its predictions and therefore allows input parameters to be defined as probability distributions rather than values. This range is based on ‘Golder Associates’ experience of partition coefficients in sand and loam’ (⇓Golder 1996). The implied retardation ranges from 1 to about 318 assuming density and porosity as above. In other words, there is a 1% chance the retardation factor will be less than 4.2. This seems rather optimistic given the various observations both in the field and in laboratory experiments described below.
Oxidation
Under oxidizing conditions, ammonium is converted to nitrite which is then almost immediately converted to nitrate depending on the pH. This reaction is generally accomplished by micro‐organisms and is therefore a form of biodegradation. Most groundwaters derived from recent recharge are oxidizing in nature and would be expected to assist the oxidation process. In some contaminant plumes, such oxidation would occur only at the edges of the plumes.
There is no doubt that oxidation is an important mechanism in the attenuation of ammonium. It seems likely that because it depends on microbial activity the mathematics of the process will be related to exponential decay (i.e. the rate at which the material decays depends on how much material there is). Another reason supporting the postulated presence of degradation in the process is the simple observation that, at the many monitoring points around UK Landfills, ammonium is rarely recorded at distances over a few 100 metres even around very old landfills. If ammonium were only being retarded, it would appear eventually at all downstream points.
Summary
Neither of the two processes described above exactly fit the mathematics of retardation or exponential decay. However it seems likely that a combination of the two formulations may provide a reasonable empirical representation of the process for use in the field. The question remains as to what is the best combination of the two processes to represent the transport of ammonium.
The answer to this question has been investigated in this paper by inspection of the ammonium and chloride breakthrough curves recorded at monitoring points close to ammonium sources, at three different scales. Curve fitting to the simple form of the Ogata–Banks equation given above may provide some insight to the relative contributions of the two processes.
Observed data
Scales of investigation are very important because both dispersion and chemical processes appear to be scale dependent. Three distinct scales are considered in this paper which are laboratory scale, unsaturated zone scale and aquifer scale. The order of magnitudes of the distances involved in the derivation of the data presented below are respectively 1 m, 30 m and 300 m. The soils involved in the three case studies presented are not the same and they must be considered only as examples.
Laboratory scale
Experiments performed by ⇓Thornton et al. (1995) were carried out using landfill leachate in Permo‐Triassic sandstone. The experiments were carried out through columns of packed sandstone about 10 cm in diameter and 1 m long. The residence time was 21 to 23 days.
Some of the data gained from the ammonium and chloride analysis are reproduced as ⇑Fig. 1. In this example, the A‐phase leachate was used which had typical concentrations of 2705 mg/l of chloride and 1398 mg/l of ammonium. In this experiment, clean groundwater replaced the leachate at the time marked ‘groundwater flush’. It is clear that degradation of ammonium is minimal since the ammonium comes through at full strength. The authors suggest that the retardation factor of ammonium was between 1.28 and 1.39.
Since one pore volume represents about 22 days travel time and the duration of the experiments was about 200 days, it is possible that the duration was not long enough to detect any degradation.
Unsaturated zone scale
Observations at Burnstump Landfill (⇓Lewin et al. 1994) suggest that between 1978 and 1991 the chloride front advanced about 17 m in the unsaturated zone. The ammonium front advanced about 7 m in the same time period and does not seem to advance at concentrations above about 20% of full strength. Although a calculation is not presented, we have analysed the data as shown in ⇓⇓Figs 2 and 3.
Least‐squares analysis was not used in order to include an appreciation of the independent data constraints and some degree of expert opinion and common sense. In matching this curve, the equation has five variables (C_{0}, α, v, t and x), all of which can be constrained to some extent by data independent from the breakthrough curve itself. The strength of the leachate is not known and has been assumed to be 2000 mg/l (chloride) and 1000 mg/l as N (ammonium) which is consistent with a leachate generated from domestic and commercial waste.
The theoretical curve presented in ⇑⇑Figs 2 and 3, is based on the parameters in ⇓Table 2. C_{B} is the background concentration in the groundwater (mg/l). H is the half‐life of the degradation rate.
The tendency of the chloride concentration behind the front to be much lower than at the front (see ⇑Fig. 2) is attributed by the authors to a reduction in the strength of the leachate being produced. It is also noted that the very low dispersivity is probably a consequence of an intergranular flow system (at least vertically) with no fissures to disperse the contaminants.
The fit between data and theoretical curve for the ammonium concentration is poor, particularly with C_{0} constrained at 1000 mg/l. The point behind the front cannot be matched but this could be a consequence of reduction in source strength as with chloride.
Both at laboratory scale and unsaturated zone scale, no firm conclusion can be drawn on degradation but retardation is well observed. At laboratory scale the factor was about 1.3 to 1.4 and in the unsaturated zone about 2.75.
Aquifer scale
Llwn Isaf is a landfill in North Wales with an established contaminant plume. The aquifer consists of unconsolidated sands and gravels.
The breakthrough curve for chloride is very clear at several of the downstream boreholes (see ⇓Fig. 4). It is particularly good at BH20 and reasonable for BH21.
The chloride curve has been matched at Boreholes 20 and 21 using equation (1) in ⇑Fig. 4. The parameters used for this model are chloride (160 mg/l), background chloride 12 mg/l, distance 200 m, groundwater gradient 0.01, hydraulic conductivity 2 m/d and porosity 0.35. dispersivity is set at 10 m and the process has been started in December 1986.
In this case, t and x can be fairly well constrained. For example, the distance to the source is between 150 m (the distance to the closest point of the landfill) and 400 m (the distance to the furthest point). The landfill was apparently started in 1982, although the parameter t is not fully constrained for two reasons. Firstly, waste was on the site before this date. Secondly, the travel time through the unsaturated zone may be a few years, and clearly the landfill does not begin to act as a source until the leachate has arrived in the aquifer.
The source concentration C_{0} can be given an upper bound by the analyses of leachate in the landfill. The uncertainty is that the leachate is diluted as it enters the aquifer by the regional groundwater flow. Both this and the leachate leakage rate are hard to constrain and it is approximately the ratio of these two which defines the source concentration.
Velocity of groundwater is even more difficult to define. If direct measurements are not available, it can be calculated from the measured parameters: hydraulic conductivity (a parameter which frequently varies spatially by more than an order of magnitude), the hydraulic gradient (usually well constrained) and the effective porosity. The effective porosity takes into account the existence of fast pathways or secondary permeability. For example in the Chalk aquifer, the total porosity may be up to 30%, but because a pollutant travels through the fissures the correct effective porosity over short distances is the fissure porosity which is generally closer to 1%.
Finally the dispersivity, while not constrained by independent on‐site data, can be constrained by the quantity of dispersion data available from the rest of the world. Analyses by ⇓Lallemand‐Barres & Peaudecerf (1978) and ⇓Gelhar (1986) show that dispersivity tends to be close to 10% of the scale of measurement. In the context of this landfill, the likely range for dispersivity is roughly 3 to 300 m. Matching the chloride curve (⇑Fig. 4) gave a dispersivity of 10 m.
⇓Figure 5 shows that the transport of ammonium is retarded. It is actually retarded differently at BH20 and BH21 since breakthrough has not occurred at BH20—possibly because of locally clayey conditions around the borehole.
At BH21, breakthrough is starting to occur (see ⇑Fig. 5). The three datapoints suggest that the break‐through has been fairly sharp. It is difficult to match this curve without reducing the dispersivity. There could be various explanations for a reduction in dispersivity between chloride and ammonium. The favoured explanation is that the mechanism of ion exchange may be able to sharpen the front. The linear isotherm formulation may be too simplistic and sorption sites may be occupied if they are available, rather than occupied in order to make the amount sorbed in equilibrium with the water concentration. This is the assumption made by the plug flow approach, which results in a breakthrough showing zero dispersivity.
There has been a significant reduction in ammonium concentration from its assumed source concentration of 60 mg/l. This ‘source concentration’ was calculated assuming the same groundwater dilution ratio as chloride. A similar effect where the ammonium does not increase to the concentrations expected was noted in the Burntstump data. It seems conceivable that degradation is the reason for this reduction.
Degradation results in the concentration gradually reaching a steady‐state equilibrium where degradation is balanced by advection. The equation of this concentration reached at infinite time is
Curve fitting
The theoretical curves presented in ⇑Fig. 5, are based on the parameters in ⇓Table 3. All the curves use the same values for x (200 m), ν (0.057 m/d) and the starting time (December 1986).
The fourth curve is included to illustrate the problem in matching curves without much degradation. The ‘steady‐state’ level at the target settles at a much higher level than is observed in the field.
Any of the other three curves presented could conceivably fit the data obtained, given the scatter that seems to affect ammonium data. Two of these curves are based on the hypothesis that dispersion is lower for ammonium than it is for chloride. Certainly if the plug flow approach to CEC were correct, then fronts would have extremely low dispersion.
One problem with this hypothesis is that the retardation needs to be very low to match the data. This is not considered credible and, on the whole, curve (1) may be the most appropriate with R = 1.4 and H = 6 years. Perhaps, at Llwn Isaf, time will tell.
Discussion
Retardation and degradation at the three scales of investigation are estimated in the three case studies above as shown in ⇓Table 4. The case studies seem to show that the ammonium breakthrough curves can be modelled by processes including degradation, and retardation by a factor of 3 or less.
At present, typical predictive assessments following the procedure laid out in LandSim tend to overestimate retardation and underestimate or neglect degradation. The result may be that the two errors compensate for each other and the model agrees with the observed data. In practice, these observed data amount to the absence of ammonium at observation boreholes fairly close to the source. However, predictions for the future including only retardation will eventually produce a breakthrough, whereas the solutions balancing retardation and degradation will reach a steady‐state distribution. It must be emphasized that there is a fundamental difference between these approaches and they will produce different predictions.
The inclusion of a degrading source term (as used in LandSim) is a method for obtaining predictions which do not predict an ammonium breakthrough in the distant future. This is a different conceptual model from the version presented in this paper where the contaminant degrades in the aquifer. The results arising from this approach have not been assessed in this paper.
Conclusions

Ammonium is the most important List II contaminant arising from Domestic Waste landfills and the most likely to impact water resources or the environment via a groundwater pathway.

There are not enough data available on the transport of ammonium at aquifer scale. Given the number of landfills in the UK that are well monitored, it is surprising that more data are not available. Monitoring at Llwn Isaf site, and at other similar landfills, must continue in order to improve understanding of the nature of ammonium transport.

The plug flow and retardation approaches to calculation of time delay in arrival of ammonium are fundamentally different. The data presented by ⇓Thornton et al. (1995) appear to suggest that the retardation approach is the more representative.

Indications both from the field and the comparison with the plug‐flow CEC equation suggest that retardation probably does not exceed 3 (in the aquifer) and the partition coefficient, K_{d}, therefore is less than 0.5 l/kg in an unconsolidated aquifer. This is in some contrast to current practices as recommended by the EA (e.g. the LandSim manual suggests a range of 0 to 50 l/kg for ammonium from experience ‘in sand and loam’).

The effect of degradation in the aquifer may be important.

Typical predictive assessments at present following the procedure laid out in LandSim tend to over‐estimate retardation and underestimate or neglect degradation. The result may be that the two alterations compensate for each other and agree with observed data. However predictions for the future including only retardation will eventually produce a breakthrough, whereas the solutions balancing retardation and degradation will reach a steady‐state distribution.

The inclusion of a degrading source term (as used in LandSim) is not the same as a contaminant that degrades in the aquifer, although the difference in results has not been assessed in this paper.
Acknowledgments
The permission of Gwynedd Council to publish data from Llwn Isaf Landfill collected as part of their monitoring programme is gratefully acknowledged.
 © 2000 The Geological Society of London