Methods for determining the methane generation potential and methane generation rate constant for the FOD model: a review

Abstract

In the first order decay (FOD) model of landfill methane generation, the methane generation potential (L₀) and methane generation rate constant (k) for both bulk municipal solid waste (MSW) and individual waste components have been determined by a variety of approaches throughout various literature. Differences in the determination methods for L₀ and k are related to differences in our understanding of the waste decomposition dynamics. A thorough understanding of the various available methods for determining L₀ and k values is critical for comparative study and the drawing of valid conclusions. The aim of this paper is to review the literature on the available determining methods and the ranges for L₀ and k values of both bulk MSW and individual waste components, while focusing on understanding the decomposition of waste, including the role of lignin. L₀ estimates in the literature are highly variable and have been derived from theoretical stoichiometric calculations, laboratory experiments, or actual field measurements. The lignin concentration in waste is correlated with the fraction of total degradable organic carbon (DOC_f) that will actually anaerobically degrade in the landfill. The k value has been determined by precipitation rates, laboratory simulations, aged-defined waste sample, and model fitting or regression analysis using actual gas data. However, the lignin concentration does not correlate well with the k value, presumably due to the impact of lignin arrangement and structure on cellulose bioavailability and degradation rate. In sum, this review summarizes the literature on the measurement of L₀ and k values, including the dynamics and decomposition of bulk MSW and individual waste components within landfills.

Keywords

Landfill municipal solid waste first-order decay model methane generation potential methane generation rate constant

Introduction

Landfills that are managed to minimize environmental impact and promote waste degradation can be integrated with technologies that include energy recovery systems. Many of the technologies that have been used to promote more sustainable landfills focus on the methods to foster waste treatment. Sustainable landfill practices address how best to manage the landfill, including leachate and landfill gas (LFG). Landfills are usually considered to be anthropogenic sources of methane (CH₄), which has historically been the largest source of greenhouse gas (GHG) emissions from the waste sector (Bogner et al., 2008). Time dependent quantitative estimation of LFG production is the primary criterion that should determine the choice of method of gas utilization. Due to the difficulties in precisely monitoring CH₄ emissions of whole landfill sites, modeling approaches are applied. These approaches include first-order decay (FOD) LFG generation models, including the US EPA’s LFG emissions model (LandGEM), e-pollutants release and transfer registers (E-PRTR) (Fr) model, Intergovernmental Panel on Climate Change (IPCC) model, and Afvalzorg model (Kamalan et al., 2011; Mou et al., 2014). The E-PRTR (Fr) and LandGEM models are single-phase models, whereas the IPCC and Afvalzorg models are multi-phase models, which operate with a number of more detailed waste categories (Mou et al., 2014). The effect of the age of waste on CH₄ production is incorporated into the first-order model. For each unit amount of waste, the FOD models consider that the CH₄ generation rate decays exponentially with time (Rajaram et al., 2012):

G = W L_{0} k e^{- k t}

(1)

where G is the CH₄ generation rate in volume per time, W is the mass of waste in place, L₀ is the CH₄ generation potential in volume per mass, k is the first-order rate constant in reciprocal time, and t is the time elapsed after disposal of the waste.

The basic condition to obtain modeling results that are as suited as possible to the actual production of gas is the right choice of assumption, with regard to the constants of the CH₄ generation potential (L₀) and CH₄ generation rate (k). L₀ represents the total volume of CH₄ generated from a specified quantity of disposed waste. The k value controls the predicted time over which CH₄ is generated from the specified waste stream (Amini et al., 2012). These parameters are strongly dependent on the chemical composition, properties of waste, and the condition of the process (e.g., waste density, pH, and moisture content). For this reason, the examination and critical estimation of the biochemical properties of wastes that take into consideration the controlling LFG emissions are of substantial importance for determining the L₀ and k values. As essential parameters, L₀ and k values for both bulk municipal solid waste (MSW) and individual waste components are widely studied and reported in the literature. Furthermore, various review studies have been performed on anaerobic decomposition, the methane generation potential of MSW, biogas generation processes, LFG generation models, and CH₄ oxidation processes (Abushammala et al., 2014; Barlaz, 2006; Fei et al., 2016; Gunaseelan, 1997; Kamalan et al., 2011; Krause et al., 2016a; Mao et al., 2015; Micales and Skog, 1997; Oonk, 2010; Scheutz et al., 2009).

The aim of this paper is to review the literature on the available determining methods and the ranges for L₀ and k values of both bulk MSW and individual waste components, with the review focusing on understanding the decomposition of waste, including the role of lignin. The following section reviews a wide range of L₀ values and their determining methods, and provides a brief description of L₀ in a landfill definition and discussion of the relationship between lignin and the extent of decomposition for individual waste components. The last section of the paper provides a summary and analysis of the literature on the degradation rate of both bulk MSW and individual waste components in both landfills, and laboratory- and field-scale simulations thereof.

Methods for determining L₀

Overview of L₀ values from the literature

The L₀ of wastes is defined as the volume of CH₄ that can be produced per unit mass of waste under idealized conditions for CH₄ formation (Krause et al., 2016a). The L₀ is often used to refer to the ultimate CH₄ yield, i.e., the maximum amount of CH₄ produced per unit mass of waste under anaerobic conditions. It should be noted that it is misleading to refer to L₀ as the CH₄ generation potential in the landfill, because the value of L₀ includes a number of physical and environmental factors (e.g., moisture, temperature, and particle size) that influence CH₄ generation (Wang et al., 2013a). The CH₄ generation potentials in field settings are lower, because landfills do not function as efficiently as anaerobic digesters or laboratory experiments (Bogner and Matthews, 2003; Fei et al., 2016).

In the literature, various methods are used to measure the L₀ of solid waste. Table 1 presents a range of L₀ values from solid waste landfill, and methods for determining L₀. As observed in these studies, L₀ values vary greatly among the different landfills, which are mainly due to differences between their waste compositions (Fei et al., 2016). In general, L₀ values have been determined by a number of methods: the stoichiometric method (Machado et al., 2009; Mor et al., 2006; Sanderson et al., 2008); experimental methods (Cho et al., 2012; Jeon et al., 2007; Tolaymat et al., 2010); model fitting or regression analysis using gas data (Amini et al., 2012; Wang et al., 2013a); and the IPCC model (Govindan and Agamuthu, 2014; Kumar et al., 2004; Thompson et al., 2009).

Table 1.

L₀ values at landfill level taken from the literature, and corresponding determination methods (DOC: degradable organic carbon, DOC_f: fraction of DOC that can decompose, MCF: CH₄ correction factor for aerobic decomposition).

Landfill site		DOC	DOC_f	MCF	L₀^a (m³ CH₄ Mg⁻¹)	Method	References
Metropolitan center landfill, Salvador, Brazil		0.273	0.263	1	67.0	Stoichiometric equations with biodegradable fraction	Machado et al. (2009)
Loma Los Colorados landfill, Montenegro, Chile		–	-	-	105.0	Stoichiometric equations with biodegradable fraction	Sanderson et al. (2008)
Gazipur landfill, Delhi, India		0.0835	0.580	1	45.2	Carbon content	Mor et al. (2006)
India		0.11–0.16	0.77	0.4	31.6–46.0	Waste composition with the IPCC model	Kumar et al. (2004)
Jeram landfill, Selangor, Malaysia	Bulk waste approach	0.12	0.5	0.8	44.8		Govindan and Agamuthu (2014)
Jeram landfill, Selangor, Malaysia	Waste composition approach	0.08	0.5	0.8	29.9		Govindan and Agamuthu (2014)
Canada	Ontario	0.176–0.205	0.77	1	126–147		Thompson et al. (2009)
	Nova Scotia	0.175–0.227			126–147
	Quebec	0.249–0.283			179–203
	Alberta	0.195–0.228			140–164
	British Columbia	0.212–0.261			153–188
Korea	Sudokwon landfill site 1	0.18–0.30	0.57–0.63	1	56–88	Waste composition with waste-component specific CH₄ generation potential	Jeon et al. (2007)
Korea	Sudokwon landfill site 2	0.13–0.21	0.55–0.60	1	37–58		Jeon et al. (2007)
Outer Loop landfill, USA		–	–	–	54.8		Tolaymat et al. (2010)
Landfills in Florida, USA		–	–	–	67 (traditional landfills) 70 (wet cell)		Amini et al. (2012)
23 metro cities, India		–	–	–	30.2–52.1		Kumar and Sharma (2014)
USA	National average waste composition	–	–	–	59.1		Staley and Barlaz (2009)
	State average waste composition	–	–	–	63.9
	Outer Loop landfill	–	–	–	48.4±14
USA		–	–	–	46		Kaplan et al. (2009)
4 landfills, Denmark	Afvalzorg	–	–	–	22–31		Krause et al. (2016b)
4 landfills, Denmark	IPCC				63–89		Krause et al. (2016b)
Landfills, USA	A	–	–	–	140	Waste composition with waste-component specific CH₄ generation potential and calibration	Amini et al. (2013)
	B	–	–	–	74
	C	–	–	–	93
USA	10 landfills	–	–	–	100	Waste composition with waste-component specific CH₄ generation potential and minimizing the SSE	Wang et al. (2013)
USA	T landfill	–	–	–	85		Wang et al. (2013)
Sudokwon landfill site 2, Korea		–	–	–	56–69	Waste composition and waste-component specific CH₄ generation potential and a correction factor	Cho et al. (2012)
Ämmässuo landfill, Finland		–	–	–	100	Model fitting using field data	Sormunen et al. (2013)
Muribeca landfill, Brazil					123.9	Model fitting using field data	Maciel and Jucá (2011)
Sudokwon landfill site 1, Korea		–	–	–	18–20	Nonlinear regression using field data	Park et al. (2012b)
Three landfills		–	–	–	76		Faour et al. (2007)
SSWMC					115
Landfill A					95
CSWMC					87
21 landfills					100

An F value of 0.5 is used, and the density of CH₄ is assumed to be 0.714 kg/m³.

Table 2 presents a range of L₀ values for individual waste components. Food waste with high moisture content has a low L₀, whereas paper wastes have a high L₀. Over the lifetime of the landfill, the slowly degrading components, especially paper and card waste, make the most significant overall contribution to CH₄ emissions (Donovan et al., 2011). Therefore to achieve significant reduction in LFG generation, the reduction and sorting of paper, card, and green waste should be prioritized (Pan and Voulvoulis, 2007).

Table 2.

L₀ values for individual waste components taken from the literature.

Country	Component		DOC	DOC_f	MCF	L₀ (m³ CH₄ Mg^-1)	References
USA	Leaves		Source: Eleazer et al. (1997)			30.6	Kaplan et al. (2009)
	Grass					136.0
	Branches					62.6
	Old newsprint					74.3
	Cardboard					152.3
	Office paper					217.3
	Phone books					74.3
	Books					217.3
	Old magazines					84.4
	3rd Class mail					150.8
	Mixed paper					103.7
	Food waste					300.7
USA	Household waste		0.16-0.20	0.50	0.5	74.7-93.4	Manfredi et al. (2009)
	Kitchen organics		0.10-0.12	0.64		59.8-71.7
	Newspapers		0.36-0.44	0.20		67.2-82.2
	Office paper		0.30-0.36	0.88		246.5-295.8
	Cardboard		0.30-0.38	0.45		126.1-159.7
	Wood		0.40-0.45	0.23		85.9-96.6
Hokkaido, Japan	Paper		BMP test			214.4	Ishii and Furuichi (2013)
Hokkaido, Japan	Kitchen waste		BMP test			126.7	Ishii and Furuichi (2013)
Thailand	Food waste		0.15	0.5	0.65	45.5	Wangyao et al. (2010)
	Papers		0.40			121.4
	Wood		0.43			130.5
	Textiles		0.24			72.8
Denmark	Shredder		Laboratory test			6.2-9.1	Mou et al. (2014)
	Street cleaning					7.2-7.4
	Mixed bulky					5.4-7.0
	Sludge					52.0-70.0
USA	Yard waste		BMP test			49.0	Yazdani et al. (2012)
Korea	Food wastes	Stoichiometric	0.36	0.68	1.0	117.1	Jeon et al. (2007)
	Food wastes	Organic carbon	0.33	0.73		117.1
	Paper	Stoichiometric	0.72	0.70		239.1
	Paper	Organic carbon	0.79	0.63		239.1
	Wood	Stoichiometric	0.56	0.44		116.0
	Wood	Organic carbon	0.57	0.43		116.0
	Textile	Stoichiometric	1.00	0.45		215.8
	Textile	Organic carbon	0.89	0.51		215.8
	Misc. organics	Stoichiometric	0.39	0.59		109.3
	Misc. organics	Organic carbon	0.40	0.58		109.3
	Sludge	Stoichiometric	0.14	0.29		19.1
	Sludge	Organic carbon	0.12	0.33		19.1
Italy	Mechanically sorted organic residues		Laboratory test			115.1±4.2	De Gioannis et al. (2009)
Italy	Mechanically-aerobically pretreated waste					9.2±1.5	De Gioannis et al. (2009)
Italy	Mechanically-aerobically pretreated waste					12	Di Maria et al. (2013)
England	Mechanically-aerobically pretreated waste					49.5	Siddiqui et al. (2013)
Germany	Mechanically-anaerobically-aerobically pretreated waste					17.7

Another possible solution for the reduction of LFG generation is mechanical biological treatment (MBT; Di Maria et al., 2013). MBT leads to a significant reduction of LFG generation from landfills as compared to the raw waste. De Gioannis et al. (2009) reported that 91% reduction of the LFG generation potential was achieved after 8 weeks of aerobic treatment. In addition, there is a concept of anaerobic bioreactor landfill. In comparison with the traditional dry sanitary landfill, this method allows for better use of the energy potential of biogas and reduces the risk of uncontrolled LFG emissions.

Stoichiometric method

The CH₄ yield (B₀) can be calculated by assuming the total stoichiometric conversion of the organic matter to CH₄ and carbon dioxide (CO₂) using Buswell’s equation (Raposo et al., 2011):

B_{0} = \frac{[(a / 2) + (b / 8) - (c / 4)] \times 22400}{(12 a + b + 16 c)}

(2)

Empirical formulae (C_aH_bO_c) can be designed from experimental elemental analysis determination. However, a limitation of this equation is associated with the stoichiometric estimates of waste fractions, which are not biodegradable, the moisture limitations, and also toxins, some fraction of the waste that is not accessible.

Organic matter can be fractionated into easily biodegradable compounds (carbohydrates, lipids, and proteins), and poorly biodegradable compounds (fibers, humic, and fulvic acids) (Batstone et al., 2002; Lesteur et al., 2010). If the organic fraction composition (lipids, proteins, and carbohydrates) is known, the CH₄ yield can be estimated using the following general equation (Raposo et al., 2011):

\begin{array}{l} B_{0} = 415 \times % Carbohydrates + \\ 496 \times % Proteins + 1014 \times % Lipid \end{array}

(3)

The coefficients in this equation are derived from stoichiometric conversion of model compounds representing average formulae for carbohydrates (C₆H₁₀O₅), proteins (C₅H₇O₂N), and lipids (C₅₇H₁₀₄O₆) (Angelidaki and Sanders, 2004; Raposo et al., 2011).

However, in practice, not all of the organic matter in waste is subject to microbial degradation. This makes the production of LFG much lower than the theoretical value. The elemental composition value therefore overestimates the biochemical methane potential (BMP) value (Lesteur et al., 2010). It is important to note that the theoretical CH₄ potential must be adjusted by a biodegradability factor.

L₀ values for waste can be calculated using the theoretical CH₄ potential and the biodegradable portion (BF) of the waste, as shown in (Machado et al., 2009):

L_{0} = \frac{B_{0} \times B F}{1 + w}

(4)

The water content, w, is used to consider only the dry mass of potentially degradable organic matter. The BF value can be calculated using the ratio between the BMP value and the values predicted by stoichiometric equation (equation (2)). For example, the BF value at the Metropolitan Landfill, Salvador, Brazil is found to be 0.263, excluding plastic and rubber content (Machado et al., 2009).

The linear relationship between BF and lignin has been modelled by Chandler et al. (1980). Several kinds of substrate, such as manure, newspaper, straw, leaves, and other agricultural materials, were used to develop the model, predicting the effect of lignin content on BF (Lesteur et al., 2010). Chandler’s model is as follows:

BF = 0.83 - (0.028 \times lignin)

(5)

where lignin (0 < lignin < 20%) is the VS lignin content.

LFG is formed as a result of the biodegradation of organic carbon in the waste: stoichiometry shows that per kilogram of organic carbon (= 83.3 mol) that anaerobically degrades, about 1.87 m³ of LFG normalized to 1 atm and 0°C (= 83.3 mol × 22.4 L/mol) is produced (Scharff and Jacobs, 2006). Anaerobic decomposition can be hindered in specific microenvironments, due to unsuitable environmental conditions, and the heterogeneity of the waste composition. This is accounted for by assuming that only a fraction (ζ) of the waste is converted into LFG. It may be said that BF and ζ have a similar meaning. ζ is typically of the order of 0.5 (Bogner and Matthews, 2003), and Mor et al. (2006) suggested a value of 0.58. ζ increases with temperature, and can be as high as 0.8. At 35°C, almost 80% of the degradable organic carbon may be dissimilated (Bingemer and Crutzen, 1987). However, this value was obtained in ideal conditions, so it is not likely that the value in real landfills exceeds 0.7 (Mor et al., 2006):

α_{t} = ζ 1.87 A C_{0} k e^{- k t}

(6)

where α_t is the LFG formation at a certain time (m³ yr⁻¹), ζ is the dissimilation factor, k is the degradation rate constant (yr⁻¹), A is the amount of waste deposited (Mg), C₀ is the amount of degradable organic carbon in the waste (kg Mg⁻¹) at the time of deposition, t is the time elapsed in years since deposition (yr), and the factor 1.87 has the dimensions m³ kg⁻¹.

Measuring the elemental composition and organic carbon is very fast, taking only a few hours. But, it should be noted that the application of results obtained from these methods to a full-scale landfill remains difficult, because the methods simulate only average landfill conditions, and do not account for variations brought about by climatic and operational events.

Experimental methods

L₀ values have been measured by BMP test, lysimetry, and field-scale experiments. The L₀ value from full-scale landfills would be the best indicator. However, such data are very limited, if not non-existent, and are difficult to acquire, given the complexity of biochemical interactions within a landfill, the lack of uniform and reliable data collection protocols, the inherent uncertainty of gas collection methods employed at various sites, and the maturation stage at which a landfill might be during a monitoring period (El-Fadel et al., 1997). In contrast, laboratory experiments are better controlled, and employ operating procedures to enhance microbial activity. For these reasons, laboratory experiments produce more predictable result, compared to field monitoring studies (Fei et al., 2016).

In order to determine L₀, several authors have used the BMP value of mixed waste based on the weighted average of waste components (Cho et al., 2012; Jeon et al., 2007; Tolaymat et al., 2010). BMP assay is described by Owen et al. (1979), and has been modified by some researchers (Shelton and Tiedje, 1984; Strömberg et al., 2014). The L₀ from landfill depends on the composition of waste (Cho et al., 2012). It should be noted that it is not possible to predict L₀ for landfills with inaccurate waste composition data (Amini et al., 2013).

The BMP value can be used as an index of the anaerobic biodegradation potential. The BMP is the experimental value of the maximum quantity of CH₄ produced per gram of volatile solid. For this reason, BMP test also involves certain problems related to obtaining acceptable data for determining the L₀.

Firstly, DOC and BMP values are closely related (Machado et al., 2009). DOC is the organic carbon in wastes that is accessible to biochemical decomposition under anaerobic conditions, which includes the biochemical processes in a cell or organism. In other words, DOC is the amount of organic carbon that is ultimately degraded under optimal anaerobic conditions. Similarly, the BMP assay measures the quantity of anaerobically degradable organic carbon present in a sample under optimal conditions (Lesteur et al., 2010; Mou et al., 2015a, 2015b; Wang et al., 1994).

Secondly, there are many international and national standards available on how to perform a BMP test, but they differ in the experiment set-up, and are frequently modified and adapted to the specific researcher’s purpose (Raposo et al., 2011). Due to this, it is often difficult to evaluate results from different studies, as the values and level of information can substantially differ. Many studies demonstrate the importance of considering the temperature, pressure, particle size, origin of inoculum, inoculum-to-substrate ratio, and mixing rate when performing BMP test (Angelidaki et al., 2009; Strömberg et al., 2014; Walker et al., 2009).

Finally, the L₀ value obtained via the BMP test is greater than that obtained from a lysimeter experiment and full-scale data. A lysimeter is a simulate form of sanitary landfill in the sense of control device (Rafizul et al., 2012). Generally, lysimeters are smaller, more self-contained and better monitored than landfills. Their small scale allows their location in a laboratory, where it is convenient to perform extensive monitoring (Stessel and Murphy, 1992).

The lysimeter experiments use a few kilograms of sample. Therefore in contrast to the BMP test, the lysimeter experiment uses sample amounts that are more representative of the mixed waste without segregation, and so provides more reliable and valid data. However, the lysimeter experiments are limited, since a very long time is required (e.g., a number of years) to collect acceptable data (Cho et al., 2012).

The CH₄ generation for wastes in the lysimeter would be low, due to the larger size of the tested sample, and restricted mass transfer of the substrate and nutrients in the lysimeter, compared with those in the case of the BMP test (Cho et al., 2012). Thus, Cho et al. (2012) suggested

L_{0, l a n d f i l l} = f \times \sum_{i = 1}^{n} (L_{0, i, B M P} \times {(w t . f r a c t i o n)}_{i})

(7)

which means that the L₀ obtained from BMP test (L_0,i,BMP) needs to be corrected using a correction factor (f), based on the BMP assay and lysimeter study.

Sil et al. (2014) published correction factors to estimate CH₄ emission using the LandGEM model. The correction factors are 0.94, 0.13, and 0.74 for food waste, mixed un-segregated MSW, and vegetable wastes, respectively.

With respect to hydraulic conductivity, the disadvantage of the lysimeter test is the hydraulic retention time (HRT). The HRT of a lysimeter may not allow for sufficient residence time for carbon degradation in leachate (Park et al., 2012a). In contrast, previous studies reported that less than 4% of the total input carbon is emitted through leachate in landfills (IPCC, 2006; Lornage et al., 2007; Kim et al., 2011; Manfredi et al., 2009; Valencia et al., 2009). The low proportion of DOC emitted through leachate can be explained by the low hydraulic conductivities of compacted MSW, which impedes water flow. The literature review shows that the hydraulic conductivities of waste at landfills range from 1.36 × 10⁻³ to 1.03 × 10⁻⁷ cm s⁻¹ (Petrovic, 2016). It should be noted that carbon emitted via leachate needs to be considered to determine L₀ using a lysimeter.

Model fitting and regression analysis

The LFG generation models may rely on some site-specific data on CH₄ recovery, emission, and oxidation, which are all important to calibrate or validate the LFG models. Thus, L₀ and k can be determined on the basis of the experimentally determined values in the landfill, and their feasibility can be determined by comparison of the modelled CH₄ generation with the CH₄ recovery or CH₄ generation (Sormunen et al., 2013). This methodology enables more precise CH₄ generation estimates compared with models based only on the recovered CH₄.

Generally, the Gompertz and logistic models fit better than the first-order equation for experimental values (Nielfa et al., 2015). Ware and Power (2017) argued that when actual experimental data of a CH₄ production are available, sigmoidal models (Gompertz, Richards, Stannard, and logistic models) should be applied in order to determine the model of best fit. Park et al. (2012b) developed two models obtained by differentiating the Modified Gompertz and Logistic models to determine L₀ and k values. The L₀ and k values can be determined by regression analysis using the two models and actual LFG collection data. However, the models need long-term LFG data from landfill to determine the L₀ and k values. Faour et al. (2007) argued that the exponential rise in the gas volume curve is often delayed, perhaps as a result of the acclimation of microorganisms, non-optimal gas recovery, or lack of landfill cover. Therefore, the mixed-effects model is developed to account for this lag. There are three parameters in the mixed-effects model, k, L₀, and the specific volume of CH₄ collected at the end of the lag phase. However, it should be noted that if collected gas data with changing gas collection efficiency over time, rather than generated gas data, is used to perform regression analysis, different L₀ values can be reached. Furthermore, CH₄ emission modelling has been carried out using LFG extraction data and assumptions for extraction efficiency and CH₄ oxidation, resulting in major uncertainties being introduced (Scharff and Jacobs, 2006).

IPCC method

The IPCC (2006) model uses characteristics of the waste (DOC and DOC_f) and the landfill site (MCF and F) to prediction CH₄ generation. In the IPCC (2006) model, L₀ can be calculated using

{DDOC}_{m} = DOC \times {DOC}_{f} \times MCF

(8)

L_{0} = \frac{D D O C_{m} \times F \times \frac{16}{12}}{0.714}

(9)

Decomposable degradable organic carbon (DDOC_m) is the part of the organic carbon that will degrade under the anaerobic conditions in landfill. DOC is the organic carbon in waste that is accessible to biochemical decomposition. DOC_f is the fraction of DOC that can decompose. MCF is the CH₄ correction factor for aerobic decomposition. F is the CH₄ volume concentration in the gas, 16/12 is the molecular weight ratio of CH₄ and C, and 0.714 is the CH₄ density (0°C, 1 atm)

DOC

Previously research reported that DOC in MSW ranges from 8% to 30% (Bingemer and Crutzen, 1987). It is interesting to note that for the CH₄ emission source of landfill in Japan, tsunami sediment is included in that of landfill. Part of the tsunami sediment generated by the Great East Japan Earthquake, which occurred on 11 March 2011, is finally disposed of. Since disposed tsunami sediment includes organic matters, CH₄ emissions from this source are estimated using the emission factor for wood by expert judgement. The carbon content of tsunami sediment (4.5%) is calculated by multiplying the fraction of organic matter in tsunami sediment by the fraction of carbon contents in the organic matter; assuming the fraction of organic matter in tsunami sediment finally disposed of is 10%, and 45.2% of the fraction of carbon content for wood is substituted for tsunami sediment (GIO et al., 2016).

Total carbon can be measured with a CHN analyzer. Götze et al. (2016) present an overview of physicochemical waste characterization data for individual waste material fractions available in the literature. Figure 1 shows box–whisker plots and the corresponding quantiles for carbon content (Götze et al., 2016). The largest data variation for carbon content is found in combustibles (textiles, rubber, leather, sanitary products, and wood), plastic, and food waste.

To measure organic carbon in total carbon, it is necessary to distinguish between organic carbon and inorganic carbon. Thus, sample should be acid washed to eliminate inorganic carbon prior to analysis (Wang et al., 2015a). This is particularly important for paper samples, because some paper products (e.g., copy paper) contain inorganic carbon in the form of CaCO₃ as fillers (Wang et al., 2015a). Mou et al. (2014) used the assumption that 2 mL of sulfurous acid (5% H₂SO₃ solution) was added to approximately 0.5 g of powder to remove inorganic carbon. An alternative method for determining organic carbon is the total organic carbon (TOC) analyzer. There are numerous methods and variations of the alternative methods for the quantitation of TOC. The wet oxidation method is a commonly used approach to determine TOC content. Among the low-cost and easy-to-use alternative TOC determinations, spectroscopic techniques such as near-infrared (NIR) and mid-infrared (MIR) spectroscopy are very attractive (Wang et al., 2012). In addition, it is necessary to distinguish between fossil carbon and biogenic carbon to measure the DOC. The fossil carbon comes from petroleum-derived products such as plastics and synthetic textiles. Biogenic (biodegradable) carbon originates from vegetative and animal matter (e.g., food and yard waste, paper, and wood) (De la Cruz et al., 2013; Moora et al., 2017). The biogenic carbon that is not degraded is stored within the landfill.

Theoretically, the DOC value of waste fractions must be lower than the TOC value because some organic carbon, such as fossil carbon, is non-degradable (De la Cruz et al., 2013). Recently, two different approaches have been established to determine the fraction of biogenic carbon. One of the approaches derives the fraction of biogenic carbon from the BMP result (Mou et al., 2014; Puyuelo et al., 2011). The DOC can be calculated using (Mou et al., 2014):

\begin{array}{l} {CH}_{4} recovery = (BMP \times 1 0^{- 3}) / \\ (TOC \times F \times 16 / 12) \times 100 % \end{array}

(10)

where BMP is determined via batch tests and presented as kg-CH₄ Mg⁻¹ waste, TOC is presented as % (kg-OC kg⁻¹ waste), F is the volume fraction of CH₄ in generated gas, and 16 and 12 are the molar masses of CH₄ and carbon, respectively, and

DOC = {CH}_{4} recovery \times TOC

(11)

where DOC is presented as % (kg-C kg⁻¹ waste, wet weight).

The other approach is a modern carbon analysis method that uses the decay of the radioactive isotope carbon-14 (¹⁴C, half-life: 5370 years). Biogenic carbon is that which has been recently derived from CO₂ in the atmosphere via photosynthesis. Because ¹⁴C is present in the atmosphere as a result of the cosmic ray bombardment of nitrogen, photosynthesis results in the incorporation of some ¹⁴C into organic matter. While fossil fuel derived organic materials contained ¹⁴C at the time of their formation, it has decayed to negligible levels over time. Fellner and Rechberger (2009) suggest a method to determine the ¹⁴C content of biogenic matter in waste, resulting in the radiocarbon content of MSW of 115.2±3.5 pMC (percent modern carbon). Thus, De la Cruz et al. (2013) carried out a modern carbon analysis method to calculate the fraction of biogenic carbon. The fraction of biogenic carbon is calculated by equation (11), which assumes that waste is a two-component mixture of modern biogenic carbon with a ¹⁴C value of 115.2±3.5 pMC, and a fossil contribution of 0 pMC. It is based on fossil fuels having zero radiocarbon, whereas biogenic materials are enriched in ¹⁴C, and reflect the ¹⁴CO₂ abundance of the ambient atmosphere. The fraction of carbon can be determined by carbon dating by accelerator mass spectrometry, after converting the organic carbon in the samples to graphite. The DOC can be calculated using the following equations:

F_{bc} \times 115.2 + F_{f} (0) = Measured pMC value

(12)

DOC = TOC \times Fraction of biogenic C

(13)

where F_bc represents the fraction of biogenic carbon, F_f represents the fraction of fossil carbon, and F_bc + F_f = 1.

It should be noted that the ¹⁴C contents calculated from Fellner and Rechberger (2009) are only used for biogenic waste fractions in 2009. In the future, the radiocarbon content of biogenic matter will decline, due to a steady decrease of the atmospheric ¹⁴CO₂ level. Thus, the ¹⁴C contents of biogenic waste fractions generated in the future should be calculated.

DOC_f

Methods for determining DOC_f

The parameter DOC_f is the fraction of DOC that will actually degrade in the landfill. With respect to the DOC_f, IPCC (2006) recommends 0.5 of DOC_f as a default value including lignin, indicating that 50% of the DOC in the waste is released as gases. In contrast, laboratory studies of solid waste decomposition from the United States, Germany, and Italy have shown that the DOC_f ranges from negligible to a maximum of 0.17–0.47 (Bogner and Matthews, 2003; Bogner and Spokas, 1993; Lornage et al., 2007).

The DOC_f value is dependent on many factors, such as temperature, moisture, pH, and composition of waste. It should be noted that for laboratory experiments, there are certain difficulties in reproducing the real conditions of landfilling (Machado et al., 2009).

Two different approaches have been established to determine the DOC_f. In one of the approaches, the extent of decomposition is the measured CH₄ yield divided by the yield calculated assuming 100% conversion of the cellulose (Cel) and hemicellulose (H) (and protein in the case of food waste) to CH₄ and CO₂ (Eleazer et al., 1997). The content of cellulose and hemi-cellulose of waste is well correlated with L₀ (Fei et al., 2016). According to Wang et al. (2015a), the extent of carbon conversion can be calculated based on carbon loss through the anaerobic experiment test. The extent of carbon conversion is defined as the fraction of the organic carbon converted to CH₄ and CO₂, which is equivalent to the DOC_f as used by the IPCC. The other approach can be quantified using the ratio of cellulose plus hemicellulose to lignin (L). Typically, cellulose and hemicellulose are the major degradable components of MSW (Baldwin et al., 1998). This indicator of decomposition decreases as materials degrade, due to the biodegradation of cellulose and hemicellulose, and the recalcitrance of lignin under anaerobic conditions. Lignin is known to be non-degradable in anaerobic environments, since its initial fragmentation requires molecular oxygen (Komilis and Ham, 2003). Equation (14) is based on the assumption that lignin is recalcitrant under anaerobic conditions, thus the amount of lignin is constant over time, i.e., M_initialL_initial = M_finalL_final (Wang et al., 2013b):

{DOC}_{f} = (M_{initial} X_{initial} - M_{final} X_{final}) / (M_{initial} X_{initial})

(14)

where M_{initial or final} is the weight of the initial or final sample and X_{initial or final} represents the ratio of cellulose plus hemicellulose content (%) in the initial or final excavated sample.

De la Cruz et al. (2013) argued that when normalized to the initial sample mass, the amount of biogenic C decreases with decreasing (Cel+H)/L, as shown in Figure 2. A higher (Cel+H)/L indicates waste with relatively more biodegradable carbon, and also represents fresher waste. As (Cel+H)/L decreases, more of the biogenic carbon is present as lignin, whereas at high (Cel+H)/L, more of the biogenic carbon is cellulose and hemicellulose. This is because lignin is recalcitrant under anaerobic conditions that exist in landfills, and therefore limits the bioavailability of cellulose and hemicellulose, which are structurally associated with lignin (De la Cruz et al., 2014).

The cellulose and hemicellulose can be measured based on enzymatic neutral detergent fiber (ENDF) and acid detergent fiber (ADF). ENDF and ADF are gravimetric techniques that have been used to characterize fiber from a nutritional perspective (Barlaz, 2006). The sum of cellulose, hemicellulose, and lignin can be determined in accordance with ENDF. The sum of cellulose and lignin fraction can be determined by ADF (Ximenes et al., 2008). However, the gravimetric technique is likely to include some non-cellulosic material as cellulose, and thus may give artificially high results (Barlaz, 2006). A technique is developed using high-pressure liquid chromatography (HPLC). The basic procedure is hydrolysis of a solid sample in 72% (w/v) H₂SO₄, followed by a secondary hydrolysis in 3% (w/v) H₂SO₄. The hydrolyses convert cellulose and hemicellulose to their respective monomeric sugars, glucose, xylose, mannose, arabinose, and galactose, which are quantified by HPLC equipped with a pulsed electrochemical detector. The eluents are water, and a solution containing 200 mM sodium hydroxide and 60 mM sodium acetate (Wang et al., 2013b, 2015a). Klason lignin is the most common method utilized to determine lignin. Klason lignin is determined by loss on ignition (2 h, 550°C) of the solids remaining after the acid hydrolysis. In the Klason lignin method, any organic material that does not dissolve in sulfuric acid will be counted as lignin. However, this method assumes that all non-cellulosic organic material is lignin, which is not perfectly accurate. Plastics and rubber are likely to be counted as lignin in this method (Barlaz, 2006).

DOC_f in relation with lignin and moisture

Table 3 presents a literature overview of the DOC_f values for individual components of MSW. Food waste and grass have a high DOC_f, whereas paper, and in particular wood, have a low DOC_f within the landfill. CH₄ generation occurs predominantly from cellulose and hemicellulose (Bareither et al., 2012). In contrast, lignin is not easily degraded under anaerobic conditions. Several studies have demonstrated that lignin inhibits cellulose decomposition in waste, and lignin concentration has been related to both the rate and extent of cellulose plus hemicellulose degradation (Baldwin et al., 1998; Barlaz, 2006; De la Cruz et al., 2014; Eleazer et al., 1997; Wang et al., 1994). The higher lignin content in newsprint, which is generally made from mechanical pulp, resulted in the lowest CH₄ yield (Wang et al., 2015a). Greater decomposition of copy paper with lower lignin content relative to newsprint has also been reported in field study (Wang et al., 2013b). Lignin interferes with the digestion of cell-wall polysaccharides by acting as a physical barrier to microbial enzymes (Moore and Jung, 2001).

Table 3.

Literature overview of the DOC_f value of each waste.

Reference		Wang et al. (2011)	Wang et al. (2013b)		Wang et al. (2015a)	Wang and Barlaz (2016)	Eleazer et al. (1997)	Ximenes et al. (2008)
Method		The ratio of cellulose plus hemicellulose to lignin			The ratio of carbon loss from cellulose and hemicellulose
MSW		–	–	–	–		0.58	–
Grass		–	–	–	–		0.76–0.94	–
Leaves		–	–	–	–		0.28	–
Branch		–	–	–	–		0.28	–
Food		–	–	–	–		0.84	–
Hardwood		0.19	0.08–0.19	0.02	–	0.171–0.285	–	0.00–0.17
Softwood		0.05	0.00–0.02	0.12	–	0.000–0.095	–	0.00–0.18
Oriented strand board		0.50	0.08–0.39	0.08–0.38	–		–	–
Plywood		0.00	0.15–0.19	0.00–0.08	–		–	–
Particleboard		0.02	0.00–0.14	0.00–0.18	–		–	–
Medium-density fiberboard		0.00	0.00–0.19	0.00–0.21	–		–	–
Newsprint		–	0.59–0.81	0.69–0.81	0.21–0.29		0.31	–
Corrugated containers		–	0.70–0.96	–	–		0.54	–
Coated paper		–	–	–	–		0.39	–
Copy paper		–	0.71–0.95	–	(eucalyptus fiber) 0.24(acacia fiber) 0.96		0.55	–
Magazine	Chemical pulp	–	–	–	0.82		–	–
Magazine	Mechanical fiber				0.28

Figure 3 shows that there is a relationship between lignin and DOC_f, although the lignin may be more inhibitory in other components than grass (Barlaz, 2006). For grass, lignified grass tissues can be digested to leave only thin-walled indigestible residues (Moore and Jung, 2001). Jung and Vogel (1986) demonstrated that the relationship of lignin with forage digestibility is curvilinear, and the inhibiting effect of lignin declined at higher lignin concentration. Additionally, it has been reported that there is an inverse relationship between (Cel+L) and the biodegradability of several organic wastes (Buffiere et al., 2006). As a consequence, although it is difficult to draw a definitive conclusion, the lignin content could be used as an abatement indicator for the DOC_f of individual MSW components.

Most studies have concluded that the most critical factor in landfill decomposition is the amount of moisture in the waste; if sufficient moisture is not available, then gas formation will not proceed, and in some cases will not start at all (Baldwin et al., 1998; Hartz and Ham, 1983; Meima et al., 2008; Micales and Skog, 1997). At low moisture content, which means below 16%, the biological activities will decrease to zero (Hartz and Ham, 1983; Meima et al., 2008). Thus, Meima et al. (2008) presented that the water function is defined as a straight line, with a water factor (f(w)) of 0.0 at 16%, and a water factor of 1.0 at complete saturation, which is usually at a water content (w) of approximately 50%. The water factor can be calculated using

f (w) = 2.76 w - 0.44

(15)

The CH₄ production rate and maximal cumulative CH₄ production appear to be linearly correlated to the moisture content (Mora-Naranjo et al., 2004; Pommier et al., 2007). Consequently, there is a linear relationship between the moisture content and cumulative CH₄ production, and the CH₄ production has been predicted based on this linear relationship. Therefore, in order to evaluate DOC_f, equation (14) can be used to translate an equation that is given by DOC_f = 2.76w − 0.44 (Chong et al., 2016).

The biogas production depends on the waste temperature. Manna et al. (1999) applied an equation whereby the relation between the organic carbon fraction and the total available organic carbon fraction is strictly linked to temperature values, as follows:

ω = [0.014 \times (T_{w} - 273.15) + 0.28] ω_{t}

(16)

where T_w is the absolute temperature value (K), ω is the biodegradable carbon content of the waste, and ω_t is the TOC content of the waste.

This relation is valid up to T_w = 324.6 K, which is the optimum temperature value for anaerobic thermophilic bacteria. For higher values of up to T_w = 353.15 K, ω is the biodegradable carbon content, which practically coincides with the TOC content (Manna et al., 1999). However, not considered in detail are the nutrient and inhibitor concentrations, which may also be significant. Inhibitors and nutrients would accumulate and continuously affect the biochemical reaction processes, causing their effect on the CH₄ generation to be overestimated.

MCF and F

MCF is defined as the portion of organic materials that decompose anaerobically. The default value of MCF for semi-aerobic landfills is set as 0.5, which implies that 50% of organic matter is decomposed aerobically and the remaining 50% is decomposed anaerobically. This means that a semi-aerobic landfill emits just one-half of CH₄, compared to an equal size anaerobic landfill. Matsufuji et al. (1997) carried out a comparison of solid waste stabilization between semi-aerobic landfill and anaerobic landfill. The results gave the ratio of generated gases to leached contaminants of 8:2 for the semi-aerobic, and 4:6 for the anaerobic. Thus based on this result, IPCC (2006) recommend MCF of 0.5 as a default value.

Matsuto et al. (2015) emphasized that when considering a semi-aerobic landfill as an aerobic landfill technology, the layout of the pipe network should be designed with respect to the possible air flow paths. Both the leachate collection pipe and the passive gas vents are key elements in a semi-aerobic landfill, because the former functions as a conduit supplying air to the landfill, while the latter functions as an exit for the heated air. Thus, it is not necessary to connect the gas vents to the leachate collection pipe, because the connection only increases the air flow through the pipe, and this has little effect on aeration. Jeong et al. (2015) insist that validation of the MCF default value using field measurement is necessary. A semi-aerobic landfill site can be in an anaerobic condition when the outflow port of the leachate collection system is swamped, the system is full of water, it holds retention of leachate, or the leachate collection/gas extraction system is not properly extended (GIO et al., 2016).

The MCF accounts for the factor whereby an unmanaged landfill produces less CH₄ from a given amount of waste than an anaerobic landfill (IPCC, 2006). The MCF ranges from 0.4 to 1.0, depending on the landfill condition. Wangyao et al. (2010) established that the best fitting values of the CH₄ correction factor are 0.65, 0.20, 0.15, and 0.1 for deep landfills, shallow landfills, deep dumpsites, and shallow dumpsites, respectively. The MCF values are thus lower than the IPCC default values. Govindan and Agamuthu (2014) use 0.8 of MCF, because a study landfill is categorized as unmanaged landfill with an amount of deep buried waste (more than 5 m depth), and with high water content within the waste.

Most landfill generates a gas with approximately 50% CH₄. Thus, IPCC (2006) suggests that the parameter F refers to the fraction of CH₄ in generated LFG. However, the fraction of CH₄ in generated LFG should not be confused with the measured CH₄ in gas emitted from the landfill. Losses of CO₂ by leachate have to be considered, because CO₂ is much more soluble in water than CH₄ (IPCC, 2006, Kjeldsen and Fisher, 1995). Absorbed CO₂ might have deposited as carbonates in the drainage layer, since carbonate concentrations in solid, liquid or gas phases are dependent on the chemical equilibrium governed by the pH of the system (Rittmann et al., 2003; Valencia et al., 2009; VanGulck et al., 2003).

Semi-aerobic landfill does not provide the waste body with an adequate delivery of oxygen, which results in only a partial reduction of methanogenesis. CH₄ concentration in LFG from semi-aerobic landfills decreases to 10–30% (Matsufuji et al.,1993; Huang et al., 2008), which means that F for semi-aerobic landfill should be considered to be lower than 0.5. In contrast, Jeong et al. (2015) emphasized that the actual meaning of F is the fraction of CH₄ in the generated gas by the breakdown of organic matter in the absence of oxygen, which implies that the F value for semi-aerobic landfill is 0.5.

Methods for determining k

Characteristics of the k value

The k value is the biodegradation half-life value in years⁻¹ for landfilled waste. There have been efforts to estimate k value, as this parameter governs the rate at which CH₄ is produced. Although the organic part of each waste type is considered to have different decay rates (Thompson et al., 2009), most models assume a single overall value for k.

The k value is found to increase with higher moisture contents and higher temperature (Baldwin et al., 1998; Ishii and Furuichi, 2013). However, Amini et al. (2012) reported similar k values for the wet cell (0.10 yr⁻¹) and traditional landfill (0.08 yr⁻¹), because all the study landfills were located in Florida, which has relatively high annual precipitation rates. Barlaz et al. (2010) showed that there is no apparent relationship between k and the wet weight water content. This is likely due to the heterogeneity of water content in the varying material fractions of waste, as well as uneven wetting due to channelized flow, resulting in a wide range of water contents over the lateral and vertical dimensions of a landfill.

The value of k reflects the rate of degradation, and is affected by waste depth, density, pH, climate, and moisture content (Levis and Barlaz, 2011; Machado et al., 2009; Sormunen et al., 2013). The DOC_f is also affected by these conditions. Figure 4 shows the k values associated with DOC_f for each waste. The laboratory-scale k values of MSW components translate into field-scale k values (Wang and Barlaz, 2016). The field-scale k values are average rates estimated for a traditional landfill scenario (k = 0.04 yr⁻¹). There is no relationship between k and DOC_f. However, it is interesting to note that grass, which is highly lignified, has a high k value and DOC_f, whereas office paper with the lowest lignin has a low k value. This suggests that the lignin concentration does not correlate well with the decay rate, presumably due to the impact of lignin arrangement and structure on cellulose bioavailability. This phenomenon can be explained by the moisture content of waste. For example, the moisture contents for food waste and grass are 70% and 60%, respectively (De la Cruz and Barlaz, 2010), indicating that high moisture content may promote the biodegradation process. Moisture provides the basis for the hydrolysis of organic carbon. According to the processes of degradation and solubilization of organic compounds, hydrolysis can be regarded as the rate-limiting step within the bio-degradation processes (El-Fadel et al. 1989; Sanders et al., 2000; Trzcinski and Stuckey, 2012).

Another possibility is that the high contents of slowly hydrolysable compounds may delay the whole biodegradation process, consequently reducing the k value (Haarstrick et al., 2001). Grass does not contain a slowly hydrolysable carbon fraction, whereas the slowly hydrolysable carbon fractions are approximately 31%, 45%, and 82% of the total solid carbon in food waste, mixed paper, and branches (Komilis, 2006). Barlaz (2006) referenced that newspaper ink covered cellulose fiber, and reduced its bioavailability.

Classification of methods for determining k

The literature describes various methods to measure the k value of solid waste. Table 4 presents ranges of k values from solid waste landfill, and methods for determining k. In general, k values have been determined by a number of methods: determination of decay rates based on precipitation rates (Kumar and Shama, 2014; Thompson et al., 2009; US EPA, 2004); laboratory simulations (De La Cruz and Barlaz, 2010; Mou et al., 2015; Wang and Barlaz, 2016); samples excavated from landfills (Ishii and Furuichi, 2013; Kim and Townsend, 2012); and model fitting or regression analysis using actual gas data (Amini et al., 2012, 2013; Machado et al., 2009; Tolaymat et al., 2010; Wang et al., 2013a).

Table 4.

k values at landfill level taken from the literature, and corresponding determination methods.

Landfill site		Method	k (yr⁻¹)	References
Metropolitan center landfill in Salvador, Brazil		Model fitting with calculated L₀	0.200	Machado et al. (2009)
Outer Loop landfill, USA			0.060 (traditional landfill)0.110 (bioreactor)	Tolaymat et al. (2010)
Jeram landfill, Selangor, Malaysia	Bulk waste approach		0.080	Govindan and Agamuthu (2014)
Jeram landfill, Selangor, Malaysia	Waste composition approach		0.090	Govindan and Agamuthu (2014)
USA	9 landfills	Model fitting with SSE minimization at varied L₀	0.090–0.170	Wang et al. (2013a)
USA	2 landfills	Model fitting with SSE minimization at varied L₀	0.040	Wang et al. (2013a)
USA	9 landfills	Model fitting with SSE minimization	0.070–0.190	Wang et al. (2015b)
USA	2 landfills	Model fitting with SSE minimization	0.040	Wang et al. (2015b)
USA	3 landfills	Model fitting with assumed L₀	0.050–0.350	Barlaz et al. (2010)
Smiths Creek landfill in Michigan, USA	Septage bioreactor		0.296	Zhao et al. (2013)
Smiths Creek landfill in Michigan, USA	Leachate bioreactor		0.082	Zhao et al. (2013)
Landfills in Florida, USA		Model fitting with R² maximization at calculated L₀	0.080 (traditional landfill)0.100 (bioreactor)	Amini et al. (2012)
Landfills, USA	A		0.060	Amini et al. (2013)
B			0.090
C			0.040
Shanghai landfill, China		Aged-defined waste samples and regression	0.060	Youcai et al. (2001)
North Central Florida, USA	Alachua County Southwest landfill		0.470(bioreactor)	Kim and Townsend (2012)
North Central Florida, USA	New River Regional landfill		0.210(bioreactor)	Kim and Townsend (2012)
Sudokwon landfill site 1, Korea		Nonlinear regression using field data	0.100–0.140	Park et al. (2012b)
Wet landfills	Three landfills		0.280	Faour et al. (2007)
	SSWMC		0.210
	Landfill A		0.110
	CSWMC		0.120
	21 landfills		0.300
Canada	British Columbia	Annual precipitation rate	0.048	Thompson et al. (2009)
	Alberta		0.023
	Ontario		0.037
	Quebec		0.042
	Nova Scotia		0.056
23 metro cities, India			0.030–0.080	Kumar and Sharma (2014)

Table 5 presents k values for individual components of MSW. Grass and food waste showed a high k value, whereas paper, wood, and low-organic wastes showed a low k. In particular, the low-organic wastes showed lower k values in comparison to the default k values in the IPCC (Mou et al., 2015). Thus, long-term emissions from landfills are probably attributable to the slowly degrading paper and wood fraction (Donovan et al., 2010; Pan and Voulvoulis, 2007).

Table 5.

k values for individual waste components taken from the literature.

Country	Component	Method	k (yr⁻¹)	References
Hokkaido, Japan	Paper	Aged-defined waste samples and regression	0.050	Ishii and Furuichi (2013)
Hokkaido, Japan	Kitchen waste		0.062	Ishii and Furuichi (2013)
France	Paper-cardboards		0.110	Francois et al. (2006)
4 landfills, Denmark	Combustible	Half-life time using lab test	0.024–0.025	Mou et al. (2015)
	Shredder		0.016–0.017
	Sludge		0.16–0.19
	Mixed bulky		0.013–0.014
	Street cleansing		0.070
USA	Textile	Multiplying the laboratory-scale rates with a correction factor	0.015–0.088	De la Cruz and Barlaz (2010)
	Wood		0.007–0.045
	Food waste		0.072–0.432
	Leaves		0.085–0.512
	Grass		0.149–0.895
	Branches		0.007–0.045
	Miscellaneous organics		0.066–0.393
	Newspaper		0.017–0.099
	Office paper		0.015–0.088
	Coated paper		0.061–0.365
	Corrugated containers/ Kraft bags		0.010–0.059
	Mixed paper		0.016–0.094
USA	Hardwood		0.027–0.048	Wang and Barlaz (2016)
USA	Softwood		0.000–0.127	Wang and Barlaz (2016)
USA	Yard waste	Model fitting with calculated L₀ by minimizing the SSE	0.082	Yazdani et al. (2012)
France	Paper and cardboard	Evolutions of organic fractions with age	0.200	Lefebvre et al. (2007)
Thailand	Food waste	Model calibration with calculated L₀ using IPCC default values	0.347	Wangyao et al. (2010)
	Papers		0.069
	Wood		0.035
	Textiles		0.069
Italy	Mechanically-biologically pretreated waste	Linear regression using a two-stage model	0.039	De Gioannis et al. (2009)
Italy	Mechanically-biologically pretreated waste	Linear regression using a two-stage model	0.308	Di Maria et al. (2013)

Precipitation rates

Garg et al. (2006) indicate that precipitation is the most important parameter to estimate the k value. Thus, the k value for a bulk waste can be calculated based on precipitation rates (US EPA, 2004):

k = (3.2 \times 1 0^{- 5} \times annual precipitation in mm) + 0.01

(17)

The US EPA (2004) provides default values based on an emission factor, which is a k of 0.04 yr⁻¹ above 25 inches (635 mm) of precipitation for emission inventories that are considered more representative of MSW landfills where no leachate recirculation is occurring (Faour et al., 2007). On the other hand, research in some cases has found the US EPA (2004) default decay rate to be substantially lower (Amini et al. 2012; Wang et al., 2013a, 2015b). Wang et al. (2013a) maintained that there is no relationship between annual precipitation and k value.

Laboratory simulations

Several studies have presented CH₄ yield measurements for individual components of MSW to determine their k values (De la Cruz and Barlaz, 2010; Mou et al., 2015; Wang and Barlaz, 2016). Mou et al. (2015) suggest that assuming the organic carbon in the waste follows the FOD equation,

N_{t} = N_{0} \times e^{- k t}

(18)

the k value can be calculated by

k = - l n (N_{t} / N_{0}) / t

(19)

where N_t is the quantity (g) of degraded organic carbon (DOC) after a period of time (t), N₀ is the initial quantity (g) of DOC, and t is the organic carbon degradation time (yr).

Laboratory k values are orders of magnitudes higher than field k values because laboratory conditions are more ideal (Lamborn, 2012; Fei et al., 2016). Therefore, it is necessary to develop a correction factor that can be used to adjust lab-scale k values to match field-scale values (De la Cruz and Barlaz, 2010; Karanjekar et al., 2015). De la Cruz and Barlaz (2010) presented a correction factor (f) to translate the laboratory-scale decay rates (k_lab,i) of MSW components into field-scale rates (k_field,i). It is assumed that the weighted average decay rate for a waste mixture is equal to the bulk MSW decay rate. The k value of waste (k_field,MSW) can be calculated from the weighted average of the k of each biodegradable component (k_lab,i), as described in

k_{f i e l d, M S W} = f \times \sum_{i = 1}^{n} k_{l a b, i} \times {(w t . f r a c t i o n)}_{i}

(20)

k_{f i e l d, i} = f \times k_{l a b, i}

(21)

where i is the ith waste component.

Karanjekar et al. (2015) published a multiple linear regression (MLR) equation from laboratory data for estimating a correction factor. The MLR equation is considered the effect of annual rainfall and ambient temperature for estimating the k value.

Aged-defined waste samples and regression

This approach is to collect samples of landfilled waste, and then measure their biodegradability of waste as a function of waste age (Ishii and Furuichi, 2013; Kim and Townsend, 2012). As biodegradability is a surrogate for landfilling age, lower biodegradability would be expected in older samples. The biodegradability of waste is typically evaluated using the BMP. An advantage to this approach compared to using gas collection data is that the efficiency of the in-place gas collection system does not influence the results (Kim and Townsend, 2012). This approach consists of three steps, as shown in Figure 5.

First, working reports of the landfill site are investigated to predict the composition of the landfilled waste, the annual amount of landfilled waste, and the distribution of landfilled waste over space and time (Ishii and Furuichi, 2013). Sample age can be estimated from landfill waste placement records (Kim and Townsend, 2012). Second, sampling of age-defined wastes from the study landfill site is conducted. The waste composition, moisture, volatile matter and ash contents, and methane generation potential are analyzed, as shown in Figure 6. In the third step, the k values for each type of wastes are estimated using time series data on the methane generation potential (Ishii and Furuichi, 2013). The methane generation potential of waste is P_t at t years after landfilling, which means that the remaining methane generation potential of waste can be described by the FOD equation:

P_{t} = P_{0} e^{- kt}

(22)

where P_t is the methane generation potential of waste at t years after landfilling, P₀ is the methane generation potential of waste at 0 years after landfilling, and k is the methane generation rate constant (year⁻¹). Figure 7 shows the curve-fitted lines obtained using equation (22) to determine the k value.

A disadvantage of this approach is the relatively heterogeneous nature of MSW samples collected in the field. Furthermore, given that biodegradable waste components (e.g., food waste, paper) typically become reduced in size as waste stabilization progresses, simple separation of the fine fraction to remove soil prior to the BMP may be problematic (Kim and Townsend, 2012). For this reason, Kim and Townsend (2012) suggest the procedure presented in Figure 8. Identifiable biodegradable components can be processed and analyzed separately from large, non-biodegradable components and soil, thus providing a more accurate and repeatable measurement of this important fraction. The intermediate fraction (0.042–0.475 cm), often rich in degraded organic wastes (similar to compost), can similarly be homogenized without the interference of soil or other non-biodegradable wastes. Finally, the fine fraction (<0.042 cm) can be tested, and although the CH₄ yields are typically low because it is predominantly soil, this fraction’s contribution to overall CH₄ yield can be considered.

Biodegradability-test methods that are based on the use of aerobic respiration indices have been recently reviewed for waste biodegradability assessment. In contrast to the BMP test, the aerobic biodegradability tests do not assess the ultimate methane yield of a sample, but rather its activity. Thus, these aerobic biodegradability tests could not determine the L₀ value of a sample. The basic principle of the test for the biodegradability estimation is the amount of carbon that can be mineralized. Accordingly, aerobic biodegradability tests have been proposed to overcome the limits of anaerobic biodegradability tests. These aerobic biodegradability tests measure the respiration activity using the oxygen (O₂) consumption or the amount of carbon dioxide (CO₂) that is released under aerobic conditions. Although these tests are conducted under aerobic conditions, they are currently used to assess the methane production potential of waste under anaerobic conditions. A good correlation has been found between the anaerobic and aerobic tests for the characterization of the biodegradability of solid wastes (Binner and Zach, 1999). The aerobic tests offer the advantage of lesser time consumption compared with the anaerobic tests, and they can be implemented with all kinds of waste (Kallel et al., 2003; Lesteur et al., 2010). However, complex organic matter including cellulose is not taken into account in the aerobic tests (Lesteur et al., 2010).

The (Cel+H)/L ratio is often used to assess refuse decomposition. This ratio is unaffected by the presence of inert material (e.g., soil, ceramic, and glass), does not depend on visual identification of waste materials, and decreases as waste degrades (Bareither et al., 2012; Mehta et al., 2002; Wang et al., 1994; Wang et al., 2013b). Fresh waste typically has a (Cel+H)/L ratio of between about 3 and 4 (Barlaz, 2006). Figure 9 shows that the amount of biogenic carbon increases with increasing (Cel+H)/L. A regression analysis of the (Cel+H)/L with waste age has a coefficient of determination (R²) of 0.55, and the R² of biogenic carbon is 0.67. In addition, the degradation coefficient for waste sample is approximately 0.16 yr⁻¹.

Model fitting or regression analysis using actual gas data

The k value can be determined on the basis of the experimentally determined values in the landfill, and the feasibility of these values can be determined by comparison of the modelled CH₄ generation with the measured CH₄ recovery or CH₄ generation (Sormunen et al., 2013). Garg et al. (2006) suggest a fuzzy model to estimate the k value. Four major parameters, of precipitation, temperature, waste biodegradability, and landfill depth, are used as inputs to the model. The model indicates that precipitation is the most weighted parameter. However, the model does not consider differences in waste composition.

Mathematical models are normally built to fit a wide range of data and circumstances. These models need to be validated with measured or observed data to verify the results generated. For this reason, calibration of numerical values for k by site-specific data is reported to be essential when applying FOD models to estimate whole-site LFG generations (Amini et al. 2012; Scharff and Jacobs, 2006; Sormunen et al., 2013). To find the optimal set of gas generation parameters, error function analysis is used. This entails the minimization of the difference between the calculated gas generation rates and the actual rates to determine the optimal set of gas generation parameters, using error function for statistical analysis (Wangyao et al., 2010). Estimation of k for a landfill can be carried out by the estimated L₀ in conjunction with k value by curve fitting of the collected LFG data with minimizing the sum of squared errors (SSE) or R² near one for the modeled vs. measured data (Amini et al., 2012, 2013; Tolaymat et al. 2010; Wang et al., 2013a, 2015b). It should be noted that when the k value is estimated using field data, errors in the used L₀ can significantly affect the estimates of k, as shown in Figure 10.

Summary and conclusion

This review highlights current approaches for determining L₀ and k values with their wide ranges from detailed experiments conducted within bulk MSW and individual waste components. Tables 6 and 7 compare different methods for determining L₀ and k.

Table 6.

Comparison of different methods for determining L_0..

Method	Description	Advantages	Drawbacks
Stoichiometric methods	- use a stoichiometric equation based on the chemical composition of the waste	- simple and easy to analyze- take only a few hours	- no distinction between biodegradable and non-biodegradable matter- do not account for variations brought about by climatic and operational events- overestimate CH₄ potential
Experimental methods	- use BMP value of mixed waste based on the weighted average of waste components	- provide a more predictable result, compared to field monitoring studies- can determine L₀ for individual waste components	- BMP value is similar to DOC- overestimate CH₄ potential compared to full-scale data- require a correction factor- limited in reproducing the real conditions of landfilling
Model fitting or regression analysis	- use site-specific data on CH₄ recovery and emission	- can determine accurate site-specific L₀	- need long-term LFG data- need assumptions for CH₄ oxidation
IPCC method	- uses characteristics of the waste (DOC and DOC_f) and landfill site (MCF and F)	- simple and easy to determine L₀	- needs to distinguish between fossil carbon and biogenic carbon to measure DOC- needs to analyze DOC_f for individual waste components

Table 7.

Comparison of different methods for determining k.

Method	Description	Advantages	Drawbacks
Precipitation rate	- uses US EPA equation based on precipitation rates	- simple and easy to determine k value	- does not account for differences in landfill conditions (waste composition, temperature, cover soil)
Laboratory simulations	- use regression analysis of obtained laboratory biogas data	- can determine k values for individual waste components	- overestimates k values compared to field k values- need to adjust lab-scale k values
Aged-defined waste sample and regression	- uses time series data on the biodegradability of waste	- can determine site-specific k value	- heterogeneous nature of MSW samples
Model fitting or regression analysis using actual gas data	- use curve fitting of collected LFG data	- more accurate site-specific k value- can be validated with measured LFG data	- need long-term LFG data- errors in the used L₀ can significantly affect the estimates of k

The L₀ values in field settings are lower, because landfills do not function as efficiently as anaerobic digesters or laboratory experiments. Thus, the L₀ should be used to refer to the CH₄ yield, i.e., the amount of CH₄ produced per unit mass of waste under actual anaerobic conditions within a landfill. L₀ estimates in the literature are highly varied, and have been derived from theoretical stoichiometric calculations, laboratory experiments, or actual field measurements from landfill. Theoretical stoichiometric calculations are very fast, taking only a few hours, whereas the application of results obtained from these methods to a full-scale landfill remains difficult, because they do not account for variations brought about by climatic and operational events.

Laboratory experiments are better controlled, and employ operating procedures to enhance microbial activity. For these reasons, laboratory experiments produce more predictable results, compared to field monitoring studies. However, the BMP test could not provide direct estimation of L₀. The BMP value can be assumed equal to the DOC, because the BMP value generally represents the ultimate amount of CH₄ produced under optimal anaerobic conditions.

The FOD model parameters are highly dependent on environmental conditions and the capture efficiency. Significant differences exist between the conditions in the laboratory experiments, and the landfills. For this reason, if LFG collection data are available, calculating site-specific L₀ from model fitting or regression analysis is recommended as the best approach. However, most authors in the literature associate the problem with the lack of long-term LFG data. Thus, more data from full-scale landfills are needed with complete data sets that provide descriptions of gas collection systems, gas quality and quantity, waste placement rates, and moisture conditions. Moreover, data from the analyzed sites should be updated, since currently very few sites have such data available.

The IPCC model uses characteristics of the waste (DOC and DOC_f) and the landfill site to predict CH₄ generation. Determination of DOC needs to distinguish between organic carbon and inorganic carbon, resulting from acid washed to eliminate inorganic carbon prior to analysis. BMP or modern carbon analysis methods of waste components may be the most direct estimations of DOC. The DOC_f is the measured CH₄ yield divided by the yield calculated assuming conversion of 100% of the cellulose and hemicellulose (and protein in the case of food waste) to CH₄ and CO₂. In addition, the (Cel+H)/L ratio is often used to assess DOC_f. Although the content of lignin of waste is correlated with DOC_f, further studies are required to assess the relationship between lignin and DOC_f for individual waste components.

In the literature, the k value has been determined by precipitation rates, laboratory simulations, aged-defined waste sample, and model fitting or regression analysis using actual gas data. Precipitation is the most important parameter to estimate the k value. Thus, the k value for a bulk waste can be calculated using the US EPA equation based on precipitation rates. However, this equation does not account for differences in landfill conditions.

Laboratory simulations can determine k values for individual waste components. It should be noted that this approach is likely the upper limit of the rates in landfills, as these laboratory-scale rates are measured under optimal conditions. Thus, it is necessary to develop a correction factor that can be used to adjust lab-scale k values to match field-scale values.

The aged-defined waste sample method is to collect samples of landfilled waste, and then measure their biodegradability of waste as a function of waste age. However, it may be difficult to accurately characterize heterogeneous wastes.

When the k value is estimated using field data, errors in the used L₀ can significantly affect estimates of k. Thus, L₀ is fixed within a plausible range, and k should be optimized by curve fitting of the collected LFG data with minimizing the SSE or R² near one for the modelled vs. measured data.

Many countries have banned the landfilling of organic waste (Manfredi et al., 2010; Mou et al., 2014). Due to this trend, the composition of disposed waste at landfills in these countries is expected to change, as it is expected that organic waste will be recycled or incinerated. Thus, CH₄ emission from landfills must be accurately quantified to establish appropriate CH₄ reduction. Site-specific input parameters, in place of default values, significantly improve the model-estimated gas-generation results (Mou et al., 2015a).

Considering the recognition given to using the model in the literature, model fitting or regression analysis to estimate L₀ and k is recommended as the optimum method if LFG data are available. When such data are not available, k can be determined by aged-defined waste sample and regression analysis using the first-order model. Additionally, L₀ can be selected using disposed MSW composition, laboratory component specific methane potential values, and a correction factor based on site conditions (Amini et al., 2012).

To further the knowledge base on waste decomposition processes and rates, expanded efforts will be needed to accurately quantify L₀ and k values for both bulk MSW and individual waste components, and a reliable representation of their decomposition dynamics through time. In particular, there is currently insufficient field evidence to determine the proportions of carbon from each waste that are potentially lost through degradation through emission as CO₂, and as CH₄.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (grant number 2016R1A2B4011548).

ORCID iD

Jin-Kyu Park

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Methods for determining the methane generation potential and methane generation rate constant for the FOD model: a review

Abstract

Keywords

Introduction

Methods for determining L0

Overview of L0 values from the literature

Stoichiometric method

Experimental methods

Model fitting and regression analysis

IPCC method

DOC

DOCf

Methods for determining DOCf

DOCf in relation with lignin and moisture

MCF and F

Methods for determining k

Characteristics of the k value

Classification of methods for determining k

Precipitation rates

Laboratory simulations

Aged-defined waste samples and regression

Model fitting or regression analysis using actual gas data

Summary and conclusion

Footnotes

Declaration of conflicting interests

Funding

ORCID iD

References

Methods for determining L₀

Overview of L₀ values from the literature

DOC_f

Methods for determining DOC_f

DOC_f in relation with lignin and moisture