A novel time-series-based kinetic model for degradation of municipal solid waste under different oxygen concentrations

Highlights

	● A model is proposed for calculating the reaction rate constant of organic matters.
	● The relationship between oxygen concentration and reaction rate is proposed.
	● The gas generation during degradation of organic matters degradation is superposed.
	● SDOM model is more accurate in calculating the CO2 production during degradation.

Abstract

Aeration is pivotal in accelerating landfill stabilization. Biodegradation kinetic models of landfills have not fully accounted for the uneven distribution of oxygen during aerobic in situ stabilization, owing to the high heterogeneity of landfills. In this study, a successive degradation of organic matter (SDOM) model is proposed to calculate the reaction rate constant of municipal solid waste (MSW). The SDOM model assumes that organic matter (OM) is composed of n independent shares, with each share starting to degrade at different times. However, all fractions degrade according to first-order kinetics once they enter the reaction phase. In this study, degradation tests of typical organic matter in landfills were conducted under varying oxygen concentrations, and the reaction rates for each degradation test were calculated using the SDOM model. Subsequently, a model was developed to simulate the variation in the reaction rate constant with the oxygen concentration. Superposition tests on multiple types of organic matter were conducted to further validate the superposition principle of the degradation process. Model verification using real waste data revealed a reaction rate constant of 0.12, demonstrating a better fit compared to the Monod model and traditional first-order kinetic model, as well as the highest accuracy in the calculation of CO₂ produced in the degradation process. The SDOM model can help to understand the degradation mechanism of the aerobic in situ stabilization of landfills in a better manner.

Graphical abstract

Keywords

Landfill / Time-series-based model / Aerobic stabilization / Organic matter biodegradation

1 Introduction

Landfilling continues to be the primary method for municipal solid waste (MSW) disposal, with approximately 54% and 85% of solid waste being landfilled in the United States and China, respectively (Lou et al., 2014; Bian et al., 2018). In China, the accumulated MSW stock exceeds 8 × 10⁹ t, covering an area of approximately 5.5 × 10⁸ m² and over 27000 temporary landfills require urgent restoration (Zhang and Wu, 2013). These sites often contain high levels of organic matter (OM) that requires an extended stabilization period (Feng et al., 2021). The aerobic stabilization of landfills leads to a switch from anaerobic to aerobic degradation of OM, which is the predominant method for landfill restoration (Guo et al., 2023). Aeration can accelerate the degradation of landfills by 5–30 times. Through this process, the environmental impacts can simultaneously reduce pollutants (Read et al., 2001; Ahmadifar et al., 2016; Zhang, 2019).

Oxygen plays a significant role in aerobic stabilization. However, due to the high heterogeneity and variations in saturated and unsaturated areas in landfills, the uneven oxygen distribution leads to landfill degradation at different oxygen concentrations. The gas-production process of MSW in landfills is complicated, and following air injection, the gas-production characteristics of the landfill undergo alteration. A viable approach to determine the gas production behavior is to establish a kinetic landfill gas production model (Vieru, 2020). A previous study developed a numerical model that considered changes in landfill gas caused by biochemical reactions (Ma et al., 2020). Given the highly complex oxygen-filled environments of aeration landfills, it is necessary to develop a biodegradation kinetic model to simulate multicomponent degradation under different oxygen concentrations (Lavagnolo et al., 2018). However, many studies have used empirical Monod expressions to express the effect of the oxygen concentration on the reaction rate. To reflect the effect of oxygen concentration on degradation more accurately, we conducted experimental tests in which the oxygen half-saturation constant was calculated. In landfills, the gas production rate is considered an important indicator of stabilization that can provide a theoretical basis for the MSW degradation mechanism and simulate and predict the process of aerobic restoration (Wang et al., 2021; Avinash and Mishra, 2024).

Revealing the degradation mechanisms in landfills is challenging because of the high complexity and diversity of the waste fractions (Xiao et al., 2022). The components of degradable solid-phase OM in MSW can be classified as total sugar, protein, fat, cellulose, lignin, etc. (Qu et al., 2005; Chen, 2014; Li et al., 2023). Total sugar, protein, and fat originate predominantly from food waste, whereas cellulose is the primary component of paper and yard waste. As the reaction rate of lignin is slow, it is often not considered during the aerobic degradation process. The composition of the MSW in the different landfills varied significantly. For example, China produces a high proportion of food waste in landfills. Therefore, if the degradation rate of MSW is characterized simply by a specific value or range derived from empirical equations or references to studies on aeration landfills, it may lead to a misunderstanding of the degradation process owing to the neglect of MSW components. A previous study has conducted degradation tests on the components in MSW (Yang et al., 2008), aiming to elucidate the unknown mechanisms underlying the impact of waste composition. Furthermore, to apply the law of degradation of individual organic matter to landfills, it is necessary to consider the mechanism of co-degradation of organic matter. Since the components of MSW are complex and diverse, it is essential to consider the superposition of degradation mechanisms for individual organic matter components in order to establish an accurate kinetic model. The reaction rate constant of the degradation is usually determined experimentally and then used in a kinetic model. Some studies have used stoichiometric equations and empirical parameters (Haarstrick et al., 2001; Xiao et al., 2018) to calculate reaction rate constants. However, these equations are typically empirical and lack theoretical support, which can introduce errors. Monod models consider mixed processes of multiple microorganisms and reactions (Gawande et al., 2010; Fathinezhad et al., 2022), including biochemical reactions, organic compound adsorption, and gasification into account (Gutiérrez et al., 2017; Nguyen et al., 2019). However, when the substrate concentration is very low or high, the accuracy of Monod’s method may decrease.

OM degradation in landfills can also be described using first-order kinetics (Feng et al., 2017; Omar and Rohani, 2017). During waste degradation, the gas generation rate first reached its peak and then gradually decreased, exhibiting an “inverted V-shaped” curve. However, the observed trend does not align with the first-order kinetics model because the rate should reach its maximum at the initial stage. In addition, the volume of gas produced from the degradation can be determined by integrating the reaction rate curve. Therefore, the direct application of a first-order kinetic model for gas production calculations may result in an overestimation of the predicted gas yield. This means that the misapplication of an inappropriate dynamic model could lead to errors in estimating carbon emissions from landfills.

To better fit the degradation rate curve, previous studies have described the degradation process using two- or three-stage models, such as the Sheldon-Arleta model, with each stage corresponding to a degradation rate constant. A two-stage gas generation rate model has been proposed in previous studies (Tang, 1998; Hu et al., 2022), in which the gas production rate of the first stage is proportional to the gas production time, whereas the gas production rate of the second stage decreases exponentially with time. This model overcomes the problem of the gas production rate peaking at the beginning, which is similar to the Scholl Canyon model (Rafey and Siddiqui, 2023). However, this description did not reveal the mechanism of degradation; the reaction rate was calculated only from the observed curve. To truly reflect the degradation mechanism in the kinetic model, it is necessary that the model not only describes the trend of the gas generation rate rising first and then decreasing but also reflects that the degradation process conforms to first-order kinetics.

This study aimed to develop a novel kinetic model for OM degradation during aerobic stabilization in landfills from the perspective of successive time sequences under different oxygen concentrations. In this study, degradation tests of individual OM under different oxygen concentrations were performed, the oxygen half-saturation constants of different OM were calculated, and the superposition of OM degradation was verified experimentally. The results will provide useful theoretical support for gas injection restoration in landfills, and the kinetic model will serve as a fundamental basis for understanding landfill stabilization.

2 Materials and methods

2.1 Degradation test of individual organic matter

In this study, protein, starch, fat, and cellulose were identified as typical degradable OM components in landfills. To validate the kinetic model, degradation tests were conducted on the four substances under varying oxygen concentrations. Additionally, tests involving the pairwise stacking of OM were performed. The degradation substrates utilized for the individual OM degradation experiments were cellulose, protein, and starch purchased from Macklin Ltd. and crude fat from Acker Ltd. The inoculum used in the degradation tests consisted of waste sourced from an old landfill site in Shenzhen, China. The waste was processed by sampling and sieving to acquire the inoculum. The basic properties of the inoculum were as follows: pH = 7.8; TS, 40% (w/w). The experiment focused on the degradation test of individual components, conducted in a reactor with a 600 mL capacity, as depicted in Fig.1. The reactor has an inlet and outlet, each equipped with an on/off valve. These valves were maintained in a closed position throughout the experiment, except during sampling operations. To ensure effective purging for gas exchange, we connected the inlet to a hose extending to the bottom of the reactor.

Fig.1 Diagram of the laboratory-scale reactor of (a) individual OM degradation, (b) simulated aerobic degradation.

Full size|PPT slide

The initial moisture content in the reactor was adjusted to 60% using deionized water. The oxygen concentrations were set to 2%, 5%, 10%, and 21%. The oxygen concentration was controlled using a flow meter, where N₂ and air were passed through one to reach the mixing ratio, and the nitrogen gas (N₂) and oxygen were 99.99% pure (AR grade). Then, the gas flowed out of the flow meter and passed through a three-way valve, where it was fully mixed and connected to the air intake. Prior to initiating the reaction, N₂ was injected at a rate of 100 mL/min for 5 min, followed by the injection of gas with a preset oxygen concentration at the same rate and time. The gas was sampled with a 20 mL syringe at the outlet, and the concentration of the gas was tested using a gas chromatograph. To eliminate stratification of the gas inside the reactor, a syringe was used to extract the gas repeatedly during the sampling of the air outlet before each sampling. After each sampling, the headspace gas was replenished by injecting the mixed gas again, the concentration of which was the same as the initial oxygen concentration in the reaction.

Each reactor containing 40 g of substrate was incubated at 55 °C in a constant temperature incubator. At the beginning of the experiment, a specific proportion of the inoculum (25% of the mass of the material to be degraded) was added to the reactor. Sampling commenced 13 h after the start of the test, spanning a total duration of approximately three weeks. Initially, samples were collected approximately every 7 h, with the interval extending in later stages as the gas generation rate declined. The test controlled the initial temperature, oxygen concentration, and water content in the reactor but did not adjust the initial pH. To determine whether gas generation from the mixed substances was additive, 20 g of each typical OM was combined in pairs and tested under identical conditions as the individual component tests. The mass and source of the inoculum, as well as the testing procedure, remained consistent throughout the experiment.

2.2 Degradation test of simulated waste

The mixed waste was comprised of 50% kitchen waste, 20% wood waste, 5% shredded paper, and 5% shredded plastic, the chemical compositions of which are listed in Tab.1. Simultaneously, a certain amount of inoculum (20%) and deionized water were added in proportion to regulate the inoculated microorganisms and water content. Wood waste included leaves, shredded grass, and wood. The inoculum content was set to be consistent with the results of the previous experiments. The waste materials were crushed into a size of less than 2 cm and loaded into the reactor. The mass of waste in the reactor was 640 g (wet mass), with an initial density of 480 kg/cm³, which is close to the density range in landfills (Ali et al., 2018).

Tab.1 Initial chemical composition of waste

Organic fraction	Protein	Fat	Total sugar	Cellulose	Lignin
(%, Dry basis)*	8.5	4.21	14.5	8.47	9.89

Note: * Test after removal of plastic and inorganic components.

The top of the reactor is equipped with an air inlet and outlet, each with an on/off valve. The inlet was connected to a tube deep in the bottom, and the top of the reactor was sealed with an adhesive gasket to ensure airtightness. The leachate outlet at the bottom of the reactor was closed. The external heating band of the reactor for the waste experimental process was set at 30 °C to minimize heat loss inside the reactor because of the low room temperature. Degradation tests simulating actual waste degradation involved the use of synthetic waste and injecting air into the reactor at a rate of 25 mL/min to ensure continuous aeration. Sampling was initiated 24 h after the start of the test. Each test lasted for 30 d. During the first 10 d, gas samples were collected 1–2 times per day, increasing to 3–5 times per day in the subsequent period.

2.3 Physiochemical analysis

A gas chromatograph (7820A, Agilent, USA) was used to analyze the gas components, employing a Porapak Q column (1/8 in, 2 mm, 60/80 mesh) for the quantitative determination of CO₂. The methods for the detection of fat, cellulose, and protein were in accordance with the standards GB/T6433-2022, GB/T6434-2022, and GB/T6432-2022, respectively. The total sugar content was quantified using the DNS colorimetric method.

2.4 Statistical analysis

The experimental data were organized and analyzed using Origin 2023 software. Statistical analyses were performed using the Statistical Package for the Social Sciences (SPSS) Statistics software (version 27.0; IBM, USA). Student’s t-test was used to assess differences in the data, with the significance threshold set at P < 0.05.

3 Model development

As mentioned in the Introduction, the variation trend of the gas generation rate curve cannot be explained from the viewpoint of the reaction mechanism using a two- or three-stage model. The reaction rate curve shows that the organic matter is not a whole but has n independent degradation shares, and each share starts to degrade at different times. When all shares began to degrade, the gas generation rate reached a maximum and then declined as the substrate was continuously consumed. In this study, we assumed that all shares were degraded following a first-order kinetic model, as shown in Eq. (1):

(1)$Y(t)=Y_0\mathrm{e}\mathrm{x}\mathrm{p}(kt),$

where Y(t): the gas generation of OM at t, [L³]; t: the calculation time, [T]; Y₀: the gas generation potential of OM (theoretical maximum gas generation), [L³]; k: the first order rate constant of degradation OM, [/T].

3.1 Linear SDOM model

Assuming that the time at which the gas generation rate is maximized is t_m, OM has n independent degradation shares that start the gas generation phase sequentially in a certain time period (e.g., linear or arithmetic increase). For linear models, the first share starts to degrade at t₀, followed by the second share at t₀ + Δt, ..., and at t₀ + nΔt = t_m starts with the last share. Δ where t is the time step, as expressed in Eq. (2):

(2)$\mathrm{\Delta }t=\frac{t_{\mathrm{m}}-t_0}{n},$

where t is the calculation time, counting from the beginning of the OM into the reaction system (including the gas generation lag time) [T]; t₀ is the gas generation lag time (i.e., from the time the OM starts the reaction system to the beginning of the gas generation time) [T]; n is the number of shares into which the OM is divided; Δt the time step [T]; t_m is the time at which the gas generation rate reaches its maximum value (counting from the time when the OM starts the reaction system) [T]. When t = t₀, the first share begins to degrade, and by t = t_m, all OM begins to degrade; thus, the cumulative gas generation reaches a maximum at t_m. From t₀ to t_m the total gas generation rate is the sum of all the shares of the degradation gas generation rate. After t_m, no more OM began to degrade, and the gas generation rate began to decline. During the degradation process, all shares conformed to the first kinetic model.

Based on this assumption the SDOM model is proposed as Eq. (3):

(3)$\begin{array}{rl}Q(t)=& \sum _{i=1}^{n}q\left(t-i\mathrm{\Delta }t-t_0\right)=\\ & k\sum _{i=1}^n{Y}_i\exp \left[-k\left(t-i\mathrm{\Delta }t-t_0\right)\right]\\ & q\left(t-i\mathrm{\Delta }t-t_0\right)=0\mathrm{f}\mathrm{o}\mathrm{r}t-i\mathrm{\Delta }t-t_0<0,\end{array}$

where Q(t) is the gas generation rate at time t [L³/T], k is the gas generation rate constant of the OM [/T], q(t) is the gas generation rate at time t [L³/T], Y_i is the gas generation potential of the i^th share, and [L³] is the${\displaystyle \sum _{i=1}^n{Y}_i=Y_0}$. For linear timings,$Y_i=Y_0/n$.

Y₀ is defined as the area under curve Q(t) of the gas generation rate curve with time as it approaches 0. Under this assumption, there may still be some OM that has not been degraded and this share is considered non-degradable. If a share did not generate gas, it represented a relatively high proportion of non-degradable gases.

3.2 Arithmetic increase model

As the reaction begins and the degradation conditions improve, the OM undergoes increasing degradation. Assuming that time is an arithmetic incremental time, the gas generation potential Y_i at the i^th is given by Eq. (4):

(4)$Y_i=\frac{1-f}{n}{Y}_0+i\mathrm{\Delta }y,$

(5)$\mathrm{\Delta }y=\frac{Y_{0}f}{{\displaystyle \sum _{i=1}^n}}i,$

where f is the proportion of the incremental component, and Δy is the increment of time. Each share starts independently, becoming part of a periodic increment in gas generation, owing to possible inhibition phenomena. If all shares enter the reaction simultaneously, the value of f is close to 0, and if most shares start at different times and rates, then f is close to 100%. Therefore, if the gas generation potential Y₀, lag time t₀, and time at which the gas generation rate reaches its maximum value t_m are known, the reaction rate constant k can be calculated from the measured Q(t)–t data according to the trial algorithm.

The degradation test of different OM was carried out at different oxygen concentrations to determine the relationship between the oxygen concentration and the reaction rate. The coefficient of variation of the volume fraction of oxygen for the aerobic degradation reaction rate was proposed based on existing studies (Mason, 2008) as shown in Eq. (6):

(6)$k_{{\mathrm{O}}_2}=\frac{a{c}_{{\mathrm{O}}_2}}{c_{{\mathrm{O}}_2}+K_{\mathrm{O}}},$

where $c_{{\mathrm{O}}_2}$ is the volume fraction of oxygen [%], K_O is the oxygen half-saturation constant, and a is the correction constant.

3.3 Influence factors of SDOM model

Environmental factors affecting the kinetic parameters in a landfill, such as oxygen, temperature, and moisture content, are expressed in Eq. (7) (Haug, 1993):

(7)$\frac{\mathrm{d}{C}_{\mathrm{s}}}{\mathrm{d}t}=-kf\left({\mathrm{O}}_2\right)f(T)f(C/N)f\left(C_{\mathrm{w}}\right)C_{\mathrm{s}},$

where f represents the coefficient of variation of the degradation rate constant, reflecting the effects of the oxygen concentration, temperature, carbon-to-nitrogen ratio, and moisture content; C_s is the biodegradable solid waste concentration [kg/m³]; and k is the biodegradation rate [/s]. To represent the important parameters affecting the reaction rate constants in the kinetic model, the corrected aerobic reaction rate constant was further improved, as shown in Eq. (8):

(8)$k=k_{{\mathrm{O}}_2}f\left(C_{\mathrm{w}}\right)f(T),$

where the temperature and moisture content change functions are respectively (Lin et al., 2008; Petric and Mustafić, 2015) as Eq. (9):

(9)$f(T)=\frac{\left(T-T_{max}\right){\left(T-T_{min}\right)}^2}{\left(T_{\mathrm{o}\mathrm{p}\mathrm{t}}-T_{min}\right)\left[\left(T_{\mathrm{o}\mathrm{p}\mathrm{t}}-T_{min}\right)\left(T-T_{\mathrm{o}\mathrm{p}\mathrm{t}}\right)-\left(T_{\mathrm{o}\mathrm{p}\mathrm{t}}-T_{max}\right)\left(T_{\mathrm{o}\mathrm{p}\mathrm{t}}+T_{min}-2T\right)\right]},$

where $T_{\mathrm{o}\mathrm{p}\mathrm{t}}$ value is 50 °C, $T_{\mathrm{m}\mathrm{i}\mathrm{n}}$ value is 0 °C and $T_{max}$ value is 65 °C.

(10)$f(C_{\mathrm{w}})=\frac{1}{{\mathrm{e}}^{\left(-17.684C_{\mathrm{w}}+7.0622\right)}+1}$

.

The reaction rate constants (k), which describe the law of degradation, were determined using the SDOM model and were compared with those derived from other common models. At the same time, the SDOM model was verified according to waste degradation, and the procedure was shown in Fig.2. The above algorithm was compiled into software, and the data are available on request.

Fig.2 Calculation procedure and diagram of SDOM model.

Full size|PPT slide

4 Results and discussion

4.1 The reaction rate constants of different organic matters

Degradation tests of typical organic matter were conducted at various O₂ concentrations (Fig.3). The result showed that gas generation rates of the proteins, starch, cellulose, and fat decreased sequentially. Interestingly, we found that the times at which the maximum gas generation rate was achieved by various typical OM under different oxygen concentrations were quite similar. The reaction in each group reached a maximum gas generation rate at approximately 61–85 h after the start of the experiment. In the experimental group (21% O₂), the maximum gas generation rates of starch, protein, fat, and cellulose were 0.11, 0.29, 0.014, and 0.06 L-CO₂/d, respectively.

Fig.3 Gas generation rates at the oxygen concentrations of 2%, 5%, 10%, and 21% at t = 55 °C of (a) starch, (b) protein, (c) fat, and (d) cellulose.

Full size|PPT slide

Other studies have shown that proteins are degraded faster than other OMs. The protein contains a large amount of nitrogen, which significantly enhances microbial metabolism. A previous research has discovered that the hydrolase activity of proteins was most pronounced at the onset of hydrolysis, leading to the highest cumulative gas generation from proteins (Jones and Grainger, 1983). The gas generation rate of cellulose was the slowest, particularly at elevated O₂ concentrations, which was attributed to the slower consumption rate of cellulose by the microorganisms. Cellulose, a crucial component of landfill stabilization, is decomposed by microorganisms at a slower pace during this process, resulting in a lower cumulative gas generation rate than starch and protein.

The gas generation rate began to flatten 20 d after the start of the experiment; however, the gas generation of fat continued to increase, indicating that a large portion of fat was either non-degradable or limited. In this study, the degradation of crude fat was influenced by its use as a feed additive and external treatment with antioxidants for easier storage. Besides, it has been proved that hydrolysis was the rate-limiting step in the fat degradation process, with methanogens suggested as essential for fat hydrolysis (Miron et al., 2000). The laboratory-scale experiment was not entirely consistent with the actual conditions of aerobic landfilling because the landfill itself was initially anaerobic and the methanogens were active before air injection. Therefore, the absence of methanogens may have contributed to the slow fat degradation rate.

It was demonstrated that the reaction rate increases with increasing oxygen concentration; however, the increase in the rate constant slows when the oxygen concentration surpasses 10% (Fig.4). The reaction rate constants of OM are listed in Tab.2.

Tab.2 Reaction rate constant k of organic matters at different oxygen concentration

O2 concentration	Protein	Starch	Cellulose	Fat
2%	0.123	0.086	0.046	0.148
5%	0.144	0.104	0.054	0.173
10%	0.164	0.14	0.088	0.182
21%	0.178	0.15	0.105	0.188

Fig.4 Relationship between the reaction rate constant and oxygen concentration.

Full size|PPT slide

The relationship between the O₂ concentration and reaction rate constant can be obtained, and the oxygen half-saturation constant corresponding to different OM values can be calculated. Equations (11)–(14) show the relationship between the oxygen concentration and the reaction rate constants of starch, protein, fat, and cellulose, respectively. The effect of oxygen on the reaction rate was first proposed by Haug (1993), and the oxygen half-saturation constant was defined as 2. In some studies of landfill coupling models (Feng et al., 2021; Li et al., 2021), the oxygen half-saturation constant was uniformly defined as 0.7, but the effect of MSW composition is not taken into account. The results of this study accurately reflect the effects of the waste components.

(11)$k_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{h}}=\frac{0.16C_{{\mathrm{O}}_2}}{C_{{\mathrm{O}}_2}+2.12},$

(12)$k_{\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{i}\mathrm{n}}=\frac{0.18C_{{\mathrm{O}}_2}}{C_{{\mathrm{O}}_2}+1.06},$

(13)$k_{\mathrm{f}\mathrm{a}\mathrm{t}}=\frac{0.19C_{{\mathrm{O}}_2}}{C_{{\mathrm{O}}_2}+0.61},$

(14)$k_{\mathrm{c}\mathrm{e}\mathrm{l}\mathrm{l}\mathrm{u}\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{e}}=\frac{0.13C_{{\mathrm{O}}_2}}{C_{{\mathrm{O}}_2}+4.85}.$

4.2 Superposition analysis of organic matter degradation

In landfills, organic matter exists in mixed forms. However, the basic unit of landfill degradation is individual OM. A degradation test of mixed substances was carried out to prove the superposition of the relationship between the mixed substrates and the individual OM and to make the model applicable to the aeration landfill scenario. If the degradation of MSW and mixed substances is consistent, the organic matter is relatively independent of the degradation process, and the experimental results of individual and mixed substrates can be further calculated to estimate the MSW degradation gas generation rate.

The effect of superposition on OM degradation was investigated by mixing typical OM and assessing the gas-generation characteristics, as shown in Fig.5. During the rapid gas-generation phase, the measured values slightly exceeded the predicted values, suggesting potential interactive effects. This interaction could stem from the specialization of different microorganisms in decomposing various types of OM, which in turn might enhance the overall degradation efficiency (Zhao et al., 2015). The diversity of microbial communities and complexity of metabolic pathways may accelerate biodegradation process (Wang et al., 2008; Zhao et al., 2023). Kunath et al. (2018) identified an interaction among closely related species within a colony that enhanced metabolic diversity. However, the independent sample t-test results within the group indicated no significant variability between the measured and theoretical values (P > 0.05), suggesting that mixed substance degradation can be regarded as a superposition of individual degradations.

Fig.5 Gas generation characteristics between individual and mixed OM with time: (a) protein and fat, (b) protein and starch, (c) fat and starch, (d) cellulose and fat, (e) protein and cellulose, (f) cellulose and starch; (g) simulated and measured values of gas generation characteristics of protein and starch at 10% oxygen concentration.

Full size|PPT slide

4.3 Model verification by real waste

A degradation test on real waste was conducted to verify the SDOM model. The change in gas generation over time was calculated according to the organic matter content in the waste, and the cumulative gas generation curves of the OM were plotted (Fig.6). After 40 d of degradation, the measured cumulative CO₂ generation was approximately 78.53 L, which was less than 1% of the calculated value. Summing the cumulative gas generation curves resulted in a good fit with the measured values, indicating that the OM degradation exhibited superposition. The reaction rate constant calculated by the SDOM model was 0.12, whereas the reaction rate of real waste was slower than that of individual OM, possibly because of a more uniform degradation system. Previous model studies have proposed that the maximum aerobic rate is 0.1–0.2 per day (Cao et al., 2018; Yan et al., 2020), which belongs to the range of SDOM calculation. There have also been studies in which the aerobic rate was 1/d (Fytanidis and Voudrias, 2014), the reason for which could be related to reaction conditions and MSW composition. Since the real waste degradation was conducted at a temperature of 30 °C, the effect of temperature was accounted for in calculating the reaction rate. The result showed that the correlation coefficient for the fitted curves of the SDOM model was 0.96, indicating a good fit of the model and its capability to represent the degradation process of real waste. After approximately 10 d of degradation, when the reaction rate began to decline, there was a difference between the measured value and the fitted curve. The slow degradation of cellulose and lignin in waste may be the main reason for this discrepancy. In addition, the water content may change during continuous aeration; however, this was not fully considered in this study.

Fig.6 Effect of SDOM model verification (a) comparison of gas production of individual OM and real waste, (b) comparison of SDOM model versus first-order and Monod model of gas production rate with time.

Full size|PPT slide

For the SDOM model, after the last share entered degradation, all organic matter degraded in a first-order kinetic manner; therefore, the SDOM model and the first-order kinetic model have a similar trend in the stage of gas generation rate decline. The first-order kinetic model indicated a rate constant of 0.101. However, because the first-order kinetic model assumes that the rate reaches a maximum at the beginning, which deviates from the actual degradation process, the fitting effect is affected, especially in the initial stage of degradation. The correlation coefficients between the fitted curve and the measured values were calculated using Pearson analysis. This analysis revealed that the correlation coefficient for the SDOM model was 0.92, compared to 0.86 of the first-order kinetic model and 0.76 for the Monod model. The SDOM model cannot only accurately calculate the reaction rate constant, especially in the case of known MSW components, but also reflect the degradation process from the perspective of dynamics.

According to the gas generation curve, the cumulative CO₂ generation during degradation calculated by the Monod model, first-order kinetic model, and SDOM model was 91, 84.9, and 78.5 L, respectively. Although the Monod model fit well, the CO₂ production calculated by the model was high, which could be attributed to the utilization of empirical parameters, particularly the initial biomass concentration. The cumulative CO₂ calculated using the first-order kinetic model exceeded the measured value. The relative error is defined as the ratio of the residual to the measured value. The relative errors of the Monod, first-order kinetic, and SDOM models were 16.2%, 6.9%, and 1%, respectively. Compared to other dynamic models, the SDOM model demonstrated superior accuracy in calculating CO₂ generation, primarily because of its incorporation of waste components and precise representation of degradation gas generation from a mechanistic perspective.

5 Conclusions

In this study, we propose a novel kinetic model for the degradation of MSW at different oxygen concentrations in landfills. The model assumed that the MSW exhibited non-monolithic behavior with independent degradation shares, and each commenced degradation at different times. To elucidate the gas-generation characteristics of the organic matter, we conducted degradation tests on four typical degradable organic components: total sugar, protein, fat, and cellulose. According to the results, the reaction rate constants were calculated using the SDOM model, and the relationship between oxygen concentration and reaction rate was established. Additionally, the results of the superposition analysis of the degradation test showed that the characteristics of mixed substrate degradation were indeed superimposable. The SDOM model was further proven to be effective in simulating real waste degradation, and the application of the model requires further validation and research to enhance its comprehensiveness and applicability.

References

[1] Ahmadifar M, Majid Sartaj, & M. Abdallah.. (2016). Investigating the performance of aerobic, semi-aerobic, and anaerobic bioreactor landfills for MSW management in developing countries. Journal of Material Cycles and Waste Management, 18(4): 703–714

[2] Ali M, Zhang J, Raga R, Lavagnolo R C, Pivato A, Wang X, Zhang Y, Cossu R, Yue D. (2018). Effectiveness of aerobic pretreatment of municipal solid waste for accelerating biogas generation during simulated landfilling. Frontiers of Environmental Science & Engineering, 12(3): 73–85

[3] Avinash L S, Mishra A. (2024). Comparative evaluation of artificial intelligence based models and kinetic studies in the prediction of biogas from anaerobic digestion of MSW. Fuel, 367: 131545

[4] Bian R, Xin D, Chai X. (2018). A simulation model for methane emissions from landfills with interaction of vegetation and cover soil. Waste Management, 71: 267–276

[5] CaoB Y, Feng S J, LiA Z (2018). CFD modeling of anaerobic-aerobic hybrid bioreactor landfills. International Journal of Geomechanics, 18(7): 04018072.04018071–04018072.04018010

[6] Chen Y m. (2014). A fundamental theory of environmental geotechnics and its application. Chinese Journal of Geotechnical Engineering, 36(1): 1–46

[7] Fathinezhad A, Jafari N H, Oldenburg C M, Caldwell M D. (2022). Numerical investigation of air intrusion and aerobic reactions in municipal solid waste landfills. Waste Management, 147: 60–72

[8] Feng S J, Lu S F, Chen H X, Fu W D, Lu F. (2017). Three-dimensional modelling of coupled leachate and gas flow in bioreactor landfills. Computers and Geotechnics, 84(APR): 138–151

[9] Feng S J, Wu S J, Fu W D, Zheng Q T, Zhang X L. (2021). Slope stability analysis of a landfill subjected to leachate recirculation and aeration considering bio-hydro coupled processes. Geoenvironmental Disasters, 8(1): 29

[10] Feng S J, Shen Y, Zheng Q T, Shi J L. (2022). Multi-functional direct shear apparatus for geosynthetic interfaces with its application on various GMB/GCL interfaces. Acta Geotech, 17(3): 993–1008

[11] Fytanidis D K, Voudrias E A. (2014). Numerical simulation of landfill aeration using computational fluid dynamics. Waste Management, 34(4): 804–816

[12] Gawande N A, Reinhart D R, Yeh G T. (2010). Modeling microbiological and chemical processes in municipal solid waste bioreactor, part II: application of numerical model BIOKEMOD-3P. Waste Management, 30(2): 211–218

[13] Guo S, Yu W, Zhao H, Lai C, Bian S, Jin P, Liang S, Yuan S, Huang L, Wang S. . (2023). Numerical simulation to optimize passive aeration strategy for semi-aerobic landfill. Waste Management, 171: 676–685

[14] Gutiérrez M C, Siles J A, Diz J, Chica A F, Martín M A. (2017). Modelling of composting process of different organic waste at pilot scale: biodegradability and odor emissions. Waste Management, 59: 48–58

[15] Haarstrick A, Hempel D C, Ostermann L, Ahrens H, Dinkler D. (2001). Modeling of the biodegradation of organic matter in municipal landfills. Waste Management & Research, 19(4): 320–331

[16] HaugR T (1993). The Practical Handbook of Compost Engineering. New York: Lewis Publishers

[17] Hu X, Yang Y, Zhou K, Tian G, Liu B, He H, Zhang L, Cao Y, Bian B. (2022). Verification of agricultural cleaner production through rice-duck farming system and two-stage aerobic composting of typical organic waste. Journal of Cleaner Production, 337: 130576

[18] Jones K L, Grainger J M. (1983). The application of enzyme activity measurements to a study of factors affecting protein, starch and cellulose fermentation in domestic refuse. European Journal of Applied Microbiology & Biotechnology, 18(3): 181–185

[19] Kunath B J, Delogu F, Naas A E, Arntzen M Ø, Eijsink V G H, Henrissat B, Hvidsten T R, Pope P B. (2019). From proteins to polysaccharides: lifestyle and genetic evolution of Coprothermobacter proteolyticus. ISME Journal, 13(3): 603–617

[20] Lavagnolo M C, Grossule V, Raga R. (2018). Innovative dual-step management of semi-aerobic landfill in a tropical climate. Waste Management, 74: 302–311

[21] Li K, Chen Y M, Xu W J, Zhan L T, Ling D S, Ke H, Hu J, Li J L. (2021). A thermo-hydro-mechanical-biochemical coupled model for landfilled municipal solid waste. Computers and Geotechnics, 134: 104090

[22] Li K, Xu W, Chen Y, Zhan L, Ke H, Xu H, Xiao D. (2023). Biochemical, hydrological and mechanical behaviors of high food waste content MSW landfill: numerical simulation analysis of a large-scale experiment. Waste Management, 171: 557–567

[23] Lin Y P, Huang G H, Lu H W, He L. (2008). Modeling of substrate degradation and oxygen consumption in waste composting processes. Waste Management, 28(8): 1375–1385

[24] Lou Z, Chai X, Zhao Y, Song Y, Zhu N, Jia J. (2014). Indicating landfill stabilization state by using leachate property from Laogang Refuse Landfill. Frontiers of Environmental Science & Engineering, 8(3): 405–410

[25] Ma J, Liu L, Yu X, Fei X, Bi Y. (2020). Simulation of gas concentration during the process of air injection and extraction in a landfill. Environmental Progress & Sustainable Energy, 39(5): e13406

[26] Mason I G. (2008). An evaluation of substrate degradation patterns in the composting process. Part 2: Temperature-corrected profiles. Waste Management, 28(10): 1751–1765

[27] Miron Y, Zeeman G, Lier J B V, Lettinga G. (2000). The role of sludge retention time in the hydrolysis and acidification of lipids, carbohydrates and proteins during digestion of primary sludge in CSTR systems. Water Research, 34(5): 1705–1713

[28] Nguyen D, Wu Z, Shrestha S, Lee P H, Raskin L, Khanal S K. (2019). Intermittent micro-aeration: new strategy to control volatile fatty acid accumulation in high organic loading anaerobic digestion. Water Research, 166: 115080

[29] Omar H, Rohani S. (2017). The mathematical model of the conversion of a landfill operation from anaerobic to aerobic. Applied Mathematical Modelling, 50(10): 53–67

[30] Petric I, Mustafić N. (2015). Dynamic modeling the composting process of the mixture of poultry manure and wheat straw. Journal of Environmental Management, 161: 392–401

[31] Qu X, He P, Shao L, Li G. (2005). Biomass compositions fermentation in initial stage of fresh municipal solid waste degradation in bioreactor landfill. Journalof Environmental Sciences, 9: 1219–1225

[32] Rafey A, Siddiqui F Z. (2023). Modelling and simulation of landfill methane model. Cleaner Energy Systems, 5: 100076

[33] Read A D, Hudgins M, Phillips P. (2001). Perpetual landfilling through aeration of the waste mass; lessons from test cells in Georgia (USA). Waste Management, 21(7): 617–629

[34] TangW (1998). Study on Generation and Control of Landfill Gas for Municipal Solid Waste. Dissertation for the Doctoral Degree. Beijing: Tsinghua University

[35] Vieru D. (2020). Mathematical modeling of landfill gas (MSW)—production of gas with methane gas content from landfills (MSW). Journal of Geoscience and Environment Protection, 8(12): 36–62

[36] Wang H, Cao Q M, Yang J F, Tang S M. (2008). Effect of soil biodiversity on nutrients and water used by plants. Acta Ecologica Sinica, 28(3): 1240–1246

[37] Wang K, Yun S, Xing T, Li B, Abbas Y, Liu X. (2021). Binary and ternary trace elements to enhance anaerobic digestion of cattle manure: focusing on kinetic models for biogas production and digestate utilization. Bioresource Technology, 323: 124571

[38] Xiao D, Chen Y m, Xu W j, Zhan L T, Ke H, He H j, Liu Y f. (2022). Experimental study on aerobic accelerated stabilization and carbon and nitrogen migration of municipal solid waste. Zhongguo Huanjing Kexue, 42(5): 2204–2212

[39] XiaoD, Xu W, ZhanL, ChenY (2019). A model for aerobic biochemical degradation of municipal solid waste. In:　Proceedings of the 8th International Congress on Environmental Geotechnics Volume 3. Hangzhou, China, October 28–November 1, 2018

[40] Yan H, Sedighi M, Xie H. (2020). Thermally induced diffusion of chemicals under steady-state heat transfer in saturated porous media. International Journal of Heat and Mass Transfer, 153: 119664

[41] Yang B, Wang H, Lu W, Qian H. (2008). Anaerobic digestion of single material waste for landfill conditions. Journal of Tsinghua University (Science and Technology), 48(9): 1445–1448

[42] ZhangJ (2019). Simulation Test and Mumerical Modeling of Old Municipal Solid Waste Landfill in-situ Aeration. Dissertation for the Doctoral Degree. Shanghai: Huazhong University of Science and Technology

[43] Zhang P, Wu H. (2013). Research progress of landfill evapotranspiration cover. Journal of Shenyang University, 25(4): 271–274

[44] ZhaoT, Zhang K, GuJ, ZhangS, WangX, SongW, Shi L, YanF, PanH (2015). Characteristics of lignocellulose degradation and the microbial diversity of FWD1. Journal of AGRO-Environmenta Science, 34(8): 1582–15881588

[45] Zhao Y, Liu Z, Zhang B, Cai J, Yao X, Zhang M, Deng Y, Hu B. (2023). Inter-bacterial mutualism promoted by public goods in a system characterized by deterministic temperature variation. Nature Communications, 14(1): 5394

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 42177177).

Conflict of Interests

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

RIGHTS & PERMISSIONS

2025 Higher Education Press 2025