An integrated mathematical model for co-composting of agricultural solid wastes with industrial wastewater

A review of mathematical models for composting

Composting is a valuable method to treat and valorize organic waste. However, the process is defined by its dynamic nature and governed by a multitude of operating parameters. As such, mathematical modelling of the process offers a powerful tool to simulate and predict the variable outcomes of the process, allowing for its optimization. This can include improving efficiency, lowering costs and reducing environmental impact. To aid with the development of future models, we provide an up to date review and assessment on the state of the art of composting modelling. By reviewing 40 years of literature, this review paints the most complete picture of the field to date. This includes an analysis of trends in composting modelling: looking at the type of systems that are targeted, the aim of the models and the approaches to kinetics and mass and heat transfer. Regarding modelling approaches, we explore the fractionation of both substrates and microorganisms, the biological processes that can be included (disintegration, hydrolysis, uptake and death) and their kinetics (first-order, Monod-type), energy balances (biological generation, convection, conduction) and mass balances. We also provide a review of the results of sensitivity analyses performed on composting models, finding that models are most sensitive to microbial growth and death rates, as well as consumption rates and product yields. In the final portion of the review, we identify, explore, and provide guiding recommendations for work on emerging areas and areas requiring development in composting modelling (volume change, pH, maturation, artificial intelligence, etc.).

Modelling for reactor-style aerobic composting based on coupling theory of mass-heat-momentum transport and Contois equation

This study establishes an optimal mathematical modelling to rationally describe the dynamic changes and spatial distribution of temperature and oxygen concentration in the aerobic composting process using coupling mass-heat-momentum transfer based on the microbial mechanism. Two different conditional composting experiments, namely continuous aeration and intermittent aeration, were performed to verify the proposed model. The results show that the model accurately predicted the dynamic changes in temperature (case I: R² = 0.93, RMSE = 1.95 K; case II: R² = 0.86, RMSE = 4.69 K) and oxygen concentration (case I: R² = 0.90, RMSE = 1.26%; case II: R² = 0.75, RMSE = 2.93%) in the central point of compost substrates. It also systematically simulated fluctuations in oxygen concentration caused by boundary conditions and the spatial distribution of the actual temperature and oxygen concentration. The proposed model exhibits good applicability in simulating the actual working conditions of aerobic composting process.

Centralized management of sewage sludge and agro-industrial waste through co-composting

In this research study, the co-composting process of a waste mixture containing strawberry extrudate, fish waste, sewage sludge and bulking agent (SEFW, 190:1:22:90 ratio) was carried out in a dynamic-solid respirometer at pilot scale. The aerobic biodegradability of the mixture was previously ensured in a static-liquid respirometer. The advantages and drawbacks of the SEFW co-composting process were subsequently identified through the determination of respirometric activity and the physical-chemical characterization of the waste, as well as the monitoring of odor emissions. The evolution of the physical-chemical variables showed that pH increased slightly and that the organic matter concentration, expressed as volatile solids (VS, %) or oxidable organic carbon (C_OXC, %), decreased by around 15% in both cases and by approximately 56% in its biodegradable form (total organic carbon, TOC, %). The low odor emission rate (OER) in the least favorable scenario (the maximum odor generation) during SEFW composting was 1.59 ou_E/s, whereas this figure reached 3.52 ou_E/s when only the organic fraction of municipal solid waste (OFMSW) was composted. Consequently, the co-composting of SEFW is more favorable in terms of odor emission and permits the simultaneous treatment of different types of waste.

Particle-Scale Modeling of Methane Emission during Pig Manure/Wheat Straw Aerobic Composting

Inefficient aerobic composting techniques significantly contribute to the atmospheric methane (CH4) levels. Macro-scale models assuming completely aerobic conditions cannot be used to analyze CH4 generation in strictly anaerobic environments. This study presents a particle-scale model for aerobic pig manure/wheat straw composting that incorporates CH4 generation and oxidation kinetics. Parameter estimation revealed that pig manure is characterized by high CH4 yield coefficient (0.6414 mol CH4 mol(-1) Cman) and maximum CH4 oxidation rate (0.0205 mol CH4 kg(-1) VS(aero) h(-1)). The model accurately predicted CH4 emissions (R(2) = 0.94, RMSE = 2888 ppmv, peak time deviation = 0 h), particularly in the self-heating and cooling phases. During mesophilic and thermophilic stages, a rapid increase of CH4 generation (0.0130 mol CH4 kg(-1) VS h(-1)) and methanotroph inactivation were simulated, implying that additional measures should be performed during these phases to mitigate CH4 emissions. Furthermore, CH4 oxidation efficiency was related to oxygen permeation through the composting particles. Reducing the ambient temperature and extending the aeration duration can decrease CH4 emission, but the threshold temperature is required to trigger the self-heating phase. These findings provide insights into CH4 emission during composting and may inform responsible strategies to counteract climate change.

Integrating particle physical geometry into composting degradation kinetics

The study was carried out to integrate physical geometry of compost particle with degradation kinetics to model biological reactions, which revealing additional dynamic approaches. A sphere and its circumscribing cube were used to represent compost particles. An inner sphere, representing anaerobic zone, was introduced to describe variations of substrate volume without sufficient oxygen supply. Degradation of soluble substrates and hydrolysis of insoluble substrates were associated with the particle geometry. Transportation of soluble substrates produced from hydrolysis was expressed using Fick's law. Through the integration of degradation kinetics with geometry models, degradation models could describe varying volume of composting materials involving aerobic or anaerobic digestion and transportation of soluble substrates in a unit compost particle.

Modelling nitrogen and carbon interactions in composting of animal manure in naturally aerated piles

Composting animal manure with natural aeration is a low-cost and low-energy process that can improve nitrogen recycling in millions of farms world-wide. Modelling can decrease the cost of choosing the best options for solid manure management in order to decrease the risk of loss of fertilizer value and ammonia emission. Semi-empirical models are suitable, considering the scarce data available in farm situations. Eleven static piles of pig or poultry manure were monitored to identify the main processes governing nitrogen transformations and losses. A new model was implemented to represent these processes in a pile considered as homogeneous. The model is based on four modules: biodegradation, nitrogen transformations and volatilization, thermal exchanges, and free air space evolution. When necessary, the parameters were calibrated with the data set. The results showed that microbial growth could reduce ammonia volatilization. Greatest nitrogen conservation is achieved when microbial growth was limited by nitrogen availability.

Mathematical modeling of olive mill waste composting process

The present study aimed at developing an integrated mathematical model for the composting process of olive mill waste. The multi-component model was developed to simulate the composting of three-phase olive mill solid waste with olive leaves and different materials as bulking agents. The modeling system included heat transfer, organic substrate degradation, oxygen consumption, carbon dioxide production, water content change, and biological processes. First-order kinetics were used to describe the hydrolysis of insoluble organic matter, followed by formation of biomass. Microbial biomass growth was modeled with a double-substrate limitation by hydrolyzed available organic substrate and oxygen using Monod kinetics. The inhibitory factors of temperature and moisture content were included in the system. The production and consumption of nitrogen and phosphorous were also included in the model. In order to evaluate the kinetic parameters, and to validate the model, six pilot-scale composting experiments in controlled laboratory conditions were used. Low values of hydrolysis rates were observed (0.002841/d) coinciding with the high cellulose and lignin content of the composting materials used. Model simulations were in good agreement with the experimental results. Sensitivity analysis was performed and the modeling efficiency was determined to further evaluate the model predictions. Results revealed that oxygen simulations were more sensitive on the input parameters of the model compared to those of water, temperature and insoluble organic matter. Finally, the Nash and Sutcliff index (E), showed that the experimental data of insoluble organic matter (E>0.909) and temperature (E>0.678) were better simulated than those of water.

Mechanism and kinetics of organic matter degradation based on particle structure variation during pig manure aerobic composting

Characterization of the dynamic structure of composting particles may facilitate our understanding of the mechanisms of organic matter degradation during pig manure-wheat straw aerobic composting. In this study, changes in the size, shape, pores, chemical compositions, and crystal structures of pig manure particles during composting were investigated. The results showed that the median diameter (D50) decreased exponentially, while the particle aspect ratio and sphericity were unchanged, suggesting that particles were degraded uniformly along different radial directions. Pores had a mean diameter of 15-30 μm and were elliptical. The particle porosity increased linearly mainly because of hemicellulose degradation. Furthermore, the influence of particle structure variation on the first order rate constant (k) of organic matter degradation was corrected, which may facilitate the optimization of operation conditions. The k value was proportional to the reciprocal of D50 according to the specific surface area of particles, and it decreased with increased porosity due to the stabilized chemical compositions and crystal structures of particles. However, the applicability of these data to other composting materials should be verified.

Biodegradation of naphthalenesulphonate polymers: the potential of a combined application of fungi and bacteria

The potential of several fungi and their synergy with bacterial biomasses were evaluated as a solution for the removal of 2-naphthalensulphonic acid polymers (2-NSAPs) from petrochemical wastewater, characterized by a chemical oxygen demand (COD) greater than 9000 mg/L. The ability of fungi to grow on 2-NSAP mixtures was preliminarily investigated using a solid medium, and then the action of the selected strains, both in suspended and immobilized form, was evaluated in terms of degradation, depolymerization, sorption and an increase in biodegradability of 2-NSAP. Among the 25 fungi evaluated two, in particular, Bjerkandera adusta and Pleurotus ostreatus, have been found to significantly depolymerize 2-NSAP yielding to the corresponding monomer (2-naphthalenesulphonic acid, 2-NSA), which has been further degraded by a bacterial consortia selected in a wastewater treatment plant (WWTP). The fungal treatment alone was able to reduce the COD value up to 44%, while activated sludge removed only 9% of the initial COD. In addition, the combined treatment (fungi and bacteria) allowed an increase in the COD removal up to 62%.

Characterization of the dynamic thickness of the aerobic layer during pig manure aerobic composting by Fourier transform infrared microspectroscopy

A new method for characterizing the aerobic layer thickness in pig manure based on Fourier transform infrared microspectroscopy (FTIRM) is presented to improve the anaerobic/aerobic co-process mechanism, to ensure adequate oxygen supply and, thus, minimize methane emissions during aerobic composting. Freeze-dried manure particles were microtomed into 10 μm thick sections; the spectral range, spectral resolution, and pixel dimensions in the transmission spectra were 4000-650 cm(-1), 16 cm(-1), and 6.25 × 6.25 μm, respectively. A mean spectrum of 16 scans was used for the second-derivative analysis with nine smoothing points. This is the first attempt at determining the oxidation profile of composting particles according to the radial variations in second-derivative spectra at 2856 and 1568 cm(-1), which are attributed to the reactants and products of the oxidation, respectively. In addition, an intermediate area is detected between the aerobic layer and anaerobic core. The experimental values of the aerobic layer thickness are consistent with the estimates, and an exponential increase is observed, which is influenced by multiple dynamic factors. However, the contribution of each factor to dynamic variations in the aerobic layer thickness should be investigated using available methods.

COP-compost: a software to study the degradation of organic pollutants in composts

Composting has been demonstrated to be effective in degrading organic pollutants (OP) whose behaviour depends on the composting conditions, the microbial populations activated and interactions with organic matters. The fate of OP during composting involves complex mechanisms and models can be helpful tools for educational and scientific purposes, as well as for industrialists who want to optimise the composting process for OP elimination. A COP-Compost model, which couples an organic carbon (OC) module and an organic pollutant (OP) module and which simulates the changes of organic matter, organic pollutants and the microbial activities during the composting process, has been proposed and calibrated for a first set of OP in a previous study. The objectives of the present work were (1) to introduce the COP-Compost model from its convenient interface to a potential panel of users, (2) to show the variety of OP that could be simulated, including the possibility of choosing between degradation through co-metabolism or specific metabolism and (3) to show the effect of the initial characteristics of organic matter quality and its microbial biomass on the simulated results of the OP dynamic. In the model, we assumed that the pollutants can be adsorbed on organic matter according to the biochemical quality of the OC and that the microorganisms can degrade the pollutants at the same time as they degrade OC (by co-metabolism). A composting experiment describing two different (14)C-labelled organic pollutants, simazine and pyrene, were chosen from the literature because the four OP fractions simulated in the model were measured during the study (the mineralised, soluble, sorbed and non-extractable fractions). Except for the mineralised fraction of simazine, a good agreement was achieved between the simulated and experimental results describing the evolution of the different organic fractions. For simazine, a specific biomass had to be added. To assess the relative importance of organic matter dynamics on the organic pollutants' behaviour, a sensitivity analysis was conducted. The sensitivity analysis demonstrated that the parameters associated with organic matter dynamics and its initial microbial biomass greatly influenced the evolution of all the OP fractions, although the initial biochemical quality of the OC did not have a significant impact on the OP evolution.

Novel bioevaporation process for the zero-discharge treatment of highly concentrated organic wastewater

A novel process termed as bioevaporation was established to completely evaporate wastewater by metabolic heat released from the aerobic microbial degradation of the organic matters contained in the highly concentrated organic wastewater itself. By adding the glucose solution and ground food waste (FW) into the biodried sludge bed, the activity of the microorganisms in the biodried sludge was stimulated and the water in the glucose solution and FW was evaporated. As the biodegradable volatile solids (BVS) concentration in wastewater increased, more heat was produced and the water removal ratio increased. When the volatile solids (VS) concentrations of both glucose and ground FW were 120 g L(-1), 101.7% and 104.3% of the added water was removed, respectively, by completely consuming the glucose and FW BVS. Therefore, the complete removal of water and biodegradable organic contents was achieved simultaneously in the bioevaporation process, which accomplished zero-discharge treatment of highly concentrated organic wastewater.

Simulation of carbon degradation in a rotary drum pilot scale composting process

This paper studies the simulation of carbon degradation in pilot scale solid waste composting processes using first-order kinetic models previously calibrated by laboratory experiments at different temperatures. Different solid biowastes (olive mill waste, winery waste, sewage sludge and reed biomass) were used. Three mixtures were prepared from combinations of the materials listed above, and they were used in both the laboratory kinetic experiments and the pilot scale composting experiments. Lab experiments were conducted in small reactors with temperature (T) control and forced aeration of the solid mixture. Each biowaste mixture was treated at four different temperatures, 25, 40, 50 and 60 °C, with controlled moisture; the carbon (C) concentration of the samples was measured weekly. Two different kinetic models were used to fit the carbon mineralisation curves: the 2C model, which considers two organic fractions (biodegradable and non-biodegradable), and the 3C model, which considers three fractions (easily biodegradable, slowly biodegradable and non-biodegradable). In both cases, the kinetic rate constants were calculated by mathematical fitting. The influence of temperature on the rate constants was also studied for both models using a T-dependent equation. The theoretical k(T) curves showed classical shapes, and the temperatures for optimum k values and thermal inactivation were obtained. Once the C degradation rate constants and their T dependence equations were available, it was possible to simulate the evolution of C degradation in an actual pilot scale rotary drum composting process under varying temperatures and using the same biowaste mixtures. The comparison between the theoretical profiles and the experimental data showed that the thermophilic stage could be accurately simulated; however, errors and lower levels of model accuracy occurred when the maturation stage was simulated. The simulation was valid for all of the viewed biowaste mixtures. The 2C and 3C simulation profiles were quite similar in all cases for much of the process duration; the differences between the profiles only occurred after the end of the thermophilic stage. It was concluded that the 2C model would be only valid for shorter experimental periods, until the readily biodegradable carbon fraction was removed, while the 3C model reproduced the subsequent degradation in the maturation stage more closely.

Kinetic modeling of sporulation and product formation in stationary phase by Bacillus coagulans RK-02 vis-à-vis other Bacilli

A logistic kinetic model was derived and validated to characterize the dynamics of a sporogenous bacterium in stationary phase with respect to sporulation and product formation. The kinetic constants as determined using this model are particularly important for describing intrinsic properties of a sporogenous bacterial culture in stationary phase. Non-linear curve fitting of the experimental data into the mathematical model showed very good correlation with the predicted values for sporulation and lipase production by Bacillus coagulans RK-02 culture in minimal media. Model fitting of literature data of sporulation and product (protease and amylase) formation in the stationary phase by some other Bacilli and comparison of the results of model fitting with those of Bacillus coagulans helped validate the significance and robustness of the developed kinetic model.

Integrating mixed microbial population dynamics into modeling energy transport during the initial stages of the aerobic composting of a switchgrass mixture

A mathematical model which integrates empirically derived microbial growth kinetics with heat and mass transfer phenomena and substrate degradation kinetics has been developed to capture the dynamics of the aerobic composting of a switchgrass and dog food mixture over a period of 64 h. The model incorporated three microbial populations of yeasts, bacteria and fungi that metabolized composting material consisting of sugars and starches, cellulose and hemicelluloses to produce heat and utilize oxygen in a static, cylindrical reactor employing forced aeration. Model predictions captured well the dynamics obtained experimentally between physical and microbial variables and the model has the potential to become a predictive tool for substrate degradation during aerobic composting processes.

Quantitative effects of composting state variables on C/N ratio through GA-aided multivariate analysis

It is widely known that variation of the C/N ratio is dependent on many state variables during composting processes. This study attempted to develop a genetic algorithm aided stepwise cluster analysis (GASCA) method to describe the nonlinear relationships between the selected state variables and the C/N ratio in food waste composting. The experimental data from six bench-scale composting reactors were used to demonstrate the applicability of GASCA. Within the GASCA framework, GA searched optimal sets of both specified state variables and SCA's internal parameters; SCA established statistical nonlinear relationships between state variables and the C/N ratio; to avoid unnecessary and time-consuming calculation, a proxy table was introduced to save around 70% computational efforts. The obtained GASCA cluster trees had smaller sizes and higher prediction accuracy than the conventional SCA trees. Based on the optimal GASCA tree, the effects of the GA-selected state variables on the C/N ratio were ranged in a descending order as: NH₄+-N concentration>Moisture content>Ash Content>Mean Temperature>Mesophilic bacteria biomass. Such a rank implied that the variation of ammonium nitrogen concentration, the associated temperature and the moisture conditions, the total loss of both organic matters and available mineral constituents, and the mesophilic bacteria activity, were critical factors affecting the C/N ratio during the investigated food waste composting. This first application of GASCA to composting modelling indicated that more direct search algorithms could be coupled with SCA or other multivariate analysis methods to analyze complicated relationships during composting and many other environmental processes.

Simulation of substrate degradation in composting of sewage sludge

To simulate the substrate degradation kinetics of the composting process, this paper develops a mathematical model with a first-order reaction assumption and heat/mass balance equations. A pilot-scale composting test with a mixture of sewage sludge and wheat straw was conducted in an insulated reactor. The BVS (biodegradable volatile solids) degradation process, matrix mass, MC (moisture content), DM (dry matter) and VS (volatile solid) were simulated numerically by the model and experimental data. The numerical simulation offered a method for simulating k (the first-order rate constant) and estimating k(20) (the first-order rate constant at 20 degrees C). After comparison with experimental values, the relative error of the simulation value of the mass of the compost at maturity was 0.22%, MC 2.9%, DM 4.9% and VS 5.2%, which mean that the simulation is a good fit. The k of sewage sludge was simulated, and k(20), k(20s) (first-order rate coefficient of slow fraction of BVS at 20 degrees C) of the sewage sludge were estimated as 0.082 and 0.015 d(-1), respectively.