A review of mathematical models for composting

Highlights

• Comprehensive and exhaustive review of 40 years of composting modelling.

• Identification of trends in the aim and approach of composting models.

• Representative overview of composting kinetics, heat balances and mass balances.

• Complete inventory of kinetic correction functions.

• In-depth discussion and guiding perspective on future developments in the field.

Abstract

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.).

Introduction

Approximately 50% of the waste generated worldwide is composed of organic matter, generally coming from food, human and animal waste, and garden and wood products (Hoornweg and Bhada-Tata, 2012). Currently, this waste is most often intended for disposal by landfill (Hoornweg and Bhada-Tata, 2012). Landfilling is an environmentally unsustainable method for waste treatment, resulting in contamination of the surrounding land and groundwater, large amounts of greenhouse gas (GHG) emissions, and important spatial requirements (El-Fadel et al., 1997). However, with growing interest in sustainable development and circular economies, industry and governmental leaders are turning their eyes towards biological biomass conversion technologies such as composting to address the waste issue (Walling et al., 2019). This transition has involved the implementation of multiple laws and directives aiming to either limit or ban landfilling, generally classifying it as a last recourse. Examples of this include the Landfill Directive of the European Union (EU) (EU, 1999) that has led to the near elimination of landfilling in countries such as Austria, Belgium, Germany, the Netherlands and Sweden, and with the recent adoption of the Circular Economy Action Plan that proposes to revise previous legislation to limit landfilling to a maximum of 10% of municipal waste by 2030. Similarly, countries such as Canada have also sought to limit landfilling through national diversion goals and provincial bans currently in place in multiple provinces (CCME, 2014).

Composting is the biological process in which organic matter is aerobically decomposed by bacteria, fungi and worms into compost. The process allows for the reduction of the weight and volume of the residual matter, while simultaneously killing off pathogens and organisms and leading to a value-added product (Hay and Kuchenrither, 1990). The resulting product, i.e. compost, is a humus-like substance that is rich in carbon and nutrients, thus promoting its use as an organic fertilizer or as a soil amendment. As such, compost has been demonstrated to increase the nutrient supply, increase crop yield, decrease soil erosion, and increase soil workability, all the while sequestering carbon and acting as a pesticide against certain insects (Lairon, 2010, Lazcano et al., 2014). There are also the added benefits derived from avoiding landfilling, such as reducing GHG emissions and decreasing soil and groundwater contamination. Furthermore, compost is a generally accepted product by the general population, in contrast to products of other biomass conversion processes, such as the digestate from anaerobic digestion and biochar from pyrolysis and gasification which, for the time being, require work to establish themselves in the eyes of the consumers (Al Seadi and Lukehurst, 2012, Dahlin et al., 2015, Dahlin et al., 2017, Riding et al., 2015, Torrijos, 2016).

To favor the development and implementation of composting processes, mathematical models have been developed for the past few decades. These models aim at furthering our understanding of the processes, consequently reducing the time and energy spent on their optimization and allowing for simulation and assessment of process modifications. Only three reviews have explored the modeling of composting: Hamelers (2004) reviewed the approaches for modelling composting kinetics, notably focusing on the differences between inductive and deductive models. This was followed by Mason (2006) who looked at the structure and kinetic foundations of composting models, paying attention to their simulation capabilities and performance. The more recent review by Li et al. (2013) examined the importance of certain factors and their impact on the composting of food waste, as well as looking at modeling approaches and how models deal with uncertainty. However, since these reviews, there has been significant work in the field of composting modelling, with over 1600 papers having been published on the subject since 2013, more than the amount (1450) published between 1990 and 2010 (based on the Web of Science database).

Given these recent developments and the increasing growth in the field, a new review on the current state of composting modelling could be very beneficial. Therefore, the aim of this review is to examine the state of the art while highlighting areas requiring further development. Section 2 presents the methodology used during the review, as well as general trends identified from the composting literature. Section 3 investigates in detail the mathematical modelling of the composting process, providing a comprehensive overview of the work that has been done in this field by focusing on kinetics, heat and mass balances, and the significance of model parameters, gleaned from an assessment of sensitivity analyses. Section 4 identifies and discuses emerging areas and areas requiring development in the field of composting modelling, while Section 5 provides some concluding remarks.