We develop a non-linear model to maximize the economic profit of an anaerobic digester.
The model consists of technical and economical equations.
Increasing the feeding time in between feedstock inputs increases economic profit.
Feeding individual streams of feedstock separately to the system increases economic profit.
A non-linear programming model was developed to maximize the economic profit from an anaerobic co-digester. The model consists of a combination of technical and economic equations, linked through the biogas production variable. Five scenarios were simulated. These differed with regard to substrate inlet mass flow rate, organic loading rate and hydraulic retention time. The impact on biogas production was investigated and an economic analysis was undertaken based on the concepts of profitability and Net Present Value. The model results indicate that varying the substrate inlet mass flow rate and organic loading rate could have a positive impact on the profitability of co-digesters in Flanders. This can be achieved either by increasing the interval time between feedstock input, or by feeding individual streams of feedstock separately into the system, while at the same time reducing the hydraulic retention time.
- Non-linear programming;
- Kinetic model;
- Biogas plant;
- Economic profit;
- Organic loading rate
1.1. Objectives of the work
The objective of this research paper is to look for strategies and solutions that operators of anaerobic digesters can apply to improve their economic performance and profitability. More specifically, in this paper, we focus on maximizing profit by optimizing biogas production through optimizing substrate inlet mass flow rate, organic loading rate (OLR) and hydraulic retention time (HRT).
Most research conducted so far has focused either on improving system stability and biogas yield by investigating the microbiological parameters of anaerobic digestion (AD), such as pH, changes in volatile fatty acid (VFA) and ammonia concentration at a laboratory scale, or on economic parameters such as investment costs and subsidies for full-scale anaerobic digesters. Our research is innovative in seeking to bridge the gap between the technical and economic AD models by looking at operational system parameters on the unit-process level, namely substrate inlet mass flow rate, OLR and HRT for a real-life co-digester in Flanders, and linking these to economic parameters.
1.2. Challenges of anaerobic digestion in Flanders
With an estimated average investment cost of €4800 and an operational cost of €520 per kWe installed capacity , the Flemish biogas sector represents almost half a billion euros in investment over the past 5 years and an annual turnover of around €50 million. Nevertheless, the sector is faced with loss-making businesses, bankruptcy and deferred investments . It is therefore important to technically and economically optimize the processes involved in biogas production.
Construction and operation of a biogas plant is a combination of economic and technical considerations. Obtaining the maximum biogas yield, through complete digestion of the substrate, requires a long HRT, and subsequently a larger digester size. In practice, the choice of system design, or of applicable HRT, is always based on a compromise between attaining the highest possible biogas yield, on the one hand, and ensuring that the plant is economically justifiable on the other . The industrial viability of AD requires a suitable combination of physical and chemical process parameters and low-cost substrates, hence the need for process optimization . Unfortunately, commercial AD processes often operate well below their optimal performance due to a variety of factors, such as a too low OLR, basic design considerations that try to determine the right balance between the construction practicalities of both mixing and heat loss, and the mixing regime  and . Additionally, AD of single substrates presents some drawbacks linked to substrate characteristics. Anaerobic co-digestion overcomes these drawbacks and improves the plant’s economic viability . In what follows, referrals to the term AD can be applied to mono- as well as co-digestion.
1.3. AD modeling
In addition to the numerous experiments conducted in the laboratory or in field studies to optimize the AD process, several models have been developed to help understand, simulate and predict the AD process. Modeling is always a goal-driven exercise, and many alternative models have been proposed in the literature, depending on the aim, e.g. process understanding, dynamic simulation, optimization, or control . These models can be divided into two types of models, i.e. biochemical models and economic-financial models.
AD is characterized by high complexity and non-linearity and the difficulties in collecting large amounts of informative experimental data for modeling purposes . The fact is that AD is itself a complicated, multi-stage, dynamic process that requires the concerted efforts of several bacterial groups. The composition of such groups varies in an unknown manner with changes in HRT, feedstock, temperature, reactor type, and other operating conditions . An important variability exists in values reported for the kinetic parameters, even when the same operational and environmental conditions have been evaluated. One of the consequences thereof is a variety of approaches to modeling and parameter identification . While complex models like ADM1  are well suited for process simulation, they are substantially limited when applied to process control and optimization . Because these models demand a substantial quantity of specialized data, they are not accessible to farmers and other stakeholders with limited scientific knowledge on the issue of anaerobic digestion. Therefore, a number of simple calculators were developed to estimate the applicability of the AD process to a specific farm and provide information to a farmer or decision maker .
As demand for renewable, clean, local energy increases, so will the need for more accurate and detailed economic information on the financial feasibility of anaerobic digesters . Economic-financial AD models have been developed and described by Anderson et al. , Gebrezgabher et al.  and Walla and Schneeberger , amongst others. They looked at developing tools for assessing the financial feasibility of farm-based anaerobic digesters, disposal of digestate in an economically and environmentally sustainable manner, and optimal size for biogas plants. These and other previous studies have generally found ADs to be a poor investment for private firms, without assistance , , , ,  and . It is therefore in the interests of the sector to increase the profitability of commercial AD applications.
The goal of our research was to link together biochemical and economic-financial models, by maximizing profit at the commercial AD level through optimizing biogas production. Biogas operators are not typically involved in AD experiments at the microbiological level, as they are processing large amounts of feedstock every day for their livelihoods. To maximize their profit, we have looked at strategies to increase biogas yield, and hence economic profit, by proposing small adjustments in their daily operational management. We propose a new type of black-box optimization model, based on algebraic equations, which takes into account the operational parameters of AD, as opposed to reaction mechanisms and experimental measurements for a multitude of parameters, to monitor the operating conditions and performance of an AD treatment process at a small-scale commercial facility.
2. Materials and methods
The aim of our research is to optimize (maximize) economic profit based on the biogas yield of a mesophilic anaerobic farm-scale digester co-digesting three types of feedstock. Our case is a theoretical, hypothetical one but is based on a case study of similar digesters in Flanders . Due to the complexity of the AD process, each type of model has been developed for a different purpose . Since our purpose is to improve the profitability of commercial anaerobic digesters by providing operators with hands-on practical ways to achieve this, we do not focus on the biological or physico–chemical parameters of the process, or on the kinetics of bacterial growth. Rather, the core modeling efforts focus on the operational parameters, such as substrate inlet mass flow rate, OLR and HRT, to calculate substrate degradation and biogas formation.
The model is based on the observation that different types of biomass have different speeds of degradation and different bio-methanisation potentials (BMP). In commercial biogas reactors, AD is a continuous process, meaning that there is a daily in- and outflow of biomass. The difference in degradation and BMP for the different input streams for co-digestion implies that some of the biomass will have spent a relatively short time in the reactor and therefore might not have achieved its full potential in gas production before it is pumped out of the reactor. Currently, biogas operators can deal with this challenge, either by installing a secondary, post-digestion reactor which will allow for additional gas production of 5–15%, or by separating the digested biomass and recycling the fiber fraction to extend the HRT for slowly decomposing materials . However, these adaptations imply a trade-off between additional cost and extra gas yield. Our model simulates the in- and outflow of the biomass in a co-digester and identifies the optimal quantity and ratio for each type of feedstock to be inserted at a certain time, as well as the optimal HRT for each ‘batch’ of feedstock inserted at a certain time, with the aim of increasing biogas yield without additional costs. We assume that co-digestion takes place under optimal mixing conditions. Mixing in an anaerobic digester keeps the solids in suspension and homogenizes the incoming feed with the active microbial community within the digester content. Experimental investigations have shown that the mixing mode and mixing intensity have direct effects on the biogas yield, even though there are conflicting views on mixing design . In this study, however, we do not take into account the possible effects of different mixing modalities on the biogas yield.