Keywords

25.1 Introduction

Anaerobic digestion (AD) is a process in which biodegradable organic wastes are broken down in the absence of oxygen by microbes to produce biogas and digestate which can be used for energy and fertilizer, respectively [3]. AD systems are considered as an environmental friendly technology for dealing with various organic waste including wastewater.

In global terms, with increasing populations, the amount of sludge is expected to increase and wastewater AD plants are constantly faced with the challenge of increasing the throughput through their systems [10]. Hence, optimal values of digester operating parameters are usually found for AD systems so that the quality and quantity of biogas and effluent produced can be improved [2, 7, 11]. However, optimising just the digester might not result in the most efficient design and components in the system, other than the digester, also need to be taken into account. Furthermore, in addition to the technical performance of the system, the financial and environmental performances also need to be optimised.

Some researchers did perform multi-objective optimisation of a system where they aimed to simultaneously improve the technical, financial and environmental performance however, their work was not limited to just the AD process and included other technologies such as composting, gasification and pyrolysis [14]. Where research was focused on just AD, it predominantly looked at finding optimal combination of technologies and pathways that improved the performance of the system and these studies did not consider optimisation of AD system design parameters [5]. Yan et al. [17] and Li et al.’s [13] work were the only two studies that optimised both system parameters and the combination of technologies in an AD system. Nonetheless, a limitation of their work was that they used correlations between temperature and biogas yields, found in literature, to predict biogas yields values and not a comprehensive model such as the state of the art Anaerobic Digestion Model No. 1 (ADM1). Hence, there is a need for a multi-objective optimisation of an AD system, which integrates an extensive digester model with an optimisation algorithm, to improve the performance of an AD system.

This paper aims to outline an optimisation problem that couples ADM1 with multi-objective optimisation, to improve the technical and financial performance of an AD system. The model is demonstrated for a wastewater anaerobic digestion system where optimal values of different system design parameters are found.

In the following section, the methodology is outlined and a rationale for the chosen objectives functions and decision variables is given. An overview of the case study system is outlined in Sect. 25.3 and a detailed model is described in Sect. 25.4. The results and discussion are provided in Sect. 25.5 and the paper concludes with the key findings from the study and recommendations for future work.

25.2 Methodology

The multi-objective optimisation model developed in this study uses ADM1 to predict biogas yields from a digester and optimises values of different design parameters for a wastewater AD system. The model was demonstrated for a case study AD plant and predicted biogas yield values were validated with measured data. Objective functions and decision variables were representative of the current challenges faced by the case study’s plant owners. Semi-structured interviews and plant performance data were used to identify these challenges. Analysis of the data and the interview results showed that at present, sludge often has to be strategically moved through the wastewater treatment plant because the AD side is at full capacity. Furthermore, the plant owners would also like to determine the optimal ratio of biogas that should be sent between the CHP and Biogas Upgrading Units (BUU) so that overall energy output from the plant is maximised and the energy costs are kept low. Based on these findings, the decision variables were defined to be the substrate feeding rates for each of the digester and the ratio of biogas sent between the CHP and BUU. The objectives set were to maximise the sludge throughput through the AD plant, maximise the overall energy output and minimise the running costs. Objective functions were normalised and a single utility function was created and minimised using genetic algorithm (GA) in Python.

25.3 Case Study Plant

Thickened sewage sludge is blended with water and divided between eight digesters. Biogas produced goes either into a CHP where it is converted into electricity, or a BUU where it is converted to biomethane and sent to the grid. Data recorded from the plant consists of the substrate feeding rate (m3/day) for each of the digesters and the total energy generated, in megawatt hours (MWh), from the CHP and biomethane sent over the grid.

Figure 25.1 shows a schematic of the plant layout and the plant components and Table 25.1 shows values of the parameters associated with the case study system.

Fig. 25.1
A schematic layout represents the wastewater anaerobic digestion plant. The components of the plant are balance tanks, thickening centrifuges 1 to 5, a thickened sludge holding tank, C D E screen, pre-digestion blending tanks, digesters 1 to 8, de-watering tanks, and others.

Layout of the waste water anaerobic digestion plant

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Table 25.1 Values of the different parameters associated with the case study system
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25.4 Models/Theory

25.4.1 Using ADM1 to Determine Biogas Yield

To predict biogas yield values, a modified ADM1 model by [15] was used and the ADM1 coefficients and substrate initial conditions for sewage sludge were taken from Rosen and Jeppsson’s [16] work. The assumption made was that the sewage sludge modelled by Rosen and Jeppsson [16] would be representative of the sludge processed at the case study plant.

Before predicted biogas yields were validated with measured data, ADM1 was calibrated for ten days to allow the model to adjust to the system. During this time, the flowrate of sludge was gradually increased from 0 to 90 m3, in increments of 10 m3. Since the case study plant consisted of eight digesters, with different flowrates and digester volumes, ADM1 was run individually for each digester and then the total predicted biogas yield was determined by adding the biogas yields from each of the individual digesters. The overall measured biogas yield values were determined using the plant data. Equations (25.2) and (25.3) were used to back calculate the biogas entering the CHP and BUU, using the energy values given in the plant data. The predicted and measured biogas yield values were compared for the months of October 2020 and September 2021.

25.4.2 Optimisation Problem

Once the objective functions and decision variables were defined the optimisation problem was formulated. Equation 25.1 shows how the objective functions were normalised and added together to form a utility function.

$$\min f\left( x \right) = \sum\limits_{x \in R} { - \frac{F\left( x \right)}{{\left| {F\left( {x\_{\text{raw}}} \right)} \right|}} - \frac{E\left( x \right)}{{\left| {E\left( {x\_{\text{raw}}} \right)} \right|}} + \frac{C\left( x \right)}{{\left| {C\left( {x\_{\text{raw}}} \right)} \right|}}}$$
(25.1)
$$\begin{array}{*{20}c} {0 < x_{1} < 109, x \in R} & {0 < x_{2} < 140, x \in R} & {0 < x_{3} < 109, x \in R} \\ {0 < x_{4} < 140, x \in R} & {0 < x_{5} < 133, x \in R} & {0 < x_{6} < 133, x \in R} \\ {0 < x_{7} < 133, x \in R} & {0 < x_{8} < 133, x \in R} & {0 < x_{9} < 1, x \in R} \\ \end{array}$$

where, F(x) is the total sludge added through the AD plant (m3/day), E(x) is the total energy produced by the system (MWh) and C(x) is the total running cost of the plant ($), x1 to x8 are the substrate feeding rates for each of the digesters (m3/day) and x9 is the ratio of biogas sent between the BUU and the CHP.

The electricity produced from the CHP was determined using the energy content of biogas and the CHP efficiency.

$${\text{E}}_{{{\text{CHP}}}} = { }\frac{{{\text{B}}_{{{\text{CHP}}}} {\eta }_{{{\text{CHP}}}} }}{{{\text{B}}\_{\text{energy}}}}$$
(25.2)

where, \({ }E_{CHP}\) is the electricity from the CHP (MWh), \(B_{CHP}\) is the biogas sent to the CHP (m3/day), \(\eta_{CHP}\) is the electrical efficiency of the CHP unit (%) and \(B\_energy\) is the energy content of biogas (m3/MWh).

The energy produced from the BUU was calculated using the amount of methane in biogas and the methane recovery ratio of the BUU.

$${\text{E}}_{{{\text{G}}2{\text{G}}}} = { }\frac{{{\text{B}}_{{{\text{G}}2{\text{G}}}} {\eta }}}{{{\text{B}}\_{\text{energyB}}\_{\text{ch}}4}}$$
(25.3)

where, \({ }E_{G2G}\) is the energy from the biomethane sent to the grid (MWh), \(B_{G2G}\) is the biogas sent to the BUU (m3/day), \(\eta\) is the methane recovery percentage of the BUU (%) and \(B\_ch4\) is the concentration of methane in biogas (%).

The total energy was determined by adding the amount of electricity produced by the CHP unit and the biomethane sent to the grid.

The total running cost of the system was determined by calculating the energy needed to heat the digesters and heat loss through the digesters walls using the input parameters shown in Table 25.1 and equations in [4]. The running costs of the CHP and BUUs were determined by multiplying the energy produced from those systems with the cost values shown in Table 25.2.

Table 25.2 Values of the input parameters used in the model
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25.5 Results and Discussion

25.5.1 Validating ADM1 with Measured Data

Figure 25.2 shows a comparison between the predicted and measured biogas yields for October 2020 and September 2021.

Fig. 25.2
2 line and scatter plots, a and b of biogas versus time in days. Both have the line for A D M 1 and plots for measured. The line has a fluctuating trend and the plots are scattered in and around the line.

Predicted biogas yield versus measured for the months of October 2020 and September 2021

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It can be seen that a good agreement exists between predicted and measured biogas yields for both months hence, this model can be used in the optimisation study to predict biogas yields. The small discrepancy between the results can be improved by characterising the feedstock used in this case study plant instead of using generic sludge ADM1 coefficients found in literature.

25.5.2 Current Versus Optimised System

Figure 25.3 shows the substrate feeding rates for each of the digesters 1–8 in the current and optimised system.

Fig. 25.3
4 line graphs, a to d, of substrate feeding rate versus date. A and B plot 4 lines each for dig 1, dig 2, dig 3, and dig 4 in cubic meters per day. C and D plot 4 lines each for dig 5, dig 6, dig 7, and dig 8 in cubic meters per day. All the graphs follow a fluctuating trend with peaks and troughs.

Substrate feeding rate for each of the digesters 1–4 and 5–8 in the current (a, c) and optimised system (b, d), respectively

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At present, the substrate feeding rate for each of the digesters 1–3 and 5–8 are approximately similar to each other. However, the optimiser suggests different feeding rates for each of the digesters based on their maximum allowable capacity. This results in higher and more consistent daily sludge volumes through the plant and allows for more stable operation (Fig. 25.4a, b). Furthermore, optimising sludge volumes for each of the digesters based on their capacity allows them to perform at their optimal capacity, increases their lifetime and reduces their operation and maintenance costs.

Fig. 25.4
4 line graphs. A and B of substrate feeding rate and biogas produced versus date plot 2 fluctuating lines for total flow rate and biogas in cubic meters per day. C and D of energy and cost versus date have 3 fluctuating lines of biomethane and electricity in megawatts-hour, and the cost in dollars.

Electricity and biomethane produced and the running cost of current (a) and optimised (b) AD system

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Figure 25.4 shows the overall substrate feeding rate and biogas produced from the system and the amount of electricity and biomethane produced along with the running costs of the plant, for the current and optimised system.

Electricity from the CHP is the predominant downstream pathway for biogas in the current system however, this causes the running cost of the plant to be inconsistent and higher throughout the month. The optimiser suggests to produce more biomethane as that results is an overall higher energy from the plant and lower running costs. More consistent and higher sludge volumes are now also processed through the plant and this allows the system performance to be more consistent and predictable. Table 25.3 shows the percentage change in the value of the objective functions, for September 2021, after implementing the multi-objective optimisation approach. The amount of sludge processed through the plant and overall energy output have increased by 17.7% and 3.0%, respectively. The running cost of the plant has reduced by 6.2%. These are significant improvements in system performance achieved by making minor modifications to the plant such as optimising the sludge feeding rates for each of the digesters and the ratio of biogas sent between the CHP and BUU.

Table 25.3 Change in the values of the objective functions after applying the multi-objective optimisation approach
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25.6 Conclusion and Further Work

Results from this optimisation study show that higher and more consistent sludge volumes can now be processed through the case study AD plant. This will meet the current challenge of having to process large volumes of sludge through the wastewater AD plant, while keeping the running costs low. By implementing the multi-objective optimisation approach, the total sludge volumes processed through the plant increased by 17.7% and the energy costs reduced by 6.2%. The ratio of biogas converted to electricity and biomethane was also optimised so that higher overall energy can be achieved from the plant.

The optimiser can be extended to determine whether sending biomethane to the grid is the most optimal choice or would another end use of biomethane be more suitable. The environmental performance of the plant can also be added as an objective function in the optimisation study so that any biogas flaring and greenhouse gas (GHG) emissions from the plant can be taken into account. Results from the optimisation study can be communicated back to case study partners so that their suggestions and feedback can be incorporated into the model to further optimise the system’s performance.