Defossilizing feedstocks of industrial clusters has increasingly attracted attention due to potential impacts on climate change mitigation targets. However, the transition from fossil-based feedstocks to alternative carbon sources (ACS) presents both environmental and economic challenges in terms of performance and feasibility. One issue is the large uncertainties regarding the techno-economic feasibility in terms of investment decisions, which has been barely studied in the literature at cluster level. This study considers market price fluctuations of raw materials, products and energy over time to evaluate the profit and risk associated with individual plants for decision-making purposes. By adopting Modern Portfolio Theory (MPT), a portfolio optimization problem is defined to provide a risk-return-based guidance framework for transitioning to alternative carbon feedstocks. The proposed optimization model obtains investment portfolios and corresponding production capacity distributions based on the optimal constituents among fossil-based and ACS-based plants. The Port of Rotterdam, the Netherlands, is considered as a case study to assess the defossilization of feedstocks at the cluster level. The results show that integrating ACS-based plants into the cluster requires substantial capital investment, and reduces the Return on Investment (RoI) relative to the associated risk, making full defossilization economically challenging to achieve. However, applying a price-allocation method for re-costing ACS-based (by-)products considering governmental financial supports, the transition to alternative carbon sources can become attractive to investors at specific production capacities, as identified through optimal risk–return portfolios.

Temperature plays a critical role in performance and stability of anaerobic digestion processes, subject to frequent meteorological fluctuations. However, state-of-the-art modeling and process control approaches for anaerobic digestion often do not consider the temporal dynamics of the temperature, which can influence microbial communities, kinetics, and chemical equilibrium, and consequently, biogas production efficiency. Therefore, to account for anaerobic digesters operating under fluctuating meteorological conditions, the Anaerobic Digestion Model no. 1 (ADM1) is mechanistically extended in this paper to incorporate temporal changes into temperature-dependent parameters by defining inhibition functions for microbial activities using the cardinal temperature model, and accounting for the lag in microbial adaptation to temperature fluctuations using a time-lag adaptation function. Thereafter, given that temperature fluctuations are a significant disturbance, a control framework based on Model Predictive Control (MPC) is developed to regulate the feeding flow rate and to ensure stable production rates despite temperature disturbances without relying on direct temperature control. An adaptive MPC approach is formulated based on a linear input–output model, where the parameters of the linear model are updated online to capture the nonlinear dynamics of the process and frequent changes in the dynamics accurately. In addition, a fuzzy logic system is employed to assign a reference trajectory for the production rate based on the temperature and its rate of change. Integrating this fuzzy logic system with the MPC controller enhances the production rate on warm days and avoids the operational failure in production on cold days. Additionally, to enhance biogas production rates, the feasibility of utilizing a portion of the produced biogas for external heating purposes is also investigated. It is demonstrated that by utilizing the proposed MPC approach, the additional amount of feed for the digester to produce methane required for a self-consumption biogas-fueled heating system can be calculated according to the meteorological variations. This enhances the process performance and stability. Finally, a thermally optimized dome digester semi-buried in the ground, operating under climate conditions of The Netherlands is considered as a case study to validate the extended model in agreement with biological and physicochemical behaviors of real-world applications, and to demonstrate the effectiveness of the proposed control system in handling temperature changes and enhancing performance.

This paper focuses on the development of linear Switched Box–Jenkins (SBJ) models for approximating complex dynamical models of biological wastewater treatment processes. We discuss the adaptation of these processes to the SBJ framework, showing the model's generality and flexibility as a class of switched systems that can offer accurate predictions for complex and nonlinear dynamics. This approach of modeling enables real-time data reconciliation from experiments and allows the design of model-based control strategies. Through the extension of the Outer Bounding Ellipsoids (OBEs) algorithm, the paper introduces an online two-stage parameter identification algorithm that effectively handles bounded disturbances for SBJ models. Using the OBE method relaxes the stochastic assumptions on disturbances, which may not be satisfied in practice, particularly for biological and environmental fluctuations. The proposed decomposed OBE algorithm separately identifies the switching patterns and parameters of linear submodels, conducting parameter identification in two distinct phases for input/output and disturbance/output submodels. The efficacy of this approach is shown via simulation results validated against both ADM1 and PBM models, demonstrating the proposed algorithm's capability to accurately predict outputs from different biological wastewater treatment models.

Purple Phototrophic Bacteria (PPB) are increasingly being applied in resource recovery from wastewater. Open raceway-pond reactors offer a more cost-effective option, but subject to biological and environmental perturbations. This study proposes a hierarchical control system based on Adaptive Generalized Model Predictive Control (AGMPC) for PPB raceway reactors. The AGMPC uses simple linear models updated adaptively to project the complex process dynamics and capture changes. The hierarchical approach uses the AGMPC controller to optimize PPB growth as the core of the system. The developed supervisory layer adjusts set-points for the core controller based on two operational scenarios: maximizing PPB concentration for quality, or increasing yield for quantity through effluent recycling. Lastly, due to competing PPB and non-PPB bacteria during start-up phase, an override strategy for this transition is investigated through simulation studies. The Purple Bacteria Model (PBM) simulates this process, and simulation results demonstrate the control system's effectiveness and robustness.

Purple phototrophic bacteria (PPB) show an underexplored potential for resource recovery from wastewater. Raceway reactors offer a more affordable full-scale solution on wastewater and enable useful additional aerobic processes. Current mathematical models of PPB systems provide useful mechanistic insights, but do not represent the full metabolic versatility of PPB and thus require further advancement to simulate the process for technology development and control. In this study, a new modelling approach for PPB that integrates the photoheterotrophic, and both anaerobic and aerobic chemoheterotrophic metabolic pathways through an empirical parallel metabolic growth constant was proposed. It aimed the modelling of microbial selection dynamics in competition with aerobic and anaerobic microbial community under different operational scenarios. A sensitivity analysis was carried out to identify the most influential parameters within the model and calibrate them based on experimental data. Process perturbation scenarios were simulated, which showed a good performance of the model.

Dynamical systems and processes that either exhibit non-smooth behaviours (e.g. through logic control or natural phenomena) or work in different modes of operation are usually represented using hybrid systems models, i.e. mathematical models that combine continuous dynamics with discrete-event dynamics. Identification of a hybrid system includes finding switching patterns and identification of model parameters to obtain a data-driven model. This survey paper provides a systematic review of models (how to parameterize the system) and methods (how to identify unknown parameters) proposed for hybrid system identification with an exposition of recent advances and developments, and further research directions.