Uncertainty plays a crucial role in strategic supply chain design. In this study, we explore robust approaches to model uncertainty when the non-deterministic parameters are placed in the independent term, on the right-hand side (RHS) of the constraints. We consider the "disjunctive adjustable column-wise robust optimization" (DACWRO), a disjunctive formulation introduced previously in our group, and compare it with the adjustable column-wise robust optimization (ACWRO) formulation, a specific technique for solving robust optimization problems when the original robust optimization approach may assume too-conservative results. Given that the proposed method is based on the generalized disjunctive programming (GDP) technique, it is a higher lever modelling approach that represents the discrete nature of the decision process. In addition, it provides alternative MILP representations that can be further tested and compared. The analysis assesses the computational performance and reformulat... [more]

This study presents an integrated approach combining the Analytic Hierarchy Process (AHP) with a Mixed-Integer Multi-Objective Linear Programming (MOMILP) model to evaluate sustainable power generation alternatives for Pamplona, Colombia. The MOMILP model includes solar, wind, biomass, and diesel technologies, aiming to minimize costs (net present value) and CO2 emissions while considering design, operational, and budget constraints. The AHP method evaluates multiple criteria such as social acceptance, job creation, technological maturity, and environmental impact. The results show that solar panels are prioritized, with small diesel plants added due to resource limitations. The most sustainable option is a hybrid system with 49% solar, 29% wind, 14% biomass and 8% diesel, generating a net present value of 121,360 USD and 94,720 kg of CO2 emissions. The proposed methodology can be applied to assess and select the most feasible alternative within a wide range of new projects for the int... [more]

Bayesian optimization is known to be able to search for the optimal conditions based on a small number of experiments. However, these experiments are insufficient to understand the experimental condition space. In contrast, we report the development of an algorithm that combines a low-confounding definitive screening design with Bayesian optimization, allowing for rapid optimization and ensuring sufficient experiments to understand the experimental condition space with a low confounding.

Electricity and carbon trading towards carbon reduction are highly coupled. The research on joint trading is essential for helping companies identify optimal strategies and enabling policymakers to detect potential policy loopholes. This study presents a novel game theory optimization model involving both power generation companies (GenCos) and factories to explore optimal operation strategies under electricity-carbon joint trading. By fully capturing the operational characteristics of power generation units and the technical energy consumption of electricity-consuming enterprises, it describes the relationship between renewable energy, fossil fuels, electricity, and carbon emissions detailedly. Considering the correlation between production volume and price of the same product, the case actually encompasses three trading systems: electricity, carbon, and commodities. Transforming this nonlinear model into a mixed-integer linear form through piecewise linearization and discretization,... [more]

Mechanical compression heat pumps are indispensable to facilitate the transition from thermally driven processes to renewable energy by electrification, upgrading low-temperature waste heat to recycle it at a higher temperature level. However, the implementation of such heat pumps up to date encounters limitations, due to equipment limitations and a lack of tools for the design of process concepts for the application of high-temperature heat pumps. The optimal design of heat pumps relies heavily on the selection of an appropriate refrigerant, as the thermodynamic properties significantly affect the heat pump cycle design and performance. While existing methods are capable of identifying thermodynamically beneficial refrigerants, they do not directly account for practical constraints such as limitations on the compressor discharge temperature, compression ratio, and vacuum operation. The current study proposes a fast-screening approach for arbitrary heat pump applications, considering a... [more]

In process systems engineering (PSE), obtaining accurate process models for optimization can be expensive and time-consuming. Black-box Bayesian Optimization (BO) with Gaussian process (GP) surrogates offers a promising approach. However, full black-box optimization neglects valuable prior knowledge, which could otherwise improve the optimization process. This work explores methods of integrating prior knowledge in the form of low-fidelity data into BO by evaluating these methods on synthetic multi-fidelity test functions. Our results highlight possibilities for improved convergence of the BO optimization. However, our work further highlights potential pitfalls of these multi-fidelity models, such as bias, convergence to local optima, and overfitting on low-fidelity data. Hence, leveraging low-fidelity data in multi-fidelity models can improve BO convergence, but there are instances where the algorithms are more susceptible to failure.

This work approaches a detailed characterization of the aspects inherent to the innovative paradigm of Water and Energy Integration Systems (WEIS). These consists in conceptual physical systems which consider all potential energy-using and water-using processes in a site, all potential recirculation of material and energy streams between these and the integration of several categories of state-of-the-art technologies. The WEIS have the ultimate aim to promote the sustainability character associated to existing installations (through the reduction of energy and water input and contaminants output). The specific characteristics of WEIS are compared to existing similar process integration methodologies and a set of performance indicators are determined, having as a basis two previous case-studies approached for the Engineering project of WEIS. The performed analysis in this work revealed that the innovative paradigm is able to constitute Engineering projects with associated sustainability... [more]

Addressing challenges in process design and optimisation, especially with complex models and data uncertainties, requires effective tools for model development, selection, and identification. Techniques such as Model-based Design of Experiments (MBDoE) help support this task by screening and discriminating between models and, eventually, calibrating them. Open-source and user-friendly Python packages have implemented some model identification techniques. However, the need for a tool that can couple with various model simulators and account for the steps of model identification as well as physical constraints of systems in design of experiments remains unmet. In that light, we present the python package MIDDOE (Model-(based) Identification, Discrimination, and Design of Experiments) to address this gap. It integrates rival models screening, parameter estimation, uncertainty analysis, and MBDoE techniques, while adapting to various process constraints. These functionalities are demonstra... [more]

This paper introduces the Updated Absolute Expected Value Solution, U-AEEV, a heuristic for solving multi-stage stochastic programming (MSSP) problems with type 2 endogenous uncertainty. U-AEEV is an evolution of the Absolute Expected Value Solution, AEEV [1]. This paper aims to show how U-AEEV overcomes the drawbacks of AEEV and performs better than AEEV. To demonstrate the performance of U-AEEV, we solve 6 MSSP problems with type 2 endogenous uncertainty and compare the solutions and computational resource requirements.

This article aims to tutorial a few important extremum seeking control approaches that can be used for the model-free optimization of industrial processes in various fields. The application of several methods is illustrated with a simple case study related to the production of algal biomass in photobioreactors. Other methods and applications are briefly reviewed.

Monitoring chemical composition is key in several industrial-scale chemical processes. However, traditional composition sensors usually convey drawbacks, including high costs, short lifetimes, and frequent calibration requirements. As an alternative, software (soft) sensors have gained attention in recent years due to their accuracy, ease of training, and potential of integrating widely known machine learning techniques. This study presents the methodology followed to train a soft sensor for hydrogen sulfide monitoring in the gas treatment section of an industrial facility in Italy. In particular, this methodology includes a novel approach for steady-state determination from historical plant data in the presence of several steady states and noise. Unfortunately, only four steady states were found in the plant data, which was insufficient for accurate soft sensor training. As an alternative, these steady states were used to develop and validate a rigorous Aspen HYSYS process simulation.... [more]

The application of Real-time Optimization (RTO) to dynamic operations is challenging due to the complexity of the nonlinear problems involved, making it difficult to achieve robust solutions. The literature on RTO in Pressure Swing Adsorption (PSA) units relies on Model Predictive Control (MPC) and Economic Model Predictive Control (EMPC), which rely heavily on an accurate model representation of the industrial plant. Given the importance of PSA systems on multiple separation operations, establishing alternatives for control and optimization in real-time is in order. With that in mind, this work aimed to explore alternative model-free RTO techniques that depend on simple control elements, as is the case of Extremum Seeking Control (ESC).The chosen case study was Syngas Upgrading. Extremum Seeking Control successfully optimized the CO2 productivity in PSA units for syngas upgrading/H2 purification. The results demonstrate that ESC can be a valuable tool in optimizing and controlling PSA... [more]

Implementing Model Predictive Control (MPC) for large-scale nonlinear systems is often computationally challenging due to the intensive online optimization required. To address this, various reduced-order linearization techniques have been developed. The Koopman operator linearizes a nonlinear system by mapping it into an infinite-dimensional space of observables, enabling the application of linear control strategies. While Artificial Neural Networks (ANNs) can approximate the Koopman operator in a data-driven manner, training these networks becomes computationally intensive for high-dimensional systems as the lifting into a higher-dimensional observable space significantly increases data size and complexity. In this work, we propose a technique, combining Proper Orthogonal Decomposition (POD) with an efficient ANN structure to reduce the training time of ANN for large order systems. By first applying POD, we obtain a low order projection of the system. Subsequently, we train the ANN w... [more]

Hydrogen isotope separation is a critical component of the fusion fuel cycle, particularly for achieving the desired purity levels of deuterium and tritium while minimising tritium inventory. This study investigates the cryogenic distillation of hydrogen isotopes, with a focus on the effects of isotopic equilibrium reactions at reduced temperatures and different system configurations. A one-column architecture was analysed to evaluate the impact of feed and side stream equilibrator temperatures and flowrates on separation performance and tritium inventory. Additionally, a two-column architecture was studied, incorporating multiple isotopic equilibrators in interconnecting streams, to further reduce unwanted heteronuclear isotopologues and improve system efficiency. Comparative analysis of the proposed configurations highlights significant operational advantages of optimising equilibrator temperatures, including reduced tritium contamination and inventory. Results indicate that reducing... [more]

The definition of strategies for operation of process networks is a key research focus in process systems engineering. This challenge is commonly formulated as a numerical constraint satisfaction problem, where most practical algorithms are limited to identifying inner approximations to the feasible operational envelope. Sampling-based approaches so far have only been developed for formulations that required coordinated operation of the units within the network. We propose a decomposition approach that enables decentralized operation for acyclic muti-unit processes by sampling. Our methodology leverages problem structure to decompose unit-wise and deploys surrogate models to couple the resultant subproblems. We demonstrate it on a serial, batch chemical reactor network. In future research, we will extend this framework to consider the presence of uncertain unit parameters robustly.

Reaction processes require optimization to enhance key performance indicators (KPIs) such as yield, conversion, and selectivity. Techniques like Bayesian Optimization (BO), Model-Based Design of Experiments (MBDoE), and Goal-Oriented Optimal Experimental Design (GOOED) play pivotal roles in achieving these objectives. BO efficiently explores the design space to identify optimal conditions, while MBDoE maximizes the information gain by reducing kinetic model uncertainty. In contrast, GOOED focuses solely on maximizing the KPIs without considering the system uncertainty, identifying reactor conditions in the design space guaranteeing optimal performance. This study compares BO, MBDoE, and GOOED in optimizing methane oxidation in an automated flow reactor. Performance is assessed based on optimal methane conversion, reduced system uncertainty and minimal experimental efforts to achieve maximum conversion. BO quickly identifies high-conversion conditions, MBDoE minimizes experimental runs... [more]

This study presents a deterministic optimization methodology for the design of shell-and-tube heat exchangers with twisted tape turbulence promoters, focusing on minimizing the total annualized cost (TAC) while balancing thermal performance and energy consumption. A sensitivity analysis was carried out as Case I (Methanol-Water), it reveals that increasing the twist ratio (TR) reduces flow turbulence, resulting in lower fluid velocity, pressure drop (?Pi), and overall heat transfer coefficient (U). Among the turbulence promoters evaluated, twisted tapes with V-cuts achieved a 21.1% increase in U with a 52.27% increase in pressure drop, demonstrating an optimal balance between thermal enhancement and energy cost. In contrast, promoters with circular rings and multiple perforations showed the highest U improvements (26.7% and 25.8%, respectively) but incurred significant pressure drops (93.5% and 97.9%). The optimization problem has been stated as a nonlinear programming (NLP) problem an... [more]

Vacuum (pressure) swing adsorption (V(P)SA) has received considerable attention in the past decades. Existing studies typically estimate vacuum pump energy consumption using an approximate constant energy efficiency or an empirical energy efficiency correlation, leading to inaccurate representation of realistic vacuum pump performance. In this paper an enhanced computational approach is proposed for simulation and optimisation of V(P)SA through simultaneous integration of realistic vacuum pump data and adsorption bed fluidisation limits. The computational results show that the developed prediction models accurately represent the actual performance curves of the vacuum pump. Incorporation of the vacuum pump prediction models and fluidisation constraints in V(P)SA optimisation leads to significantly different optimal solutions compared to when these factors are not considered.

Predicting processes’ future behavior based on past data is vital for automatic control and dynamic optimization in engineering. Recent advances in deep learning, particularly Artificial Neural Networks, have improved predictions in various engineering fields. Recurrent Neural Networks (RNNs) are well-suited for time series data, as they naturally evolve through dynamic systems with recurrent updates. Despite their high predictive power, RNNs may underperform if their training ignores the model's future application. In Model Predictive Control, for example, the model evolves over time using only current information, relying on its own predictions at later steps. A model trained for one-step-ahead predictions may fail when tasked with multi-step-ahead forecasting in autoregressive mode. This study explores deep recurrent neural network models for predicting critical operational time series of a large-scale Electric Submersible Pump system. We present an innovative training approach, fra... [more]

Optimal energy scheduling for sector-coupled multi-energy systems is becoming increasingly important as renewable energies such as wind and photovoltaics continue to expand. They are very volatile and difficult to predict. This creates a deviation between generation and demand that can be compensated for by energy storage technologies. For these, rule-based control is well established in industry, and mixed-integer model predictive control (MPC) is an area of research that promises the best results, usually regarding minimal costs. Drawbacks of MPC include the need for an adequate system model, often associated with high modeling effort, high computational effort for larger prediction horizons, and complications with stochastic variables. In this work, Reinforcement Learning is used in an attempt to overcome these difficulties without applying elaborate mixed-integer linear programming. The self-learning algorithm, which requires no explicit knowledge of the system behavior, can learn... [more]

Real-time optimization (RTO) is a model-based technique that drives plants to optimal operating conditions. Modifier Adaptation (MA) is a class of methods that adjusts the optimization problem using gradient information. This enables the plant to reach the optimum operating point or batch trajectory without the need of a precise model which reduces the necessary modeling efforts. However, computing the gradients of the cost function or of the plant outputs with respect to the inputs online is a challenging task. Modifier Adaptation with Quadratic Approximation (MAWQA) integrates MA with Quadratic Approximation (QA), which helps mitigate the challenges of estimating gradients from noisy measurements by utilizing historical operating data. However, the distribution of these past operating points significantly affects the effectiveness of the MAWQA strategy. To address this issue in this contribution, new methods to compute probing points which lead to fast convergence to the optimum are... [more]

Middle vessel batch distillation (MVBD) is an alternative configuration of the conventional batch distillation with improved sustainability index. This article presents a comparison of model-based control approaches for MVBD column. Specifically, two control approaches - sequential (open-loop optimization followed by closed-loop control) and simultaneous (closed-loop optimization and control) are pursued. These two approaches are compared in terms of their effectiveness, overall performance, and robustness to plant-model mismatch. The effectiveness of these control strategies is illustrated using a simulation case study of a ternary mixture separation consisting of benzene, toluene and o-xylene.

This work addresses a practical challenge in batch process optimization: the need for sample efficient learning methods due to the high cost and time-intensive nature of running physical batch processes. While reinforcement learning (RL) offers a promising framework for optimizing batch processes, traditional approaches require numerous experimental runs to converge to optimal policies. A novel sample efficient RL method that leverages Gaussian Processes (GPs) to accelerate learning from limited batch data is proposed. However, the direct application of GPs becomes computationally intractable as data accumulates batch-to-batch, and their performance degrades when training distributions shift during policy improvement. To address these challenges, an integrated framework that combines Q-learning with GPs was developed and a strategic subset selection mechanism using determinantal point processes is introduced to maintain computational efficiency while preserving diverse, high-performing... [more]

Industrial decarbonization is considered one of the key objectives in mitigating global climate change. To achieve a net-zero industry requires actively transitioning from fossil fuel-based energy sources to renewable alternatives. However, the intermittent nature of renewable energy sources poses challenges to a reliable and robust supply of energy for industrial sites. Therefore, the integration of renewable energy systems with existing industrial processes, subject to energy storage solutions and main grid interconnections, is essential to enhance operational reliability and overall energy resilience. This study proposes a novel framework for the design and optimization of industrial utility systems integrated with renewable energy sources. A monthly-based analysis is adopted to consider variable demand and non-constant availability in renewable energy supply. Moreover, carbon capture is considered in this work as a viable decarbonization measure, which can be strategically combined... [more]

This work presents a Lyapunov-based framework for safe reinforcement learning (RL) applied to the control of an unstable reactor. The proposed method imposes stability constraints on the value and Q-functions through a Lyapunov candidate function defined as the negative of these functions, L(s)=-V(s) and L(s,a)=-Q(s,a). Constraints enforce positivity of the Lyapunov candidate function and non-positive time derivatives, promoting monotonic behavior aligned with Lyapunov stability conditions. The framework was tested on both on-policy (PPO) and off-policy (SAC, TD3, and DDPG) RL algorithms, with performance evaluated against their baseline versions and a nonlinear Model Predictive Controller (NMPC). Results showed that stability constraints significantly improved control performance across all tested algorithms, yielding consistently higher cumulative rewards, reduced overshoot, and decreased variability. Derivative-based constraints successfully mitigated abrupt changes and oscillatory... [more]