Developing ultra- or high-performance liquid chromatography (HPLC) methods for analysis or purification requires significant amounts of material and manpower, and typically involves time-consuming iterative lab-based workflows. This work demonstrates in two case studies that an autonomous HPLC platform coupled with a mechanistic model that self-corrects itself by performing parameter estimation can efficiently develop an optimized HPLC method with minimal experiments (i.e., reduced experimental costs and burden) and manual intervention (i.e., reduced manpower). At the same time, this HPLC platform, referred to as Smart HPLC Robot, can deliver a calibrated mechanistic model that provides valuable insights into method robustness.

Catalysis design and reaction condition optimization are considered the heart of many chemical and petrochemical processes and industries; however, there are still significant challenges in these fields. Advances in machine learning (ML) have provided researchers with new tools to address some of these obstacles, offering the ability to predict catalyst behaviour, optimal reaction conditions, and product distributions without the need for extensive laboratory experimentation. In this contribution, the potential applications of ML in heterogeneous catalysis and photocatalysis are explored by analysing datasets from different reactions, including Fischer-Tropsch synthesis and photocatalytic pollutant degradation. First, datasets were collected from literature. After cleaning and preparing the datasets, they were employed to train and test several models. The best model for each dataset was selected and applied for optimization.

Operational decision-making in Process Systems Engineering (PSE) has achieved high proficiency at specific levels, such as supply chain optimization and unit-operation optimization. However, a critical challenge remains: integrating these layers of optimization into a cohesive, hierarchical decision-making framework that enables sustainable and automated operations. Addressing this challenge requires systems capable of coordinating multi-level decisions while maintaining interpretability and adaptability. Multi-agent frameworks based on Large Language Models (LLMs) have demonstrated significant promise in other domains, successfully simulating traditional human decision-making tasks and tackling complex, multi-stage problems. This paper explores their potential application within operational decision-making for PSE, focusing on sustainability-driven objectives. A realistic Gas-Oil Separation Plant (GOSP) network is used as a case study, mimicking a hierarchical workflow that spans from... [more]

Process synthesis is a fundamental step in process design. The aim is to determine the optimal configuration of unit operations and stream flows to enhance key performance metrics. Traditional methods provide just one optimal solution and are strongly dependent on user-defined technologies, stream connections, and initial guesses for unknown variables. Usually, a single solution is not sufficient for adequate decision-making, especially, when properties such as flexibility or reliability are considered in addition to the process economics. Wastewater Treatment network synthesis and design is a complex problem that demands innovative approaches in design, retrofits, and maintenance strategies. Considering this, an enhanced framework for improving reliability in wastewater transportation networks based on graph theory and machine learning is presented. Machine learning models were developed to predict failure probability, where the XGBoost model provided the best predictions. To select t... [more]

The electrification of industrial heat is a promising pathway for decarbonization, yet challenges persist in balancing capital costs, operating costs, and emissions reduction. While previous studies have assessed electrification through heat integration and graphical methods, these approaches do not inherently determine the optimal hybrid technology configuration. This study introduces an optimization-based framework that systematically evaluates the cost-optimal allocation of electrified and conventional heating technologies. Formulated as a Mixed-Integer Linear Programming (MILP) model and implemented in Gurobi, the framework minimizes Total Annualized Cost (TAC) while satisfying heat demand, technology constraints, and emissions targets. Applied to an industrial case study, the model compares three scenarios: a fully conventional system relying on steam boilers and fired heaters, a fully electrified system utilizing high-temperature heat pumps, electrode boilers, and electric heater... [more]

Currently, state-of-the-art approaches to solving complex optimization problems have focused solely on methods requiring high computational time and unable to find the global optimal solution. In this work, a methodology based on quantum computing is presented to overcome these drawbacks. The novelty of this framework stems from the quantum computer’s architecture and taking into consideration the quantum phenomena that take place to solve optimization problems with specific structure. The proposed methodology includes steps for the transformation of the initial optimization problem into an unconstrainted optimization problem with binary variables and its embedding onto a quantum device. Moreover, different resolution levels for the transformation step and different architectures for the embedding process are utilized. To illustrate the procedure, a case study based on Haverly’s pooling and blending problem is examined while demonstrating the potential of the proposed approach. The res... [more]

Optimization under uncertainty is inherent to many PSE applications ranging from process design to RTO. Reaching process true optima often involves learning from experimentation, but actual experiments involve a cost (economic, resources, time) and a budget limit usually exists. Finding the best trade-off on cumulative process performance and experimental cost over a finite budget is a Partially Observable Markov Decision Process (POMDP), known to be computationally intractable. This paper follows the nonmyopic Bayesian optimization (BO) approximation to POMDPs developed by the machine-learning community, that naturally enables the use of hybrid plant surrogate models formed by fundamental laws and Gaussian processes (GP). Although nonmyopic BO using GPs may look more tractable, evaluating multi-step decision trees to find the best first-stage candidate action to apply is still expensive with evolutionary or NLP optimizers. Hence, we propose modelling the value function of the first-st... [more]

One of the most successful continuous high-performance liquid chromatography (HPLC) processes for drug manufacturing is the Simulated Moving Bed (SMB). SMB is a multi-column, continuous, chromatographic process that can handle much higher throughputs than regular batch chromatographic processes. The process is initially transient, but eventually arrives at a cyclic steady state, which makes optimization very challenging, even more so when superstructure optimization is involved. To simplify the optimization problem, many researchers fixed the SMB structure, optimizing only the continuous variables, so they cannot be considered superstructure optimization. In this work, an SMB superstructure that can simultaneously optimize column structure and operation is proposed. The results showed that the superstructure proposed is reliable, and it is more efficient compared to current optimization approaches if the optimal column structure has to be identified.

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]

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.

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 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.

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]

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.

By capturing carbon dioxide from biomass flue gases, energy processes with negative carbon footprint are achieved. Among carbon capture methods, the fluidized temperature swing adsorption (TSA) column is a promising low-pressure alternative, but it has been developed on small scales. This work aims to model, simulate and optimize a fluidized TSA multi-stage equilibrium system to obtain a cost estimate and a conceptual design for future process scale up. A mathematical model described adsorption in multiple stages, each with a heat exchanger, coupled to the desorption operation. The model was based on elementary macroscopic molar and energy balances, coupled to pressure drops in a fluidized bed designed to operate close to the minimum fluidization velocity, and coupled to thermodynamics of adsorption equilibrium of a mixture of carbon dioxide and nitrogen in solid sorbents (the Toth equilibrium isotherm was used). The complete fluidized TSA process has been optimized to minimize costs,... [more]

The dividing wall column (DWC) has significant energy saving potential compared to conventional column sequences. However, to reach these savings in practice, it is essential that the control structures can track the optimal operation point despite inevitable changes in feed properties, performance characteristics and other uncertainties. Otherwise, the energy consumption may rise significantly or, more commonly, the DWC becomes unable to produce pure products even at its maximum reboiler duty. Extremum seeking control (ESC) is a model-free optimisation technique that may mitigate off-optimal operation in this environment. By active perturbation of selected manipulative variables, the algorithm infers gradient properties of the measured cost function and, by that, enables tracking of a moving optimum. Extremum seeking control can be used also in combination with other approaches, e.g. self-optimising control. Applied to the DWC, the presented perturb-and-observe algorithm, which can be... [more]

This work explores Aotearoa-New Zealand’s potential to fully electrify and source industrial process heat demands from renewable energy for 286 industrial sites while exploring the feasibility of green methanol production using excess electricity. Most energy models rely on spatially aggregated supply and demand, which limits the accurate representation of energy value chains. To address this limitation, the model incorporates industrial sites with varied temperature profiles, enabling the use of diverse heating technologies such as heat pumps, electrode boilers, bubbling fluidised bed reactors and biomass boilers. The proposed Mixed-Integer Linear Programming energy model uses the Accelerated Branch-and-Bound (ABB) algorithm, which is implemented within the P-graph framework to optimise the system. The model considers different energy transportation modes, including road transport for biomass and grid infrastructure for electricity. The multi-period design determines optimal heating t... [more]

This work presents a plantwide model of a Haber-Bosch ammonia synthesis loop (HB-loop) in a PtA plant, consisting of heat exchangers, compressors, steam turbines, flash separators and catalytic reactor beds. The total electrical power utility of the HB-loop is a combination of compressor power, refrigeration power, and steam turbine power. We optimise the HB-loop operating parameters, subject to constraints for maximum reactor temperatures, compressor choke and stall, minimum steam temperature, and maximum loop pressure. The loop features six degrees of freedom (DOFs) for the optimisation: three reactor temperatures, reactor N2/H2-ratio, separator temperature, and loop pressure. The optimisation minimises the total loop power utility for a given hydrogen make-up feed flow, with the PtA load varied by ranging the hydrogen make-up feed flow from 10 % to 120 % of the nominal. Across this load range, different constraints become active, with the compressor surge limit being particularly cr... [more]

The optimization of the power conversion system, responsible for thermal-to-electrical energy conversion, for a pulsed fusion power plant is presented. A spherical tokamak is modelled as three heat sources, all pulsed, with different stream temperatures and available amounts of heat. A thermal energy storage system is considered in the design to compensate for the lack of thermal power during a dwell. Thermal storage enables continued power generation during a dwell and can avoid thermal transients in sensitive components like turbomachines. Multiple lower grade heat sources are integrated into the process through parallel preheating trains. The evaluation of a dynamic model of the power conversion system is used to define an objective function with multiple criteria. A bi-objective optimization problem is defined to investigate the trade-off between the size of the thermal energy storage system and the variability in turbine power output during a dwell. The set of non-dominated design... [more]

Solar Thermal Power Plants (STPPs) use solar energy for large-scale electricity production but face significant operational challenges. These include variations in solar radiation, cloud cover, electricity demand fluctuations, and the need for frequent shutdowns if energy storage is inadequate. Deciding an optimal STPP operating conditions is challenging due to these factors. While revenue maximization has been used as an objective in existing literature, current models are often static and fail to capture the dynamic nature of STPPs. In contrast, this work proposes a dynamic model-based revenue optimization approach that accounts for plant dynamics and operational constraints, such as solar radiation variability and changing electricity demand. The objective function is designed to maximize revenue while considering power generation and fluctuating electricity prices. A simulation model of 1 MWe hybrid solar thermal power plant in Gurgaon, India, featuring two solar fields—Parabolic T... [more]

Enhanced weathering (EW) of alkaline minerals in chemical reactors with a controlled environment is recognized as a promising approach for gigaton-level carbon dioxide removal. However, reactor configuration and operating conditions must be optimized to balance the interfacial areas between gas, liquid and solid phases prior to industrial application. We developed a physics-based and data-driven hybrid modelling approach, coupled with multi-objective optimization, to study and compare three typical chemical reactors, i.e., trickle bed, packed bubbling columns, and stirred slurry reactors, and the optimal design to improve CO2 capture rate and reduce energy and water consumptions. Then an adaptive optimization is proposed to dynamically adjust the operating of the reactors in response to intermittent CO2 emission and renewable energy supply. Results indicated that forced stirring enhances CO2 capture rates by accelerating mass transport but increases energy consumption. Trickle bed reac... [more]

Seawater desalination is considered as the only available solution that can cope with the increasing demand for freshwater around the world. Improving the desalination techniques may help to cut off the cost and increase sustainability. In this paper, a mathematical model describing the MED process is developed within gPROMs software. The model includes all the necessary mass and energy balance equations together with thermodynamic and physical properties equations. The model predictions are validated against the actual plant data before using the model for optimizing the process to achieve minimum heat transfer area. For two different operating conditions (summer and winter) and a fixed production demand, the heat transfer area is minimised while optimising different parameters of the MED process. The results showed that a 10.4% reduction in the heat transfer area can be achieved under summer operating conditions and around 26% decrease in the heat transfer area can be met under winte... [more]

Asserting the phase stability of multi-component mixtures is an important task in computer-aided mixture/blend design (CAMbD), but it is often hindered by the lack of reliable and tractable models. In this paper, we propose a group-contribution machine-learning (GC-ML) method to predict phase coexistence for a large set of ternary mixtures consisting of two solvents and one (fixed) solute. Each solvent is represented by a vector of functional group numbers, encoded by integer values. The solvent vectors are combined with mixture composition and temperature to form the input features to a GC-ML surrogate classifier, which distinguishes between four types of stable phase configurations as possible outputs: liquid (L), solid-liquid (SL), liquid-liquid (LL) or solid-liquid-liquid (SLL). To explore the performance of the trained GC-ML multi-classifier, it is embedded as a surrogate phase-stability constraint in the optimisation of an ibuprofen crystallisation process. A two-step solution s... [more]

Process systems are negatively impacted by manufacturing uncertainties, and increasingly by unknown-unknown disruptive events. To this effect, systems need to be designed with the inherent flexibility and resilience to overcome the impacts of uncertainties and disruptions respectively as it is more challenging to retrofit existing systems with such capabilities. To this end, we propose a methodology based on flexibility analysis to systematically explore the feasibility of design alternatives under parameter uncertainty and discrete disruption scenarios simultaneously. Multi-parametric programming is utilized to generate explicit relationships between design decisions and the resulting system’s ability to maintain feasible operations under uncertainty and disruptive events. We capture this ability by introducing the Combined Flexibility-Resilience Index (CFRI), which describes the likelihood that the system is feasible under the relevant uncertainty and disruption sets. With explicit f... [more]

Model-based control and optimisation strategies can play a key role in improving energy efficiency and reducing emissions into produced water re-injection facilities. However, building a model that adequately describes the plant is challenging and can also be used in online decision-making procedures. This work proposes a simple model based on a real water re-injection facility operating on the Norwegian continental shelf. The results demonstrate the model's flexibility, which could be fitted to different plant operating points while being fast to solve when embedded in optimisation problems. The developed model is expected to aid the implementation of strategies like self-optimising control and real-time optimisation on produced water re-injection facilities.