The state task network (STN) representation is a widely used modeling approach for optimal multipurpose batch production scheduling. In practice, STNs have been traditionally formulated as mixed-integer programming (MIP) problems and solved using general-purpose MIP solvers relying on branch-and-bound and branch-and-cut. In the meantime, alternative modeling and solution paradigms for optimization have been developed, enabling the incorporation of alternative variable types and optimization algorithms. Specifically, this work relies on the Hexaly software, which introduced set-based models and their solution through general-purpose hybrid algorithms, i.e., methods that combine traditional MIP with constraint programming, local search, large neighborhood search, among other tools. So far, Hexaly has shown promising results when tackling optimal scheduling problems, however, set-based models and solution approaches for STN optimization have not been studied in the literature. Aiming to f... [more]

This paper presents a Europe-wide optimisation framework for designing and operating a multi-period Carbon Capture and Storage (CCS) supply chain across Europe. A MATLAB preprocessing pipeline constructs an auditable techno-economic dataset (emission nodes, ports, aquifers, candidate pipeline/shipping arcs and costs) and exports it to a GAMS optimisation model. The planning problem is formulated as a two-stage stochastic MILP, where scenario-independent first-stage decisions select discrete pipeline and shipping capacity bands and port operating modes, while scenario-dependent second-stage decisions allocate capture, transport and sequestration flows. Uncertainty is represented through correlated scenarios of capture unit costs for four capture technologies (CV=0.35, rho=0.8, Ns=20). To address the computational burden induced by inter-temporal binary investments and scenario replication, we apply a two-phase arc-screening heuristic: an LP relaxation on the full network identifies prom... [more]

Flowsheet synthesis is an integral step in process design, entailing the selection of a set of unit operations and their connectivity to convert raw materials to products. Superstructure optimisation represents a promising class of synthesis approaches, allowing for the systematic exploration of the flowsheet design space. Despite this, many superstructure formulations suffer from numerical instabilities, combinatorial explosion, and/or rely on restrictive assumptions on the types of flowsheet alternatives that can be considered. The modified state-operator network (MSON) formalism has recently been proposed to address some of these issues for isobaric flowsheets. The constant-pressure assumption restricts the applicability of the MSON to real process applications as pressure is a key process variable in many unit operations, such as distillation, reaction, and extrusion, and is necessary to elicit flow. In this work, we present the extended MSON (E-MSON) which inherits the numerical s... [more]

In this study, we propose a method to uniquely determine robust operating conditions for simulated moving bed (SMB) chromatography, an essential continuous liquid-phase separation technique in the pharmaceutical industry, in the form of explicit algebraic equations. The proposed method incorporates process robustness-defined as the probability of meeting the target purities under flow-rate uncertainty due to pump errors-without requiring computationally expensive dynamic simulations. In a computational demonstration, the method achieved a joint probability of 0.960 for simultaneously attaining 99.9% purity in both extract and raffinate products.

To improve the energy efficiency of distillation processes, various process intensification concepts have been proposed, including direct heat integration and thermal coupling. Identifying the most suitable alternative for a given separation task requires a rigorous and consistent techno-economic optimization. Superstructure models typically rely on isobaric operation and fixed HETP values, in order to avoid treating column hydraulics when solving the already challenging mixed-integer nonlinear optimization problems. In order to overcome this limitation and evaluate the effect of the simplification, the current work extends a rigorous equilibrium-stage superstructure model to account for tray-specific pressure drop and HETP values. A polylithic solution approach is implemented to improve the convergence for the resulting optimization problems. The proposed approach is demonstrated for the optimization of heat-integrated distillation sequences operated at close to atmospheric and vacuum... [more]

This work aims to systematically generate intensified process designs by integrating reinforcement learning (RL)-driven process synthesis and phenomena-based modeling via Generalized Modular Framework (GMF). Rather than considering flowsheet synthesis with conventional unit-operations, GMF utilizes fundamental building blocks, also known as mass and heat exchange modules, to describe the physiochemical phenomena and to enhance novel process discovery. At its core are driving forces which characterize the mass transfer feasibility based on the total change in Gibbs free energy of the system. RL is integrated with this phenomena-based modeling strategy to drive flowsheet generation by exploring much of the total action space and minimizing pre-postulation of stream connections. All possible inlets, outlets, and interconnections between modules are contained in a stream matrix. Deep Q-Network is used as the RL agent, which contains a multi-layer convolution neural network followed by a mu... [more]

Although solvent-based crystallization is widely adopted for separation and purification of crystalline pharmaceutical products, solvent choice and utilisation critically influence product quality, manufacturing cost, and the environmental performance of the pharmaceutical process. Escalating demands to reduce process mass intensity (PMI), together with increasing vulnerabilities in the supply chains, necessitate the development of more efficient and resilient process designs, incorporating solvent and active pharmaceutical ingredient (API) recycling. The conceptual design of crystallization processes offers a viable route to identify flowsheets with substantially reduced solvent consumption. In this paper we present a computer-aided molecular and process design (CAMPD) formulation to explore the benefits of solvent/API recycle for two processes/APIs: (i) a continuous cooling crystallization process for mefenamic acid (MA) employing a binary solvent mixture and (ii) a batch cooling cry... [more]

Industrial decarbonization is crucial to reducing global emissions. Efficient processes lower energy use and reduce the environmental impacts, such as material use and waste, decreasing the overall industrial footprint. In this context, the present study explores the impact of reducing steam consumption (thermal energy) during the ammonia regeneration process in the production of sodium carbonate. A key feature of the Solvay process is ammonia recycling, which significantly reduces raw material consumption and ensures both economic and environmental sustainability. However, this stage is highly energy-intensive. To enhance energy efficiency in soda ash production, a study was conducted to analyze variation in temperature, pressure, and steam flow introduced into the ammonia regeneration system. The objective is to understand its impact on both ammonia recovery and the process's energy consumption. Variations in steam pressure do not impact on energy consumption of the process. By reduc... [more]

To effectively distribute power to a system of multiple electrolyzer stack units, control strategies have been developed that now need to be applied to heterogeneous electrolysis systems. These are the 'segment principle', the 'slow start principle' and the 'start-stop principle'. As there are many possible combinations to the system composition of a modular heterogeneous electrolysis system together with the most suitable control strategy, a discrete multi-criteria optimisation problem can be formulated. To solve this discrete multi-criteria optimisation problem, two discrete decision variables are introduced. One is the electrolysis system composition, represented by the power ratio/configuration (C). A total of 17 different configurations were used for this, consisting of different proportions of alkaline electrolysis (AEL) and proton exchange membrane electrolysis (PEMEL). The other one are the control strategies (R). For the control strategies, the conventional strategies, mention... [more]

In the pursuit of decarbonisation, process industries are turning to electrification as a solution to avoid fossil fuels for heating and processing raw material. Transitioning to renewable electricity couples the processes to varying electricity availability and requires more consideration for production timing and scheduling to support grid stability and avoid high electricity prices. However, practical challenges limit the capability for unforeseen rescheduling for large processes. This paper explores the idea of auxiliary flexibility in an electrified steel production process, where only the auxiliary systems can react to changing conditions. We model an H2-DRI-EAF inspired process with controllable Air-Separation unit, water electrolysis, pressurized hydrogen storage, gas liquefaction units, and a battery energy storage system to react to a production related demand delay. First, we compare hourly and 15-minute DA pricing and observe that without fast flexibility the cost differenc... [more]

Black-box optimization (BBO) deals with problems involving functions that are either unknown, imprecise, or costly to evaluate. Current BBO methods encounter multiple challenges, such as high computational demands from excessive function evaluations, difficulties in handling complex constraints, lack of theoretical convergence guarantees, and unstable performance due to significant variations in solution quality. This work presents a machine learning-powered feasible path (MLFP) framework for general BBO problems involving complex constraints. An adaptive sampling strategy is first proposed to explore optimal regions and pre-filter potentially infeasible points, thereby reducing the number of evaluations. Machine learning algorithms are utilized to build surrogates for black-box functions. The feasible path algorithm is integrated to accelerate theoretical convergence by updating only independent variables instead of all variables. Computational experiments demonstrate that MLFP can ra... [more]

Simulated Moving Bed (SMB) chromatography is widely used for a variety of separations, yet, when applicable, these systems are typically operated using offline optimization strategies. Over time, process degradation and unforeseen disturbances may cause SMB units to deviate from the calculated optimal conditions, reducing overall performance. Real-Time Optimization (RTO) offers a promising solution by continuously monitoring and adjusting operating conditions to maintain optimal performance, despite such perturbations. However, experimental implementation of RTO in industrial SMB processes is costly and requires significant interdisciplinary coordination.To address this challenge, a virtual framework is proposed for the preliminary development of a model-based RTO system. The methodology employs a virtual plant-model pair, in which a representative plant model generates in silico experimental data, while a structurally distinct predictive model reproduces these results. Structural mism... [more]

Efficient deployment of carbon capture, utilisation, and storage (CCUS) within industrial clusters requires coordinated CO2 allocation under economic, technical, and environmental constraints, particularly when CO2 availability is limited. This paper presents a centralised optimisation framework for allocating captured CO2 from nine industrial sources to six utilisation and storage sinks within an industrial park in Qatar. A multi-objective mixed-integer linear programming (MILP) model is developed to minimise total system cost while accounting for capture, purification, transport, and utilisation processes, and enforcing an environmental feasibility constraint to ensure net CO2 reduction. The model is evaluated under four scenarios: a baseline case with sufficient CO2 to satisfy all sink demands, and three scarcity scenarios in which 15%, 25%, and 35% of total source emissions are available. Results show that under scarcity, allocations prioritise large EOR sinks supplied by high-volu... [more]

Dimethyl ether (DME) is a promising clean fuel and chemical intermediate, yet its synthesis from synthesis gas remains highly sensitive to both catalyst formulation and operating conditions. In this work, a data-driven framework is developed that combines machine learning surrogate modeling with multi-objective optimization to support systematic decision-making in DME synthesis. The novelty lies in the systematic comparison of different optimization approaches applied to an identical machine learning surrogate model for DME synthesis, thereby highlighting their respective strengths and limitations as decision-support tools under limited-data conditions. A dataset compiled from published literature includes catalyst composition, preparation methods, physicochemical descriptors, and operating conditions, with CO conversion and DME selectivity as performance indicators. After data preprocessing, feature analysis using correlation analysis and principal component analysis (PCA) is applied... [more]

Nonlinear model predictive control (NMPC) can substantially improve performance and constraint handling for (bio)chemical processes, but its adoption is still limited by the effort required to build maintainable first-principles models and to implement efficient dynamic optimization-based controllers. This paper presents GlycoPy, an open-source, equation-oriented and object-oriented Python framework that supports hierarchical model construction and integrated workflows for simulation, parameter estimation, dynamic optimization, and NMPC. The case study of the monoclonal antibody glycosylation process based on a multiscale model demonstrates the capability of GlycoPy.

Dynamic simulation of distillation columns and chemical reactors remains essential for plant design, controllability analysis, and economic optimization. High-purity separations of close-boiling mixtures present significant computational challenges due to nonlinear thermodynamic behavior and stiff differential-algebraic equation (DAE) systems. This work presents a unified Python/JAX framework integrating four computational modules: (1) Peng-Robinson thermodynamics with complex-step differentiation, (2) nonlinear solvers (Newton, Broyden, Newton-Krylov) with automatic Curtis-Reid scaling, (3) DAE solver with Radau IIA collocation and intelligent auto-selection, and (4) constrained optimization using the Augmented Lagrangian Method with JAX automatic differentiation. The framework leverages JAX's just-in-time compilation (JIT), vectorization (vmap), and automatic differentiation (AD) to achieve near-compiled-language performance. Validation includes: nonlinear solver benchmarks with Newt... [more]

Type your abstract text here. This work presents an essential methodological framework oriented to the implementation of sustainability promotion measures in process industries. It makes use of a previously developed paradigm, designated as Water and Energy Integration Systems (WEIS), which are fundamentally conceptual systems based on the implementation of several technologies implemented with the end to minimize water use, energy use and related environmental burdens. The primarily conceptual nature of these systems is significant that these have not been significantly implemented in real-life, and that these have been essentially implemented in the virtual basis of digital twin-based computational models. This work extensively presents a methodology developed for the assessment of the integrity of WEIS models, which have been developed using the capacities of a customised computational tool designated as ThermWatt. Two previously approached case-studies have been considered to perfo... [more]

Modular process simulators are widely used in industry due to their robust and detailed unit operation models. However, their application to gradient-based process optimization remains challenging, as these simulators are typically treated as black boxes, limiting access to internal equations and derivatives. As a result, finite difference methods are commonly employed for gradient estimation, despite their sensitivity to numerical noise and poor scalability. While previous studies have demonstrated the benefits of analytical derivatives in modular simulators, these approaches have largely relied on tangent differentiation modes. This work proposes a non-intrusive methodology that couples analytical derivatives with the adjoint mode of automatic differentiation to efficiently compute gradients for process optimization in modular simulators. The approach preserves the robustness of existing simulation tools by performing simulations normally to convergence, followed by external adjoint-... [more]

Modular plant design requires assessing whether independently characterized process requirements and module capabilities are compatible-a challenge that established methods address incompletely. Feasibility and flexibility analysis, as well as Quality by Design, typically assume integrated single-domain models where all variables belong to one coherent description, yet modular design involves domains that originate from different sources, evolve independently, and connect through interface variables. This work proposes Quantified Constraint Satisfaction Problems (QCSPs) as a formulation for interface-level suitability assessment: universal quantification encodes properties that must hold across their entire admissible range (e.g., physical properties, uncertain or environment-dependent characteristics requiring robustness), while existential quantification encodes variables where at least one feasible value must exist (e.g., critical process parameters, control inputs, configuration op... [more]

Global optimization of industrial-scale chemical process flowsheets remains challenging due to nonlinearity, nonconvexity, and large problem scale. While equation-oriented modeling frameworks enable high-fidelity representation of industrial processes, obtaining globally optimal solutions is often computationally intractable for off-the-shelf solvers. In this work, we present a decomposition-based global optimization strategy that solves a high-fidelity flowsheet model from the IDAES framework with the Structured Nonlinear Global Decomposition (SNoGloDe) framework. The proposed approach exploits spatial decomposability by partitioning the flowsheet into coupled subproblems linked through a small set of complicating variables and solving them within a prioritized spatial branch-and-bound framework. The methodology is demonstrated on a hydrodealkylation (HDA) process for benzene production, a nonconvex and industrially relevant case study. The flowsheet is decomposed into reactor and sep... [more]

Hierarchical optimization problems such as (generalized) semi-infinite optimization problems and bilevel problems appear in various disciplines of process systems engineering, such as flexibility analysis or parameter estimation. Adaptive discretization-based algorithms are a family of methods to solve these problems. In these methods, the original problem is decomposed into subproblems, which are solved with a standard optimization solver and then refined iteratively. Several related algorithms have been published. Until recently, computational studies have typically been performed using publication-specific implementations and benchmark problems. We recently published a software package - libDIPS - comprising existing adaptive discretization-based algorithms and a library of test problems for comparison. Several of the algorithms implemented in libDIPS exhibit strong parallelization potential in their algorithmic steps: In the algorithms of Mitsos [Optimization 60:1291-1308 (2011)] a... [more]

As chemical processes become increasingly complex and costs of experimentation increase, understanding the practical effectiveness of Active Learning methodologies is essential. In this regard, an ongoing debate is occurring within the research community about the use of Design of Experiments (DOE) and Bayesian Optimisation (BO). However, this debate is limited by the scarcity of systematic comparative studies. Therefore, this work provides a comparative analysis of two widely adopted data-driven optimisation approaches: DOE and BO. The comparison is conducted across two distinct case studies reflecting different levels of complexity, regarding the quantity and variety of input variables involved. The first case study represents a realistic in silico experimental scenario, with multiple decision variables of different types (continuous, categorical and mixture), and two distinct single-objective optimisation goals, while the second one considers a simpler, well-known benchmark model wi... [more]

Sonochemical reactors are a promising technology in process intensification, offering a sustainable and energy-efficient means of enhancing chemical reactions. By harnessing acoustic cavitation - the formation, oscillation and violent collapse of bubbles in a liquid medium - these systems generate local hotspots that can accelerate reaction kinetics. Despite its potential, efficient design and scale-up of sonochemical reactors remain major challenges, mostly because the cavitation phenomena take place close to the ultrasonic transducer. This work presents a simulation-based framework for the optimization of sonochemical batch reactors by coupling microscopic-level bubble behavior with macroscopic-level reactor performance, focusing on the placement of transducers to maximize reaction activity.

In today's competitive LNG market, reducing energy consumption is critical for enhancing both profitability and sustainability. The hot section of the LNG processing, which includes inlet receivers, acid gas removal, and dehydration units, is the most thermally demanding. Previous optimisation methods targeted each unit separately. On the other hand, this work details the development of a data-driven optimisation framework to minimise energy across these interdependent units. Preliminary application of the framework has yielded encouraging results. Utilising HYSYS process simulation data, the study successfully identifies critical operating variables-such as reboiler duty, amine circulation rate, and air-to-furnace stoichiometry-that drive production efficiency and energy consumption. Results indicate that a baseline condensate mass flow of 2, 048.71 kg/h is achieved at a stripper bottom temperature of 137.74 °C, while the AGRU produces sweet gas with 0.18 ppm H2S. Optimisation using P... [more]

Copper refining via electrolysis is a core metallurgical process that takes place in tankhouses, subject to strict temporal, spatial, and operational constraints. The efficiency and stability of this process depend critically on the coordinated scheduling of crane operations responsible for handling anodes, cathodes, and auxiliary tasks. In industrial practice, crane scheduling must simultaneously satisfy long-term production targets and short-term operational feasibility, while respecting process-dependent timing constraints imposed by electrochemical parameters. Inefficient or inconsistent schedules can lead to process delays, suboptimal resource utilization, and degraded electrolysis performance, ultimately affecting product quality and operational stability. This paper presents a modeling approach for optimizing tankhouse operations. The uniqueness of this case lies in the broad range of constraints, including human capacity, energy restrictions, metallurgical rules, and logistical... [more]