Solvent selection is a critical decision-making process that balances economic, environmental, and societal factors. The vast chemical space makes evaluating all potential solvents impractical, necessitating pre-selection strategies to identify promising candidates. Predictive thermodynamic models, such as the UNIFAC model, are commonly used for this purpose. Recent advancements in deep learning have led to models like the Gibbs-Helmholtz Graph Neural Network (GH-GNN), which overall offers higher accuracy in predicting infinite dilution activity coefficients over a broader chemical space than UNIFAC. This study presents a systematic comparison of solvent pre-selection using GH-GNN and UNIFAC-IL in the context of liquid-liquid extraction. The original GH-GNN model is extended to simultaneously predict organic and ionic systems. This extended GH-GNN model predicts more than 92 % of the logarithmic IDACs with an absolute error of less than 0.3. By comparison, UNIFAC-based models only achi... [more]

Recent advancements in material design have made adsorption a more energy-efficient alternative to traditional thermally driven separation processes. Accurate modelling of adsorption thermodynamics is crucial for designing and operating equilibrium-limited adsorption systems. High-quality open-source packages like PyIAST, PyGAPsare available for processing adsorption data in Python. They provide a robust set of features for processing and analysing isotherms. However, they have no support for automatic differentiation and are not targeted for performance. Langmuir.jl addresses these limitations by leveraging Julia's composable and differentiable programming ecosystem. Langmuir.jl includes tools for processing adsorption thermodynamics data—loading data, fitting isotherms with most often used models, predictive multicomponent adsorption through Ideal Adsorption Solution Theory (IAST) — and, importantly, enabling accurate derivative calculations through Julia's automatic differentiation... [more]

This study introduces a novel methodology that combines Gaussian process regression (GPR) with alpha shape design space reconstruction to visualize multi-dimensional design spaces. The proposed GPR surrogate approach incorporates a kernel optimization step, employing a greedy tree search strategy to identify the optimal combinatorial kernel from a selection of base kernels. This approach efficiently evaluates design spaces around specific points of interest, enabling alpha shape reconstruction. The methodology's adaptability is demonstrated through its application to both lower-dimensional (2D and 3D) cases and more complex, higher-dimensional systems (up to 7D), showcasing its scalability and versatility. Its effectiveness is further validated by its ability to generate accurate surrogate models from limited data. Overall, this study presents a robust framework that leverages GPR surrogate modeling and alpha shape reconstruction to facilitate design space evaluation in complex, multid... [more]

Second-order optimization algorithms that leverage the exact Hessian or its approximation have been proven to achieve a faster convergence rate than first-order methods. However, their applications on training deep neural networks models, partial differential equations-based optimization problems, and large-scale non-convex problems, are hindered due to high computational cost associated with the Hessian evaluation, Hessian inversion to find the search direction, and ensuring its positive-definiteness. Accordingly, we propose a new search direction based on an interval Hessian and incorporate it into a line-search framework. We apply our algorithm to a set of 210 problems and show that it converges to a local minimum for 70% of the problems. We also compare our algorithm with other approaches. We illustrate that our algorithm is competitive to other methods in finding a local minimum using a smaller number of O(n3) operations.

In the domain of process systems engineering, developing software embedded with advanced computational methods is in great demand to enhance the kinetic comprehension and facilitate industrial applications. Polymer production, characterized by complex reaction mechanisms, represents a particularly intricate process industry. In this work, a scientific software is developed for polymerization modelling and simulation with insight on microscopic resolution. From a software architecture perspective, the software is built on a self-developed process modelling platform that allows flexible user customization. A specific design for polymer species with microscopic chain structure information is conducted. From an algorithm perspective, the software offers high-performance solution strategies for polymerization process modelling by utilizing advanced computation approaches. A Ziegler-Natta copolymerization is presented to demonstrate the software’s capability in capturing the microscopic stru... [more]

Anomaly detection is a key technique for maintaining process suitability and safety; however, the quality of process data often deteriorates due to missing or noisy values caused by sensor malfunctions. Such data imperfections may obscure real faults. If anomaly detection models are too sensitive to such abnormal data, they may cause false positives resulting in unnecessary alarms, which may obstruct detection of true process faults. Thus, deterioration of the quality of process data may affect process performance and safety. We propose a new anomaly detection method that utilizes graph Laplacian regularization as a loss function considering data-specific temporal relationships. Graph Laplacian regularization is a mathematical tool used in image processing and denoising to smooth data. We assume that successive process data temporally close to each other have similar values and maintain temporal dependencies among variables. In this study, Laplacian regularization imposes significant p... [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.

Heuristic decomposition schemes like moving horizon schemes are a common approach to approximately solve large-scale mixed-integer programs. The authors propose Bayesian optimization as a methodological approach to systematically tune parameters of decomposition schemes for mixed-integer programs. This paper discusses detailed results of three studies of the Bayesian optimization-based approach using hoist scheduling as a case study: Firstly, two objectives of the tuning problem are examined considering sequences of incumbent solutions found by the Bayesian optimization. Secondly, the Bayesian optimization is applied to a set of test instances of the hoist scheduling problem using four types of acquisition functions; they are compared with respect to the convergence of the tuning problem solutions. Thirdly, the scaling behaviour of the Bayesian optimization is studied with respect to the dimension of the space of tuning parameters. The results of the three studies show that the solutio... [more]

A new method for efficient process development is the direct scale-up from laboratory scale to production scale using mechanistic models [1]. The integration of the Quality by Design approach into this scale-up concept may prove beneficial for a variety of product- and process-related aspects. This paper presents a workflow for the digital twin-supported direct scale-up of processes and process plants, which integrates elements of the Quality by Design methodology. To illustrate the concept, the workflow is implemented for the example of an esterification reaction in a stirred tank reactor. Finally, benefits of the implementation of Quality by Design in the direct scale-up using digital twins regarding the product quality and the process development are discussed as well as its limitations.

Sustainability is increasingly recognized as a critical global issue. Multi-objective optimization is an important approach for sustainable decision-making, but problems with four or more objectives are hard to interpret due to its high dimensions. In our group’s previous work, an algorithm capable of systematically reducing objective dimensionality for (mixed integer) linear Problem has been developed. In this work, we will extend the algorithm to tackle nonlinear many-objective problems. An outer approximation-like method is employed to systematically replace nonlinear objectives and constraints. After converting the original nonlinear problem to linear one, previous linear algorithm can be applied to reduce the dimensionality. The benchmark DTLZ5(I, M) problem set is used to evaluate the effectiveness of this approach. Our algorithm demonstrates the ability to identify appropriate objective groupings on benchmark problems of up to 20 objectives when algorithm hyperparameters are app... [more]

Process design deals with the problem of finding the best process set-up, subject to a set of constraints defining the design space (DSp). This selection is guided primarily by economic considerations. Flexibility may also play an important factor in process design, since it embodies “how far” from the design space’s bounds are the candidate optimal designs, which in some cases may lead to off-spec products. This work proposes a novel approach for flexibility assessment. In design problems where the design space is constrained by a set of affine bounds, flexibility may be expressed either as the minimum or the maximum distance with respect to the feasible (design) space bounds. For any point in the DSp, the minimum distance provides a good indicator on the minimum flexibility, as the direction that represents the highest risk of violating the constraints. An analogous conclusion can be drawn between the maximum distance and maximum flexibility. These distances can be computed exactly v... [more]

In the chemical industry, soft sensors are deployed to reduce equipment cost or allow for a continuous measurement of process variables. Soft sensors monitor parameters not via physical sensors but infer them from other process variables. On the one hand, the precision of a soft sensors is affected by its architecture, the choice of parametric equations like balances and thermodynamic or kinetic dependencies in the soft sensor model. On the other hand, uncertainty that is inherent to the input variable values propagates through the soft sensor model and impacts the output uncertainty. The latter is affected by the configuration of physical sensors in the chemical process. This paper proposes an approach for the combined optimization of soft sensor architecture and physical sensor configuration. For this purpose, the method combines an automatic extraction of all possible soft sensor architectures from a set of system equations with an uncertainty-based evaluation of sensor configuratio... [more]

Artificial neural networks are widely used as data-driven models for capturing complex, nonlinear systems. However, suboptimal training remains a significant challenge due to the nonlinearity of activation functions and the reliance on local solvers, which makes achieving global solutions difficult. One solution involves reformulating activation functions as piecewise linear approximations to convexify the problem, though this approach often requires substantial CPU time. This study demonstrates that a tailored branch-and-bound algorithm can effectively address these challenges by efficiently navigating the solution space using linear relaxations. The proposed method achieves minimal training error, offering a robust solution to the training bottleneck. Unlike traditional mixed-integer programming approaches, which often struggle to converge within reasonable CPU times, the SOSX algorithm shows superior scalability, with computational demand growing almost linearly rather than exponent... [more]

In applications involving fine powders and small particles, the accuracy of numerical simulations, particularly those employing the Discrete Element Method (DEM) to predict granular material behavior, can be significantly affected by uncertainties in critical parameters. These uncertainties include the coefficients of restitution for particle-particle and particle-wall collisions, viscous damping coefficients, and other related factors. In this study, we use stochastic expansions based on point-collocation non-intrusive polynomial chaos to perform a sensitivity analysis of a fluidized bed system. We treat four key parameters as random variables; each assigned a specific probability distribution over a designated range. This uncertainty is propagated through high-fidelity Large Eddy Simulation (LES)-DEM simulations to statistically quantify its impact on the results. To effectively explore the four-dimensional parameter space, we analyze a comprehensive database comprising over 1,200 si... [more]

Random signals are crucial in chemical and process engineering, where industrial plants generate big data that can be used for process understanding and decision-making. This makes it necessary to unveil the underlying probability histograms from these signals with a finite number of bins. However, the search for the optimal number of bins is still based on empirical optimisation and general rules of thumb. In this work, we introduce an alternative and general method to unveil probability histograms. Our method employs a novel variable-order QMOM, which adapts automatically based on the relevance of the information contained in the random data. The number of bins used to recover the underlying histogram is found to be proportional to the information entropy, where a search algorithm is developed that generates bins and assigns probabilities to them. The algorithm terminates when no more significant information is available for assignment to the newly created nodes, up to a user-defined... [more]

Waste lubricant oil (WLO) is a hazardous residual that requires proper management, being WLO regeneration the preferred approach. However, regeneration is only viable if the WLO does not coagulate in the equipment. Otherwise, the process needs to be shut down for cleaning and maintenance. To mitigate this risk, a laboratory test is currently used to assess the WLO coagulation potential before it enters the process. This laboratory test is, however, time-consuming, presents several safety risks, and is subjective. To expedite decision-making, process analytics technology (PAT) and machine learning were used to develop a model to classify WLOs according to their coagulation potential. Three approaches were followed, spanning linear and non-linear models. The first approach (benchmark) uses partial least squares for discriminant analysis (PLS-DA) and interval PLS combined with standard chemometric preprocessing techniques (27 model variants). The second approach uses wavelet transforms to... [more]

Bilevel optimization is an active area of research within the operations research community due to its ability to capture the interdependencies between two levels of decisions. This study introduces a metamodeling approach for addressing mixed-integer bilevel optimization problems, exploiting the approximation capabilities of neural networks. The proposed methodology employs neural network embeddings to approximate the optimal follower's response, bypassing the inner optimization problem by parametrizing it with continuous leader’s decisions. The use of Rectified Linear Unit (ReLU) activations allows the forward pass of the neural network to be represented as a set of mixed-integer linear constraints. Thereby, the bilevel structure is simplified into a single-level optimization model. A case study based on a two-echelon supply chain demonstrates the effectiveness of the approach, with solutions comparable to traditional bilevel optimization methods. The results suggest that neural netw... [more]

New research on complex intensified distillation schemes has popularized the use of several commercial process simulation software. The interfaces between process simulation and optimization-oriented software have allowed the use of rigorous and robust models. This type of optimization is mentioned in the literature as "Black Box Optimization", since successive evaluations exploits the information from the simulator without altering the model that represents the given process. Among process simulation software, Aspen Plus® has become popular due to their rigorous calculations, model customization, and results reliability. This work proposes a comparative study for Aspen Plus software and Microsoft Excel VBA®, Python® and MATLAB® interfaces. Five distillation schemes were analyzed: conventional column, reactive column, extractive column, column with side rectifier and a Petlyuk column. The optimization of the ?????? (Total Annual Cost) was carried out by a modified Simulated Annealing A... [more]

In this work, we introduce a quantum-enhanced reinforcement learning (RL) framework for process design synthesis. RL-driven methods for generating process designs have gained momentum due to their ability to intelligently identify optimal configurations without requiring pre-defined superstructures or flowsheet configurations. This eliminates reliance on prior expert knowledge, offering a comprehensive and robust design strategy. However, navigating the vast combinatorial design space poses computational challenges. To address this, a novel approach integrating RL with quantum machine learning (QML) is proposed. QML leverages theoretical advantages over classical methods to accelerate searches in large spaces. Built upon our prior work, the approach begins with a maximum set of available unit operations, represented in a flowsheet structure using an input-output stream matrix as RL observations. A Deep Q-Network (DQN) algorithm trains a parameterized quantum circuit (PQC) in place of a... [more]

The performance of chemical plants is inevitably related to knowledge about the current state of the system. However, both process and equipment drifts may distort state information. Deviations of process values caused by equipment malfunction may be misinterpreted as process drifts and vice versa. Determining the cause of the drift is further complicated by the fact that equipment drifts typically occur in combination with process drifts. This paper presents a method that uses available additional equipment data to reliably detect and decouple combined equipment and process drifts in chemical plants by combining statistical methods with model-based approaches. The utility of additional equipment information is assessed based on its effect on the decoupling of process and equipment drifts. First results demonstrate the feasibility of the approach in a real plant.

Industrial process monitoring can benefit from utilizing historical data, providing insights for decision-making and operational efficiency. This study develops a soft-sensor-based approach leveraging multi-fidelity modeling to correct discrepancies between online sensors and laboratory analyses. A Gaussian process-based strategy is used to predict deviations between high-frequency low-fidelity sensor data and less frequent high-fidelity laboratory measurements. By exploring static and dynamic modeling frameworks, we assess their suitability for capturing process dynamics and addressing time-dependent variability. The multi-fidelity soft sensor noticeably improves predictive accuracy, outperforming high-fidelity and low-fidelity methods. This approach demonstrates applicability across various industrial settings where integrating diverse data sources enhances real-time process control and monitoring, reducing reliance on costly laboratory sampling.

Artificial Photosynthetic Bio-Electrochemical Systems (AP-BES) offer a promising approach for converting CO2 to valuable bioproducts, addressing carbon mitigation and sustainable production. This study employs a stochastic techno-economic assessment (TEA) to estimate the viability of rhodopsin driven AP-BES, from carbon capture to product purification. Unlike traditional deterministic TEAs, this approach uses Monte Carlo simulations to model uncertainties in key technoeconomic parameters, including energy consumption, CO2 conversion efficiency, and bioproduct market prices. The analysis generates probability distributions for economic metrics such as Operational Expenditure (OPEX), Capital Expenditure (CAPEX), and profit. Enhancements in light-harvesting efficiency and advancements in reactor materials were predicted to reduce the payback period to just one year, thereby making large-scale deployment a feasible option.

Liquid-liquid extraction stages often deviate from equilibrium due to factors like insufficient mixing, making accurate efficiency modeling essential for process simulation. This study addresses the limitations of Aspen Plus (AP), which distorts equilibrium calculations by directly multiplying efficiency with the distribution coefficient. A modified Murphree efficiency definition, more suitable for liquid-liquid systems but absent in AP's Extraction Column module, was implemented using Aspen Custom Modeler (ACM). The custom multi-stage extraction column model replaces mole fractions with mole flows to better represent mass transfer and phase interactions, enhancing simulation accuracy when imported into AP. Two test cases validated the custom model's effectiveness. Test Case I, utilizing the UNIQ-RK thermodynamic model, compared the ACM model to AP's built-in module, revealing that the ACM model provides a more realistic representation of extraction processes under varying stage effici... [more]

Surrogate models are widely used to improve the tractability of process optimization. Some commonly used surrogate models are obtained via machine learning such as multi-layer perceptrons (MLPs), Gaussian processes, and decision trees. Recently, a new class of machine learning models named Kolmogorov Arnold Networks (KANs) have been proposed. Broadly, KANs are similar to MLPs, yet they are based on the Kolmogorov representation theorem instead of the universal approximation theorem for the MLPs. Compared to MLPs, it was reported that KANs require significantly fewer parameters to approximate a given input/output relationship. One of the bottlenecks preventing the embedding of MLPs into optimization formulations is that MLPs with a high number of parameters (larger width or depth) are more challenging to globally optimize. We investigate whether the parameter efficiency of KANs relative to MLPs can be translated to computational benefits when embedding them into optimization problems an... [more]

Developing piping and instrumentation diagrams (P&IDs) is a fundamental task in process engineering. For designing complex installations, such as petroleum plants, multiple departments across several companies are involved in refining and updating these diagrams, creating significant challenges in data exchange between different software platforms from various vendors. The primary challenge in this context is interoperability, which refers to the seamless exchange and interpretation of information to collectively pursue shared objectives. To enhance the P&ID creation process, a unified, machine-readable data format for P&ID data is essential. A promising candidate is the Data Exchange in the Process Industry (DEXPI) standard. We present pyDEXPI, an open-source implementation of the DEXPI format for P&IDs in Python. pyDEXPI makes P&ID data more efficient to handle, more flexible, and more interoperable. We envision that, with further development, pyDEXPI will act as a central scientific... [more]