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]

The green transition accelerates innovations and developments targeting the integration of green hydrogen in the chemical industry. However, all new hydrogen pathways and process designs must be tested on operability and safety. A big challenge is the typical fluctuating characteristic of green hydrogen supply that contrasts the steady-state operation of most conventional chemical processes. Therefore, to adequately assess control and monitoring techniques, a benchmark model tailored to the relevant aspects of the hydrogen economy is required. We introduce a benchmark model based on the production of green ammonia using the Haber-Bosch process that remains operable when coupled to a fluctuating hydrogen supply from water electrolysis. The main section of the process model is an adiabatic indirect cooled reactor system that provides realistic modeling of industrial applications. Like the ammonia reactor, all process units and the underlying control structure are precisely dimensioned to... [more]

Rapid and robust simulation of chemical production processes is critical to address core scientific questions related to process design, optimization, and sustainability. Efficiently solving a chemical process, however, remains a challenge due to their highly coupled and nonlinear nature. Graph abstractions of the underlying physical phenomena within unit operations may help identify potential avenues to systematically reformulate the network of equations and enable more robust convergence of flowsheets. To this end, we further refined a flowsheet graph-theoretic abstraction that consists of a mesh of interconnected variable nodes and equation nodes. The new network of equations is formulated at the phenomenological level agnostic to the thermodynamic property package by extending equation formulations widely used to solve multistage equilibrium columns. Decomposition of the graph by phenomena linearizes material and energy balances across the flowsheet by decoupling phenomenological n... [more]

A key step in developing high-performance industrial products lies in the design of their constituent molecules. Computer-aided molecular design (CAMD) has garnered significant attention for its potential to accelerate and improve the design process. The mainstream method involves using property prediction models to predict the properties of potential molecules and selecting the best candidates based on these predictions. However, prediction errors are inevitable, introducing unreliability into the design. To address this issue, this paper proposes a novel component property modeling framework based on a molecular similarity coefficient. By calculating the similarity between a target molecule and those in an existing database, the framework selects the most similar molecules to form a tailored training dataset. The similarity coefficient also quantifies the reliability of the property predictions. In tests across various properties, this framework not only provides a quantifiable evalu... [more]

Process systems engineering optimization problems may be challenging. These problems often exhibit nonlinearity, non-convexity, discontinuity, and uncertainty, and often only the values of objective and constraint functions are accessible. Additionally, some problems may be computationally expensive. In such scenarios, black-box optimization methods may be appropriate to tackle such problems. A general-purpose multi-agent framework for optimization has been developed to automate the configuration and use of hybrid optimization, allowing for multiple optimization solvers, including different instances of the same solver. Solvers can share solutions, leading to better outcomes with the same computational effort. Alongside cooperation, competition is introduced by dynamically allocating more computational resource to solvers best suited to the problem. Each solver is assigned a priority that adapts to the evolution of the search. The scheduler is priority-based and uses similar algorithms... [more]

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]