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Model-based predictive control for pneumatic separation and classification of materials in lithium-ion battery recycling 基于模型的锂离子电池回收物料气动分离分类预测控制
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-19 DOI: 10.1016/j.compchemeng.2025.109358
Antonio I. García , Oscar A. Marín , Edelmira D. Gálvez
{"title":"Model-based predictive control for pneumatic separation and classification of materials in lithium-ion battery recycling","authors":"Antonio I. García ,&nbsp;Oscar A. Marín ,&nbsp;Edelmira D. Gálvez","doi":"10.1016/j.compchemeng.2025.109358","DOIUrl":"10.1016/j.compchemeng.2025.109358","url":null,"abstract":"<div><div>Due to the considerable number of lithium-ion batteries (LIBs) required for telecommunication systems, electric transport, and renewable energy storage, among other applications, the recycling of spent LIBs is considered an increasingly critical operation. The improvement of this operation can reduce manufacturing costs, the consumption of raw materials, and the environmental footprint produced by their disposal. The present work is focused on implementing advanced control strategies for the separation and classification stages in spent LIBs recycling. The control strategies used correspond to model-based predictive control (MPC). The methodology consisted of implementing a phenomenological model that represents the operation of a device that separates and classifies materials based on their physical properties and uses an air jet as a suspension media. The study presents five control scenarios simulated considering performance approaches and one scenario regarding economic approach. The two manipulated variables example obtained the highest relative error for the output variable concerning the set point, with 1.7125%. Implementing MPC controllers for the material separation stage in LIBs recycling would allow the improvement of these processes in both performance and economic aspects.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"204 ","pages":"Article 109358"},"PeriodicalIF":3.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144926066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bayesian optimization with search space movement for cooling crystallization process 基于搜索空间移动的冷却结晶过程贝叶斯优化
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-19 DOI: 10.1016/j.compchemeng.2025.109350
Tae Hoon Oh , Kazuki Kato , Osamu Tonomura , Ken-Ichiro Sotowa
{"title":"Bayesian optimization with search space movement for cooling crystallization process","authors":"Tae Hoon Oh ,&nbsp;Kazuki Kato ,&nbsp;Osamu Tonomura ,&nbsp;Ken-Ichiro Sotowa","doi":"10.1016/j.compchemeng.2025.109350","DOIUrl":"10.1016/j.compchemeng.2025.109350","url":null,"abstract":"<div><div>Experimental automation equipped with data-driven optimization is attracting significant attention as an effective platform for finding optimal operating conditions. The key is to automate the decision-making procedure using Bayesian optimization. However, the optimization performance depends heavily on the search space, which is typically selected manually by an expert with domain knowledge. This study proposes a new Bayesian optimization algorithm with a search space movement strategy to automate the search space selection procedure. Simulation studies of two benchmark problems show that the proposed method can determine the optimal conditions with fewer trials than existing methods. Furthermore, the proposed method was applied to maximize the productivity of batch cooling crystallization. The experimental results indicate that the proposed Bayesian optimization algorithm can automatically and robustly find the proper search space and thus improve productivity by up to 46%.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109350"},"PeriodicalIF":3.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A knowledge-graph-based pharmaceutical engineering chatbot for drug discovery 基于知识图谱的药物发现制药工程聊天机器人
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-19 DOI: 10.1016/j.compchemeng.2025.109318
Naz Pinar Taskiran, Chia-En Jacklyn Tsai, Shuxin Huang, Arijit Chakraborty, Venkat Venkatasubramanian
{"title":"A knowledge-graph-based pharmaceutical engineering chatbot for drug discovery","authors":"Naz Pinar Taskiran,&nbsp;Chia-En Jacklyn Tsai,&nbsp;Shuxin Huang,&nbsp;Arijit Chakraborty,&nbsp;Venkat Venkatasubramanian","doi":"10.1016/j.compchemeng.2025.109318","DOIUrl":"10.1016/j.compchemeng.2025.109318","url":null,"abstract":"<div><div>Despite their success in day-to-day applications, ChatGPT and other large language models (LLMs) have not covered as much ground in scientific and engineering domains. One key challenge is the abundance of domain-specific terminology, which an LLM is not trained to extract in accordance with the underlying physical laws. Such black-box models can also lead to unreliable results or hallucinations. Hybrid AI, which combines data-driven and symbolic methods, leverages domain knowledge to add explainability and reliability to answers. Our group has previously developed a domain-informed ontology-based information extraction tool called SUSIE, which extracts key terms and their context to present them to the user as knowledge graphs (KGs). Although KGs are used to visualize relationships between different entities, they are not easily accessible for user questions. However, they serve as a structured input for LLMs. Thus, KGs can efficiently query a corpus of pharmaceutical documents, streamlining drug discovery and manufacturing processes. In this work, we propose methods to improve the information extraction capabilities of SUSIE by expanding its knowledge base and improving its ability to understand scientific material through a sentence-restructuring module. Additionally, we present a customized question-and-answer module that enables the user to query from generated KGs and get an answer in natural language. Unlike black-box models such as those purely powered by OpenAI’s models and the LangChain GraphQA packages, combining our KGs with Neo4j limits hallucinations and provides reliable and traceable answers in a user-friendly chatbot interface.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109318"},"PeriodicalIF":3.9,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144863217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Model predictive control for continuous pharmaceutical manufacturing with mass retention constraints 具有质量保留约束的连续制药模型预测控制
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-18 DOI: 10.1016/j.compchemeng.2025.109332
Zheming Wang , Chenyang Gu , Bo Chen , Shuwang Du
{"title":"Model predictive control for continuous pharmaceutical manufacturing with mass retention constraints","authors":"Zheming Wang ,&nbsp;Chenyang Gu ,&nbsp;Bo Chen ,&nbsp;Shuwang Du","doi":"10.1016/j.compchemeng.2025.109332","DOIUrl":"10.1016/j.compchemeng.2025.109332","url":null,"abstract":"<div><div>The pharmaceutical industry is undergoing a significant shift from batch to continuous production processes in pursuit of enhanced productivity and profitability. This motivates the research of control techniques for continuous pharmaceutical manufacturing. Unlike batch processing, continuous pharmaceutical manufacturing involves a single input of raw materials, with all subsequent steps operating in an uninterrupted flow. This paper presents the application of constrained model predictive control (MPC) for the feeding and mixing units in continuous pharmaceutical manufacturing with mass retention constraints. Based on mechanistic modeling, we develop a dynamic model of the continuous pharmaceutical process by introducing two integral state variables, which allow to characterize mass retention constraints. With this model, we then design a MPC scheme to track the desired outlet mass flow subject to mass retention constraints. Finally, the effectiveness of the proposed MPC scheme is validated by a simulation example.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109332"},"PeriodicalIF":3.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Development of approximate scheduling-adaptive controllers for multi-products continuous chemical processes using deep learning techniques and model predictive control 基于深度学习和模型预测控制的多产品连续化工过程近似调度自适应控制器的研究
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-18 DOI: 10.1016/j.compchemeng.2025.109359
M. Abou El Qassime , A. Shokry , A. Espuña , E. Moulines
{"title":"Development of approximate scheduling-adaptive controllers for multi-products continuous chemical processes using deep learning techniques and model predictive control","authors":"M. Abou El Qassime ,&nbsp;A. Shokry ,&nbsp;A. Espuña ,&nbsp;E. Moulines","doi":"10.1016/j.compchemeng.2025.109359","DOIUrl":"10.1016/j.compchemeng.2025.109359","url":null,"abstract":"<div><div>Recently, Machine learning (ML) techniques are increasingly used to enhance process control. However, most ML-based control solutions treat control problems in isolation from higher-level decision-making layers (scheduling in this study), which they must interact with and adapt to during operation. Consequently, they often become ineffective or inapplicable when scheduling scenarios vary (e.g., product types, sequences, quantities, or qualities).</div><div>Therefore, this work proposes a new Deep Learning-based Scheduling-Adaptive Controller (DL-SAC) that approximates Model Predictive Control (MPC) solutions while explicitly incorporating scheduling-layer decisions. DL-SAC learns how variations in product sequence, production rates, and quality specifications influence optimal closed-loop control actions. It is trained using a dataset generated by solving the nonlinear MPC problem under diverse scheduling scenarios. Each training instance includes state and control trajectories along with scheduling features such as production rates and product quality specifications, thereby embedding scheduling-contextual information into the control approximation.</div><div>The proposed approach is validated on a benchmark multi-product continuous chemical process subject to various scheduling configurations and process disturbance. Across these scenarios, DL-SAC achieves a Normalized Root Mean Square Error (NRMSE) of 1.19 % in predicting control actions, while reducing the online computational time required to solve the MPC problem by approximately 98.8 %. These results demonstrate the method’s capability to deliver accurate, real time control approximations while maintaining adaptability to variations in scheduling decisions and process dynamics. The approach (i) enhances real-time operational flexibility and adaptability of chemical plants and (ii) provides basis for improved integration between control and scheduling, enabling more unified and responsive process optimization.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"204 ","pages":"Article 109359"},"PeriodicalIF":3.9,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144926068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Using large language models for solving textbook-style thermodynamic problems 使用大型语言模型来解决教科书式的热力学问题
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-17 DOI: 10.1016/j.compchemeng.2025.109333
Rébecca Loubet , Pascal Zittlau , Luisa Vollmer , Marco Hoffmann , Sophie Fellenz , Fabian Jirasek , Heike Leitte , Hans Hasse
{"title":"Using large language models for solving textbook-style thermodynamic problems","authors":"Rébecca Loubet ,&nbsp;Pascal Zittlau ,&nbsp;Luisa Vollmer ,&nbsp;Marco Hoffmann ,&nbsp;Sophie Fellenz ,&nbsp;Fabian Jirasek ,&nbsp;Heike Leitte ,&nbsp;Hans Hasse","doi":"10.1016/j.compchemeng.2025.109333","DOIUrl":"10.1016/j.compchemeng.2025.109333","url":null,"abstract":"<div><div>Large Language Models (LLMs) have made significant progress in reasoning, demonstrating their capability to generate human-like responses. This study analyzes the problem-solving capabilities of LLMs in the domain of thermodynamics. A benchmark of 22 textbook-style thermodynamic problems to evaluate LLMs is presented that contains both simple and advanced problems. Five different LLMs are assessed: GPT-3.5, GPT-4, and GPT-4o from OpenAI, Llama 3.1 from Meta, and le Chat from MistralAI. The answers of these LLMs were evaluated by trained human experts, following a methodology akin to the grading of academic exam responses. The scores and the consistency of the answers are discussed, together with the analytical skills of the LLMs. Both strengths and weaknesses of the LLMs become evident. They generally yield good results for the simple problems, but also limitations become clear: The LLMs do not provide consistent results, they often fail to fully comprehend the context and make wrong assumptions. Given the complexity and domain-specific nature of the problems, the statistical language modeling approach of the LLMs struggles with the accurate interpretation and the required reasoning. The present results highlight the need for more systematic integration of thermodynamic knowledge with LLMs, for example, by using knowledge-based methods.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"204 ","pages":"Article 109333"},"PeriodicalIF":3.9,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144893669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Physics-guided transfer learning for Bayesian optimization of chemical port-Hamiltonian systems 化学端口-哈密顿系统贝叶斯优化的物理引导迁移学习
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-17 DOI: 10.1016/j.compchemeng.2025.109331
Negareh Mahboubi, Junyao Xie, Biao Huang
{"title":"Physics-guided transfer learning for Bayesian optimization of chemical port-Hamiltonian systems","authors":"Negareh Mahboubi,&nbsp;Junyao Xie,&nbsp;Biao Huang","doi":"10.1016/j.compchemeng.2025.109331","DOIUrl":"10.1016/j.compchemeng.2025.109331","url":null,"abstract":"<div><div>Bayesian optimization (BO) has emerged as a powerful black-box optimization approach for complex systems, making sequential decisions through Gaussian process (GP) models to explore complex search spaces. However, conventional BO faces certain challenges when applies to optimizations of chemical systems, particularly with limited measurement data and physical constraints. This paper proposes an adaptive framework combining transfer learning with physics-informed GP to enhance BO performance for chemical process optimization. By incorporating physics-based priors through Gaussian Process Port-Hamiltonian Systems (GP-PHS) in the point-by-point transfer learning methodology, the proposed approach dynamically leverages knowledge from related source domains while satisfying physical constrains. The framework’s effectiveness is demonstrated across three chemical systems including a water tank, an electrochemical cell, and an isothermal continuous stirred tank reactor (CSTR). Results show improvements in both optimization accuracy and convergence speed compared to traditional BO methods. This proposed approach bridges the gap between data-driven optimization and physical principles, offering a robust solution for complex chemical system optimization under data scarcity.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109331"},"PeriodicalIF":3.9,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144863216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Physics-Informed Neural Network (PINN) framework for generic bioreactor modelling 通用生物反应器建模的物理信息神经网络(PINN)框架
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-17 DOI: 10.1016/j.compchemeng.2025.109354
Monesh kumar Thirugnanasambandam , José Pinto , Ekaterina Moskovkina , Rafael S. Costa , Rui Oliveira
{"title":"A Physics-Informed Neural Network (PINN) framework for generic bioreactor modelling","authors":"Monesh kumar Thirugnanasambandam ,&nbsp;José Pinto ,&nbsp;Ekaterina Moskovkina ,&nbsp;Rafael S. Costa ,&nbsp;Rui Oliveira","doi":"10.1016/j.compchemeng.2025.109354","DOIUrl":"10.1016/j.compchemeng.2025.109354","url":null,"abstract":"<div><div>Many previous studies have explored hybrid semiparametric models merging Artificial Neural Networks (ANNs) with mechanistic models for bioprocess applications. More recently, Physics-Informed Neural Networks (PINNs) have emerged as promising alternatives. Both approaches seek to incorporate prior knowledge in ANN models, thereby decreasing data dependency whilst improving model transparency and generalization capacity. In the case of hybrid semiparametric modelling, the mechanistic equations are hard coded directly into the model structure in interaction with the ANN. In the case of PINNs, the same mechanistic equations must be “learned” by the ANN structure during the training. This study evaluates a dual-ANN PINN structure for generic bioreactor problems that decouples state and reaction kinetics parameterization. Furthermore, the dual-ANN PINN is benchmarked against the general hybrid semiparametric bioreactor model under comparable prior knowledge scenarios across 2 case studies. Our findings show that the dual-ANN PINN can level the prediction accuracy of hybrid semiparametric models for simple problems. However, its performance degrades significantly when applied to extended temporal extrapolation or to complex problems involving high-dimensional process states subject to time-varying control inputs. The latter is primarily due to the more complex multi-objective training of the dual-ANN PINN structure and to physics-based extrapolation errors beyond the training domain.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109354"},"PeriodicalIF":3.9,"publicationDate":"2025-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144890351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal control of uncertain batch processes via Koopman expectation-assisted gradient methods 基于Koopman期望辅助梯度法的不确定批处理最优控制
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-16 DOI: 10.1016/j.compchemeng.2025.109353
Danijel Zadravec, Nenad Ferdelji
{"title":"Optimal control of uncertain batch processes via Koopman expectation-assisted gradient methods","authors":"Danijel Zadravec,&nbsp;Nenad Ferdelji","doi":"10.1016/j.compchemeng.2025.109353","DOIUrl":"10.1016/j.compchemeng.2025.109353","url":null,"abstract":"<div><div>Batch processes are indispensable in the chemical industry for producing low-volume, high-value products, leveraging their inherent flexibility to adapt to evolving market demands. While process control optimization promises significant potential for improving efficiency and profitability, discrepancies between plant behavior and model predictions, stemming from imperfect models and measurements, can lead to suboptimal or even infeasible outcomes. To address these challenges, our work focuses on developing efficient gradient-based methods for optimizing batch processes under parametric uncertainty, with the goal of satisfying process chance constraints. Central to our approach is the use of the Koopman expectation method, a novel and computationally efficient alternative to Monte Carlo simulations for propagating uncertainty in nonlinear dynamic systems. We explore two optimization procedures: Direct iterative optimization, which fully integrates the Koopman expectation into the gradient calculation loop, and Backoff-assisted iterative optimization, which combines deterministic optimization with probabilistic constraint corrections informed by the Koopman expectation. The Direct iterative optimization demonstrates robustness and is straightforward to implement, albeit with significant computational demands. In contrast, the Backoff-assisted method significantly reduces computational burden while maintaining satisfactory optimization results. Both methods are successfully applied to a case study involving the minimum time problem in batch distillation, demonstrating their effectiveness in achieving constraint satisfaction under uncertain initial conditions and model parameters. The proposed methodology is further applied to a batch crystallization case study, illustrating its broader applicability and effectiveness across different batch processing scenarios.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109353"},"PeriodicalIF":3.9,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convex envelope method for T,p flash calculations for mixtures with an arbitrary number of components and arbitrary aggregate states 凸包络法的T,p闪速计算具有任意数量的组分和任意聚合状态的混合物
IF 3.9 2区 工程技术
Computers & Chemical Engineering Pub Date : 2025-08-16 DOI: 10.1016/j.compchemeng.2025.109326
Quirin Göttl, Natalie Rosen, Jakob Burger
{"title":"Convex envelope method for T,p flash calculations for mixtures with an arbitrary number of components and arbitrary aggregate states","authors":"Quirin Göttl,&nbsp;Natalie Rosen,&nbsp;Jakob Burger","doi":"10.1016/j.compchemeng.2025.109326","DOIUrl":"10.1016/j.compchemeng.2025.109326","url":null,"abstract":"<div><div><span><math><mrow><mi>T</mi><mo>,</mo><mi>p</mi></mrow></math></span> flash calculations determine the correct number of phases at phase equilibrium and their compositions for fixed temperature and pressure. They are essential for chemical process simulation and optimization. The convex envelope method (CEM) is an existing approach that employs the tangent plane criterion to determine liquid phase equilibria for mixtures with an arbitrary number of components without providing the number of phases beforehand. This work extends the CEM to include also vapor and solid phases. Thus, any phase equilibrium of a given mixture with an arbitrary number of components and phases can be calculated over the whole composition space. The CEM results are presented for various vapor–liquid and solid–liquid phase equilibria examples of up to four components. We show how the CEM can be used for parameter fitting of <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>E</mi></mrow></msup></math></span>-models. As an outlook, we demonstrate how the CEM can be combined with a machine learning-based tool for property prediction to construct phase equilibria.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"203 ","pages":"Article 109326"},"PeriodicalIF":3.9,"publicationDate":"2025-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144864004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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