{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T01:56:36Z","timestamp":1774922196963,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T00:00:00Z","timestamp":1742428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62273215"],"award-info":[{"award-number":["62273215"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2021SFGC1101"],"award-info":[{"award-number":["2021SFGC1101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"publisher","award":["62273215"],"award-info":[{"award-number":["62273215"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"publisher","award":["2021SFGC1101"],"award-info":[{"award-number":["2021SFGC1101"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In coal chemical industries, the optimal allocation of gas and steam is crucial for enhancing production efficiency and maximizing economic returns. This paper proposes an optimal scheduling method using operating zone models and entropy weights for an energy system in a gas-to-methanol process. The first step is to develop mechanistic models for the main facilities in methanol production, namely desulfurization, air separation, syngas compressors, and steam boilers. A genetic algorithm is employed to estimate the unknown parameters of the models. These models are grounded in physical mechanisms such as energy conservation, mass conservation, and thermodynamic laws. A multi-objective optimization problem is formulated, with the objectives of minimizing gas loss, steam loss, and operating costs. The required operating constraints include equipment capacities, energy balance, and energy coupling relationships. The entropy weights are then employed to convert this problem into a single-objective optimization problem. The second step is to solve the optimization problem based on an operating zone model, which describes a high-dimensional geometric space consisting of all steady-state data points that satisfy the operation constraints. By projecting the operating zone model on the decision variable plane, an optimal scheduling solution is obtained in a visual manner with contour lines and auxiliary lines. Case studies based on Aspen Hysys are used to support and validate the effectiveness of the proposed method.<\/jats:p>","DOI":"10.3390\/e27030324","type":"journal-article","created":{"date-parts":[[2025,3,20]],"date-time":"2025-03-20T12:23:11Z","timestamp":1742473391000},"page":"324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Scheduling of Energy Systems for Gas-to-Methanol Processes Using Operating Zone Models and Entropy Weights"],"prefix":"10.3390","volume":"27","author":[{"given":"Xueteng","family":"Wang","sequence":"first","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mengyao","family":"Wei","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2635-8724","authenticated-orcid":false,"given":"Jiandong","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yang","family":"Yue","sequence":"additional","affiliation":[{"name":"Shandong Rongxin Group Co., Ltd., Zoucheng 273517, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/j.resconrec.2017.03.006","article-title":"History and future of the coal and coal chemical industry in China","volume":"124","author":"Li","year":"2017","journal-title":"Resour. Conserv. Recycl."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"113684","DOI":"10.1016\/j.apenergy.2019.113684","article-title":"Investigation and optimization analysis on deployment of China coal chemical industry under carbon emission constraints","volume":"254","author":"Huang","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/j.fuel.2016.11.008","article-title":"Carbon dioxide utilization in a gas-to-methanol process combined with CO2\/Steam-mixed reforming: Techno-economic analysis","volume":"190","author":"Zhang","year":"2017","journal-title":"Fuel"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1794","DOI":"10.1007\/s11244-018-0993-3","article-title":"Efficient way of carbon dioxide utilization in a gas-to-methanol process: From fundamental research to industrial demonstration","volume":"61","author":"Zhang","year":"2018","journal-title":"Top. Catal."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"104845","DOI":"10.1016\/j.jngse.2022.104845","article-title":"Review on technologies for conversion of natural gas to methanol","volume":"108","author":"Salahudeen","year":"2022","journal-title":"J. Nat. Gas Sci. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"878","DOI":"10.1016\/j.enpol.2011.11.037","article-title":"China\u2019s growing methanol economy and its implications for energy and the environment","volume":"41","author":"Yang","year":"2012","journal-title":"Energy Policy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"318","DOI":"10.1016\/j.enconman.2016.12.010","article-title":"Coke oven gas to methanol process integrated with CO2 recycle for high energy efficiency, economic benefits and low emissions","volume":"133","author":"Gong","year":"2017","journal-title":"Energy Convers. Manag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"822","DOI":"10.1016\/j.renene.2022.05.123","article-title":"A review on the integrated optimization techniques and machine learning approaches for modeling, prediction, and decision making on integrated energy systems","volume":"194","author":"Alabi","year":"2022","journal-title":"Renew. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Dong, J., Song, Z., Zheng, Y., Luo, J., Zhang, M., Yang, X., and Ma, H. (2024). Robust optimization research of cyber\u2013physical power system considering wind power uncertainty and coupled relationship. Entropy, 26.","DOI":"10.3390\/e26090795"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Xu, R., Lin, F., Shao, W., Wang, H., Meng, F., and Li, J. (2024). Multi-time-scale optimal scheduling strategy for marine renewable energy based on deep reinforcement learning algorithm. Entropy, 26.","DOI":"10.3390\/e26040331"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"3144","DOI":"10.1016\/j.enbuild.2011.08.010","article-title":"Multi-objective approach in thermoenvironomic optimization of a small-scale distributed CCHP system with risk analysis","volume":"43","author":"Abdollahi","year":"2011","journal-title":"Energy Build."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1016\/j.enconman.2015.07.009","article-title":"Operation optimization of a distributed energy system considering energy costs and exergy efficiency","volume":"103","author":"Yan","year":"2015","journal-title":"Energy Convers. Manag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1016\/j.energy.2017.10.122","article-title":"A novel multi-period mixed-integer linear optimization model for optimal distribution of byproduct gases, steam and power in an iron and steel plant","volume":"143","author":"Zeng","year":"2018","journal-title":"Energy"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.jclepro.2019.05.086","article-title":"Optimization of a regional energy system including CHP plants and local PV system and hydropower: Scenarios for the County of V\u00e4stmanland in Sweden","volume":"230","author":"Daraei","year":"2019","journal-title":"J. Clean. Prod."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"114834","DOI":"10.1016\/j.applthermaleng.2019.114834","article-title":"A MINLP model for multi-period optimization considering couple of gas-steam-electricity and time of use electricity price in steel plant","volume":"168","author":"Wei","year":"2020","journal-title":"Appl. Therm. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"40337","DOI":"10.1109\/ACCESS.2020.2976835","article-title":"Two-layer optimization scheduling model of integrated electricity and natural gas energy system considering the feasibility of gas-fired units\u2019 reserve","volume":"8","author":"Zhou","year":"2020","journal-title":"IEEE Access"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Alhumaid, Y., Khan, K., Alismail, F., and Khalid, M. (2021). Multi-input nonlinear programming based deterministic optimization framework for evaluating microgrids with optimal renewable-storage energy mix. Sustainability, 13.","DOI":"10.3390\/su13115878"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"114249","DOI":"10.1016\/j.enconman.2021.114249","article-title":"Design optimization of multi-energy systems using mixed-integer linear programming: Which model complexity and level of detail is sufficient?","volume":"240","author":"Wirtz","year":"2021","journal-title":"Energy Convers. Manag."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"115147","DOI":"10.1016\/j.enconman.2021.115147","article-title":"Multi-objective bi-level quantity regulation scheduling method for electric-thermal integrated energy system considering thermal and hydraulic transient characteristics","volume":"253","author":"Guo","year":"2022","journal-title":"Energy Convers. Manag."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3057","DOI":"10.1002\/ese3.1188","article-title":"Multi-objective economic\/emission optimal energy management system for scheduling micro-grid integrated virtual power plant","volume":"10","author":"Lamari","year":"2022","journal-title":"Energy Sci. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103984","DOI":"10.1016\/j.est.2022.103984","article-title":"Developing optimal energy management of integrated energy systems in the hybrid electricity and gas networks","volume":"48","author":"Monfaredi","year":"2022","journal-title":"J. Energy Storage"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"116680","DOI":"10.1016\/j.enconman.2023.116680","article-title":"Development and assessment of an integrated wind-solar based energy system for sustainable communities","volume":"277","author":"Dincer","year":"2023","journal-title":"Energy Convers. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"118071","DOI":"10.1016\/j.enconman.2024.118071","article-title":"A joint solution framework for the optimal operation and evaluation of integrated energy systems based on exergy","volume":"301","author":"Chen","year":"2024","journal-title":"Energy Convers. Manag."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2944","DOI":"10.1002\/ese3.1798","article-title":"Optimal scheduling of regional integrated energy systems with hot dry rock enhanced geothermal system based on information gap decision theory","volume":"12","author":"Liu","year":"2024","journal-title":"Energy Sci. Eng."},{"key":"ref_25","unstructured":"Incropera, F.P., DeWitt, D.P., Bergman, T.L., and Lavine, A.S. (1996). Fundamentals of Heat and Mass Transfer, Wiley."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"432","DOI":"10.3182\/20140824-6-ZA-1003.01510","article-title":"Dynamic modeling and simulation of compressor trains for an air separation unit","volume":"47","author":"Dominic","year":"2014","journal-title":"IFAC Proc. Vol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1016\/j.simpat.2008.05.017","article-title":"Steam turbine model","volume":"16","author":"Chaibakhsh","year":"2008","journal-title":"Simul. Model. Pract. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1016\/j.procir.2018.03.271","article-title":"Model-based method for condition monitoring and diagnosis of compressors","volume":"72","author":"Engelberth","year":"2018","journal-title":"Procedia CIRP"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1194","DOI":"10.1016\/j.energy.2019.03.160","article-title":"Modeling of a steam boiler operation using the boiler nonlinear mathematical model","volume":"175","author":"Trojan","year":"2019","journal-title":"Energy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2649","DOI":"10.1109\/TCST.2019.2943469","article-title":"Alarm monitoring for multivariate processes based on a convex-hull normal operating zone","volume":"8","author":"Yu","year":"2020","journal-title":"IEEE Trans. Contr. Syst. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Shen, Y., Li, D., and Wang, W. (2024). Multi-energy load prediction method for integrated energy system based on fennec fox optimization algorithm and hybrid kernel extreme learning machine. Entropy, 26.","DOI":"10.3390\/e26080699"},{"key":"ref_32","unstructured":"Aspen Technology, Inc. (2019). Aspen HYSYS Unit Operations V11 Reference Guide, Aspen Technology, Inc.. Available online: https:\/\/esupport.aspentech.com\/S_Article?id=000052892."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/324\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:57:20Z","timestamp":1760029040000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/3\/324"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,20]]},"references-count":32,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["e27030324"],"URL":"https:\/\/doi.org\/10.3390\/e27030324","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,20]]}}}