{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:17:34Z","timestamp":1760242654407,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,12,29]],"date-time":"2017-12-29T00:00:00Z","timestamp":1514505600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Leakage through microscale or nanoscale cracks is usually hard to observe, difficult to control, and causes significant economic loss. In the present research, the leakage in a pipe was evaluated by the virtual entropy generation (VEG) method. In virtual entropy generation method, the \u201cmeasured entropy generation\u201d is forced to follow the \u201cexperimental second law of thermodynamics\u201d. Taking the leakage as the source virtual entropy generation, a new pipe leakage evaluation criterion was analytically derived, which indicates that the mass leakage rate should be smaller than the pressure drop rate inside a pipe. A numerical study based on computational fluid dynamics showed the existence of an unrealistic virtual entropy generation at a high mass leakage rate. Finally, the new criterion was used in the evaluation of leakage available in the literature. These results could be useful for leakage control or industry criteria design in the future.<\/jats:p>","DOI":"10.3390\/e20010014","type":"journal-article","created":{"date-parts":[[2017,12,29]],"date-time":"2017-12-29T10:58:47Z","timestamp":1514545127000},"page":"14","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Leakage Evaluation by Virtual Entropy Generation (VEG) Method"],"prefix":"10.3390","volume":"20","author":[{"given":"Zhichao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Municipal and Environmental Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Corina","family":"Drapaca","sequence":"additional","affiliation":[{"name":"Department of Engineering Science and Mechanics, Pennsylvania State University, State College, PA 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1577-3316","authenticated-orcid":false,"given":"Zhifeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Engineering Science and Mechanics, Pennsylvania State University, State College, PA 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuaifang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Nuclear Engineering, Pennsylvania State University, State College, PA 16802, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shimei","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Municipal and Environmental Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Municipal and Environmental Engineering, Jilin Jianzhu University, Changchun 130118, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1115\/1.2734250","article-title":"Experimental Leak-Rate Measurement Through a Static Metal Seal","volume":"129","author":"Marie","year":"2006","journal-title":"J. Fluids Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.applthermaleng.2017.07.208","article-title":"The Monte Carlo based virtual entropy generation analysis","volume":"126","author":"Zhang","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1476","DOI":"10.1016\/j.applthermaleng.2016.09.051","article-title":"Virtual entropy generation (VEG) method in experiment reliability control: Implications for heat exchanger measurement","volume":"110","author":"Zhang","year":"2017","journal-title":"Appl. Therm. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, Z., and Bai, B. (2016, January 11\u201317). Critical heat balance error for a general imbalanced heat exchanger. Proceedings of the ASME 2016 International Mechanical Engineering Congress and Exposition, Phoenix, AZ, USA.","DOI":"10.1115\/IMECE2016-68049"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.energy.2017.10.023","article-title":"A quantitative energy efficiency evaluation and grading of plate heat exchangers","volume":"142","author":"Zhang","year":"2018","journal-title":"Energy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1016\/j.applthermaleng.2015.11.005","article-title":"Critical heat balance error for heat exchanger experiment based on entropy generation method","volume":"94","author":"Zhang","year":"2016","journal-title":"Appl. Therm. Eng."},{"key":"ref_7","first-page":"6","article-title":"Modeling and simulation of Maximum power point tracker in Ptolemy","volume":"1","author":"Cai","year":"2013","journal-title":"J. Clean Energy Technol."},{"key":"ref_8","unstructured":"M\u2019rio, S.A., Chatzikokolakis, K., Palamidessi, C., and Smith, G. (2012, January 25\u201327). Measuring information leakage using generalized gain functions. Proceedings of the 2012 IEEE 25th Computer Security Foundations Symposium (CSF), Cambridge, MA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"021302","DOI":"10.1115\/1.4023425","article-title":"Prediction of Leak Rates Through Porous Gaskets at High Temperature","volume":"135","author":"Grine","year":"2013","journal-title":"J. Press. Vessel Technol."},{"key":"ref_10","unstructured":"Bejan, A. (1982). Entropy Generation through Heat and Fluid Flow, Wiley."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Henrie, M., Carpenter, P., and Nicholas, R.E. (2016). Pipeline Leak Detection Handbook, Gulf Professional Publishing.","DOI":"10.1016\/B978-0-12-802240-5.00002-9"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.petrol.2013.08.007","article-title":"Modeling of incompressible flow in short pipes with leaks","volume":"109","year":"2013","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.petrol.2009.09.008","article-title":"Mechanistic modeling of pipeline leak detection at fixed inlet rate","volume":"70","author":"Kam","year":"2010","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_14","unstructured":"Tortora, G.J., and Derrickson, B.H. (2008). Principles of Anatomy and Physiology, John Wiley & Sons."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1016\/j.compchemeng.2007.08.011","article-title":"Analysis of the smallest detectable leakage flow rate of negative pressure wave-based leak detection systems for liquid pipelines","volume":"32","author":"Ge","year":"2008","journal-title":"Comput. Chem. Eng."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"(2011). Environmental Protection Agency 2011.","DOI":"10.2175\/193864711802766452"},{"key":"ref_17","unstructured":"(2010). Interstate Natural Gas Pipeline Efficiency, Interstate Natural Gas Association of America."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/j.energy.2015.06.069","article-title":"A numerical study of air preheater leakage","volume":"92","author":"Maharaj","year":"2015","journal-title":"Energy"},{"key":"ref_19","unstructured":"Bjerketvedt, D., and Mjaavatten, A. (2005, January 9\u201311). A hydrogen air explosion in a process plant: A case history. Proceedings of the 5th International Conference on Hydrogen Safety, Brussels, Belgium."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Chuka, C.E., Freedom, I.H., and Anthony O, U. (2016). Transient Model-Based Leak Detection and Localization Technique for Crude Oil Pipelines: A Case of NPDC, Olomoro, Scholars Middle East Publishers.","DOI":"10.21276\/sjeat.2016.1.2.2"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:56:00Z","timestamp":1760208960000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/1\/14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,29]]},"references-count":20,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1]]}},"alternative-id":["e20010014"],"URL":"https:\/\/doi.org\/10.3390\/e20010014","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,12,29]]}}}