{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:26:38Z","timestamp":1760243198833,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,12,24]],"date-time":"2015-12-24T00:00:00Z","timestamp":1450915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1115827, DMS-1522734"],"award-info":[{"award-number":["DMS-1115827, DMS-1522734"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005416","name":"Research Council of Norway","doi-asserted-by":"publisher","award":["Centres of Excellence funding scheme, project 223259"],"award-info":[{"award-number":["Centres of Excellence funding scheme, project 223259"]}],"id":[{"id":"10.13039\/501100005416","id-type":"DOI","asserted-by":"publisher"}]},{"name":"US Department of Energy","award":["DE-FE00135331"],"award-info":[{"award-number":["DE-FE00135331"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>In this paper, we consider a reduced computational model of methane hydrate formation in variable salinity conditions, and give details on the discretization and phase equilibria implementation. We describe three time-stepping variants: Implicit, Semi-implicit, and Sequential, and we compare the accuracy and efficiency of these variants depending on the spatial and temporal discretization parameters. We also study the sensitivity of the model to the simulation parameters and in particular to the reduced phase equilibria model.<\/jats:p>","DOI":"10.3390\/computation4010001","type":"journal-article","created":{"date-parts":[[2015,12,24]],"date-time":"2015-12-24T10:03:53Z","timestamp":1450951433000},"page":"1","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Reduced Numerical Model for Methane Hydrate Formation under Conditions of Variable Salinity. Time-Stepping Variants and Sensitivity"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5013-7943","authenticated-orcid":false,"given":"Malgorzata","family":"Peszynska","sequence":"first","affiliation":[{"name":"Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francis","family":"Medina","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wei-Li","family":"Hong","sequence":"additional","affiliation":[{"name":"College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, USA"},{"name":"CAGE (Centre for Arctic Gas Hydrate, Environment and Climate), Department of Geology, UiT The Arctic University of Norway, Tromso, Norway"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marta","family":"Torres","sequence":"additional","affiliation":[{"name":"College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,12,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0012-821X(03)00325-X","article-title":"Rethinking the global carbon cycle with a large, dynamic and microbially mediated gas hydrate capacitor","volume":"213","author":"Dickens","year":"2003","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.epsl.2004.07.029","article-title":"Gas hydrate growth, methane transport, and chloride enrichment at the southern summit of Hydrate Ridge, Cascadia margin off Oregon","volume":"226","author":"Torres","year":"2004","journal-title":"Earth Planet. Sci. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Peszynska, M., Hong, W.L., Torres, M., and Kim, J.H. (2015). Methane hydrate formation in Ulleung Basin under conditions of variable salinity. Reduced model and experiments, submitted.","DOI":"10.1007\/s11242-016-0706-y"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Liu, X., and Flemings, P.B. (2007). Dynamic multiphase flow model of hydrate formation in marine sediments. J. Geophys. Res., 112.","DOI":"10.1029\/2005JB004227"},{"key":"ref_5","unstructured":"Lake, L.W. (1989). Enhanced Oil Recovery, Prentice Hall."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Helmig, R. (1997). Multiphase Flow and Transport Processes in the Subsurface, Springer.","DOI":"10.1007\/978-3-642-60763-9"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1016\/S0309-1708(02)00014-3","article-title":"Numerical simulation of non-isothermal ultiphase multicomponent processes in porous media 2. Applications for the injection of steam and air","volume":"25","author":"Class","year":"2002","journal-title":"Adv. Water Resour."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1137\/0149044","article-title":"Mathematical structure of the black-oil model for petroleum reservoir simulation","volume":"49","author":"Trangenstein","year":"1989","journal-title":"SIAM J. Appl. Math."},{"key":"ref_9","first-page":"319","article-title":"Degenerate two-phase incompressible flow problems. I. Regularization and numerical results","volume":"5","author":"Chen","year":"2001","journal-title":"Commun. Appl. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"278","DOI":"10.2118\/79535-PA","article-title":"A Parallel Multi-Block Black-Oil Model in Multi-Model Implementation","volume":"7","author":"Lu","year":"2002","journal-title":"SPE J."},{"key":"ref_11","unstructured":"Peszy\u0144ska, M., Lu, Q., and Wheeler, M.F. (2000). Computational Methods in Water Resources, Balkema."},{"key":"ref_12","unstructured":"Wheeler, M.F., Wheeler, J.A., and Peszy\u0144ska, M. (2000). Computational Methods in Water Resources, Balkema."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1147","DOI":"10.1016\/S0309-1708(02)00105-7","article-title":"Computational Engineering and Science Methodologies for Modeling and Simulation of Subsurface Applications","volume":"25","author":"Wheeler","year":"2002","journal-title":"Adv. Water Resour."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"372","DOI":"10.2118\/50990-PA","article-title":"Compositional and black oil reservoir simulator","volume":"1","author":"Coats","year":"1995","journal-title":"SPE Reserv. Eval. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5081","DOI":"10.1029\/1998JB900092","article-title":"Predicting the occurence, distribution, and evolution of methane hydrate in porous marine sediments","volume":"104","author":"Xu","year":"1999","journal-title":"J. Geophys. Res."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Nimblett, J., and Ruppel, C. (2003). Permeability evolution during the formation of gas hydratees in marine sediments. J. Geophys. Res., 108.","DOI":"10.1029\/2001JB001650"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1016\/j.jmaa.2013.07.023","article-title":"Evolution of phase transitions in methane hydrate","volume":"409","author":"Gibson","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Peszynska, M., Showalter, R., and Webster, J. (2014). Advection of Methane in the Hydrate Zone: Model, Analysis and Examples. Mathe. Methods Appl. Sci.","DOI":"10.1002\/mma.3401"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rempel, A.W. (2012). Hydromechanical Processes in Freezing Soils. Vadose Zone J., 11.","DOI":"10.2136\/vzj2012.0045"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Sloan, E., and Koh, C.A. (2008). Clathrate Hydrates of Natural Gases, CRC Press. [3rd ed.].","DOI":"10.1201\/9781420008494"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1029\/2010GC003392","article-title":"Capillary controls on methane hydrate distribution and fracturing in advective systems","volume":"12","author":"Daigle","year":"2011","journal-title":"Geochem. Geophys. Geosyst."},{"key":"ref_22","unstructured":"Center for Hydrate Research Software CSMHYD and CSMGem. Available online: http:\/\/hydrates.mines.edu\/CHR\/Software.html."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1029\/97GL01599","article-title":"Phase equilibrium of gas hydrate: Implications for the formation of hydrate in the deep sea floor","volume":"24","author":"Zatsepina","year":"1997","journal-title":"Geophys. Res. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1315","DOI":"10.1137\/0730068","article-title":"Godunov-mixed methods for advection-diffusion equations in multidimensions","volume":"30","author":"Dawson","year":"1993","journal-title":"SIAM J. Numer. Anal."},{"key":"ref_25","unstructured":"Dawson, C.N., and Wheeler, M.F. (1991, January 8\u201312). Time-splitting methods for advection-diffusion-reaction equations arising in contaminant transport. Proceedings of the second International Conference on Industrial and Applied Mathematics, Washington, DC, USA."},{"key":"ref_26","unstructured":"Whiteman, J.R. (1987). The Mathematics of Finite Elements and Applications VI, Academic Press."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1051\/m2an:2003021","article-title":"Semi-smooth Newton methods for variational inequalities of the first kind","volume":"37","author":"Ito","year":"2003","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Ulbrich, M. (2011). Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces; Vol. 11, MOS-SIAM Series on Optimization, Society for Industrial and Applied Mathematics (SIAM).","DOI":"10.1137\/1.9781611970692"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.matcom.2013.04.021","article-title":"Gas phase appearance and disappearance as a problem with complementarity constraints","volume":"99","author":"Gharbia","year":"2014","journal-title":"Math. Comput. Simul."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Peaceman, D.W. (1977). Fundamentals of Numerical Reservoir Simulation, Elsevier Scientfic Publishing Company.","DOI":"10.1016\/S0376-7361(08)70233-4"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Ewing, R.E. (1983). The Mathematics of Reservoir Simulation, SIAM.","DOI":"10.1137\/1.9781611971071"},{"key":"ref_32","unstructured":"Peszy\u0144ska, M., Jenkins, E., and Wheeler, M.F. (2002). Recent Advances in Numerical Methods for Partial Differential Equations and Applications, American Mathematical Soc."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"LeVeque, R.J. (2007). Finite Difference Methods for Ordinary and Partial Differential Equations, Society for Industrial and Applied Mathematics (SIAM).","DOI":"10.1137\/1.9780898717839"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"709","DOI":"10.1016\/j.procs.2010.04.076","article-title":"Adaptive modeling of methane hydrates","volume":"1","author":"Torres","year":"2010","journal-title":"Procedia Computer Sci."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/1\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:54:44Z","timestamp":1760216084000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/4\/1\/1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,24]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,3]]}},"alternative-id":["computation4010001"],"URL":"https:\/\/doi.org\/10.3390\/computation4010001","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2015,12,24]]}}}