{"title":"An upscaling model for simulation of geothermal processes in stratified formations","authors":"Jinyu Tang , Yang Wang , William R. Rossen","doi":"10.1016/j.geothermics.2024.103095","DOIUrl":null,"url":null,"abstract":"<div><p>In stratified porous media, non-uniform velocity between layers combined with thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Conventional upscaling not accounting for this heterogeneity within simulation grid blocks underestimates thermal dispersion, leading to overestimation of thermal breakthrough time. We derive a model for effective longitudinal thermal diffusivity in the direction of flow, <em>α<sub>eff</sub></em>, to represent the effective thermal dispersion in two-layer media. <em>α<sub>eff</sub></em>, accounting for thermal Taylor dispersion, is much greater than the thermal diffusivity of the rock itself. We define a dimensionless number, <em>N<sub>TC</sub></em>, a ratio of times for longitudinal convection to transverse conduction, as an indicator of transverse thermal equilibration of the system during cold- or hot-water injection. For <em>N<sub>TC</sub></em> > 5, thermal dispersion in the two-layer system closely approximates a single layer with <em>α<sub>eff</sub></em>. This suggests a two-layer medium satisfying <em>N<sub>TC</sub></em> > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity <em>α<sub>eff</sub></em>. In application to a geothermal reservoir, one can apply the model to perform upscaling in stages, i.e. combining two layers satisfying the <em>N<sub>TC</sub></em> criterion in each stage. The <em>α<sub>eff</sub></em> model accounting for the fine-scale heterogeneity within simulation grid blocks would enhance the prediction accuracy of thermal breakthrough time and thus thermal lifetime.</p></div>","PeriodicalId":55095,"journal":{"name":"Geothermics","volume":null,"pages":null},"PeriodicalIF":3.5000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geothermics","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0375650524001834","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENERGY & FUELS","Score":null,"Total":0}
引用次数: 0
Abstract
In stratified porous media, non-uniform velocity between layers combined with thermal conduction across layers causes spreading of the thermal front: thermal Taylor dispersion. Conventional upscaling not accounting for this heterogeneity within simulation grid blocks underestimates thermal dispersion, leading to overestimation of thermal breakthrough time. We derive a model for effective longitudinal thermal diffusivity in the direction of flow, αeff, to represent the effective thermal dispersion in two-layer media. αeff, accounting for thermal Taylor dispersion, is much greater than the thermal diffusivity of the rock itself. We define a dimensionless number, NTC, a ratio of times for longitudinal convection to transverse conduction, as an indicator of transverse thermal equilibration of the system during cold- or hot-water injection. For NTC > 5, thermal dispersion in the two-layer system closely approximates a single layer with αeff. This suggests a two-layer medium satisfying NTC > 5 can be combined into a single layer with an effective longitudinal thermal diffusivity αeff. In application to a geothermal reservoir, one can apply the model to perform upscaling in stages, i.e. combining two layers satisfying the NTC criterion in each stage. The αeff model accounting for the fine-scale heterogeneity within simulation grid blocks would enhance the prediction accuracy of thermal breakthrough time and thus thermal lifetime.
期刊介绍:
Geothermics is an international journal devoted to the research and development of geothermal energy. The International Board of Editors of Geothermics, which comprises specialists in the various aspects of geothermal resources, exploration and development, guarantees the balanced, comprehensive view of scientific and technological developments in this promising energy field.
It promulgates the state of the art and science of geothermal energy, its exploration and exploitation through a regular exchange of information from all parts of the world. The journal publishes articles dealing with the theory, exploration techniques and all aspects of the utilization of geothermal resources. Geothermics serves as the scientific house, or exchange medium, through which the growing community of geothermal specialists can provide and receive information.