An upscaling model for simulation of geothermal processes in stratified formations

IF 3.5 2区 工程技术 Q3 ENERGY & FUELS Geothermics Pub Date : 2024-07-04 DOI:10.1016/j.geothermics.2024.103095
Jinyu Tang , Yang Wang , William R. Rossen
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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.

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模拟地层地热过程的升级模型
在分层多孔介质中,层间速度不均匀加上跨层热传导会导致热前沿扩散:即热泰勒扩散。如果不考虑模拟网格块内的这种异质性,传统的放大模型会低估热扩散,从而导致高估热突破时间。我们推导出一个流动方向上的有效纵向热扩散率模型 αeff,以表示两层介质中的有效热扩散。我们定义了一个无量纲数 NTC,即纵向对流与横向传导的时间比,作为冷水或热水注入时系统横向热平衡的指标。当 NTC > 5 时,双层体系中的热扩散非常接近于具有 αeff 的单层。这表明,满足 NTC > 5 的双层介质可以合并为具有有效纵向热扩散率 αeff 的单层介质。在应用于地热储层时,可以应用该模型分阶段进行放大,即在每个阶段将满足 NTC 标准的两层结合在一起。αeff 模型考虑了模拟网格块内的细尺度异质性,可提高热突破时间的预测精度,从而提高热寿命。
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来源期刊
Geothermics
Geothermics 工程技术-地球科学综合
CiteScore
7.70
自引率
15.40%
发文量
237
审稿时长
4.5 months
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.
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