Modeling with Constraints and Phase Transitions in Porous Media

多孔介质中的约束和相变建模

• 批准号: 1912938
• 负责人: Malgorzata Peszynska
• 金额: $ 22.44万
• 依托单位: Oregon State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-15 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1912938&HistoricalAwards=false
• 关键词: Modeling; Constraints; Phase; Transitions; Porous

The changes in sea temperatures and those in permafrost regions have influence on hydrological, climate, and human systems on the time scale of years and decades. The freezing and thawing of permafrost leads to subsidence and development of hills and depressions; these alter the direction of surface waters, and challenge the stability of construction. Warming of permafrost causes decay of biomass as well as release and transport of methane gas from hydrate and other stores underneath the frozen layers. Methane gas is a major contributor to greenhouse gas balances, and its presence, transport, and evolution, as well as that of methane hydrate, an ice-like substance, are of great interest in geophysics, climate studies, and energy engineering. Methane hydrate can dissociate to gas, and is a potential unconventional energy source, drilling hazard, and contributor to sub-sea slope instability. The realistic scenarios and case studies motivating this work include the melting of ice to water and dissociation of methane hydrate into gas in response to increased temperature or mechanical disturbance, with the liquid and gas phases traveling through the sediment. Models of similar nature also apply to bubble and steam transport, e.g., due to microbial activity, or in geysers. In this project the principal investigator will develop new mathematical results as well as those useful for geophysics, and continue interdisciplinary modeling efforts across the many fields. This project addresses mathematical and computational challenges arising in the models of phase change in porous media such as permafrost or sub-sea sediments, and the evolution and migration of the resident liquid and the dissociated gas phase. For these coupled processes of energy and mass transport, data and some nonlinear model systems of PDEs at the spatial and temporal (Darcy) scale of the reservoir are available. However, the new dynamics in the Earth's environment calls for further insights into the processes across the several interlinked spatial and temporal scales including the pore-scale.The models at the pore-scale bridge the physics between the interface and Darcy scales, account for confinement within the porous walls and complex geometries, and can be upscaled to Darcy scale. While x-ray micro-tomography can deliver unprecedented insight into pore-scale processes, at present, this data is rather sparse for conditions near phase transitions. These challenge the current knowledge and motivate the project. The research will advance the understanding of the micro-scale (pore-scale and interface scale) processes which inform the Darcy scale models. The project will develop and analyze algorithms for relevant models; many techniques and results are of independent interest. The evolution models the principal investigator will consider are complex and delicate, and involve pointwise constraints on the solutions in and out of the equilibrium.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

海洋温度和多年冻土区温度的变化在几年和几十年的时间尺度上对水文、气候和人类系统产生影响。多年冻土的冻结和融化导致丘陵和洼地的下沉和发育，改变了地表水的走向，对建筑的稳定性构成了挑战。永久冻土变暖会导致生物质的腐烂，以及甲烷气体从水合物和冻土层下的其他储存中释放和运输。甲烷气体是温室气体平衡的主要贡献者，甲烷水合物的存在、输运和演化以及甲烷水合物是地球物理、气候研究和能源工程领域的研究热点。甲烷水合物可以分解成天然气，是潜在的非常规能源、钻井危险和海底斜坡失稳的贡献者。推动这项工作的现实场景和案例研究包括：冰融化成水，甲烷水合物因温度升高或机械干扰而解离成气体，液体和气相在沉积物中传播。类似性质的模型也适用于气泡和蒸汽的运输，例如由于微生物的活动，或间歇泉。在这个项目中，首席研究员将开发新的数学结果以及那些对地球物理有用的结果，并继续在许多领域进行跨学科的建模工作。该项目解决了在多年冻土或海底沉积物等多孔介质相变模型中产生的数学和计算挑战，以及滞留液体和分离气相的演化和迁移。对于这些能量和质量传输的耦合过程，可以获得水库时空尺度上的偏微分方程组的数据和一些非线性模型系统。然而，地球环境中的新动力学需要进一步深入了解包括孔隙尺度在内的几个相互关联的空间和时间尺度上的过程。孔隙尺度上的模型在界面和达西尺度之间架起了物理桥梁，解释了多孔壁内的限制和复杂的几何形状，并且可以升级到达西尺度。虽然X射线微层析成像可以提供对孔隙尺度过程的前所未有的洞察，但目前，对于相变附近的条件，这些数据相当稀少。这些挑战了当前的知识，并激励了项目。这一研究将促进对形成达西尺度模型的微观尺度(孔尺度和界面尺度)过程的理解。该项目将开发和分析相关模型的算法；许多技术和结果是独立感兴趣的。首席研究人员将考虑的进化模型复杂而精细，涉及对均衡内外解决方案的点状限制。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Stability of a numerical scheme for methane transport in hydrate zone under equilibrium and non-equilibrium conditions

• DOI: 10.1007/s10596-021-10053-2
• 发表时间: 2021-03
• 期刊: Computational Geosciences
• 影响因子: 2.5
• 作者: M. Peszynska;Choah Shin

Numerical analysis of a parabolic variational inequality system modeling biofilm growth at the porescale

模拟孔隙尺度生物膜生长的抛物线变分不等式系统的数值分析

• DOI: 10.1002/num.22458
• 发表时间: 2020
• 期刊: Numerical Methods for Partial Differential Equations
• 影响因子: 3.9
• 作者: Alhammali, Azhar;Peszynska, Malgorzata
• 通讯作者: Peszynska, Malgorzata

Reduced Model for Properties of Multiscale Porous Media with Changing Geometry

几何形状变化的多尺度多孔介质特性的简化模型

• DOI: 10.3390/computation9030028
• 发表时间: 2021
• 期刊: Computation
• 影响因子: 2.2
• 作者: Peszynska, Malgorzata;Umhoefer, Joseph;Shin, Choah
• 通讯作者: Shin, Choah

Heterogeneous Stefan problem and permafrost models with P0-P0 finite elements and fully implicit monolithic solver

具有 P0-P0 有限元和完全隐式整体求解器的异质 Stefan 问题和永久冻土模型

• DOI: 10.3934/era.2022078
• 发表时间: 2022
• 期刊: Electronic Research Archive
• 影响因子: 0.8
• 作者: Bigler, Lisa;Peszynska, Malgorzata;Vohra, Naren
• 通讯作者: Vohra, Naren

Coupled flow and biomass-nutrient growth at pore-scale with permeable biofilm, adaptive singularity and multiple species

具有渗透性生物膜、适应性奇点和多物种的孔隙尺度的耦合流动和生物量-养分生长

• DOI: 10.3934/mbe.2021108
• 发表时间: 2021
• 期刊: Mathematical Biosciences and Engineering
• 影响因子: 2.6
• 作者: Shin, Choah;Alhammali, Azhar;Bigler, Lisa;Vohra, Naren;Peszynska, Malgorzata
• 通讯作者: Peszynska, Malgorzata