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Phase transitions in porous media across multiple scales

多尺度多孔介质中的相变

基本信息

批准号：
1522734
负责人：
Ralph Showalter
金额：
$ 38.39万
依托单位：
Oregon State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-07-15 至 2021-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1522734&HistoricalAwards=false
关键词：
Phase transitions porous media across

项目摘要

In this project the PI will develop and analyze computational models describing the evolution of methane hydrate. Methane hydrate is an ice-like substance of great interest in geophysics, climate studies, and energy engineering, because it can release methane, a powerful greenhouse gas and drilling hazard; hydrates can also serve as a potential unconventional energy source. This work will involve several spatial scales from the kilometer scale of hydrate bearing subsea sediments and Arctic permafrost regions, to the micro-scale at which one looks at the pores of the sediments. The PI's mathematical analysis of hydrate models, under some simplifying assumptions, has so far revealed very unusual features absent, e.g., in ice-water phase transitions. Based on these analyses the PI will formulate more accurate algorithms for the simplified and for more complex realistic models, which in turn can further our understanding of hydrate formation and dissociation in nature. The software the PI will develop will be shared with the geophysics community.In PI's prior work, she has framed a simplified model of methane hydrate as a parameter-dependent free boundary problem, and her analyses show that its solutions can develop multiple singularities beyond those known, e.g., for Stefan problem of ice-water phase transitions. In this project the PI will develop new techniques for the simplified model extending substantially the classical results known for the non-parametrized case, and studying fundamental research questions concerning, e.g., nonlinear degenerate diffusion and conservation laws with the particular type of parameter-dependent monotone operators. The will extend the delicate time-stepping analyses in the abstract setting, develop a priori and a posteriori error analyses, and robust algorithms for the couplings across multiple time and spatial scales. In particular, the will consider the porescale at which she formulates reduced and dynamic models for many of the constitutive relationships needed for macroscale. In additional to computational mathematics, the project will impact the geophysics community involved in hydrate modeling, and more broadly other applications in porous media.

在这个项目中，首席研究员将开发和分析描述甲烷水合物演化的计算模型。甲烷水合物是一种冰状物质，在地球物理学、气候研究和能源工程中引起了极大的兴趣，因为它可以释放甲烷，这是一种强大的温室气体和钻探危险；水合物还可以作为潜在的非常规能源。这项工作将涉及多个空间尺度，从含有水合物的海底沉积物和北极永久冻土区的千米尺度，到观察沉积物孔隙的微观尺度。迄今为止，在一些简化的假设下，PI 对水合物模型的数学分析已经揭示了冰水相变等中不存在的非常不寻常的特征。基于这些分析，PI将为简化和更复杂的现实模型制定更准确的算法，这反过来又可以进一步加深我们对自然界中水合物形成和解离的理解。 PI 将开发的软件将与地球物理学界共享。在 PI 之前的工作中，她将甲烷水合物的简化模型构建为参数相关的自由边界问题，她的分析表明，其解决方案可以产生超出已知范围的多个奇点，例如冰水相变的 Stefan 问题。在这个项目中，PI将开发简化模型的新技术，大幅扩展非参数化情况下已知的经典结果，并研究有关非线性简并扩散和特定类型的参数相关单调算子的守恒定律等基础研究问题。他们将在抽象环境中扩展微妙的时间步进分析，开发先验和后验误差分析，以及跨多个时间和空间尺度的耦合的鲁棒算法。特别是，她将考虑孔隙尺度，为宏观尺度所需的许多本构关系制定简化的动态模型。除了计算数学之外，该项目还将影响涉及水合物建模的地球物理学界，以及更广泛的多孔介质中的其他应用。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

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
通讯作者：
M. Peszynska;Choah Shin

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

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