Flow through partially frozen pores in granular media containing ice or gas hydrate plays an essential role in diverse phenomena including methane migration and frost heave. As freezing progresses, the frozen phase grows in the pore space and constricts flow paths so that the permeability decreases. Previous works have measured the relationship between permeability and volumetric fraction of the frozen phase, and various correlations have been proposed to predict permeability change in hydrology and the oil industry. However, predictions from different formulae can differ by orders of magnitude, causing great uncertainty in modeling results. We present a floating random walk method to approximate the porous flow field and estimate the effective permeability in isotropic granular media with specified particle size distributions, without solving for the entire flow field in the pore space. In packed spherical particles, the method compares favorably with the Kozeny-Carman formula. We further extend this method with a probabilistic interpretation of the volumetric fraction of the frozen phase, simulate the effect of freezing in irregular pores, and predict the evolution of permeability. Employing no adjustable parameters, our results can provide insight into the coupling between phase transitions and permeability change, which plays important roles in hydrate formation and dissociation, as well as in the thawing and freezing of permafrost and ice-bed coupling beneath glaciers.

中文翻译：

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使用浮动随机游走估计部分冻结土壤的渗透率

流经含有冰或天然气水合物的颗粒介质中部分冻结的孔隙在包括甲烷迁移和冻胀在内的多种现象中起着至关重要的作用。随着冻结的进行，冻结相在孔隙空间中生长并收缩流动路径，从而使渗透率降低。以前的工作测量了渗透率和冻结相体积分数之间的关系，并提出了各种相关性来预测水文和石油工业中的渗透率变化。然而，不同公式的预测可能存在数量级差异，导致建模结果存在很大的不确定性。我们提出了一种浮动随机游走方法来近似多孔流场并估计具有指定粒度分布的各向同性颗粒介质的有效渗透率，无需求解孔隙空间中的整个流场。在填充的球形颗粒中，该方法优于 Kozeny-Carman 公式。我们通过对冻结相体积分数的概率解释进一步扩展了该方法，模拟了不规则孔隙中冻结的影响，并预测了渗透率的演变。在不使用可调参数的情况下，我们的结果可以深入了解相变和渗透率变化之间的耦合，这在水合物形成和解离以及永久冻土和冰川下冰床耦合的解冻和冻结中起着重要作用。我们通过对冻结相体积分数的概率解释进一步扩展了该方法，模拟了不规则孔隙中冻结的影响，并预测了渗透率的演变。在不使用可调参数的情况下，我们的结果可以深入了解相变和渗透率变化之间的耦合，这在水合物形成和解离以及永久冻土和冰川下冰床耦合的解冻和冻结中起着重要作用。我们通过对冻结相体积分数的概率解释进一步扩展了该方法，模拟了不规则孔隙中冻结的影响，并预测了渗透率的演变。在不使用可调参数的情况下，我们的结果可以深入了解相变和渗透率变化之间的耦合，这在水合物形成和解离以及永久冻土和冰川下冰床耦合的解冻和冻结中起着重要作用。