A model for hysteretic constitutive relations governing multiphase flow: 2. Permeability‐saturation relations
A model for hysteretic constitutive relations governing multiphase flow: 2. Permeability‐saturation relations
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DOI：
10.1029/wr023i012p02197
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发表时间：
1987-12
影响因子：
5.4
通讯作者：
R. Lenhard;J. Parker
中科院分区：
文献类型：
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作者：
R. Lenhard;J. Parker
描述了一个理论模型，用于预测任意饱和路径下的两相（空气-水）和三相（空气-油-水）多孔介质系统中的相对渗透率-饱和度 (k-S) 关系。提出了空气、水和油相对渗透率的积分表达式，扩展了 Parker 等人的非滞后相对渗透率模型。 (1987) 适应水相和油相中截留的空气以及水相中截留的油造成的孔隙堵塞效应。积分方程中采用了论文 1（Parker 和 Lenhard，本期）的饱和压力 (S-P) 关系和流体截留参数模型，以便能够推导作为当前流体饱和度和饱和度历史函数的空气、水和石油相对渗透率的封闭式表达式。计算假设土壤的主要排水和吸入路径的三相 k-S 关系，以说明模型的使用并评估流体滞留对相对渗透率的影响程度。除高饱和度外，水渗透率-饱和度关系预计会表现出轻微的滞后效应，而透气率-饱和度关系中的滞后则更为明显。预测的石油渗透率滞后在低含水饱和度时较低，但随着含水饱和度的增加而变得相当明显。使用论文 1（Parker 和 Lenhard，本期）中的两种方法为沙土确定的模型参数，提出了假设的 NAPL 污染场景的 k-S-P 关系预测。结果表明，滞后和非润湿流体截留对 k-S-P 关系的影响可能相当大。发现对校准方法的敏感性相当小。
A theoretical model is described for the prediction of relative permeability-saturation (k-S) relations in two-phase (air-water) and three-phase (air-oil-water) porous media systems subject to arbitrary saturation paths. Integral expressions for air, water, and oil realtive permeabilities are presented which extend the nonhysteretic relative permeability model of Parker et al. (1987) to accomodate effects of pore blockage by air trapped in water and oil phases and oil trapped in the water phase. The parametric model for saturation-pressure (S-P) relations and fluid entrapment of paper 1 (Parker and Lenhard, this issue) is employed in the integral equations to enable derivation of closed-form expressions for air, water, and oil relative permeabilities as functions of current fluid saturations and saturation history. Three-phase k-S relations are calculated for main drainage and imbibition paths for a hypothetical soil to illustrate usage of the model and to evaluate the magnitude of fluid entrapment effects on relative permeabilities. Water permeability-saturation relations are predicted to exhibit mild hysteretic effects except at high saturations, while hysteresis in air permeability-saturation relations is much more pronounced. Predicted hysteresis in oil permeability is low at low water saturations but becomes quite marked as water saturation increases. Predictions of k-S-P relations for a hypothetical NAPL contamination scenario are presented using model parameters determined for a sandy soil by two methods in paper 1 (Parker and Lenhard, this issue). The results indicate that hysteresis and nonwetting fluid entrapment effects on k-S-P relations may be quite substantial. Sensitivity to calibration method is found to be rather small.