Deduction of Wetting Phase Fluid Unsaturated Hydraulic Conductivity Based on Unit-Pore-Throat Ensemble Model Framework
Date Issued
2006
Date
2006
Author(s)
Feng, Chih-Yung
DOI
zh-TW
Abstract
Based on the framework of hydraulic equivalent Unit-Pore-Throat Ensemble Model (UPTEM), this study proposed an approach to qualitatively analyze the wetting phase fluid unsaturated hydraulic conductivity for a two-phase flow system. In order to take the contact angle and the rheology of fluid interface into consideration, the method is composed of the following three issues:
1. According to the capillary pressure thresholds, design a set of proto-Pore-Throat-Units (proto-PTUs) comprised all the possible mechanisms of fluid displacement within a pore-throat unit (PTU).
2. Given several capillary pressures, numerically simulate the static equilibrium capillary surfaces within each proto-PTU and analyze the Laminar flow of the wetting phase fluid to calculate the conductance.
3. Based on the hydraulic equivalent UPTEM, ensemble the proto-PTUs to analyze the unsaturated hydraulic conductivity.
Although the PTU provides the elements of cube and equilateral triangular prism to depict the characteristics of the real soil pore structure better, the static equilibrium capillary surface cannot be described with the analytical geometry shapes due to the geometrical singular points. The shape of static equilibrium capillary surfaces within a PTU can be simulated numerically with the aid of Surface Evolver. The Surface Evolver is an interactive program that minimizes the energy of a surface subject to constraints, such as prescribed fluid volume and contact angle on the walls. According to the Surface Evolver graphical output, this study verified the critical conditions and the capillary pressure thresholds of 2 immiscible fluids displacement mechanisms within a PTU. The results revealed that the threshold of piston-type motion occurred at the intersection of cubic pore and equilateral triangular prism should be modified. Moreover, there should be another displacement mechanism, which snaps off the non-wetting phase in the pore body due to the thickening of wetting phase fluid.
For contact angle , the study designed 25 proto-PTUs and applied the no-stress boundary condition on the fluid interface to simulate the flow field. With the criteria of Reynolds number less than 0.1, the Laminar flow field of wetting phase fluid are analyzed and the variation of conductance are fitted. Results show that the function of conductance and dimensionless area of capillary surface is the exponential type for the none-full-throat configuration; meanwhile, it could be the exponential type, power type or exponential semi-variogram type for the one-full-throat configuration depends on the throat size ratio. Furthermore, the conductance in drainage process is larger than the one in imbibition process for a given capillary pressure due to the change of the fluid configuration.
To analyze the unsaturated hydraulic conductivity of a virtual wetting phase fluid based on the hydraulic equivalent UPTEM, which is deducted from the water-air soil column infiltration experiment, the study ensemble the 25 proto-PTUs by two ways and both can qualitatively depict the hysteresis phenomena. The first way employed the linear programming scheme to calculate the probability of each proto-PTU. Because the relation between probability and throat size deviated from the one of hydraulic equivalent UPTEM significantly, it overestimated the expected total pore volume, and therefore, the unsaturated hydraulic conductivity. On the other hand, the second way categorized the hydraulic equivalent UPTEM into 25 proto-PTUs based on the aspect ratio and the throat size ratio. It successfully revealed the reduction of unsaturated hydraulic conductivity due to non-wetting phase trapped during the imbibition process and simulated the scanning loops well.
Subjects
土壤水力特性函數
孔頸單元系集模型
傳導度
水力傳導係數
磁滯現象
掃瞄迴圈
soil characteristic curves
unit-pore-throat ensemble model
conductance
hydraulic conductivity
hysteresis
scanning loops
Type
thesis