Development of Unit-Pore-Throat Ensemble Model for Deduction of Capillary Pressure-Saturation Relationships in Porous Media
Date Issued
2004
Date
2004
Author(s)
Cheng, Anne Ru
DOI
zh-TW
Abstract
本研究建立「單元孔頸系集模型」，要由實際土壤中的「水─空氣」的首次退水、主進水、以及二次退水的毛細壓力─飽和度實驗資料，不經由實驗，推估在相同土壤中任意二相流體對、包含掃描迴路在內的磁滯毛細壓力─飽和度曲線。研究方法，是假設土壤孔隙可比擬為許多大小不同、平行排列的單元孔頸聚合體，根據二相流在模型中的置換原則，由「水─空氣」的退水與進水毛細壓力─飽和度試驗資料，反演模型孔、頸元件大小的分布函數，建立可以替代土壤的水力等價模型；再由模型模擬其他二相流體對的毛細壓力─飽和度曲線。
在幾何型態上，「單元孔頸系集模型」具有與孔頸網絡模型類似的擴張與收縮的「孔─頸」結構；三角形頸管與正立方體頂角銜接的簡單幾何形狀，使得角隅濕潤相能夠相互連結，有利於未來計算單元孔頸傳導度。在力學機制上，「單元孔頸系集模型」是完全由微觀流體界面力學平衡原理，計算在某特定毛細壓力下，二流體相界面的形狀、位置、飽和度，以及流體界面幾何形狀與飽和度達到臨界狀態，發生置換的門檻毛細壓力條件。在正向分析上，「單元孔頸系集模型」可以模擬微觀墨水瓶效應與汲取過程中非濕潤相的入陷，實現巨觀上的磁滯現象，同時可以表現不同接觸角對於毛細壓力─飽和度曲線的影響。在逆向演算時，「單元」和「系集」的設計，避免網絡模型的尺寸效應和聯合機率密度問題，孔頸大小分布參數和退水、進水毛細壓力─飽和度曲線的連結關係較為直接。
利用退水和進水曲線的試驗資料，嘗試不同的「大頸管徑」－「孔徑╱大頸管徑比值」兩變數的聯合機率密度函數，歸納得兩變數為一對一對應分布即可得到良好的擬合結果的結論。正向演算證實本微模型基於幾何模型和物理原理，確實具有實現巨觀上磁滯現象以及表現不同接觸角對於毛細壓力─飽和度影響的能力。唯本模型無論在正向或逆向演算上均非常繁複，並且目前反演模型參數的理論仍是基於過度簡化的假設上，雖然可以得到容易解析的好處，但是也限制模式的表現和解釋能力，還待未來研究逐步改進。
This study establishes a Unit-Pore-Throat Ensemble Model (UPTEM). It mimics the soil pore structure by many pore-throat units of different sizes which are not connecting to one another. Methodologies are developed to estimate the parameters of size distributions of pores and throats. They utilize the water-air soil experiment data of capillary pressure (Pc) and saturation (s) during primary drainage, primary imbibition and secondary drainage processes. The objective is to make the UPTEM hydraulically equivalent to the actual water-air-soil system. Provided with the UPTEM parameters, the Pc-s scanning loops of water-NAPL two-phase fluids within the same soil can be inferred without doing the characteristic-curve experiments.
The equilateral triangle throats and cubic pore morphology of pore-throat units enable the UPTEM to simulate the ink-bottle effect. The simple geometry and interconnected pore-throat edges make easy the positioning of fluid-interface balanced with the capillary pressure using Laplace Equation, as well as calculating the critical position and capillary pressure for interface displacement. Knowing the interface position, conductivity in addition to wetting- and non-wetting-phase saturations can be computed. In direct problems, UPTEM can reproduce the hysteresis effect and quantify the trapping ratio on macro-scale. For the displacement criteria are derived from fluid mechanic principles and morphology of pore-throat units, UPTEM can demonstrate the effect of contact angle on characteristic curves explicitly. The ensemble design of pore-throat units avoids the difficulties caused by size effect and the need to estimate joint distribution of network pore-throats in inverse problems. For the same reason, the size distribution parameters are more directly linked to the Pc-s curves.
Fitting the drainage and imbibition Pc-s curves with UPTEM was tried with application of different ‘large-throat’ and ‘aspect ratio’ distribution types. It is shown that using a simple one-to-one relationship between the two variables, the model can match the data reasonably well. The drawbacks of the UPTEM model are tedious calculation and over-simplified parameter estimation methodologies. Future research is needed for further improvement.
Subjects
汲取接觸角
毛細壓力
排退
墨水瓶效應
單元孔頸
二相流
單元孔頸系集模型
磁滯效應
逆向問題
掃描迴路
capillary pressure
contact angle
pore-throat unit
two-phase flow
inverse problem
htsteresis effect
drainage
ink-bottle effect
scanning loops
imbibition
unit-pore-throat ensemble model
Type
thesis