Flow Path Selection During Capillary Rise in Rock: Effects of Pore Branching and Pore Radius Variation
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Flow Path Selection During Capillary Rise in Rock: Effects of Pore Branching and Pore Radius Variation Tadashi Yokoyama1 · Masashi Yorimoto2 · Naoki Nishiyama3 Received: 22 April 2020 / Accepted: 2 September 2020 / Published online: 15 September 2020 © Springer Nature B.V. 2020
Abstract New and existing results of capillary rise experiments on five sandstones and a limestone differing in pore radius distribution were analyzed. Fitting of Lucas–Washburn equation (square of capillary rise height is linearly correlated with time and effective pore radius) showed that the effective pore radius notably smaller than the realistic pore radii in the rock needs to be used to reproduce the measured capillary rise rate. We interpreted the result using a capillary rise model in which the effect of pore branching is combined with a conventional pore radius variation model. The model is outlined as follows: (1) select three representative pore radii from measured pore radius distribution, (2) evaluate the direction at which water proceeds at the branch point of narrow pore and wide pore, (3) calculate an effective pore radius in consideration of the variation of flow path radius. The most important step is the selection of representative pore radii, the way was unknown in our previous research in which the concept of the model was first introduced. We analyzed pore radius distributions of six rocks and derived clear selection criteria of three pore radii that are commonly applicable to the rocks. The model calculations show that the majority of experimental data are explained by the advance of water toward narrow pore at the branch point and that the effective pore radius determined experimentally is successfully predicted by the model. The model is now available for predicting the rate of capillary rise of water in various porous media. Keywords Capillary rise · Meniscus · Pore radius distribution · Sandstone List of Symbols A Cross-sectional area of the rock core (length2) α Geometry correction factor of the cross section of capillary flow path (dimensionless) dgrain Average grain diameter (length) * Tadashi Yokoyama t‑yokoyama@hiroshima‑u.ac.jp 1
Graduate School of Advanced Science and Engineering, Hiroshima University, 1‑7‑1 Kagamiyama, Higashi‑Hiroshima, Hiroshima, Japan
2
Furukawa Mfg. Co., Ltd., 200‑65, Obara, Nutanishi‑cho, Mihara, Hiroshima, Japan
3
Graduate School of Life and Environmental Sciences, University of Tsukuba, 1‑1‑1 Tennodai, Tsukuba, Ibaraki, Japan
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fcum Cumulative pore volume ratio (dimensionless) ϕopen Porosity of open pore (dimensionless) ϕtra Porosity of transport pore (dimensionless) g Acceleration of gravity (9.80 m2 s−1) γ Surface tension of water–air interface (mass time−2, N m−1) k Permeability (length2) χ Volumetric water content (dimensionless) χres Residual water content (dimensionless) χsat Water content at saturated condition (dimensionless) l1 Length of narrow portion of the tube in Fig. 1b (length) l2 Length of wide
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