Water Retention Models for Scale‐Variant and Scale‐Invariant Drainage of Mass Prefractal Porous Media

This research describes the development of water retention models incorporating the effects of partial drainage in random mass prefractal porous media. The pore‐size distribution, as well as the connectivity of pores, determines the drained pore volume as a function of suction. The concept of probability of drainage leads to a general scale‐variant drainage model (GM) in which the proportion of pores that drain at a given suction level is dependent on the fractal dimension of the drained pore phase, D d , and the proportion of pores that drain at the first suction level or air entry value. Two simplified cases of the general model are also presented. The first simplified model (simplified case 1 [SC1]) is a special case of the GM in which all of the largest pores drain completely at the first suction level. The second model (simplified case 2 [SC2]) is a scale‐invariant model in which the proportion of drained pores for each suction level remains constant and is obtained by setting D d equal to the mass fractal dimension, D of the porous medium. Fitting each model to numerically simulated drainage curves for random two‐dimensional prefractal porous media with known D values shows that the GM fitted the numerical data much better than either the SC1 or SC2 models, which were less flexible at high D values. Estimates of D d for the GM and SC1 models approached D when D was less than the critical value for percolation, that is, D c ∼1.716. Independent estimates of the probability of drainage indicate that the connectivity of water‐filled pores decreases as a result of the lower porosities associated with higher D values. A novel experimental protocol is suggested for testing these theoretical observations.