Spontaneous imbibition of wetting liquids in porous media is a ubiquitous natural phenomenon which has received much attention in a wide variety of fields over several decades. Many traditional and recently presented capillary-driven flow models are derived based on Hagen-Poiseuille (H-P) flow in cylindrical capillaries. However, some limitations of these models have motivated modifications by taking into account different geometrical factors. In this work, a more generalized spontaneous imbibition model is developed by considering the different sizes and shapes of pores, the tortuosity of imbibition streamlines in random porous media, and the initial wetting-phase saturation. The interrelationships of accumulated imbibition weight, imbibition rate and gas recovery and the properties of the porous media, wetting liquids, and their interactions are derived analytically. A theoretical analysis and comparison denote that the presented equations can generalize several traditional and newly developed models from the literature. The proposed model was evaluated using previously published data for spontaneous imbibition measured in various natural and engineered materials including different rock types, fibrous materials, and silica glass. The test results show that the generalized model can be used to characterize the spontaneous imbibition behavior of many different porous media and that pore shape cannot always be assumed to be cylindrical.

Carbon dioxide (CO2) is the major contributor to greenhouse gas (GHG) emissions and the main driver of climate change. Currently, CO2 utilization is increasingly attracting interest in processes like enhanced oil recovery and coal bed methane and it has the potential to be

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2The spontaneous imbibition of water and other liquids into gas-filled 3 fractures in variably-saturated porous media is important in a variety of 4 engineering and geological contexts. However, surprisingly few studies have 5 investigated this phenomenon. We present a theoretical framework for 6 predicting the 1-dimensional movement of water into air-filled fractures 7 within a porous medium based on early-time capillary dynamics and 8 spreading over the rough surfaces of fracture faces. The theory permits 9 estimation of sorptivity values for the matrix and fracture zone, as well as a 10 dispersion parameter which quantifies the extent of spreading of the wetting 11 front. Quantitative data on spontaneous imbibition of water in unsaturated 12 Berea sandstone cores were acquired to evaluate the proposed model. The 13 cores with different permeability classes ranging from 50 to 500 mD and 14 were fractured using the Brazilian method. Spontaneous imbibition in the 15 fractured cores was measured by dynamic neutron radiography at the 16 Neutron Imaging Prototype Facility (beam line CG-1D, HFIR), Oak Ridge 17 National Laboratory. Water uptake into both the matrix and the fracture 18 zone exhibited square-root-of-time behavior. The matrix sorptivities ranged 19 from 2.9 to 4.6 mm s -0.5 , and increased linearly as the permeability class 20 increased. The sorptivities of the fracture zones ranged from 17.9 to 27.1 21 mm s -0.5 , and increased linearly with increasing fracture aperture width. The 22 dispersion coefficients ranged from 23.7 to 66.7 mm 2 s -1 and increased 23 linearly with increasing fracture aperture width and damage zone width. 24 Both theory and observations indicate that fractures can significantly 25 increase spontaneous imbibition in unsaturated sedimentary rock by 26 capillary action and surface spreading on rough fracture faces. Fractures 27 also inrease the dispersion of the wetting front. Further research is needed 28 7

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Fracture network and fractured porous media as well as their transport properties have received great attentions in many fields from engineering application and basic theoretical researches. Fracture will dynamically extend in length and aperture to form complex fracture network under some external conditions such as percussion drilling, wave propagation, desiccation and hydrofracturing. The complexity of fracture network can be well quantitatively characterized by fractal dimension. In this work, the dynamic characterization of fracture network extension in porous media under drying process is measured by the improved box-counting technique, and fractal dimensions of fracture network are respectively related to drying time, average aperture, moisture content and fracture porosity. The fractal dimension increases exponentially with drying time and average aperture, and decreases with moisture content in the form of power law. Specially, the fractal dimension is approximatively increased with porosity in the form of linearity in a narrow porosity range. The transport capacity of fracture network, described by seepage coefficient, is also related to the fractal dimension with drying time in the form of exponential function. The presented fractal analysis of fracture network could also shed light on the hydrofracturing application in subsurface unconventional oil and gas reservoirs.

Archie's equation is an empirical electrical conductivity‐porosity model that has been used to predict the formation factor of porous rock for more than 70 years. However, the physical interpretation of its parameters, e.g., the cementation exponent m, remains questionable. In this study, a theoretical electrical conductivity equation is derived based on the fractal characteristics of porous media. The proposed model is expressed in terms of the tortuosity fractal dimension (DT), the pore fractal dimension (Df), the electrical conductivity of the pore liquid, and the porosity. The empirical parameter m is then determined from physically based parameters, such as DT and Df. Furthermore, a distinct interrelationship between DT and Df is obtained. We find a reasonably good match between the predicted formation factor by our model and experimental data.