New model for estimating geometric tortuosity of variably saturated porous media using 3D synchrotron microcomputed tomography imaging

Tortuosity has a significant impact on flow and transport characteristics of porous media and plays a major role in many applications such as enhanced oil recovery, contaminant transport in aquifers, and fuel cells. Most analytical and theoretical models for determining tortuosity have been developed for ideal systems with assumptions that might not be representative of natural porous media. In this paper, geometric tortuosity was directly determined from three-dimensional (3D) tomography images of natural unconsolidated sand packs with a wide range of porosity, saturation, grain size distribution, and morphology. One hundred and thirty natural unconsolidated sand packs were imaged using 3D monochromatic and pink-beam synchrotron microcomputed tomography imaging. Geometric tortuosity was directly determined from the 3D images using the centroids of the connected paths in the flow direction of the media, and multivariate nonlinear regression analysis was adopted to develop a simple practical model to predict tortuosity of variably saturated natural unconsolidated porous media. Wetting phase saturation was found to provide a good estimate of relative tortuosity with an $R2$ value of .93, even with a porosity variation between 0.3 and 0.5 of the porous media systems. The proposed regression model was compared to theoretical and analytical models available in the literature and was found to provide better estimates of geometric tortuosity with an $R2$ value of .9 and a RMSE value of 0.117.