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We develop a rate-dependent network model that accounts for viscous forces by solving for the wetting and non-wetting phase pressure and which allows wetting layer swelling near an advancing flood front. The model incorporates a new time-dependent algorithm by accounting for partial filling of elements. We use the model to study the effects of capillary number, mobility ratio and contact angle distribution on waterflood displacement patterns, saturation and velocity profiles. By using large networks, generated from a new stochastic network algorithm, we reproduce Buckley-Leverett profiles directly from pore-scale modelling thereby providing a bridge between pore-scale and macro-scale transport.

A fast implementation of bilateral filtering is presented, which is based on an optimal expansion of the filter kernel into a sum of factorized terms. These terms are computed by minimizing the expansion error in the mean-square-error sense. This leads to a simple and elegant solution in terms of eigenvectors of a square matrix. In this way, the bilateral filter is applied through computing a few Gaussian convolutions, for which very efficient algorithms are readily available. Moreover, the expansion functions are optimized for the histogram of the input image, leading to improved accuracy. It is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions. Experimental validation is carried out in the context of digital rock imaging. Results on large 3D images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering.

Summary Networks of large pores connected by narrower throats (pore networks) are essential inputs into network models that are routinely used to predict transport properties from digital rock images. Extracting pore networks from microcomputed-tomography (micro-CT) images of rocks involves a number of steps: filtering, segmentation, skeletonization, and others. Because of the amount of clay and its distribution, the segmentation of micro-CT images is not trivial, and different algorithms exist for achieving this. Similarly, several methods are available for skeletonizing the segmented images and for extracting the pore networks. The nonuniqueness of these processes raises questions about the predictive power of network models. In the present work, we evaluate the effects of these processes on the computed petrophysical and multiphase-flow properties of reservoir-rock samples. By use of micro-CT images of reservoir sandstones, we first apply three different segmentation algorithms and assess the effects of the different algorithms on estimated porosity, amount of clay, and clay distribution. Single-phase properties are computed directly on the segmented images and compared with experimental data. Next, we extract skeletons from the segmented images by use of three different algorithms. On the pore networks generated from the different skeletons, we simulate two-phase oil/ water and three-phase gas/oil/water displacements by use of a quasistatic pore-network model. Analysis of the segmentation results shows differences in the amount of clay, in the total porosity, and in the computed singlephase properties. Simulated results show that there are differences in the network-predicted single-phase properties as well. However, predicted multiphase-transport properties from the different networks are in good agreement. This indicates that the topology of the pore space is well preserved in the extracted skeleton. Comparison of the computed capillary pressure and relative permeability curves for all networks with available experimental data shows good agreements. By use of a segmentation that captures porosity and microporosity, we show that the extracted networks can be used to reliably predict multiphase-transport properties, irrespective of the algorithms used.

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