Verifying Pore Network Models of Imbibition in Rocks Using Time‐Resolved Synchrotron Imaging

Abstract

At the pore scale, slow invasion of a wetting fluid in porous materials is often modeled with quasi‐static approximations which only consider capillary forces in the form of simple pore‐filling rules. The appropriateness of this approximation, often applied in pore network models, is contested in the literature, reflecting the difficulty of predicting imbibition relative permeability with these models. However, validation by sole comparison to continuum‐scale experiments is prone to induce model overfitting. It has therefore remained unclear whether difficulties generalizing the model performance are caused by errors in the predicted filling sequence or by subsequent calculations. Here, we address this by examining whether such a model can predict the pore‐scale fluid distributions underlying the behavior at the continuum scale. To this end, we compare the fluid arrangement evolution measured in fast synchrotron micro‐CT experiments on two rock types to quasi‐static simulations which implement capillary‐dominated pore filling and snap‐off, including a sophisticated model for cooperative pore filling. The results indicate that such pore network models can, in principle, predict fluid distributions accurately enough to estimate upscaled flow properties of strongly wetted rocks at low capillary numbers.

Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks

“…Displacement proceeds in order of capillary pressure, computed semianalytically, based on the geometry of an element and its contact angle, by snap-off, pistonlike advance and cooperative pore filling. Here we use the modification proposed by Bultreys et al [32] to obtain the initial condition for waterflooding: fluid occupancy at the end of drainage, the beginning of the waterflood, is taken directly from the micro-CT image.…”

“…The geometric inputs into the model are all determined from segmented images of the pore and grain from the experiments: these were obtained from high-quality images of the dry rock before flooding [32]. These inputs are the inscribed radii of pores and throats, the elements that they connect to, and the shape of the cross section.…”

“…In recent years, several studies have sought to validate image-based models against experimental micro-computedtomography (micro-CT) results including pore scale fluid distribution and topology [21,28,[30][31][32][33][34]. Akai et al [30] simulated an unsteady-state waterflooding experiment on a mixedwet carbonate rock using the lattice Boltzmann method incorporating locally measured contact angles [35].…”

“…This work demonstrated that a distribution of contact angle (rather than a uniform value) needs to be used as a model input to characterize wettability; however, the contact angle distribution had to be adjusted to obtain a good match to experiment. Bultreys et al [21,32] used an image-based pore network model to compare against steady-state waterflood measurements in water-wet Bentheimer sandstone. They proposed a workflow that is based on mapping the fluid distribution from an experimental image to the extracted network model.…”

“…Moreover, another challenge is to have a model that can be predictive for a range of wettability states. These image-based modeling studies [21,28,32] were all performed for water-wet samples. However, mixed-wet behavior is expected to have an even higher level of uncertainty [9,36].…”