Improving Fidelity of Network Models for Drainage and Imbibition

Abstract

Abstract Network models are a powerful method for extracting macroscopic multiphase properties from microscopic information. All network models of capillarity-controlled displacements (drainage/imbibition) require critical curvatures for pore level events as input. Techniques that ensure accurate critical curvatures in these models are therefore valuable. We describe a novel method to verify the correct choice of curvatures: a pore-by-pore comparison of displacement events predicted by a network model with those computed directly in the original pore space. The latter are obtained from LSMPQS, our implementation of the level set method for tracking fluid/fluid menisci in arbitrary confining geometry. We examine the robustness of a new, convenient criterion to estimate the critical curvature for imbibition events, derived from observing instances of Melrose's mechanistic criterion during LSMPQS simulations in about 200 individual pores. We validate the approach by comparing predictions from large, finite networks and infinite-acting networks to measured drainage/imbibition curves. A subset of a densely packed, disordered packing of spheres was used to test these concepts. More than 95% of the pores investigated have the same filled phase for network model and LSMPQS simulations at the drainage endpoint and more than 85% are the same at the imbibition endpoint. A smaller fraction (around 65%) matched in the vicinity of the percolation threshold, mainly because a small error in estimating critical curvatures in the network leads to a disproportionately large shift in the pressure-saturation curve. But the sequence of pore-filling events during drainage is very similar in the two cases. The new criterion for pore imbibition was also verified, as the imbibition curves for both simulations exhibit similar behavior, which in turn match experiments reported in the literature. The sequence of pore-filling events during imbibition differed for the network model and LSMPQS, however. This was primarily because the network model simulations did not account for coalescence of pendular rings. Capillary pressure curves from infinite acting network models showed the same percolation threshold as traditional estimates, but a larger saturation of displaced phase was obtained at the drainage/imbibition endpoints. The larger residual nonwetting phase saturation (Snwr) is consistent with estimates of residual saturation in reservoirs from tracer tests, indicating that lab-scale measurements of this quantity are influenced by boundary effects not present in the field.