Modeling immiscible displacement in variable aperture fractures
2011 (English)Conference paper (Other academic)
In this work we present numerical simulations on drainage in fractures with synthetic aperture fields using two different models, a continuum model and an invasion percolation (IP) model. In the continuum model, two-phase flow mass conservation equations are solved on the two-dimensional fracture plane with the assumption of validity of Darcy’s law. Results from the continuum approach are compared to the IP model with trapping. The comparison shows that the continuum approach can reproduce IP model results at low capillary number conditions and, furthermore, can produce meaningful results also in the high capillary number regime where viscous forces cannot be ignored and IP models are not valid. The continuum model is also used to numerically construct capillary pressure-saturation relationships for the generated fractures. These upscaled relationships can be very well fitted to both the van Genuchten and the Brook-Corey model. We also use the continuum model to examine the effect of capillary number (injection rate) on the phase invasion. When the injection rate varies from low to high, results show that the invasion pattern changes from single dominant fingers to clusters with numerous tortuous fingers. This trend is comparable to results from previous experimental observations in the literature.
We also present a new approach – adaptive circle fitting (ACF) approach to account for in-plane interfacial curvatures for modeling quasi-static immiscible displacement in horizontal variable aperture fractures. The ACF approach involves nonlinear fitting of a circle equation to the local interfaces. The fitted radius from the circle equation is then used to calculate the in-plane curvature. The fitting residuals are used to adaptively choose the number of nearby interfacial sites that determine the in-plane curvature. We have applied the ACF approach to the IP model and performed numerical simulations against experimental data on drainage processes in two horizontal rough-walled fractures. The results show that the observed invasion phase structures can be very well reproduced in the numerical simulations.
Place, publisher, year, edition, pages
Earth and Related Environmental Sciences
IdentifiersURN: urn:nbn:se:uu:diva-185039OAI: oai:DiVA.org:uu-185039DiVA: diva2:570389
AGU Fall Meeting, San Francisco, California, USA, 2011