Two‐phase flow in rough‐walled fractures: Comparison of continuum and invasion‐percolation models

Abstract

[1] We present a systematic comparison study of simulating two-phase flow (drainage) in single heterogeneous fractures by using two fundamentally different approaches, namely, a continuum-based two-phase flow model and an invasion-percolation (IP) model. We analyze both gravity neutral and gravity destabilized cases. In the continuum model, the two-phase mass conservation equations for the 2-D fracture plane are solved, based on modifications to TOUGH2, a numerical simulator for multiphase and multicomponent flow and transport in geological media. A specific capillary pressure-liquid saturation function is used to account for the sudden drainage of a local aperture location in the fracture once its local aperture-dependent nonwetting phase fluid entry pressure is exceeded. Results from the continuum model are compared to those from an IP model that includes trapping. We consider cases where the contribution of aperture-induced curvature in the capillary pressure term dominates over that of the in-plane curvature. The comparison shows that the presented continuum model can well reproduce the IP model results at low-capillarynumber conditions and furthermore can also produce meaningful results in the highcapillary-number regimes where IP models are not valid. Taking into account the viscous forces in the fluid displacement process, the continuum model is used to examine the effect of capillary number (reflecting the injection rate) on the phase invasion. When the injection rate varies from low to high, simulations using the continuum model show that the invasion pattern changes from single dominant fingers to more homogeneous spreading and/or clusters with numerous tortuous fingers. This trend is comparable to results from previous experimental observations in the literature. The continuum model is also used to numerically construct the upscaled (fracture-scale) capillary pressure-saturation relationship. The upscaled relationship can be well fitted to the van Genuchten and the Brooks-Corey porous-medium-type models. Fracture capillary behavior depends on the aperture field heterogeneity. Simulation results indicate that increasing the aperture standard deviation leads to smaller entry pressure and larger residual water saturation.Citation: Yang, Z., A. Niemi, F. Fagerlund, and T. Illangasekare (2013), Two-phase flow in rough-walled fractures: Comparison of continuum and invasion-percolation models, Water Resour. Res., 49,

Modeling of Two-Phase Flow in Rough-Walled Fracture Using Level Set Method

“…where is capillary pressure (Pa), the pressure in the NAPL (Pa), the pressure in aqueous phase liquid (Pa), Figure 2: Capillary pressure-saturation relationship at the local position in a single fracture ( is water saturation and wr the residual wetting phase saturation) [10,24]. the interfacial force (N/m), the contact angle of the two-phase fluid interface with the fracture wall (rad), and the average radius of curvature in the single rough-walled fracture (m).…”

“…To describe the process in which the NAPL displaces the aqueous phase liquid, a specific capillary pressure-saturation curve ( Figure 2) at the local position of the fracture was proposed [10,24]. At this local position for a single fracture, the NAPL entry pressure can be calculated:…”

Modeling of Fluid Intrusion Into Porous Media With Mixed Wettabilities Using Pore-Network

“…One of the methodologies that estimate soil's properties is based on the porenetwork model, which treats a pore space in a porous medium as an assemblage of pore segments and incorporates pore-level mechanisms like capillary phenomena. Since the network model for porous media was firstly proposed by Fatt [1], the pore-network approach has been applied in many disciplines, such as the petroleum engineering [2]- [4], the hydrology and soil physics [5]- [9]. Through a series of works, the structure and generation methods of pore-networks, and the algorithms for transport of fluids have evolved by new findings and the development of high-spec apparatuses [10]- [12].…”

“…For two-phase immiscible displacements governed by capillary effects in a pore-network, a special version of the percolation theory known as the invasion percolation is often applied [6]- [9]. The invasion percolation originally proposed by Wilkinson and Willemsen [3] is a dynamic percolation process, and accessibility rule is imposed for movement of interfaces between invading and defending fluids.…”

A Fast Algorithm for Invasion Percolation

“…Given that there are many ways to implement a binary tree, our purpose here is to provide the details of a fast IP algorithm. A search through the recent literature (e.g., Yang et al 2013;Chen et al 2012;Pesheva et al 2010) shows that standard IP with O(MN) execution times is still the norm. To the best of our knowledge, details of an O(M log M) IP algorithm have never been given.…”