Analytical solutions for two‐phase subsurface flow to a leaky fault considering vertical flow effects and fault properties

Abstract

Conductive faults in geologic formations can serve as leakage pathways for fluids such as CO 2 and methane, which would otherwise remain trapped beneath low-permeability layers. To estimate leakage rates and the associated pressure effects on adjacent aquifers, modeling of the flow in the vicinity of leaky faults must be performed. The flow from an aquifer to a leaky fault is controlled by aquifer properties as well as fault properties, including the fault permeability, fault width, and anisotropy in the fault permeability. Depending on aquifer properties and leakage rates, vertical flow equilibrium may not be reached in the aquifer in the vicinity of the leaky fault. Therefore, analytical solutions for leakage through faults that allow for vertical flow need to be developed. To do this, the vertically integrated form of the two-phase flow formulation based on vertical equilibrium is expanded by assuming a linearly structured vertical flow field, and steady state analytical solutions for single-phase and two-phase leakage are derived. In the case of twophase leakage, anisotropic aquifer permeabilities are shown to produce stronger vertical flow effects than in the case of single-phase leakage. Using numerical simulations, a model representing fault properties that is compatible with the analytical solutions is developed. The combination of the fault model and the analytical solutions captures the effects of leakage through faults with different properties and vertical flow effects. The incorporation of this fault model/analytical solution in larger basin-wide multiscale models can enable subgrid-scale effects due to leakage through faults to be captured with improved efficiency.

Status of CO2storage in deep saline aquifers with emphasis on modeling approaches and practical simulations

“…In terms of simplified models for fault flows, Kang et al . [] used an extension of the analysis of Nordbotten and Celia [] to derive local‐scale expressions for pressure drawdown and interface upconing around a leaky fault. Kang et al .…”

“…Kang et al . [] concluded that the properties and structure of the fault had to be included in the model for leakage, and provided a set of analytical solutions for two‐phase sharp‐interface flow in the formation with a model of the fault that was based on numerical simulations. Geochemical alterations of faults due to reactions with acidified brines have also been studied for faults, similarly to the studies for well cement degradation.…”

Identification of above-zone pressure perturbations caused by leakage from those induced by deformation

“…AZ's pressure change should be more sensitive to leakage because it should only correspond to leakage events (Meckel et al, 2013). Leakage-induced pressure changes in the IZ and AZ have been studied for CO2 storage in saline aquifers using both semi-analytical and numerical models (Birkholzer et al, 2009;Kang et al, 2014;Mathias et al, 2011;Mathias et al, 2009;Nordbotten et al, 2005;Pruess, 2011). CO2 leakage is preceded by brine leakage and the pressure change corresponding to this brine leakage can be evaluated analytically using single-phase models (Cihan et al, 2011;Nordbotten et al, 2004;Zeidouni, 2012Zeidouni, , 2014Zeidouni et al, 2011).…”

A methodology to detect and locate low-permeability faults to reduce the risk of inducing seismicity of fluid injection operations in deep saline formations

“…Though analytical solutions to estimate overpressure evolution in a homogeneous aquifers are more developed for water injection than for gas injection, several analytical solutions for twophase flow have been developed recently (e.g., Nordbotten et al, 2005;Dentz and Tartakovsky, 2009;Mathias et al, 2011;Houseworth, 2012;Vilarrasa et al, 2013a). These analytical solutions for infinite aquifers, and other solutions incorporating heterogeneities such as faults (Zeidouni, 2012;Kang et al, 2014) and compartmentalized aquifers (Zhou et al, 2008), may be incorporated in numerical solutions to speed up the calculations (Celia and Nordbotten, 2009). The performance of these solutions usually depends on the gravity number (gravity to viscous forces) (Vilarrasa et al, 2010), so this number should be evaluated to decide which solution is more appropriate in each case.…”