Applicability of vertically integrated models for carbon storage modeling in heterogeneous domains

Numerical modeling is an essential tool for studying the impacts of geologic carbon storage (GCS). Injection of carbon dioxide (CO2) into deep saline aquifers leads to multi-phase flow (injected CO2 and resident brine), which can be described by a set of three-dimensional governing equations, including mass-balance equation, volumetric flux equations (modified Darcy), and constitutive equations. This is the modeling approach on which commonly used reservoir simulators such as TOUGH2 are based. Due to the large density difference between CO2 and brine, GCS models can often be simplified by assuming buoyant segregation and integrating the three-dimensional governing equations in the vertical direction. The integration leads to a set of two-dimensional equations coupled with reconstruction operators for vertical profiles of saturation and pressure. Vertically-integrated approaches have been shown to give results of comparable quality as three-dimensional reservoir simulators when applied to realistic CO2 injection sites such as the upper sand wedge at the Sleipner site. However, vertically-integrated approaches usually rely on homogeneous properties over the thickness of a geologic layer. Here, we investigate the impact of general (vertical and horizontal) heterogeneity in intrinsic permeability, relative permeability functions, and capillary pressure functions. We consider formations involving complex fluvial deposition environments and compare the performance of vertically-integrated models to full three-dimensional models for a set of hypothetical test cases consisting of high permeability channels (streams) embedded in a low permeability background (floodplains). The domains are randomly generated assuming that stream channels can be represented by sinusoidal waves in the plan-view and by parabolas for the streams' cross-sections. Stream parameters such as width, thickness and wavelength are based on values found at the Ketzin site in Germany. Analysis of the computational results allows us to identify the limits of applicability of vertically integrated models for CO2 sequestration.