Vertically integrated models for coupled two‐phase flow and geomechanics in porous media

Abstract

Models of reduced dimensionality have been found to be particularly attractive in simulating the fate of injected CO 2 in supercritical state in the context of carbon capture and storage. This is motivated by the confluence of three aspects: the strong buoyant segregation of the lighter CO 2 phase above water, the relatively long time scales associated with storage, and finally the large aspect ratios that characterize the geometry of typical storage aquifers. However, to date, these models have been confined to considering only the flow problem, as the coupling between reduced dimensionality models for flow and models for geomechanical response has previously not been developed. Herein, we develop a fully coupled, reduced dimension, model for multiphase flow and geomechanics. It is characterized by the aquifer(s) being of lower dimension(s), while the surrounding overburden and underburden being of full dimension. The model allows for general constitutive functions for fluid flow (relative permeability and capillary pressure) and uses the standard Biot coupling between the flow and mechanical equations. The coupled model retains all the simplicities of reduced-dimensional models for flow, including less stiff nonlinear systems of equations (since the upscaled constitutive functions are closer to linear), longer time steps (since the high grid resolution in the vertical direction can be avoided), and less degrees of freedom. We illustrate the applicability of the new coupled model through both a validation study and a practical computational example.

Stable mixed finite elements for linear elasticity with thin inclusions

“…While our derivation is different, our mixed-dimensional equations coincide in the case of a single thin inclusion with the elastic equations derived in [7]. In that work, significant effort was placed into model verification, including comparison to fixed-dimensional models.…”

“…The governing equations on this manifold can be derived using vertical integration [22]; see e.g. [7] for an application regarding CO 2 storage.…”

Fast Evaluation of Fluid-rock Coupling in CO2 Storage

“…The VE assumption was found to be valid in the limit of large R 2 L . In a validation model presented by Bjørnarå et al [25] based on realistic CO 2 storage conditions at In Salah, Algeria, it was found that it holds even for reservoir thickness H up to at least 100 meters. The VEassumption implies further that since the pressure is in vertical equilibrium, then so is the phase distribution, or saturation.…”

Modelling Geomechanical Impact of CO2 Injection and Migration Using Precomputed Response Functions

“…Over time, the capabilities of such tools have been expanded to account for a considerable range of physical phenomena [27,16,17,26,1]. However, reduced models that properly account for the twoway coupling between fluid flow and rock mechanics have so far received less attention, although recent work in this field includes the linear vertical deflection model of [5].…”

“…At the theoretical level, the poromechanical framework has been used to investigate the risk of fracturing or fault slip caused by elevated pressure and reduced effective stress [34,32,6], and assess the risk of induced seismicity [7]. A reduced model for coupled flow and geomechanics, adapted to the case of CO 2 storage, was proposed by [5], whereas [9] situates geomechanics within a comprehensive modeling framework for CO 2 storage, where different physical processes are modeled depending on the spatial and temporal scale. Specific case-studies involving CO 2 injection and geomechanical impacts include Ketzin [29], In-Salah [35,30,4], Vedsted [39] and the CO2CRC Otway Project [2].…”