Tore Ingvald Bjørnarå

A pseudospectral approach to the McWhorter and Sunada equation for two-phase flow in porous media with capillary pressure

Two well-known mathematical solutions for two-phase flow in porous media are the Buckley–Leverett equation and the McWhorter and Sunada equation (MSE). The former ignores capillary pressure and can be solved analytically. The latter has traditionally been formulated as an iterative integral solution, which suffers from convergence problems as the injection saturation approaches unity. Here, an alternative approach is presented that solves the MSE using a pseudospectral Chebyshev differentiation matrix. The resulting pseudospectral solution is compared to results obtained from the original integral implementation and the Buckley–Leverett limit, when the capillary pressure becomes negligible. A self-contained MATLAB code to implement the new solution is provided within the manuscript. The new approach offers a robust and accurate method for verification of numerical codes solving two-phase flow with capillary pressure.

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

Models of reduced dimensionality have been found to be particularly attractive in simulating the fate of injected CO2 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 CO2 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.

Fast Evaluation of Fluid-rock Coupling in CO2 Storage

Modelling plays an important role in providing capacity estimates and analysing injectivity, long-term safety and risk factors for future storage sites. Hundreds and thousands of potential sites will have to be screened for suitability before more detailed studies are done. In this context, fast yet reliable methods will have to be developed involving simplified models but without losing too much of the accuracy. One key parameter for choosing a storage site is the injectivity; how fast can the CO2 be injected. The basics of hydro-mechanical modelling is explained and a conceptual model for single-phase fluid flow is defined. Various levels of complexity of the governing equations are derived, by considering standard methods and using constant and non-linear hydro-mechanical properties these models are compared. Results show that well defined input data makes the coupling to the geomechanical processes redundant, resulting in considerable savings in computational effort to get reliable and accurate estimates of injection pressure.