Vertically averaged equations with variable density for CO2 flow in porous media

Carbon capture and storage has been proposed as a viable option to reduce CO 2 emissions. Geological storage of CO 2 where the gas is injected into geological formations for practically indefinite storage, is an integral part of this strategy. Mathematical models and numerical simulations are important tools to better understand the processes taking place underground during and after injection. Due to the very large spatial and temporal scales involved, commercial 3D-based simulators for the petroleum industry quickly become impractical for answering questions related to the long-term fate of injected CO 2 . There is an interest in developing simplified modeling tools that are effective for this type of problem. One approach investigated in recent years is the use of upscaled models based on the assumption of vertical equilibrium (VE). Under this assumption, the simulation problem is essentially reduced from 3D to 2D, allowing much larger models to be considered at the same computational cost. So far, most work on VE models for CO 2 storage has either assumed incompressible CO 2 or only permitted lateral variations in CO 2 density (semi-compressible). In the present work, we propose a way to fully include variable CO 2 density within the VE framework, making it possible to also model vertical density changes. We derive the fine-scale and upscaled equations involved and investigate the resulting effects. In addition, we compare incompressible, semi-compressible, and fully compressible CO 2 flow for some model scenarios, using an in-house, fully-implicit numerical code based on automatic differentiation, implemented using the MATLAB reservoir simulation toolkit

A Finite-Volume-Based Module for Unsaturated Poroelasticity

In this chapter, we present fv-unsat, a multipoint finite-volume–based solver for unsaturated flow in deformable and nondeformable porous media. The latter is described using the mixed form of Richards’ equation, whereas the former by the equations of unsaturated poroelasticity. The module aims at flexibility, relying heavily on discrete operators and equations, exploiting the automatic differentiation framework provided by the MATLAB Reservoir Simulation Toolbox (MRST). Our examples cover two numerical convergence tests and two three-dimensional practical applications, including the water infiltration process in a nondeformable soil column and a realistic desiccation process of a deformable clay sample using atmospheric boundary conditions. The resulting convergence rates are in agreement with previously reported rates for single-phase models, and the practical applications capture the physical processes accurately.publishedVersio

Upscaled modeling of CO2 injection and migration with coupled thermal processes

A practical modeling approach for CO2 storage over relatively large length and time scales is the vertical-equilibrium model, which solves partially integrated conservation equations for flow in two lateral dimensions. We couple heat transfer within the vertical equilibrium framework for fluid flow, focusing on thermal processes that most impact the CO2 plume. We investigate a simplified representation of heat exchange that also includes transport of heat within the plume. In addition, we explore available CO2 thermodynamic models for reliable prediction of density under different injection pressures and temperatures. The model concept is demonstrated on simplified systems.publishedVersio

Wellbore Permeability Estimates from Vertical Interference Testing of Existing Wells

AbstractWellbore integrity is considered an important risk factor for leakage of CO2 and formation fluids out of geological CO2 storage sites. Quantifying the effective hydraulic parameters that control vertical migration of fluids along the wellbore involves data collection through numerous field and laboratory experiments. The vertical interference test (VIT) is a downhole test designed to measure hydraulic communication of the outside-of-casing wellbore barrier system over a selected well section. Results from these tests can be analyzed numerically to determine the average permeability of the section. Several field surveys of existing wells have resulted in 9 VIT datasets, of which three are presented here. The effective permeability estimates for the three tests span two orders of magnitude, from approximately 1 mD to more than 100 mD. When compared with companion sidewall core analyses of the cement matrix that have permeabilities in the microD range, the VIT data suggest that interfaces or defects in the cement sheath are responsible for flow. Initial analysis of the remaining 6 datasets suggests an even larger range in effective permeability values, as low as microD to more than 1 D, indicating that well permeability can be highly variable from well to well and that high values of permeability are possible. These data provide important insights into realistic wellbore integrity of typical wells in N. America, and help us constrain models for understanding and mitigating risk of leakage during CO2 storage operations

Modeling of relative permeabilities including dynamic wettability transition zones

Wettability is a pore-scale property that impacts the relative movement and distribution of fluids in a porous medium. There are reservoir fluids that provoke the surface within pores to undergo a wettability change. This wettability change, in turn, alters the dynamics of relative permeabilities at the Darcy scale. Thus, modeling the impact of wettability change in relative permeabilities is essential to understand fluids interaction in porous media. In this study, we include time-dependent wettability change into the relative permeability--saturation relation by modifying the existing relative permeability function. To do so, we assume the wettability change is represented by the sorption-based model that is exposure time and chemistry dependent. This pore-scale model is then coupled with a triangular bundle-of-tubes model to simulate exposure time-dependent relative permeabilities data. The simulated data is used to characterize and quantify the wettability dynamics in the relative permeability--saturation curves. This study further shows the importance of accurate prediction of the relative permeability in a dynamically altering porous medium

Numerical studies of long-term wettability alteration effects in CO2 storage applications

The wettability of the rock surface in porous media has an effect on the constitutive saturation functions that govern capillary pressure and relative permeability. The term wettability alteration refers to the change of this property over time by processes such as CO2 interactions with the rock. In this work, we perform numerical simulations considering a two-phase two-component flow model including time-dependent wettability alteration in a two-dimensional aquifer-caprock system using the open porous media framework. Particularly, we study the spatial distribution over time of injected CO2 into the aquifer neglecting and including wettability alteration effects. The numerical simulations show that wettability alteration on the caprock results in a loss of containment; however, the CO2 front into the caprock advances very slow since the unexposed caprock along the vertical migration path also needs to be changed by the slow wettability alteration process. The simulations also show that wettability alteration on the aquifer results in an enhancement of storage efficiency; this since the CO2 front migrates more slowly and the capillary entry pressure decreases after wettability alteration.acceptedVersio