An XFEM Model for Carbon Sequestration†

International Journal for Numerical Methods in Engineering, 2014

A two-phase flow eXtended Finite Element Method (XFEM) model is presented to analyse the injection and sequestration of carbon dioxide (CO 2) in deep saline aquifers. XFEM is introduced to accurately approximate near-injection well pressure behaviour with elements significantly larger than the injection well diameter. We present a vertically averaged multiphase flow model that combines XFEM to approximate the pressure field, with a Streamline Upwind/Finite Element Method/Finite Difference Method (SU-FEM-FDM) to approximate the distribution of CO 2 in the aquifer. Near-well enrichment functions are presented along with the solution procedure for the coupled problem. Two examples are presented: in the first, CO 2 injection into a perfectly horizontal aquifer is modelled with both XFEM and FEM-based methods. The results suggest that XFEM is able to provide low relative errors in the pressure near the well at a reduced computational cost compared with FEM. The impact and selection of the stabilization coefficient of the SU-FEM-FDM is also discussed. In the second example, the XFEM and SU-FEM-FDM model is applied to a more realistic problem of an inclined aquifer to demonstrate the ability of the model to capture the buoyancy-driven migration of CO 2 in a deep saline aquifer.

2016

Carbon sequestration in deep saline aquifers has been proposed for long term storage of CO2 as an alternative to the release of CO2 into the atmosphere. In this thesis a computationally efficient numerical model that describes the physics of CO2 injection into deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two coupled, non-linear partial differential equations a pressure equation and a saturation equation. The numerical formulation is based on sequentially coupled Finite Element Methods (FEMs). The Finite Difference Method (FDM) is used to discretize in time. The saturation equation is a nonlinear advective equation for which the application of Galerkin Finite Element Method (FEM) can lead to non-physical oscillations in the solution. Several stabilized methods are considered to control the oscillations that occur as a by-product of the approximation of the saturation equation. Th...

2017

A major cause of the attenuation levels observed in seismic data from sedimentary regions is the mesoscopic loss mechanism, caused by heterogeneities in the rock and fluid properties greater than the pore size but much smaller than the wavelengths of the fast compressional and shear waves. The main objective of this paper is to apply a numerical upscaling method to determine the plane wave complex modulus of a viscoelastic solid long-wave equivalent to a fluid saturated poroelastic (Biot’s medium) with mesoscopic-scale heterogeneities in the form of brine-CO2 patches. This is achieved by applying time-harmonic compressibility tests at a selected set of frequencies to a representative sample of bulk material. These tests are modeled as boundary value problems stated in the space-frequency domain. This numerical upscaling approach was applied using data from the CO2 sequestration Sleipner-field case. A numerical flow simulator to represent the CO2 injection and storage was combined wi...

2015

We describe the development of a compositional reservoir simulator capable of modeling multiphase transport of CO2 in brine aquifers. As an example we consider the radial injection of supercritical CO2 in a brine aquifer, and results are provided which illustrate the evolution of a 2-phase fluid system in which the injected CO2 resides in a dense supercritical phase and also dissolves into the liquid phase. Salt precipitation into a solid phase is found to occur close to the injection well where the gas phase dominates.

Greenhouse Gas Control Technologies 7, 2005

We describe the development of a compositional reservoir simulator capable of modeling multiphase transport of CO 2 in brine aquifers. As an example we consider the radial injection of supercritical CO 2 in a brine aquifer, and results are provided which illustrate the evolution of a 2-phase fluid system in which the injected CO 2 resides in a dense supercritical phase and also dissolves into the liquid phase. Salt precipitation into a solid phase is found to occur close to the injection well where the gas phase dominates.

International Journal for Numerical Methods in Engineering, 2017

A computationally efficient numerical model that describes carbon sequestration in deep saline aquifers is presented. The model is based on the multiphase flow and vertically averaged mass balance equations, requiring the solution of two partial differential equations-a pressure equation and a saturation equation. The saturation equation is a non-linear advective equation for which the application of Galerkin Finite Element Method (FEM) can lead to non-physical oscillations in the solution. In this article we extend three stabilized FEM formulations, which were developed for uncoupled systems, to the governing non-linear coupled PDEs. The methods developed are based on the Streamline Upwind (SU), the Streamline Upwind / Petrov-Galerkin (SUPG), and the Least Squares Finite Element Method (LSFEM). Two sequential solution schemes are developed: a single step (SS) and a predictor-corrector (PC). The range of Courant numbers yielding smooth and oscillation-free solutions is investigated for each method. The useful range of Courant numbers found depends upon both the sequential scheme (SS vs PC) and also the time integration method used (Forward Euler, Backward Euler, or Crank-Nicolson). For complex problems such as when two plumes meet, only the SU stabilization with an amplified stabilization parameter gives satisfactory results when large time steps are used. Copyright c

Journal of Physics: Conference Series, 2013

Carbon Dioxide (CO2) sequestration into geologic formations is a means of mitigating greenhouse effect. In this work we present a new numerical simulation technique to model and monitor CO2 sequestration in aquifers. For that purpose we integrate numerical simulators of CO2-brine flow and seismic wave propagation (time-lapse seismics). The simultaneous flow of brine and CO2 is modeled applying the Black-Oil formulation for two phase flow in porous media, which uses the Pressure-Volume-Temperature (PVT) behavior as a simplified thermodynamic model. Seismic wave propagation uses a simulator based on a space-frequency domain formulation of the viscoelastic wave equation. In this formulation, the complex and frequency dependent coefficients represent the attenuation and dispersion effect suffered by seismic waves travelling in fluid-saturated heterogeneous porous formations. The spatial discretization is achieved employing a nonconforming finite element space to represent the displacement vector. Numerical examples of CO2 injection and time-lapse seismics in the Utsira formation at the Sleipner field are analyzed. The Utsira formation is represented using a new petrophysical model that allows a realistic inclusion of shale seals and fractures. The results of the simulations show the capability of the proposed methodology to monitor the spatial distribution of CO2 after injection.

Environmental Earth Sciences, 2002

Injection of CO2 into saline aquifers is described by mass conservation equations for the three components water, salt (NaCl), and CO2. The equations are discretized using an integral finite difference method, and are solved using methods developed in geothermal and petroleum reservoir engineering. Phase change processes are treated through switching of primary thermodynamic variables. A realistic treatment of PVT (fluid) properties is given which includes salinity and fugacity effects for partitioning of CO2 between gaseous and aqueous phases. Chemical reactions and mechanical stress effects are neglected. Numerical simulations are presented for injection of CO2 into a brine aquifer, and for loss of CO2 from storage through discharge along a fault zone. It is found that simulated pressures are much more sensitive to space discretization effects than are phase saturations. CO2 discharge along a fault is a self-enhancing process whose flow rates can increase over time by more than an order of magnitude, suggesting that reliable containment of CO2 will require multiple barriers.

Energy Procedia, 2011

As CO 2 is injected into a deep saline aquifer, three regions develop: a "drying" region next to the well in which CO 2 injectate occupies 100% of the pore space, a brine region away from the injection well in which 100% of the pores are saturated with brine, and a two-phase region in which water and CO 2 coexist. Several papers describe the speeds at which those two fronts progress outward using the Buckley-Leverett fractional flow (BLFF) theory. Next to a CO 2 injection well and at early times, compositional flow theory must be implemented. It is also understood that far from the injection site, where only slight pressure elevation is felt, a single phase flow approach is sufficient because all the complexities of compositional flow could be neglected. However regulators may be wary of complex models and of the associated black box syndrome and rather may favor the simpler single-phase flow approach. This paper investigates using single-phase flow numerical models to describe compositional flow processes. Previous work already showed that results from the CMG-GEM and MODFLOW numerical codes are very similar away from the injection zone given some minor modifications in the input file of the single-phase flow code. We present a more thorough scoping analysis aiming at establishing the proposition that single-phase flow models (CMG-IMEX), given some simple treatment, can predict pressure increase as well as more complex compositional flow models (CMG-GEM).

International Journal of Greenhouse Gas Control, 2011

Carbon dioxide (CO 2) injection into saline aquifers is one of the promising options to sequester large amounts of CO 2 in geological formations. During as well as after injection of CO 2 into an aquifer, CO 2 migrates towards the top of the formation due to density differences between the formation brine and the injected CO 2. The time scales of CO 2 migration towards the top of an aquifer and the fraction of CO 2 that is trapped as residual gas depends strongly on the driving forces that are acting on the injected CO 2. When CO 2 migrates to the top of an aquifer, brine may be displaced downwards in a counter-current flow setting particularly during the injection period. A majority of the published work on counter-current flow settings have reported significant reductions in the associated relative permeability functions as compared to co-current measurements. However, this phenomenon has not yet been considered in the simulation of CO 2 storage into saline aquifers. In this paper we study the impact of changes in mobility for the two-phase brine/CO 2 system as a result of transitions between co-and counter-current flow settings. We have included this effect in a simulator and studied the impact of the related mobility reduction on the saturation distribution and residual saturation of CO 2 in aquifers over relevant time scales. We demonstrate that the reduction in relative permeability in the vertical direction changes the plume migration pattern and has an impact on the amount of gas that is trapped as a function of time. This is to our best knowledge the first attempt to integrate counter-current relative permeability into the simulation of injection and subsequent migration of CO 2 in aquifers. The results and analysis presented in this paper are directly relevant to all ongoing activities related to the design of large-scale CO 2 storage in saline aquifers.