Amir Riaz

Convective dissolution of carbon dioxide in saline aquifers.

[1] Geological carbon dioxide (CO2) storage is a means of reducing anthropogenic emissions. Dissolution of CO2 into the brine, resulting in stable stratification, increases storage security. The dissolution rate is determined by convection in the brine driven by the increase of brine density with CO2 saturation. We present a new analogue fluid system that reproduces the convective behaviour of CO2‐enriched brine. Laboratory experiments and high‐resolution numerical simulations show that the convective flux scales with the Rayleigh number to the 4/5 power, in contrast with a classical linear relationship. A scaling argument for the convective flux incorporating lateral diffusion from downwelling plumes explains this nonlinear relationship for the convective flux, provides a physical picture of high Rayleigh number convection in a porous medium, and predicts the CO2 dissolution rates in CO2 accumulations. These estimates of the dissolution rate show that convective dissolution can play an important role in enhancing storage security. Citation: Neufeld,J.A.,M.A .Hesse,A.Riaz,M. A.H allworth, H. A. Tchelepi, and H. E. Huppert (2010), Convective dissolution of carbon dioxide in saline aquifers, Geophys. Res. Lett., 37, L22404, doi:10.1029/2010GL044728.

Optimal perturbations of gravitationally unstable, transient boundary layers in porous media

We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of optimal perturbations are highly sensitive to perturbation amplification measures and also the time at which the boundary layer is perturbed. This behavior is in contrast to traditional studies of steady or non-transient diffusive boundary layers where perturbation dynamics are independent of perturbation measure or time. We demonstrate that any analysis of transient layers produced through classical methods can result in physically unrealizable perturbation structures. To resolve the issue, we propose a nonmodal stability procedure which additionally constrains the perturbation dynamics to physically admissible fields. The proposed procedure predicts that instabilities grow primarily due to unstable perturbations featuring much larger spanwise wavenumbers (modes) and smaller amplifications compared to perturbations predicted using classical methods. We validate our predictions using direct numerical simulations that emulate the onset of convection in physical systems.

Effect of viscosity contrast on gravitationally unstable diffusive layers in porous media

We investigate the effect of viscosity contrast on the stability of gravitationally unstable, diffusive layers in porous media. Our analysis helps evaluate experimental observations of various diffusive (boundary) layer models that are commonly used to study the sequestration of CO2 in brine aquifers. We evaluate the effect of viscosity contrast for two basic models that are characterized with respect to whether or not the interface between CO2 and brine is allowed to move. We find that diffusive layers are in general more unstable when viscosity decreases with depth within the layer compared to when viscosity increases with depth. This behavior is in contrast to the one associated with the classical displacement problem of gravitationally unstable diffusive layers that are subject to mean flow. For the classical problem, a greater instability is associated with the displacement of a more viscous, lighter fluid along the direction of gravity by a less viscous, heavier fluid. We show that the contrasting behavior highlighted in this study is a special case of the classical displacement problem that depends on the relative strength of the displacement and buoyancy velocities. We demonstrate the existence of a critical viscosity ratio that determines whether the flow is buoyancy dominated or displacement dominated. We explain the new behaviors in terms of the interaction of vorticity components related to gravitational and viscous effects.

Eigenspectra and mode coalescence of temporal instability in two-phase channel flow

The stability of two immiscible fluids with different densities and viscosities is examined for channel flow. A multi-domain Chebyshev collocation spectral method is used for solving the coupled Orr-Sommerfeld stability equations for the entire spectrum of eigenvalues and associated eigenfunctions. Numerical solution of the eigenvalue problem is obtained with the QZ eigenvalue solver and is validated with analytical results derived in the long and short wave limits. A parametric study is carried out to investigate the spectral characteristics and eigenfunction structures related to the shear and interfacial modes of instability. The interactions and mode switching between the two instability modes are investigated. Under certain conditions, the two modes are found to become unstable simultaneously. Mode coalescence can occur in either the stable or the unstable part of the spectrum. In general, the eigenfunction of the most dangerous mode is observed to vary sharply in the neighborhood of the interface and the critical points.

Topology preserving advection of implicit interfaces on Cartesian grids

Accurate representation of implicit interface topology is important for the numerical computation of two phase flow on Cartesian grids. A new method is proposed for the construction of signed distance function by geometrically projecting interface topology onto the Cartesian grid using a multi-level projection framework. The method involves a stepwise improvement in the approximation to the signed distance function based on pointwise, piecewise and locally smooth reconstructions of the interface. We show that this approach provides accurate representation of the projected interface and its topology on the Cartesian grid, including the distance from the interface and the interface normal and curvature. The projected interface can be in the form of either a connected set of marker particles that evolve with Lagrangian advection, or a discrete set of points associated with an implicit interface that evolves with the advection of a scalar function. The signed distance function obtained with geometric projection is independent of the details of the scaler field, in contrast to the conventional approach where advection and reinitialization cannot be decoupled. As a result, errors introduced by reinitialization do not amplify advection errors, which leads to substantial improvement in both volume conservation and topology representation.

Direct numerical simulation of incompressible multiphase flow with phase change

Abstract Simulation of multiphase flow with phase change is challenging because of the potential for unphysical pressure oscillations, spurious velocity fields and mass flux errors across the interface. The resulting numerical errors may become critical when large density contrasts are present. To address these issues, we present a new approach for multiphase flow with phase change that features, (i) a smooth distribution of sharp velocity jumps and mass flux within a narrow region surrounding the interface, (ii) improved mass flux projection from the implicit interface onto the uniform Cartesian grid and (iii) post-advection velocity correction step to ensure accurate velocity divergence in interfacial cells. These new features are implemented in combination with a sharp treatment of the jumps in pressure and temperature gradient. A series of 1-D, 2-D, axisymmetric and 3-D problems are solved to verify the improvements afforded by the new approach. Axisymmetric film boiling results are also presented, which show good qualitative agreement with heat transfer correlations as well as experimental observations of bubble shapes.

Effect of \(\hbox {CO}_2\) solubility on dissolution rate of calcite in saline aquifers for temperature range of 50–100 \(^{\circ } \hbox {C}\) and pressures up to 600 bar: alterations of fractures geometry in carbonate rocks by \(\hbox {CO}_2\)-acidified brines

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Nonlinear stability of gravitationally unstable, transient, diffusive boundary layers in porous media

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