Mixing-Limited Reactions in Porous Media

Transport in Porous Media - Acid mine drainage is generated when sulfide minerals are exposed to air and water through the porous subsurface, and it is significantly accelerated by the action of...     

In situ formation of allyl ketones via Hiyama-Nozaki reactions followed by a chromium-mediated Oppenauer oxidation

In Hiyama-Nozaki reactions of allylchromium with aldehydes the expected products are homoallylalcohols. However, oxidation products derived from these, predominantly allyl ketones, can be common side products. This can be explained by an Oppenauer-(Meerwein-Ponndorf-Verley)-type mechanism (OMPV-reaction). The amount of oxidation is strongly dependent on the substitution pattern of the reaction partners and the reaction conditions. An appropriate choice of these can lead to preferential formation of ketones instead of the alcohols. In addition to its synthetic usefulness, the oxidation-reduction equilibrium is of the utmost importance for the design of enantioselective Hiyama-Nozaki reactions because it is also a potential racemization pathway.     

Effects of CO<Subscript>2</Subscript> Compressibility on CO<Subscript>2</Subscript> Storage in Deep Saline Aquifers

The injection of supercritical CO₂ in deep saline aquifers leads to the formation of a CO₂ plume that tends to float above the formation brine. As pressure builds up, CO₂ properties, i.e. density and viscosity, can vary significantly. Current analytical solutions do not account for CO₂ compressibility. In this article, we investigate numerically and analytically the effect of this variability on the position of the interface between the CO₂-rich phase and the formation brine. We introduce a correction to account for CO₂ compressibility (density variations) and viscosity variations in current analytical solutions. We find that the error in the interface position caused by neglecting CO₂ compressibility is relatively small when viscous forces dominate. However, it can become significant when gravity forces dominate, which is likely to occur at late times of injection.     

Anomalous Dispersion in Pore-Scale Simulations of Two-Phase Flow

Transport in Porous Media - We investigate anomalous dispersion in steady-state two-phase flow though a random, artificial porous domain. A natural distribution of trapped wetting-phase fluid was...     

The effect of initial spatial correlations on late time kinetics of bimolecular irreversible reactions

We study anomalous kinetics associated with incomplete mixing for a bimolecular irreversible kinetic reaction where the underlying transport of reactants is governed by a fractional dispersion equation. As has been previously shown, we demonstrate that at late times incomplete mixing effects dominate and the decay of reactants follows a fundamentally different scaling comparing to the idealized well mixed case. We do so in a fully analytical manner using moment equations. In particular the novel aspect of this work is that we focus on the role that the initial correlation structure of the distribution of reactants plays on the late time scalings. We focus on short range and long (power law) range correlations and demonstrate how long range correlations can give rise to different late time scalings than one would expect purely from the underlying transport model. For the short range correlations the late time scalings deviate from the well mixed t⁻¹$t^{-1}$ and scale like t^−1/2α$t^{-1/2\alpha }$, where 1<α≤2$1<\alpha \le 2$ is the fractional dispersion exponent, in agreement with previous studies. For the long range correlation case it scales like t^−β/2α$t^{-\beta /2\alpha }$, where 0<β<1$0<\beta <1$ is the power law correlation exponent.     

Rapid acquisition technique for MR elastography of the liver

Magnetic resonance elastography (MRE) of the liver is a novel noninvasive clinical diagnostic tool to stage fibrosis based on measured stiffness. The purpose of this study is to design, evaluate and validate a rapid MRE acquisition technique for noninvasively quantitating liver stiffness which reduces by half the scan time, thereby decreasing image registration errors between four MRE phase offsets. In vivo liver MRE was performed on 16 healthy volunteers and 14 patients with biopsy-proven liver fibrosis using the standard clinical gradient recalled echo (GRE) MRE sequence (MREs) and a developed rapid GRE MRE sequence (MREr) to obtain the mean stiffness in an axial slice. The mean stiffness values obtained from the entire group using MREs and MREr were 2.72 ± 0.85 kPa and 2.7 ± 0.85 kPa, respectively, representing an insignificant difference. A linear correlation of R² = 0.99 was determined between stiffness values obtained using MREs and MREr. Therefore, we can conclude that MREr can replace MREs, which reduces the scan time to half of that of the current standard acquisition (MREs), which will facilitate MRE imaging in patients with inability to hold their breath for long periods.     

Localized Point Mixing Rate Potential in Heterogeneous Velocity Fields

Mixing is driven by an interplay between diffusion and flow-induced concentration gradients. Accurately describing the effect of flow heterogeneity on the mixing state of a plume is a challenging problem that has important repercussions on the modeling of plume dilution and chemical reactions. In this technical note, we propose a simple, semi-analytic measure to quantify the local mixing potential at a point based on the local properties of the flow-induced strain. Specifically, it is the trace of the local strain matrix squared, \({\text {Tr}}(\varvec{s}^2)\), which we demonstrate controls mixing from a point source over small times. Due to its mathematically similar influence to a shear flow on mixing, we propose an ansatz to attempt to use this metric as a predictor for mixing. We test its performance via random walk particle tracking simulations in heterogeneous Darcy flow through lognormal permeability fields. The ansatz appears to work better and better the more heterogeneous the flow, unlike more traditional approaches that rely on weak heterogeneity assumptions. While we cannot rigorously demonstrate why this is, we find it sufficiently promising that it may guide future model development.