Flow and mixing in complex porous media

The flow and mixing of fluids in complex porous media is important in a large range of environmental settings, from groundwater flows to the geological storage of carbon dioxide (CO$_2$). This thesis investigates two distinct and fundamental features of such flows; the mixing of miscible fluids of differing viscosity and density in both homogeneous and heterogeneous porous media, and the flow-induced deformation of soft, poroelastic media. In all cases the approach is to combine detailed numerical or experimental observations with simplified mathematical models of the key physical phenomena. Throughout this thesis the results are considered in the context of field-scale CO$_2$ sequestration case studies. In chapter 2, the dynamics of the miscible viscous-fingering instability are investigated. It is found that the dynamics can be divided into three regimes: at early times, the flow is well described by linear stability theory; at intermediate times, the flow is dominated by non-linear finger interactions; and at late times, the flow is composed of an exponentially slowing single-finger exchange-flow. In the course of this study, a critical Péclet number for the instability in the first regime is identified, an improved averaged model for the flow in the second regime is derived and a detailed explanation of the asymptotic fate of the fingering instability in the third regime is provided. In chapters 3 and 4, miscible displacements in layered heterogeneous porous media are studied. Specifically, the combined effects of viscosity and permeability variations are examined. It is found that when the permeability variations are large compared to the viscosity variations or when the injected fluid is more-viscous than the ambient, the interface is hydrodynamically stable and the flow tends to follow the permeability structure imposed. When the injected fluid is less-viscous than the ambient fluid and the viscosity variations are much larger than the permeability variations, the interface is unstable and there is a competition between the evolving wavelength of the viscous fingering and the imposed wavelength of the permeability structure. At intermediate times, depending on the relative magnitude of the viscosity and permeability variations, this competition leads to different dynamics including channelling and fingering. At late times, the dynamics are instead dominated by shear-enhanced (Taylor) dispersion, which asymptotically becomes independent of the viscosity ratio. In chapter 5, miscible displacements are considered in which the injected and ambient fluids have different densities as well as viscosities. A range of different behaviour is observed depending, on the relative importance of viscosity and density variations, including fingering, gravitational slumping and shear-enhanced dispersion. The different dynamical regimes are identified along with their dependence on the governing parameters, and simple reduced-order models for the evolution of the concentration field are derived. The final portion of this thesis (chapter 6) examines the fluid-driven compaction of a deformable porous medium. Experimental studies of water injection into a water-saturated packing of soft hydrogel spheres are presented. Solutions to a one-dimensional axisymmetric model are discussed and comparisons to the experimental results are made. In doing so, particular focus is given to the role of confinement on both the steady-state and transient dynamics of the system

Stable and unstable miscible displacements in layered porous media

The effect of permeability heterogeneities and viscosity variations on miscible displacement processes in porous media is examined using high-resolution numerical simulations and reduced theoretical modelling. The planar injection of one fluid into a fluid-saturated, two-dimensional porous medium with a permeability that varies perpendicular to the flow direction is studied. Three cases are considered, in which the injected fluid is equally viscous, more viscous or less viscous than the ambient fluid. In general it is found that the flow in each case evolves through three regimes. At early times, the flow exhibits the concentration evolves diffusively, independent of both the permeability structure and the viscosity ratio. At intermediate times, the flow exhibits different dynamics including channelling and fingering, depending on whether the injected fluid is more or less viscous than the ambient fluid, and depending on the relative magnitude of the viscosity and permeability variations. Finally, at late times, the flow becomes independent of the viscosity ratio and dominated by shear-enhanced (Taylor) dispersion. For each of the regimes identified above, we develop reduced-order models for the evolution of the transversely averaged concentration and compare them to the full numerical simulations

The dynamics of miscible viscous fingering from onset to shutdown

We examine the full ‘life cycle’ of miscible viscous fingering from onset to shutdown with the aid of high-resolution numerical simulations. We study the injection of one fluid into a planar two-dimensional porous medium containing another, more viscous fluid. We find that the dynamics are distinguished by three regimes: an early-time linearly unstable regime, an intermediate-time nonlinear regime and a late-time single-finger exchange-flow regime. In the first regime, the flow can be linearly unstable to perturbations that grow exponentially. We identify, using linear stability theory and numerical simulations, a critical Péclet number below which the flow remains stable for all times. In the second regime, the flow is dominated by the nonlinear coalescence of fingers which form a mixing zone in which we observe that the convective mixing rate, characterized by a convective Nusselt number, exhibits power-law growth. In this second regime we derive a model for the transversely averaged concentration which shows good agreement with our numerical experiments and extends previous empirical models. Finally, we identify a new final exchange-flow regime in which a pair of counter-propagating diffusive fingers slow exponentially. We derive an analytic solution for this single-finger state which agrees well with numerical simulations. We demonstrate that the flow always evolves to this regime, irrespective of the viscosity ratio and Péclet number, in contrast to previous suggestions

Horizontal miscible displacements through porous media: the interplay between viscous fingering and gravity segregation

We consider miscible displacements in two-dimensional homogeneous porous media where the displacing fluid is less viscous and has a different density than the displaced fluid. We find that the dynamics evolve through nine possible regimes depending on the viscosity ratio, strength of density variations and the strength of the background flow, as characterized by the Péclet number. At early times the interface is dominated by longitudinal diffusion before undergoing a transition to a slumping regime where vertical flow is important. At intermediate times, vertical flow and diffusion can be neglected and there are three different limiting solutions: a fingering limit; an injection-driven gravity-current limit; and a density-driven gravity-current limit. Finally at late times, transverse diffusion becomes important and there is a transition from an apparent shutdown regime to a viscously enhanced Taylor-slumping regime. In each of the regimes, the dominant scalings are identified and reduced-order models for the evolution of the concentration field are developed. Lastly, three case studies are considered to illustrate the dominant physical balances in the geophysically relevant setting of geological CO2 storage

Use of the Instantaneous Wave-free Ratio or Fractional Flow Reserve in PCI

BACKGROUND: Coronary revascularization guided by fractional flow reserve (FFR) is associated with better patient outcomes after the procedure than revascularization guided by angiography alone. It is unknown whether the instantaneous wave-free ratio (iFR), an alternative measure that does not require the administration of adenosine, will offer benefits similar to those of FFR. METHODS: We randomly assigned 2492 patients with coronary artery disease, in a 1:1 ratio, to undergo either iFR-guided or FFR-guided coronary revascularization. The primary end point was the 1-year risk of major adverse cardiac events, which were a composite of death from any cause, nonfatal myocardial infarction, or unplanned revascularization. The trial was designed to show the noninferiority of iFR to FFR, with a margin of 3.4 percentage points for the difference in risk. RESULTS: At 1 year, the primary end point had occurred in 78 of 1148 patients (6.8%) in the iFR group and in 83 of 1182 patients (7.0%) in the FFR group (difference in risk, -0.2 percentage points; 95% confidence interval [CI], -2.3 to 1.8; P<0.001 for noninferiority; hazard ratio, 0.95; 95% CI, 0.68 to 1.33; P=0.78). The risk of each component of the primary end point and of death from cardiovascular or noncardiovascular causes did not differ significantly between the groups. The number of patients who had adverse procedural symptoms and clinical signs was significantly lower in the iFR group than in the FFR group (39 patients [3.1%] vs. 385 patients [30.8%], P<0.001), and the median procedural time was significantly shorter (40.5 minutes vs. 45.0 minutes, P=0.001). CONCLUSIONS: Coronary revascularization guided by iFR was noninferior to revascularization guided by FFR with respect to the risk of major adverse cardiac events at 1 year. The rate of adverse procedural signs and symptoms was lower and the procedural time was shorter with iFR than with FFR. (Funded by Philips Volcano; DEFINE-FLAIR ClinicalTrials.gov number, NCT02053038 .)info:eu-repo/semantics/publishedVersio

Flow-induced compaction of a deformable porous medium.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.D.R.H. was supported by a Killam Postdoctoral Fellowship and a Research Fellowship at Gonville and Caius College, Cambridge. During the experimental part of this project, J.S.N. was supported by the division of Engineering Science, University of Toronto. J.A.N. is partly supported by a Royal Society University Research Fellowship.This is the author accepted manuscript. The final version is available from the American Physical Society via http://dx.doi.org/10.1103/PhysRevE.93.02311

85 Prediction of response to biventricular pacing from dyssynchrony indices: the absolute limit on predictability, and its clinical implications

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Collateral donor artery physiology and the influence of a chronic total occlusion on fractional flow reserve

Background— The presence of a concomitant chronic total coronary occlusion (CTO) and a large collateral contribution might alter the fractional flow reserve (FFR) of an interrogated vessel, rendering the FFR unreliable at predicting ischemia should the CTO vessel be revascularized and potentially affecting the decision on optimal revascularization strategy. We tested the hypothesis that donor vessel FFR would significantly change after percutaneous coronary intervention of a concomitant CTO. Methods and Results— In consecutive patients undergoing percutaneous coronary intervention of a CTO, coronary pressure and flow velocity were measured at baseline and hyperemia in proximal and distal segments of both nontarget vessels, before and after percutaneous coronary intervention. Hemodynamics including FFR, absolute coronary flow, and the coronary flow velocity–pressure gradient relation were calculated. After successful percutaneous coronary intervention in 34 of 46 patients, FFR in the predominant donor vessel increased from 0.782 to 0.810 (difference, 0.028 [0.012 to 0.044]; P=0.001). Mean decrease in baseline donor vessel absolute flow adjusted for rate pressure product: 177.5 to 139.9 mL/min (difference −37.6 [−62.6 to −12.6]; P=0.005), mean decrease in hyperemic flow: 306.5 to 272.9 mL/min (difference, −33.5 [−58.7 to −8.3]; P=0.011). Change in predominant donor vessel FFR correlated with angiographic (%) diameter stenosis severity (r=0.44; P=0.009) and was strongly related to stenosis severity measured by the coronary flow velocity–pressure gradient relation (r=0.69; P&lt;0.001). Conclusions— Recanalization of a CTO results in a modest increase in the FFR of the predominant collateral donor vessel associated with a reduction in coronary flow. A larger increase in FFR is associated with greater coronary stenosis severity

Over-expansion capacity and stent design model: an update with contemporary DES platforms

© 2016 The AuthorsBackground Previously, we examined the difference in stent designs across different sizes for six widely used Drug Eluting Stents (DESs). Although stent post-dilatation to larger diameter is commonly done, typically in the setting of long tapering segment or left-main PCI, there is an increasing recognition that information with regard to the different stent model designs has a critical impact on overexpansion results. This study aims to provide an update on stent model designs for contemporary DES platforms as well as test overexpansion results under with oversized post-dilatation. Methods and results We studied 6 different contemporary commercially available DES platforms: Synergy, Xience Xpedition, Ultimaster, Orsiro, Resolute Onyx and Biomatrix Alpha. We investigated for each platform the difference in stent designs across different sizes and results obtained after post-expansion with larger balloon sizes. The stents were deployed at nominal diameter and subsequently over expanded using increasingly large post dilatation balloon sizes (4.0, 5.0 and 6.0 mm at 14ATM). Light microscopy was used to measure the changes in stent geometry and lumen diameter after over-expansion. For each respective DES platform, the MLD observed after overexpansion of the largest stent size available with a 6.0 mm balloon was 5.7 mm for Synergy, 5.6 mm for Xience, 5.2 mm for Orsiro, 5.8 mm for Ultimaster, 5.5 mm for 4 mm Onyx (5.9 mm for the 5 mm XL size) and 5.8 mm for BioMatrix Chroma. Conclusion This update presents valuable novel insights that may be helpful for careful selection of stent size for contemporary DES based on model designs. Such information is especially critical in left main bifurcation stenosis treatment where overexpansion to larger oversized diameter may be required to ensure full stent apposition