Session M05: Porous Media Flows: Convection and Heat Transfer II

Early-time dynamics of fluid-driven cracks

Pressure-driven flow at a point source, facilitated by a needle inserted in a brittle elastic matrix, creates a radial fracture of penny shape. Although this phenomenon has been studied on a large time scale, the early time dynamics of these fluid-driven cracks are still not well understood. Here, we present our findings on the shape transition of fluid-driven fractures. At the initial stage, a crack forms and propagates in the axial direction, with respect to the orientation of the needle. The crack then shifts to a penny shape, when the propagation shifts from axial to radial, characterized by a peak in the pressure profile during the liquid infusion. We also used scaling laws to validate the radial and width profiles of these cracks for viscous and toughness-dominated regimes.    

Fluid-fluid displacement using spontaneous imbibition: effect of in-situ surfactants

This talk focuses on the displacement of a vegetable oil slug using an aqueous alkali solution within a capillary tube via spontaneous imbibition. The effect of surfactant formed in-situ due to a saponification chemical reaction between the carboxylic acids present in the vegetable oil and the aqueous alkali on the displacement process is studied by varying the alkali strength. The transient surface tension is measured using the pendant drop method and the rates of change in surface tension for different alkali strengths are used to estimate the Damkohler number. The final equilibrium surface tension is used to calculate the capillary number and the imbibition rate of displacement experiments with in-situ surfactants is compared to the previously reported surfactant-free case to quantify the effect of dynamic surface tension change. The energy dissipated in the bulk fluid due to viscous effects as well as the two contact likes is estimated as a function of dynamic contact angles at the aqueous-oil and oil-air menisci, respectively. The problem under study will be of significance to applications in microfluidics, hydrocarbon recovery, groundwater remediation, and wastewater treatment.   

Dispersive effects in buoyancy-driven flows in porous media

Buoyancy-driven flow in porous media is bookended by two canonical scenarios: a vertically descending plume and a horizontally-propagating gravity current. Whereas the former is dominated by entrainment, the latter often includes significant dispersion. Sahu and Neufeld (J. Fluid Mech., Vol. 886 ,2020) studied dispersive effects in gravity current flow, however, they considered dispersive effects only in the transverse direction, not in the longitudinal direction. Aiming to expand upon their pioneering study, we investigate dispersive effects both parallel and normal to the principle direction of flow. The resulting set of (1D) equations do not admit self-similar solutions but can be solved using standard numerical techniques. In turn, we can reproduce the kinds of gravity current profiles generated, under more restrictive assumptions, by Sahu and Neufeld (2020). Model results are validated using a complementary COMSOL model that was itself confirmed by comparison with analogue experimental results. In the spirit of the bookend cases described above, the COMSOL-based model can be adapted to study more general examples of gravity current flow i.e., gravity currents that are plume-fed and/or that lose mass and buoyancy as they propagate. The implications of our work to real geological flows (e.g. hydrogen storage in a depleted reservoir) are briefly highlighted.   

Pore-resolved direct numerical simulations of hyporheic exchange induced by bedforms and bed roughness

In aquatic environments, bedform features of the sediment induce exchange of water and solutes across the interface, which play a significant role in controlling biogeochemical processes. Our recent pore-resolved simulations of flat-bed hyporheic exchange revealed that, grain-scale bed roughness leads to significant volumetric flux into the sediment and deep subsurface flow paths that yield heavy-tail residence time distributions similar to those observed in the presence of bedforms. Here, we explore the synergistic effects of bed roughness and bedforms on the exchange flux, based on direct numerical simulations of turbulent open-channels at a friction Reynolds number of 1580 over a sand bed with immobile porous dunes. Two different arrangements of the uppermost-layer sediment grains at the interface are evaluated: regular and random. Results show that bed roughness plays an important role in affecting time-mean pressure and velocity patterns both above and below the interface. Substantially longer residence times are observed for the regular roughness than the random, while the random roughness results in stronger mixing at the interface and larger volumetric fluxes. Results suggest that the effect of small-scale bed features on the hyporheic exchange cannot be ignored.   

Not Participating

Effect of Heterogeneity on Residual Trapping of CO2

We analyze the buoyancy driven spreading of a plume of CO₂ through a subsurface permeable aquifer initially saturated with aqueous saline solution. We show that if the permeable rock includes two regions of different permeability, k₁ and k₂ say, then the volume of CO₂ in the plume spreads through the two layers in the ratio  (k₂/k₁)^{( 1/2 )} . Furthermore, in the case that there is some residual trapping of CO₂, we show that the volume of CO₂ partitions between the two layers in the ratio (k₂/k₁)^{( 1+2*gamma(s) )/( 2 + gamma(s) )} where the total volume of fluid decays with time as a power of time with exponent gamma(s) , here s is the fraction of CO₂ which is trapped in the pore-space. These results have implications for the efficiency of trapping during CO₂ sequestration.   

Directional-dependent invasion dynamics in anisotropic porous media with customised disorder

We show possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with customised pore-scale morphology and heterogeneity. Via pore-scale numerical simulations, we observe a substantially different invasion dynamics according to the medium orientation relative to the direction of fluid injection, i.e. with flow-aligned or flow-opposing oriented pillars. The porous medium anisotropy induces a lower effective resistance when the pillars are flow-opposing oriented, suppressing front roughening and capillary fingering, while promoting transverse invasion with respect to the direction of fluid injection. We argue that fluid infiltration occurs as long as the pressure drop is larger then the macroscopic capillary pressure determined by the front roughness. We present a simple approximated model, based on Darcy's assumptions, that links the macroscopic effective permeability with the directional-dependent front roughening. The model correctly predicts an intermediate flow regime, defined by a specific range of values of the ratio between the macroscopic pressure drop and the medium characteristic pore-scale capillary threshold, within which the injected viscous fluid reaches the outlet only whith flow-opposing oriented pillars. The prediction of the observed directional-dependent fluid conductance is important for e.g. the fabrication of porous materials that act as capillary valves to control the flow along certain specific directions.   

Imbibition-Induced Deformation in Nanoporous Vycor Glass

We present time-dependent macroscopic dilatometry experiments on the deformation of nanoporous monoliths (Vycor glass) upon spontaneous,capillarity-driven infiltration of water. We find two distinct dynamical regimes. One of them can be quantitatively traced to deformation originating in changes in the surface stress at the inner pore walls (dynamic Bangham's regime) upon water invasion, whereas the second results from from Laplace pressure effects [1,2,3]. Our study demostrates that it is possible to monitor imbibition dynamics by simply dilatometry measurements.

References:[1] Gennady Gor, Luca Bertinetti, Noam Bernstein, Peter Fratzl, and Patrick Huber. Elastic response of mesoporous silicon to capillary pressures in the pores. Appl. Phys. Lett. (2015) [2] Gennady Gor, Patrick Huber, and Noam Bernstein. Adsorption-induced deformation of nanoporous material - A review. Appl. Phys. Lett. (2017) [3] Gennady Gor, Patrick Huber, and Jörg Weissmüller. elastocapillarity in nanopores: Sorption strain from the actions of surface tension and surface stress. Phys. Rev. Matter. (2018)   

Not Participating

The injection of CO₂ into porous subsurface reservoirs is a technological means for removing anthropogenic emissions, which relies on a series of complex porous flow properties. During injection of CO₂ small-scale heterogeneities, often in the form of sedimentary layering, can play a significant role in focusing the flow of less viscous CO₂ into high permeability pathways, with large-scale implications for the overall motion of the CO₂ plume. In these settings, capillary forces between the CO₂ and water preferentially rearrange CO₂ into the most permeable layers (with larger pore space), and may accelerate plume migration by as much as 200%. Numerous factors affect overall plume acceleration, including the structure of the layering, the permeability contrast between layers, and the relative importance of the other, gravitational and viscous, forces that act upon the flow. However, despite the sensitivity of the flow to these heterogeneities, it is extremely difficult to acquire field measurements at the ~10cm scale of the heterogeneities owing to the vast range of scales involved, presenting an outstanding challenge. As a first step towards tackling this uncertainty, we use a simple modelling approach, based on an upscaled thin-film equation, to create ensemble forecasts for many different types and arrangements of sedimentary layers. In this way, a suite of predictions can be made to elucidate the most likely scenarios for injection and the uncertainty associated with such predictions.