Buoyancy-driven instabilities of partially miscible fluids in inclined porous media

2021 ◽  
Vol 926 ◽  
Author(s):  
Hamid Emami-Meybodi ◽  
Fengyuan Zhang
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Transition Zone ◽  
Porous Layer ◽  
Inclination Angle ◽  
Diffusive Boundary Layer ◽  
Partially Miscible ◽  
Gravity Driven ◽  
Diffusive Boundary ◽  
Critical Times

This study presents a buoyancy-driven stability analysis in a three-dimensional inclined porous medium with a capillary transition zone that is formed between a non-wetting and an underlying wetting phase. In this two-phase, two-component, partially miscible system, a solute from a non-wetting phase diffuses into a porous layer saturated with a wetting-phase fluid, creating a dense diffusive boundary layer beneath an established capillary transition zone. Transient concentration and gravity-driven velocity fields are derived for the wetting phase while the saturation field remains fixed. Linear stability analysis with the quasi-steady-state approximation is employed to determine the onset of solutal convective instability for buoyancy-dominant, in-transition and capillary-dominant systems. The analysis of the problem leads to a differential eigenvalue problem composed of a system of three complex-valued equations that are numerically solved to determine the critical times, critical wavenumbers and neutral stability curves as a function of inclination angle for different Bond numbers. The layer inclination is shown to play an essential role in the stability of the problem, where the gravity-driven flow removes solute concentrations in the diffusive boundary layer. The results indicate that the horizontal porous layer exhibits the fastest onset of instability, and longitudinal rolls are always more unstable than oblique and transverse rolls. The inclination angle has a more substantial impact on stabilizing the diffusive boundary layer in the buoyancy-dominant than in the capillary-dominant systems. Furthermore, for both buoyancy-dominant and capillary-dominant systems, the critical times and wavenumbers vary exponentially with inclination angle ≤ 60° and follow the Stirling model.

scholarly journals Instability of a Diffusive Boundary Layer beneath a Capillary Transition Zone

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 85
Author(s):  
Fengyuan Zhang ◽  
Hamid Emami-Meybodi
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Transition Zone ◽  
Co2 Concentration ◽  
Phase System ◽  
Neutral Stability ◽  
Diffusive Boundary Layer ◽  
Two Phase ◽  
Deep Saline Aquifer ◽  
Diffusive Boundary

Natural convection induced by carbon dioxide (CO2) dissolution from a gas cap into the resident formation brine of a deep saline aquifer in the presence of a capillary transition zone is an important phenomenon that can accelerate the dissolution process, reducing the risk of CO2 leakage to the shallower formations. Majority of past investigations on the instability of the diffusive boundary layer assumed a sharp CO2–brine interface with constant CO2 concentration at the top of the aquifer, i.e., single-phase system. However, this assumption may lead to erroneous estimates of the onset of natural convection. The present study demonstrates the significant effect of the capillary transition zone on the onset of natural convection in a two-phase system in which a buoyant CO2 plume overlaid a water-saturated porous layer. Using the quasi-steady-state approximation (QSSA), we performed a linear stability analysis to assess critical times, critical wavenumbers, and neutral stability curves as a function of Bond number. We show that the capillary transition zone could potentially accelerate the evolution of the natural convection by sixfold. Furthermore, we characterized the instability problem for capillary-dominant, in-transition, and buoyancy-dominant systems. In the capillary-dominant systems, capillary transition zone has a strong role in destabilizing the diffusive boundary layer. In contrast, in the buoyancy-dominant systems, the buoyancy force is the sole cause of the instability, and the effect of the capillary transition zone can be ignored. Our findings provide further insight into the understanding of the natural convection in the two-phase CO2–brine system and the long-term fate of the injected CO2 in deep saline aquifers.

Countercurrent convection in a double-diffusive boundary layer

1985 ◽  
Vol 160 ◽  
pp. 181-210 ◽  
Author(s):  
R. H. Nilson
Keyword(s):  
Boundary Layer ◽  
Vertical Wall ◽  
Similarity Solutions ◽  
Relative Strength ◽  
Diffusive Boundary Layer ◽  
Buoyancy Forces ◽  
Diffusive Boundary ◽  
Laminar Convection ◽  
Similar Solutions ◽  
Double Diffusive

Countercurrent flow may be induced by opposing buoyancy forces associated with compositional gradients and thermal gradients within a fluid. The occurrence and structure of such flows is investigated by solving the double-diffusive boundary-layer equations for steady laminar convection along a vertical wall of finite height. Non-similar solutions are derived using the method of matched asymptotic expansions, under the restriction that the Lewis and Prandtl numbers are both large. Two sets of asymptotic solutions are constructed, assuming dominance of one or the other of the buoyancy forces. The two sets overlap in the central region of the parameter space; each set matches up with neighbouring unidirectional similarity solutions at the respective borderlines of incipient counterflow.Interaction between the buoyancy mechanisms is controlled by their relative strength R and their relative diffusivity Le. Flow in the outer thermal boundary layer deviates from single-diffusive thermal convection, depending upon the magnitude of the parameter RLe. Flow in the inner compositional boundary layer deviates from single-diffusive compositional convection, depending upon the magnitude of $RLe^{\frac{1}{3}}$.

Kinetic aspects of major and trace elements in olivines from variably cooled basaltic melts

2020 ◽  
Author(s):  
Sarah Lang ◽  
Silvio Mollo ◽  
Lyderic France ◽  
Manuela Nazzari ◽  
Valeria Misiti ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Trace Elements ◽  
Crystal Growth ◽  
Cooling Rate ◽  
Crystallization Kinetics ◽  
Growth Rates ◽  
Crystal Surface ◽  
Major And Trace Elements ◽  
Diffusive Boundary Layer ◽  
Diffusive Boundary

<p>Olivine is an important mineral phase in naturally cooled basaltic rocks. The texture and composition of olivine are strictly related to the interplay between the degree of magma undercooling and crystal growth rate. Crystals formed at low undercoolings and growth rates generally show polyhedral-hopper textures and quite homogeneous compositions, while skeletal-dendritic textures and evident crystal zonations occur at high undercoolings and growth rates. In this context, we have performed equilibrium and disequilibrium (i.e., cooling rate) experiments to better understand, by a comparatively approach, the effects of crystallization kinetics on the incorporation of major and trace cations in olivine lattice. The experiments were carried out in a 1 atm vertical tube CO-CO2 gas-mixing furnace to perform experiment at atmospheric pressure and oxygen fugacity of QFM-2 using a basaltic glass (i.e., OIB) as starting materials. The equilibrium experiment was performed at 1175 °C. These target temperatures were kept constant for 240 h and then quenched. Conversely, the disequilibrium experiments were performed at the superliquidus temperature of 1250, and 1300 °C, which was kept constant for 2 h before cooling. The final target temperatures of 1150 (undercooling -ΔT = 50 °C), and 1175 °C (-ΔT = 25 °C) were attained by applying cooling rates of 2 °C/h, 20 °C/h, and 60 °C/h. Then the experimental charges were quenched. Results show that the olivine texture shifts from euhedral (i.e., equilibrium) to anhedral (i.e., disequilibrium) under the effect of cooling rate and rapid crystal growth. In equilibrium experiments, the composition of olivine is homogeneous and non chemical gradients are found in the melt next to the crystal surface. In contrast, a diffusive boundary layer develops in the melt surrounding the olivine crystals growing rapidly under the effect of cooling rate and degree of undercooling. The compositional gradient in the melt increases with increasing cooling rate and undercooling, causing the diffusive boundary layer to expand towards the far field melt. Because of the effects of crystallization kinetics, skeletal-dendritic olivines incorporates higher proportions of major and trace elements that are generally incompatible within their crystal lattice under equilibrium conditions.</p>

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