The formation and evolution of layered structures in porous media: effects of porosity and mechanical dispersion

Abstract

Horizontally layered structures can develop in porous or partially molten environments, such as hydrothermal systems, magmatic intrusions and the early Earth's mantle. The porosity f of these natural environments is typically small. Since dissolved chemical elements unlike heat cannot diffuse through the solid rocks, heat and solute influence the interstitial fluid density in a different manner: heat advects slower than solute through the liquid by the factor f, while diffusion of heat through the bulk porous medium is larger by the factor f y1 times the ratio between the thermal and chemical diffusivities. By performing numerical experiments in which a rigid low-porosity medium is heated from below, we have studied the formation and evolution of layers in an initially stably stratified liquid. Growth of a convective layer through convective entrainment, the formation of a stable density interface on top of the layer and destabilization of the next layer are intimately Ž . Ž . linked. By monitoring the heat solute fluxes, it is observed that the transport of heat solute across the interface changes Ž . from convective entrainment towards a regime in which transfer is purely diffusive dispersive . Because this transition occurs before the stage at which the lower layer arrives at the thermal equilibrium, we conclude that the layer growth stops when the density interface on top has grown sufficiently strong to keep the ascending plumes in the lower layer from convectively entraining more fluid from above. A simple balance between the most important forces, exerted on a fluid parcel in the lower layer, is proposed to determine this transition. This force balance also indicates whether a density interface keeps intact, migrates upwards or breaks down during the further evolution of the layered sequence. Finally, mechanical dispersion tends to increase transport of chemically dissolved elements across the density interface. Since this reduces the density difference between the two adjacent layers, the thickness of the lower layer increases. q

Depletion of a brine layer at the base of ridge-crest hydrothermal systems

“…In situ measurements [26], analysis of obducted ophiolites [25], and theoretical relationships [36] show that e¡ective porosity of the fracture network in the basaltic rocks is of the order of 0.1 to 10%. Since the porosity is a key parameter for the layer-forming process [18,32], we consider both P = 0.1 and 0.01. The dispersion lengths of the crust are taken as a l = 1 m and a t = 0.1 m, values which are reasonable for fractured rocks [37].…”

“…Our simulations di¡er from Gri¤ths' experiments, in the sense that both the porosity and the initial density di¡erence between the two layers are lower. Schoofs et al [18] argue that the stability of the interface is related directly to these quantities thus explain this scenery.…”

“…Previous studies, in which the formation and evolution of convective layers in porous media were investigated under idealized £uid conditions, have shown that a force balance on a £uid parcel just beneath the interface between the two £uid layers determines the stability of layered system [17,18]. In the context of the ridge-crest system, this balance states that the stability of the brine layer is mainly determined by (1) the brine salinity established by the thermodynamical conditions, and (2) the hydrological properties of the basaltic rocks that host the boundary.…”

Chaotic thermohaline convection in low-porosity hydrothermal systems

“…For downward migration to occur, convection in the upper layer has to be more vigorous as compared to that in the lower layer. The migration of density interfaces which developed in an initially linearly strati¢ed chemical concentration ¢eld is discussed in more detail by Schoofs et al [32,33]. Besides elucidating the various possible evolutionary states of the system, the three examples show an important e¡ect of the chemically dissolved elements.…”

“…Furthermore, the time-average of the chaotic heat £ux is reduced as compared to the £uxes at a lower chemical contrast, because a part of the internal energy which enters the domain through the bottom is used to transport the dense chemical elements upwards. Finally, heat (solute) £uxes are reduced especially during those periods in which an interface is present, because transport across this barrier is mainly di¡usive (dispersive) [32,33].…”