Alan W. Rempel

Formation and accumulation of gas hydrate in porous media

Vast quantities of clathrate hydrate are found in the Arctic and in marine sediments along continental margins. The clathrate structure traps enormous volumes of methane gas, which is both a possible source of global climate change and a potential energy resource. The growth rate and spatial distribution of gas hydrate in the shallow sediments are influenced by a variety of interacting physical processes. In order to quantify these processes, we develop mathematical models for hydrate formation in porous media. An analytical model is derived for the idealized problem of hydrate growth in a porous half-space which is cooled on its boundary. Our calculations predict the growth rate of a hydrate layer for a given rate of cooling and show that the volume of hydrate is strongly dependent on the two-phase equilibrium between hydrate and seawater. For a representative phase diagram we find that the volume of hydrate in the layer is less than 1% of the pore volume. Larger volumes of hydrate observed in some locations demand a sustained supply of gas and a long accumulation time. Numerical calculations are used to investigate situations that are more representative of conditions in marine sediments. A simple theoretical expression is derived for the rate of hydrate accumulation due to advection of methane gas from depth. Using typical estimates of fluid velocities in accretionary environments, we obtain an accumulation rate of 1% of the pore volume in 105 years. The predicted vertical distribution of hydrate is consistent with geophysical inferences from observed hydrate occurrences along the Cascadia margin. Similar distributions can arise from the combined effects of in situ methane production and warming due to ongoing sedimentation. Predicted differences between these two formation models may be detectable in geophysical and geochemical measurements.

Premelting dynamics in a continuum model of frost heave

Frost heave is the process by which the freezing of water-saturated soil causes the deformation and upward thrust of the ground surface. We describe the fundamental interactions between phase change and fluid flow in partially frozen, saturated porous media (soils) that are responsible for frost heave. Water remains only partially frozen in a porous medium at temperatures below

Possible displacement of the climate signal in ancient ice by premelting and anomalous diffusion

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A theory for ice-till interactions and sediment entrainment beneath glaciers

C owing both to the depression of the freezing temperature at curved phase boundaries and to interfacial premelting caused by long-range intermolecular forces. We show that while the former contributes to the geometry of fluid pathways, it is solely the latter effect that generates the forces necessary for frost heave. We develop a simple model describing the formation and evolution of the ice lenses (layers of ice devoid of soil particles) that drive heave, based on integral force balances. We determine conditions under which either (i) a single ice lens propagates with no leading frozen fringe, or (ii) a single, propagating ice lens is separated from unfrozen soil by a partially frozen fringe, or (iii) multiple ice lenses form.

Particle trapping at an advancing solidification front with interfacial-curvature effects

The best high-resolution records of climate over the past few hundred millennia are derived from ice cores retrieved from Greenland and Antarctica. The interpretation of these records relies on the assumption that the trace constituents used as proxies for past climate have undergone only modest post-depositional migration. Many of the constituents are soluble impurities found principally in unfrozen liquid that separates the grain boundaries in ice sheets. This phase behaviour, termed premelting, is characteristic of polycrystalline material. Here we show that premelting influences compositional diffusion in a manner that causes the advection of impurity anomalies towards warmer regions while maintaining their spatial integrity. Notwithstanding chemical reactions that might fix certain species against this prevailing transport, we find that—under conditions that resemble those encountered in the Eemian interglacial ice of central Greenland (from about 125,000 to 115,000 years ago)—impurity fluctuations may be separated from ice of the same age by as much as 50 cm. This distance is comparable to the ice thickness of the contested sudden cooling events in Eemian ice from the GRIP core.

Formation of ice lenses and frost heave

and frozen onto or melted from the glacier base can achieve a steady state that is in balance with the rate that latent heat is transported to or from the basal interface. At constant N, when a gradual increase in heat flow from the glacier base causes the rate of melting to decrease, h increases and continues to do so when the heat flow is great enough to produce freezing. As freezing becomes more rapid and h increases further, the rate of fluid supply to the glacier base reaches a maximum when the effective permeability is sufficiently reduced by the partial ice saturation in the fringe. Larger h can be achieved with slower freezing at the glacier base, but steady states with larger h are unstable. The maximum rate of fluid supply to the glacier base is greater at lower N, higher temperature gradients, and for sediments with higher permeabilities. Unsteady behavior can lead to large changes in h when there is a mismatch between the rate that latent heat can be extracted and the rate that fluid is supplied to the glacier base. Transient behavior driven by abrupt changes in N is characterized by rapid variations in freezing rate, followed by slower adjustments to h that are limited by the timescale for the conduction of latent heat. The resulting patterns of sediment deformation are expected to commonly be distributed over finite depth ranges even when shear is perfectly localized at any single instant in time.

The effects of flash-weakening and damage on the evolution of fault strength and temperature

We predict the maximum solidification rate, or critical velocity, Vc at which an insoluble particle suspended in a melt is pushed ahead of an advancing solidification front by intermolecular forces. At higher solidification rates the particle is incorporated within the solid. The net intermolecular force pushing the particle and the viscous resistance opposing it are both significantly influenced by the shape of the front as it conforms to the particle in response to interfacial premelting. We predict the entire shape of the front, within a thin-film approximation, accounting for the freezing-point depression due to curvature. We show how the interface shape varies with the magnitude of the surface energy and the closeness of the particle, and compare these to previous, ad hoc representations of the interface. We confirm the scaling results of previous, more approximate, analyses for the case in which the intermolecular forces are dominated by nonretarded van der Waals interactions, and provide new results for other power-law interactions. We examine how the particle behaviour changes as its radius increases so that the effect of interfacial curvature is diminished. # 2001 Elsevier Science B.V. All rights reserved.

Mega-earthquakes rupture flat megathrusts

[1] I examine the morphology of ice growth in porous media. Intermolecular forces cause premelted fluid to migrate and supply segregated ice growth (e.g., lenses) and frost heave. I account for the net effect of these microscopic interactions in a homogenized model formulated in terms of fundamental physical properties and characteristics of the porous medium that can be measured; no ad hoc parameterizations are required. Force equilibrium constraints yield the rate of fluid migration toward the ice lens boundary and predict the conditions under which new lenses are initiated. By combining this analysis with considerations of the heat flow problem in a step-freezing (Stefan) configuration, I elucidate the boundaries between different regimes of freezing behavior. At higher overburden pressures and relatively warm surface temperatures, ice lenses cannot form, and freezing of the available liquid occurs within the pore space, with no accompanying deformation. When conditions allow a lens to form, water is drawn toward it. If the fluid supply is sufficiently rapid, the lens grows faster than the latent heat of fusion can be carried away, and its boundary temperature warms until it reaches a stable steady state configuration. At lower fluid supply rates, the lens boundary temperature cools until a new lens can form at a warmer temperature beneath. With subsequent freezing this lens grows until yet another lens forms and the process repeats. An approximate treatment leads to estimates of the evolving lens thickness and spacing, as well as the accumulated total heave.

Dehydration‐induced porosity waves and episodic tremor and slip

The effects of fluid pressurization in altering the fault strength and limiting the temperature rise during earthquake slip are modeled for the case of a thin, but finite, shear zone, with state-dependent properties that are chosen to represent conditions along a mature fault at moderate seismogenic depth. We include the effects of flash-weakening at highly stressed asperity contacts by extending the model of Rice [1999; 2006] to treat the relative motion between gouge particles as equal to either 1) the slip rate or 2) the product of the particle diameter and the strain rate. At slips exceeding a few centimeters, the strength evolution is relatively insensitive to the difference between these two formulations, but the predicted temperature rise is considerably greater for the strain-rate dependent case. Our calculations demonstrate how increasing levels of damage can significantly limit the reduction in fault strength, resulting in more rapid heating and ultimately leading to the predicted onset of melting following relatively modest slips.

Mathematical models of gas hydrate accumulation

Mega-earthquakes go the flat way Megathrust faults in subduction zones cause large and damaging earthquakes. Bletery et al. argue that certain geometric features of the subduction zones relate to earthquake size. The key parameter is the curvature of the megathrust. Larger earthquakes occur where the subducting slab is flatter, providing a rough metric for estimating where mega-earthquakes may occur in the future. Science, this issue p. 1027 Large earthquakes in subduction zones are most likely to occur where the subducting slab is relatively flat. The 2004 Sumatra-Andaman and 2011 Tohoku-Oki earthquakes highlighted gaps in our understanding of mega-earthquake rupture processes and the factors controlling their global distribution: A fast convergence rate and young buoyant lithosphere are not required to produce mega-earthquakes. We calculated the curvature along the major subduction zones of the world, showing that mega-earthquakes preferentially rupture flat (low-curvature) interfaces. A simplified analytic model demonstrates that heterogeneity in shear strength increases with curvature. Shear strength on flat megathrusts is more homogeneous, and hence more likely to be exceeded simultaneously over large areas, than on highly curved faults.