A hydromechanical model for lower crustal fluid flow

Abstract

Metamorphic devolatilization generates fluids at, or near, lithostatic pressure. These fluids are ultimately expelled by compaction. It is doubtful that fluid generation and compaction operate on the same time scale at low metamorphic grade, even in rocks that are deforming by ductile mechanisms in response to tectonic stress. However, thermally-activated viscous compaction may dominate fluid flow patterns at moderate to high metamorphic grades. Compaction-driven fluid flow organizes into self-propagating domains of fluid-filled porosity that correspond to steady-state wave solutions of the governing equations. The effective rheology for compaction processes in heterogeneous rocks is dictated by the weakest lithology. Geological compaction literature invariably assumes linear viscous mechanisms; but lower crustal rocks may well be characterized by non-linear (power-law) viscous mechanisms. The steady-state solutions and scales derived here are general with respect to the dependence of the viscous rheology on effective pressure. These solutions are exploited to predict the geometry and properties of the waves as a function of rock rheology and the rate of metamorphic fluid production. In the viscous limit, wavelength is controlled by a hydrodynamic length scale δ, which varies inversely with temperature, and/or the rheological length scale for thermal activation of viscous deformation lA, which is on the order of a kilometer. At high temperature, such that δ < lA, waves are spherical. With falling temperature, as δ → lA, waves flatten to sill-like structures. If the fluid overpressures associated with viscous wave propagation reach the conditions for plastic failure, then compaction induces channelized fluid flow. The channeling is caused by vertically elongated porosity waves that nucleate with characteristic spacing δ. Because δ increases with falling temperature, this mechanism is amplified towards the surface. Porosity wave passage is associated with pressure anomalies that generate an oscillatory lateral component to the fluid flux that is comparable to the vertical component. As the vertical component may be orders of magnitude greater than time-averaged metamorphic fluxes, porosity waves are a potentially important agent for metasomatism. The time and spatial scales of these mechanisms depend on the initial state that is perturbed by the metamorphic process. Average fluxes place an upper limit on the spatial scale and a lower limit on the time scale, but the scales are otherwise unbounded. Thus, inversion of natural fluid flow patterns offers the greatest hope for constraining the compaction scales. Porosity waves are a self-localizing mechanism for deformation and fluid flow. In nature these mechanisms are superimposed on patterns induced by far-field stress and pre-existing heterogeneities.