An analytical solution for solitary porosity waves: dynamic permeability and fluidization of nonlinear viscous and viscoplastic rock

Abstract

Porosity waves are a mechanism by which fluid generated by devolatilization and melting, or trapped during sedimentation, may be expelled from ductile rocks. The waves correspond to a steady-state solution to the coupled hydraulic and rheologic equations that govern the flow of the fluid through the matrix and matrix deformation. This chapter presents an intuitive analytical formulation of this solution in one dimension that is general with respect to the constitutive relations used to define the viscous matrix rheology and permeability. This generality allows for the effects of nonlinear viscous matrix rheology and disaggregation. The solution combines the porosity dependence of the rheology and permeability in a single hydromechanical potential as a function of material properties and wave velocity. With the ansatz that there is a local balance between fluid production and transport, the solution permits the prediction of dynamic variations in permeability and pressure necessary to accommodate fluid production. The solution is used to construct a phase diagram that defines the conditions for smooth pervasive flow, wave-propagated flow, and matrix fluidization (disaggregation). The viscous porosity wave mechanism requires negative effective pressure to open the porosity in the leading half of a wave. In nature, negative effective pressure may induce hydrofracture, resulting in a viscoplastic compaction rheology. The tube-like porosity waves that form in a matrix with this rheology channelize fluid expulsion and are predicted by geometric argumentation from the one-dimensional viscous solitary wave solution.

Water Migration in the Subduction Mantle Wedge: A Two‐Phase Flow Approach

“…Our models show that water migration during subduction is not homogenous but may be localized along some water pathways. The model results are consistent with previous work on the role of fluid flow during subduction that suggests that viscous compaction may lead to focused migration of fluids in the mantle wedge (i.e., Connolly & Podladchikov, ; McKenzie, ; Wilson et al, ). Specifically, our water migration models in the subduction zone are characterized by two water pathways with a low‐porosity divide in between.…”

The Potential for Metamorphic Thermal Pulses to Develop During Compaction‐Driven Fluid Flow

“…Another issue related to the high fluid flux is that a porosity level as high as 20% (Figure b) could potentially cause fluidization under which conditions two‐phase flow degenerates to single‐phase flow and should be treated with different continuum models (Connolly & Podladchikov, ). As a result, the injected fluid fluxes at the model base of our simulations were controlled to restrict the evolved porosity inside the model domain to be below 20%.…”

“…Porosities at the bottom are fixed to a constant value of 1.2 × 10 −2 when imposing the “high fluid flux” boundary condition and to 3 × 10 −3 if the “normal fluid flux” boundary condition is desired. Basal porosities larger than 1.2 × 10 −2 will result in disaggregation of the matrix at porosity levels of about 20% inside the model domain (Arzi, ; Ashby, ; Auer et al, ; Connolly & Podladchikov, ; Vigneresse et al, ), whereas 3 × 10 −3 is on the order of background porosity (Skelton, ) but is still sufficient to generate fluid conduits. Basal thermal boundary conditions are prescribed according to section 2.1. The left and right boundaries are prescribed to be “no flux” and thermally insulated, i.e., ∂ Pe /∂ x = 0 and ∂ T /∂ x = 0, respectively.…”

Volatile Degassing From Magma Chambers as a Control on Volcanic Eruptions

“…Other processes that can produce transient permeability include filter pressing—the low‐density volatile phase forces melt through the locked crystal network (Sisson & Bacon, ); deviatoric thermal‐elastic stresses due to differential thermal expansion and the elastic response of the mineral assemblage in a rock (Joanne & Tengfong, ; Regenauer‐Lieb & Yuen, ); porosity waves initiated by the viscoporoelastic response of the crust (recurrence time of order 1–10 years, Connolly & Podladchikov, ); and dissolution of crustal rock by magmatic volatiles, for example, dissolution of carbonate samples by an aqueous carbon dioxide solution (Vanorio & Kanitpanyacharoen, ). The length scales for most of these processes are dependent on details of the magmatic‐hydrothermal system and are hence difficult to ascertain.…”