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

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 flow of the fluid through the matrix and matrix deformation. This work 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 prediction of the 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 tubelike porosity waves that form in such a rheology channelize fluid expulsion and are predicted by geometric argumentation from the one-dimensional viscous solitary wave solution.