System dynamics modeling of nonlinear solid, fluid, and porous media

Methods of fracturing rock are of importance with regard to the stimulation of marginal reservoirs. Tailored pulse stimulation has the potential of creating a system of fractures intersecting the existing fluid-bearing fractures within the rock, thus leading to an enhancement of the reservoir yield. Damage mechanics is able to provide a continuum based description of the brittle fracture process, which can be implemented in a Lagrangian finite element code for use in design calculations. A second-order tensor based elastic-damage model is formulated for porous rock, involving a thermodynamically consistent rate dependent damage evolution law, along with an approximate implementation of the pore fluid pressure effect. The model is validated using published wellbore stimulation data. A novel methodology is proposed to formulate a model rigorously coupling the solid and fluid dynamics of the porous media, combining a finite element discretization scheme with a unified bond graph approach. This results in a state space description of the system dynamics, distinct from alternative schemes based on weighted residual solutions of the governing partial differential equations. The model accounts for the energy transfer between the fluid and solid constituents, which are modeled in the Eulerian and Lagrangian frames respectively. This porous media model is suitable for use in very general simulation applications. The same methodology is successfully applied to formulate a Lagrangian model of coupled solid dynamics and heat diffusion, and an Eulerian model for viscous, compressible flow.