A generalized poroelastic model using FEniCS with insights into the Noordbergum effect. (February 2020)

• Record Type: Journal Article
• Authors: Haagenson, Ryan; Rajaram, Harihar; Allen, Jeffery
• Is Part Of: Computers & geosciences. Volume 135(2020)
• Publication Date: 2020-02
• Subjects: Poroelasticity -- Geomechanics -- FEniCS -- DOLFIN -- Model development; Environmental policy -- Periodicals; 550.5
• DOI: 10.1016/j.cageo.2019.104399
• Languages: English
• ISSNs: 0098-3004

Abstract

Abstract: Understanding the coupled behavior of fluid flow and solid deformation in porous media is often a critical aspect of geoscientific investigations, including studies of injection-induced seismicity, geological carbon sequestration, or surface deformation from pumping operations. In 1941, Biot first outlined the standard poroelastic formulation that accounted for this coupling within an isotropic and elastic porous medium. This fully coupled system of partial differential equations typically requires the use of numerical modeling for any practical purposes, necessitating either lengthy code development or the use of a complex, prebuilt model that often lacks flexibility. However, due to recent advances in automated approaches to solving systems of differential equations, problems of poroelasticity can now be easily handled in a streamlined yet flexible manner. Here, we present a poroelastic model built within the framework of FEniCS – an open source, general purpose finite element method software – which solves the system monolithically and can produce a continuous and mass-conserving solution for specific discharge. We present both a linear model and a generalized, nonlinear model. The nonlinear model allows for variable fluid density and employs a fluid pressure and volumetric strain dependent porosity relationship. The behavior of the linear model is verified with common benchmark problems, whereas results from the nonlinear model are compared to assess the impact of including its generalizations. Finally, the model is applied to a two-dimensional problem of fluid extraction meant to replicate the well-known Noordbergum effect (in which the fluid pressure in layers adjacent to the pumped layer temporarily increases during pumping). This is often referred to as "reverse water fluctuation". This showcases not only the flexibility of the model but also its ability to simulate numerically challenging scenarios. The results from this simulation suggest a novel explanation of the physical mechanism generating the Noordbergum effect: strain gradients. Highlights: Generalized poroelastic formulation with porosity relationship from solid continuity. Mixed Finite Element formulation with monolithic solve ensuring robustness. FEniCS implementation offers significant flexibility while remaining streamlined. Model benchmarked against classical Terzaghi's and Cryer's problems. Simulations of pumping suggest novel physical mechanism for the Noordbergum effect.