Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
SIMULATION OF FLOW IN SATURATED POROELASTIC MEDIA WITH ISOLATED VUGS
Submission Author:
Monique Feitosa Dali , RJ , Brazil
Co-Authors:
Monique Feitosa Dali, FREDERICO CARVALHO GOMES, Marcio CARVALHO
Presenter: Monique Feitosa Dali
doi://10.26678/ABCM.COBEM2021.COB2021-0377
Abstract
Modeling the interaction between fluids and porous structures subjected to mechanical forces is a complex problem. Because of its wide range of applications, this field has been attracted attention. Recently, substantial research effort has been directed to the study of poroelastic media in Brazil, due to the interest in determining the hydro-mechanical response of pre-salt carbonate reservoirs. Carbonates are heterogeneous formations that normally exhibit multiple spatial scales. Vuggy carbonates commonly present two different scales of pores, while even more scales can be found in fractured vuggy carbonates. Therefore, predictive modeling of flow in carbonates should take into account not only the transport processes on multi-porosity media but also the effects of geomechanical issues, such as subsidence, soil compaction and collapse of cavity regions, which can impact negatively the flow performance. We propose a finite element model for the coupled solution of flow and poromechanics in a vuggy deformable porous media, under quasi-static conditions. We construct an artificial porous medium model wherein the isolated macropores are explicitly marked regions with free flow and the microporous structure is replaced by averaged homogeneous properties. Furthermore, we apply the Stokes equation inside the vugs to model the free fluid transport, while the Biot model is used in the saturated poroelastic region. The latter is adopted to model the hydro-mechanical coupling effects of porous media based on a linear stress-strain relationship. The selected single-domain approach uses the Brinkman equation, which governs the flow interaction across both domains and vug-matrix interface, establishing a seamless transition between the two different flow regions. This flow scheme recovers Darcy's law on the fine-scale and the Stokes equation in the macropores through an appropriate choice of parameters. A two-dimensional model for the time-dependent displacement of a vuggy porous media is implemented in Python on the open-source FEniCS platform. The implementation of Biot's model is validated using two well-known poroelastic benchmark problems, the consolidation problem of Terzaghi and Mandel's problem. With the Biot-Brinkman system of equations, a load was applied to 2D porous medium samples containing circular vugs and filled with fluid, in order to evaluate pressure, displacement and flow rate response. The impact of the circular inclusions on flow was assessed, and the macroscopic equivalent properties that are relevant to large-scale production predictions were calculated.
Keywords
poroelasticity, Biot's model, Brinkman equation, finite element, Vuggy porous media
