N. Castelletto

A fully coupled 3-D mixed finite element model of Biot consolidation

The numerical solution to the Biot equations of 3-D consolidation is still a challenging task because of the ill-conditioning of the resulting algebraic system and the instabilities that may affect the pore pressure solution. Recently new approaches have been advanced based on mixed formulations. In the present paper a fully coupled 3-D mixed finite element model is developed with the aim at alleviating the pore pressure numerical oscillations at the interface between materials with different permeabilities. A solution algorithm is implemented that takes advantage of the block structure of the discretized problem. The proposed model is verified against well-known analytical solutions and successfully experimented with in realistic applications of soil consolidation.

Scalable algorithms for three-field mixed finite element coupled poromechanics

Abstract We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.

The effect of graph partitioning techniques on parallel Block FSAI preconditioning: a computational study

Adaptive Block FSAI (ABF) is a novel preconditioner which has proved efficient for the parallel solution of symmetric positive definite (SPD) linear systems and eigenproblems. A possible drawback stems from its reduced strong scalability, as the iteration count to converge for a given problem tends to grow with the number of processors used. The preliminary use of graph partitioning techniques can help improve the preconditioner quality and scalability. According to the specific theoretical properties of Block FSAI, different partitionings are selected and tested in a set of matrices arising from SPD engineering applications. The results show that using an appropriate graph partitioning technique with ABF may play an important role to increase the preconditioner efficiency and robustness, allowing for its effective use also in massively parallel simulations.

Multiscale finite-element method for linear elastic geomechanics

The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.

A coupled MFE poromechanical model of a large-scale load experiment at the coastland of Venice

A three-dimensional fully coupled mixed finite element (MFE) model based on Biot’s consolidation equations is implemented to simulate the geomechanical response of a large-scale 5-year long loading/unloading test performed at the Venice coastland, Italy. The model uses linear piecewise polynomials and the lowest order Raviart–Thomas mixed space to represent the porous medium motion and the groundwater flow rate, respectively. The approach ensures an element-wise mass conservative formulation while preserving the stability of the numerical solution and providing at the same time an accurate calculation of the flow field. With the aim of characterizing the Late Pleistocene and Holocene deposits above, which the MoSE project, i.e. the mobile barriers to protect Venice from acqua alta, is under implementation, a 20-m radius, 6.7-m tall vertically walled cylinder was built from September 2002 to March 2003 and removed in June 2007. The maximum load exerted on the ground at the completion of the building activity was 0.105 MPa. The land displacements were accurately monitored at various depths and the center and outer boundary of the embankment by sliding deformeters, leveling, global positioning system, and persistent scatterer interferometry. Moreover, in situ tests and standard lab tests were performed to define the hydrological and geomechanical properties of the soil underlying the cylinder. The model addresses the actual lithostratigraphy of the subsurface down to 50-m depth below the embankment and prescribes the land surface loading versus time as an external source of strength. A hysteretic elastic constitutive law, with the Young modulus E in the loading phase between 2 to 36 Mpa according to lithology, a ratio s=15 of loading to unloading cycle E, and a small adjustment of the hydrological parameters allow to predict quite satisfactorily most of the observed pressure behavior, together with vertical and horizontal displacements.

Hybrid Multiscale Formulation for Coupled Flow and Geomechanics

We devise a hybrid MultiScale Finite Element-Finite Volume (h-MSFE-FV) framework to simulate single-phase flow through elastic deformable porous media. The coupled problem is solved based on a two-field fine-scale mixed finite element-finite volume formulation of the governing equations, namely conservation laws of linear momentum and mass, in which the primary unknowns are the displacement vector and pressure. For the MSFE displacement stage, we develop sets of local basis functions for the displacement vector over coarse cells, subject to reduced boundary condition. This MSFE stage is then coupled with the MSFV method for flow, where coarse and dual-coarse grids are imposed to obtain approximate but conservative multiscale solutions. Numerical experiments are presented to demonstrate accuracy and robustness of the proposed h-MSFE-FV method---both as an approximate, non-iterative solver, and a preconditioner.

Fully-Implicit Solvers For Coupled Poromechanics Of Fractured Reservoirs

In this work we present a family of preconditioners for accelerating the fully-implicit solution of linear systems encountered in two practical applications: (i) Lagrange multiplier-based fault mechanics simulations using a mixed finite element approach, and (ii) multiphase poromechanics based on a mixed finite element-finite volume formulation. We consider block preconditioning strategies and focus on various Schur complement approximations that are based on a combination of physical and algebraic arguments. The performance of the proposed framework is illustrated using two challenging numerical examples---a synthetic fault mechanics test with manufactured solution and a large-scale water flooding problem.

A coupled poroelasticity model by Mixed Finite Elements for aquifer recharge simulations

In real-world applications involving complex, 3D, heterogeneous domains, the use of advanced numerical algorithms is of paramount importance to solve stably, accurately and efficiently the coupled system of partial differential equations (PDEs) governing the mass and the energy balance in deformable porous media. The present paper discusses a novel coupled 3D numerical model based on a combination of Finite Elements (FE) and Mixed FE (MFE) developed with the aim at stabilizing the numerical solution.

Compartmentalization Effects in Geologic CO 2 Sequestration. A Case Study in an Offshore Reservoir in Italy

The implementation of suitable carbon capture and storage (CCS) technologies is a mandatory requirement for reducing anthropogenic emissions of greenhouse gases (GHG) and obtaining a sustainable power generation from fossil fuels, especially coal. Carbon dioxide (CO2) sequestration within deep underground reservoirs is indicated as one of the most promising techniques which, however, implies a complex multidisciplinary effort involving a number of hydrological, geomechanical and geochemical issues. In the present contribution a geomechanical modeling study of the CO2 disposal into an offshore multi-compartment saline aquifer located at about 1500 m depth in the Northern Adriatic Sea, Italy, is discussed. The study assumes a CO2 injection rate of 1×10 6 ton/a and shows that a safe and permanent containment may be secured over a few years only for the considered distributions of the petrophysical properties and initial in-situ stress and pore pressure.