Luciano Simoni

Mechanics of Partially Saturated Porous Media

In the framework of the volume fraction theories, the governing equations of problems of mechanics of partially saturated porous media are derived. The use of general averaging principles provides the definition of averaged field variables, which allow the connection with experimental data. A finite element discretization of the governing equations is subsequently presented.

A coupled model for water flow, airflow and heat flow in deformable porous media

A fully coupled numerical model to simulate the complex behaviour of soil deformation, water flow, airflow, and heat flow in porous media is developed. The following thermal effects are taken into account: heat transfer through conduction and convection, flow, as well as viscosity and density variation of the fluids due to temperature gradients. The governing equations in terms of soil displacements, water and air pressures, and temperature are coupled non‐linear partial differential equations and are solved by the finite element method. Two examples are presented to demonstrate the model performances.

Cohesive fracture mechanics for a multi‐phase porous medium

This paper presents a mathematical model for the analysis of cohesive fracture propagation through a non‐homogeneous porous medium. Governing equations are stated within the frame of Biots theory, accounting for the flow through the solid skeleton, along the fracture and across its sides toward the surrounding medium. The numerical solution is obtained in a 2D context, exploiting the capabilities of an efficient mesh generator, and requires continuous updating of the domain as the fractures enucleate and propagate. It results that fracture paths and their velocity of propagation, usually assumed as known, are supplied directly by the model without introducing any simplifying assumption.

Standard staggered and staggered Newton schemes in thermo-hydro-mechanical problems

The aim of the paper is to compare the rates of iteration convergence of two staggered numerical schemes: one using successive substitutions and the other the Newton method. In the case of very weakly coupled problems the Newton method is one order faster, but there are specific cases when it is slower than the standard staggered algorithm. In both cases a convergence condition must be verified. The behaviour of the investigated staggered procedures in case of thermo-hydro-mechanical problems are shown on examples.

A general model for the mechanics of saturated-unsaturated porous materials

A general predictive model for the mechanical analysis of isothermal and non-isothermal saturated-unsaturated porous materials is presented. The model is developed along the lines of Biots theory and applies both for high water content and for low to medium water content in the pore space. Due to the similarity of the matrices in both situations, even if the transfer mechanisms are different, a single computer program can handle all of them. Examples belonging to both domains in the isothermal case as well as to heat and mass transfer in deforming porous media are shown.

Elastoplastic subsidence models with and without capillary effects

This paper investigates reservoir compaction and resulting surface subsidence during the exploitation of a gas reservoir and in the period after well shutdown. A substantial difference in behaviour results when assuming elastic and elastoplastic constitutive relationships for the reservoir rock and surroundings. Further, a correction is introduced to account for capillary effects, which strongly modify the behaviour especially after shutdown and may account for the ongoing subsidence observed.

Multi Field Simulation of Fracture

Abstract We present as areas of interest for multifield fracturing thermomechanical fracturing, fluid pressure induced isothermal and nonisothermal fracturing, fracturing due to radiation, drying, hydrogen embrittlement, and fractures induced by chemical effects. We discuss the most appropriate constitutive models for their simulation and choose the cohesive fracture model for quasi-brittle materials. Successively we show governing equations for a thermo-hydro-mechanical problem, which is representative for multifield problems. Possible extensions to more fields are addressed. Then methods for numerical modeling of multifield fracturing are presented and the most representative ones, i.e., interface and embedded discontinuity elements, X-FEM, thick level set and phase field models, and discrete crack approach with adaptive remeshing are discussed in some detail. After incorporating this last method in the governing equations, their numerical solution is shown together with the necessary adaptivity in time and space. This solution is validated. Successively applications to thermomechanical fracture; hydraulic fracturing in case of a pumped well and of 2D and 3D dams; fracturing of drying concrete and of a massive concrete beam and finally mechanical effects of chemical processes in concrete are shown. In the case of the pumped well with constant pumping rate, a comparison between an Extended Finite Element solution and that of the discrete crack approach with adaptive remeshing is made which allows for interesting considerations about the nature of hydraulic fracturing. The examples permit to conclude that with increasing complexity of the multifield problems that of the employed fracture models decreases, i.e., advanced fracture models have to date only been applied to problems with a limited number of fields, mainly displacement, thermal and/or pressure fields. There is hence plenty of room for improvement.

A Mechanism Contributing to Subsidence Above Gas Reservoirs and its Application to a Case Study

This paper aims to demonstrate that capillary effects and structural collapse can not be ruled out as significant factors in the development of subsidence occurring above gas fields. These phenomena provide sound explanations for continuing surface settlements when reservoir pore pressures stabilize and for additional settlements occurring even after the end of gas production. Conventional subsidence models fail to simulate this settlement behavior. Capillary effects also explain the lower rock compressibilities observed in gas-bearing strata as compared to the values obtained in the laboratory from fully saturated samples. Taking into account these aspects, the observed subsidence above a reservoir in the North Adriatic basin, Italy, is studied in detail.

Numerical Solutions of Thermo — Hydro — Mechanical Problems

This chapter summarizes the numerical techniques which complete the mathematical model and allow for the application in real cases. Both-spatial and temporal discretizations are presented in a general way, together with possible solution algorithms for the ensuing equations. The properties of the numerical solutions are then analyzed and used to discuss the possible choices of the field variables.

On compaction in gas reservoirs

Compaction in gas reservoirs is analysed here in terms of mechanics of partially saturated soils, where capillary effects are of importance. An elasto-plastic model is used for this purpose and a newsubsidence mechanism is shown, which does not appear in traditional subsidence models based on decrease of reservoir pressure only.RiassuntoViene analizzata la compattazione derivante dallo sfruttamento di giacimenti di gas, utilizzando la meccanica dei mezzi parzialmente saturi, contesto in cui assume importanza l’ effetto della pressions: capillare. A tale scopo viene utilizzato un modello elasto-plastico e viene evidenziato un nuovo mcccanismo di subsidenza, che non appare nei modelli tradizionali, basati solamente sulla diminuzione della pressione del gas nel giacimento.