Jean-Pol Radu

Numerical modelling of coupled transient phenomena

ABSTRACT The basic phenomena involved in thermo-hydro-mechanical processes in geomaterials have been described in the 1st chapter. The equations describing these phenomena are non-linear differential equations. Their solution can generally only be approximated thanks to numerical methods. This is the main subject of the present chapter. First the type of problems and the set of equations to be solved will be shortly recalled. Emphasis will be given on the non-linear contributions. In a second section, the mostly developed numerical method, i.e. the finite difference and the finite element methods will be discussed under the light of the problems to be treated. The iterative techniques allowing the solution of non linear equations will be described. A third section will be dedicated to the coupling terms and to their modelling. The question that rises then is How to model efficiently problems, which may differ highly from, the point of view of the time and length scales?

Finite elements modelling of a large water table aquifer in transient conditions

Abstract A chalky aquifer located near Liege (Belgium), is recharged by infiltration through the overlying loess. Wells and collecting tunnels produce a daily flow of 60 000 m3 out of this aquifer when hydrogeological balances have shown that an average yield of 100 000 m3/day should be possible. Finite element modelling has been developed to foresee the evolution of the water table to get some additional information especially about the main drainage axis. The transient flow constitutive laws are recalled in confined and unconfined aquifers. A new law is proposed to model the water table surface in transient conditions and with a fixed meshing network. Using the local flow equilibrium and the virtual power principle, the FEM formulation is set up. The time integration and the iteration technique are shortly discussed. The 3D discretization and the modelling of the entire aquifer has been realized. The problem requires about 3600 DOF and 2670 8-nodes isoparametric brick finite elements. The modelling has been quite delicate because of the geometric complexity of the different geological layers. This complexity justifies fully the use of the finite element method; there is indeed a great diversity of geological characteristics and the range of the different permeabilities is very wide. Sensitivity of the model to permeabilities and storage coefficient variations has been studied and various numerical problems have been notified. The calibration procedure is described in its main steps, and the most significant results are presented.

Thermal Response Test in Borehole Heat Exchangers Equipped with Fiber Optics

Four double-U borehole heat exchangers (BHEs) of 100m long were installed on the campus of the University of Liege (Liege, Belgium). The installation procedure and technical difficulties are presented. Fiber optic cables are attached along the length of one pipe loop in each BHE. Temperature is measured along the fibers based on the fiber optic distributed temperature sensing (DTS) technique. Thermal response test (TRT) is conducted in order to determine the rock thermal properties. The DTS instrument records the temperature evolution along the pipe loop during the TRT. Rock thermal conductivity through depth can be estimated based on the recorded data. A 3D model is developed using the finite element code LAGAMINE in order to simulate the TRT. The accuracy of the numerical model is improved by simulating the potential variation of the rock thermal conductivity.

Gas injection test in the Callovo-Oxfordian claystone : data analysis and numerical modelling

Abstract This paper describes a field-scale experiment on gas transport mechanisms performed at Andras Underground Research Laboratory (URL) in a clay rock. The experimental layout consists of two parallel boreholes that are equipped with multiple packer completions isolating three intervals each, which have been continuously monitoring the pore pressure evolution of the clay rock. Nitrogen gas was injected in the middle test interval of one of the boreholes at increasing rates. The entire gas test comprised six periods of controlled gas injections, each followed by a shut-in pressure recovery phase. The experimental data are presented along with their interpretation by means of numerical modelling of two-phase flow of gas and water using different numerical codes and different geometrical approaches that include axisymmetric, half-space and full 3D models. An iterative modelling process was used to show step-by-step how an accurate description of each component of the experiment system produced a satisfactory reproduction of the experimental data and an improved understanding of the relevant phenomena. For instance, the initial volume of remaining water in the test interval, and the presence of a damaged zone around the boreholes, was important for the models to obtain good agreement with the field data.

A finite element code for subsidence problems: Lagamine

ConclusionsA general concept for the numerical modelling of an aquifer subsidence has been presented. Its main advantage is the separation from the three-dimensional flow model (which is a scalar field with one variable per node) and the compaction model (which is a vector field problem coupled to a scalar field problem, with 4 variables per node). This separation is very interesting for a “plate-like aquifer” because the compaction problem is reduced to a series of unidimensional problems with a small number of degree of freedom.The finite element code LAGAMINE has been applied to the flow and compaction problem. The equilibrium equations and the constitutive laws have been developed.Applications are presented in the next papers (papers V and VI). They demonstrate some of the capabilities of numerical simulations with the finite element code LAGAMINE.

Characterization of gas transport in low-permeability media: two-phase flow analysis of an in-situ experiment

This paper describes a field-scale experiment on gas transport mechanisms performed at the Andra Underground Research Laboratory in a clay rock. The experimental layout consists of two parallel boreholes that are equipped with multiple packer completions delimiting three intervals each and which monitor continuously the pore pressure evolution of the clay rock. Nitrogen gas is injected in the middle test interval of one of the boreholes at increasing constant rates. The experimental data collected so far are presented along with their interpretation by means of 1D and 3D numerical modeling of the boundary value problem. The numerical results show that a predictive model as two-phase flow approach is able to reproduce experimental observations in large scale system, as far as the injection flow rate and the gas pressures remain moderate. Moreover permeability is not modified by gas injection, which indicates that the rock mass is not damaged by the gas pressure increase during the test.

Oil field subsidence phenomena

ABSTRACT Subsidence of an chalky oil field is described. The mechanical behaviour of the chalk partly saturated by oil and water is described and allows to model the compaction occurring within a simple reservoir model during the depletion as well as during the water injection.

Hydromechanical Coupling and Basin Tectonic Compression

This paper deals with the numerical modelling with the LAGAMINE finite element code of the large strain elastoplastic deformation of a basin taking into account the hydromechanical coupling. One describes the rock mechanics model, the flow model, and the coupling between them. Volume finite element are proposed as well as interface one. The second ones are devoted to the modelling of faults, including the water flow through the fault. Finally the code is applied to a basin compression induced by sedimentation. It is shown that depending on the fault hydromechanical properties, a fault can be activated or not.