Francesco Cecinato

Deformable Porous Media Saturated by Three Immiscible Fluids: Constitutive Modelling and Simulations of Injection and Imbibition Tests

A number of environmental and petroleum engineering applications involve the coexistence of three non-miscible fluids. In this work, basic constitutive relations and computational schemes are developed in order to simulate fluid injection and imbibition processes in a deformable rock through the finite element method. For this purpose, the following ingredients are worked out: (i) simple, but general formulas for the effective saturations; (ii) constitutive expressions for the relative permeabilities of water, oil and gas in terms of effective saturations; and (iii) constitutive capillary pressure relationships. These ingredients are introduced in a domestic finite element code where the primary variables are the solid displacement vector and the three fluid pressures. Given the abundance of experimental data in the petroleum engineering field, the whole framework is firstly tested by simulating gas injection into a rock core sample initially saturated by water and oil. Sensitivity analyses are performed upon varying key constitutive, loading and numerical parameters, to assess the physical and computational outputs of the proposed framework. Particular attention is given to the influence on the model predictions of several expressions defining relative permeabilities. Simulations of water-alternated-gas injection and of counter-current water imbibition tests are also performed, to establish the reliability of the proposed constitutive and computational framework.

Dynamical effects during compaction band formation affecting their spatial periodicity

Compaction bands (CBs) are responsible for significant anisotropy alterations of permeability in geological materials; hence, understanding their formation conditions appears of key importance to all applications involving fluid extraction/injection from/into the ground. While most of the available models to understand CB formation are focused on interpreting the onset of a single CB, little effort has been so far dedicated to understand the documented periodicity of CBs. In this paper, the role of dynamical effects in inducing the post onset evolution of CBs is analyzed by means of a dedicated model for porous media with compressible constituents, with reference to a horizontal layer of sandy, water-saturated material. Elastic waves are generated as a first CB occurs due to sudden, localized volumetric collapse. If the waves are reflected at the interface with a softer material or with a previously formed CB, they produce significant local effective stress concentrations, which can promote the formation of further CBs in a cascade fashion, according to a regular geometric pattern. The spatial distribution of dynamically generated CBs, as well as the extent of the phenomenon, depends on the geometry of the domain and on the materials permeability. Sensitivity analysis is also performed to assess the key properties that promote dynamical CB in situ formation, identifying as the most influential conditions large stratum stiffness (increasing with depth) and the presence of softer layers. In contrast, the presence of less permeable and/or stiffer layers is not believed to play a major role in the proposed mechanism.