Zero-thickness interface elements in petroleum geomechanics : sand production and hydraulic fracture

Aplicat embargamet des de la data de defensa fins el dia 20 de setembre de 2019 This thesis describes the extension of the Finite Element Method with zero-thickness interface elements (FEM+z) to 3D, large and complex problems in geomaterials, with special interest in petroleum geomechanics. This general objective has led to specific developments and applications such as the 3D code implementations and parallelization, and the specific petroleum geomechanics studies, both the macroscale (hydraulic fracture) and microscale (sand production). The extension to 3D of the hydro-mechanical formulation of double node zero-thickness interface elements proposed earlier, has been developed and implemented in the computer code, with satisfactory results in the verification examples. From the theoretical viewpoint, the formulation is generalized via the definition of \quotes{transport} matrices for both mechanical and hydraulic formulations, so that the two levels of the formulation can be separated: the nodal variables of the interface element, and the mid-plane variables. The formulation described is successfully validated with benchmarking examples based on analytical expressions of a hydraulic fracture. The parallelization of the code DRAC is achieved through the implementation of public domain library PETSc. The new code structure is conceived to perform a correct subdivision of tasks associated to each processor. For this purpose, a domain decomposition strategy has been implemented, which is crucial for an efficient matrix generation and assembly. The results obtained show a good degree of parallelization, demonstrated with a cube benchmark test. The applications to hydraulic fracture have served a dual purpose. First, the examples of a single fracture have been used to validate the proposed formulation, since it has been possible to compare the results with the predictions of analytical expressions such as GDK or PKN, and to other numerical results from the literature. Second, the examples of multiple interacting fractures have shown the capabilities to analyze large and complex cases. The studies performed have shown a number of relevant aspects of multiple fracturing such as the effect of geometry (distance between injections) and the effect of in situ stresses. Finally the thesis is devoted to the micromechanical analysis of sand production, including the generation and testing of micromechanical models based on the use of zero-thickness interface elements.