Multiscale Hybridization towards Efficient Oil and Gas Flows Simulations within Fractured Rocks

Abstract

Fractures impact the geological systems remarkably. So, their effects are included within the mathematical simulation models. Literature simulation schemes either lose the facture characteristics or are effort and time-consuming. So Hybrid-Fracture schemes are developed to overcome these drawbacks.

In the dissertation, a generalized Hybrid-Embedded Fractures (HEF) scheme is developed. It establishes a hierarchical classification based on fracture length's relation to uniform grid-cell lengths. Tall and medium-length fractures are detected from images, classified using Machine-Learning (ML) techniques, segmented based on the ML clusters intersections, and used to construct object-oriented based data-structures to simplify dealing with the fracture characteristics. A Deep-Learning (DL) design is set up for future work that is supposed to extract the fracture attributes from images directly.

Several fracture characteristics are utilized to generate physically more accurate REF matrix-fracture flux exchange parameters that validate better when compared to Discrete-Fracture-Network (DFN) scheme outcomes for similar conditions.

A generalized REF scheme that splits each fractured grid-cell into sub-grid matrices according to the fractures cutting them is designed. It extends the HEF concepts to nodal-grid based simulators and utilizes tree data-structure settings. The short-length fractures, from the hierarchical classification used, refer to the fractures and pores varying in scale from nanometers to micrometers. They form another smaller multiscale system and contribute significantly to the multiscale physical processes. Fractional order derivatives are used to deal with this scale, utilizing their additional degree of freedom, which is the order of the fractional order derivatives.

A hybrid cell-centered Physics Preserving Averaging (PPA) scheme is introduced to discretize the fractional order derivatives. Each fractional order derivative is expanded to left-side and right-side derivatives. The PPA scheme discretizes one of them using the original Grunwald-Letnikov (GL) formula, and the other using a shifted GL formula. The original part preserves more physical properties, and the shifted part maintains the stability of the system. PPA scheme also creates symmetrical coefficient matrices that help significantly when converting to higher dimensions, or applying to Multi-Point Flux Approximation configurations, or Multiple Interacting Continua configurations. Additional future work expansions are discussed using pore-scale network analysis and inverse solution methods.