Banca de QUALIFICAÇÃO: PEDRO AUGUSTO PIMENTEL PINHEIRO

Uma banca de QUALIFICAÇÃO de MESTRADO foi cadastrada pelo programa.
STUDENT : PEDRO AUGUSTO PIMENTEL PINHEIRO
DATE: 31/05/2026
TIME: 15:00
LOCAL: Ambiente virtual
TITLE:

Mathematical and Computational Modeling of Compressible Two-Phase Flow in Porous Media

KEY WORDS:

Mathematical and Computational Modeling; Compressible Two-Phase Flow; Porous Media; Mixed Finite Element Method; Finite Volume Method; Geological CO2 Storage

PAGES: 79
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

The numerical simulation of compressible two-phase flow in porous media constitutes a problem of great scientific and technological relevance, with applications in various fields of engineering and geosciences, such as oil and gas reservoir exploration, the analysis of contaminated aquifer remediation, and the efficiency of underground gas storage processes. This Master's qualification thesis presents the derivation of a mathematical and computational model for the two-phase flow of compressible fluids in porous media. The mathematical modeling is given by the mass conservation equations and the generalized Darcy's law for each fluid phase, including capillary pressure effects and the dependence of fluid densities on the pressure field. Summing the mass conservation equations for each phase yields the total mass balance, where the total mass flux is formulated in terms of a global pressure that eliminates the explicit dependence on saturation gradients. The saturation transport equation is obtained through a mass fractional flow decomposition, resulting in advective and capillary diffusive terms. Adopting a sequentially coupled formulation, the discretization of the hydrodynamic problem is performed using the mixed finite element method, ensuring local mass conservation and continuity of the normal flux at the element interfaces. For the transport equation, the finite volume method with an implicit Upwind scheme is employed, ensuring stability in capturing solutions that present strong gradients or discontinuities. Furthermore, to treat the second-order term arising from the capillarity effect, a central difference discretization using the TPFA method is applied. The linearization of both subproblems is handled by an iterative scheme based on Newton's method. Numerical simulations are performed to validate the proposed mathematical and computational model, analyzing the temporal evolution of the pressure, saturation, and total mass flux fields. As an application, the computational model will be applied to the numerical simulation of the carbon dioxide (CO2) injection process in saline aquifers, within the context of geological carbon storage as a greenhouse gas emission mitigation strategy.

COMMITTEE MEMBERS:
Externo ao Programa - 1288120 - ADRIANO DOS SANTOS - nullExterno à Instituição - LEONARDO ASFORA DE OLIVEIRA - IFRN
Presidente - 1646718 - SIDARTA ARAUJO DE LIMA