Advanced numerical methods for modeling pressure maintenance strategies during secondary and tertiary oil recovery in stratified petroleum reservoirs

Summarization: The current thesis focuses on the numerical modeling of pore-to-field scale couplings in hydrodynamic dispersion and immiscible flows in porous media using the standard finite element framework provided by the commercially available software COMSOL Multiphysics. The single-phase flow is handled through the study of hydrodynamic dispersion during an ideal tracer injection by using COMSOL’s readily available Physics interfaces. The coefficient of hydrodynamic dispersion is explicitly calculated through rigorous pore-scale simulations in 2D porous domains and from the results obtained, a homogeneous model for porous media is defined using the calculated effective transport properties. The upscaling from the pore-scale to the REV-scale as far as transport properties of the porous medium are concerned is evaluated through the hydrodynamic dispersion coefficient and an appropriate volume-averaged expression of the mass conservation equation. Results indicated that statistical properties conveniently derived at the REV-scale, can successfully be used for the precise calculation of pore-scale transport properties. The two-phase incompressible flow during a waterflooding oil recovery process in a stratified petroleum reservoir is simulated via two numerical models; one that includes the gravitational terms and one that omits them. The equations of the mathematical flow model are derived under specific assumptions and formulated according to the fractional flow approach. The PDE modes in the general and coefficient form for time dependent analysis are utilized for their numerical implementation in COMSOL Multiphysics. An appropriate, numerically stable, formulation of the black oil model is then used for the simulation of two-phase compressible flow during a waterflooding process in an undersaturated petroleum reservoir. The model is based on the oil phase pressure and total velocity formulation. Its implementation in COMSOL is made with the time-dependent PDE interfaces. The physical models of the waterflooding processes are also implemented in ECLIPSE 100 simulator and the results from the two simulators are compared so as to evaluate the performance of the newly-developed COMSOL PDE modules in quantifying and interpreting relevant physical phenomena. The results from the incompressible fluid flow modeling revealed that both COMSOL models are generally in good agreement with ECLIPSE 100 as far as recovery is concerned, with the COMSOL model that neglects the gravity exhibiting a better matching. The results obtained from the implemented formulation of the black oil model are also very close to the ones from ECLIPSE 100 regarding hydrocarbons production rates. That indicates that COMSOL Multiphysics can efficiently be used as a trustworthy tool in hydrocarbons recovery predictions and also for the solution of more complex physics phenomena in reservoir simulation problems.