ADVANCED LINEARIZATION SCHEMES FOR FULLY COUPLED GOVERNING EQUATIONS FOR CARBONATE RESERVOIRS

Abstract

Accurate multiphase flow simulation in carbonate reservoirs remains challenging due to high heterogeneity, strong nonlinearity, and complex phase behavior. This thesis presents a comprehensive investigation of advanced linearization methods aimed at enhancing the accuracy, stability, and computational efficiency of multicomponent multiphase flow simulations in highly heterogeneous carbonate reservoirs. Several linearization schemes, including finite forward difference (FDF), the finite backward difference (FDB), the finite central difference (FDC), and the residual accelerated Jacobian (RAJ) method were implemented within an in-house multiphase simulator and evaluated for computational efficiency, accuracy, and reliability of reservoir simulations, particularly under challenging conditions such as high heterogeneity and multi-component multiphase flow systems. Methods were benchmarked against analytical solutions and commercial simulators across three model types. For the dead oil model, OBL excelled in 1D Buckley–Leverett tests while FDC proved more accurate and computationally efficient in the second test. For the black oil model on unstructured grids, FDC showed superior accuracy in heterogeneous cases, motivating the development of the new technique RAJ, designed to improve accuracy and convergence speed while reducing cost. Although RAJ shows promising initial results, broader testing across varied reservoir configurations is needed to confirm its reliability. For compositional models, results were benchmarked against a commercial legacy simulator. OBL proved most efficient for multicomponent multiphase gas reservoirs; FDB excelled in ten-component hydrocarbon mixtures; and RAJ, designed to accelerate Jacobian assembly and reduce convergence iterations, showed potential in cases without gas injection but required broader evaluation. This thesis offers a systematic evaluation of advanced linearization techniques for multiphase multicomponent flow in highly heterogeneous carbonate reservoirs, combining analytical benchmarks, commercial simulator comparisons, and complex case studies. The RAJ method advances nonlinear solution strategies through improved convergence and reduced computational effort. The findings confirm that no single technique is universally optimal, effective simulation requires context-dependent scheme selection, and establish a foundation for developing more robust and efficient frameworks for complex subsurface systems.

Date of Award	2026
Original language	American English
Awarding Institution	HBKU College of Science and Engineering