Access to energy resources is indispensable for the growth and development of modern society. As the majority of these resources are obtained through the extraction of fossil fuels, there is a consequential increase in CO2 emissions which contribute to the greenhouse effect. This necessitates the urgent implementation of efficient fossil fuel production methods during the transition to cleaner energy sources, and the development of strategies for capturing and sequestering CO2 in geological formations. Understanding flow and displacement phenomena in porous media is central to these endeavors. However, given the scarcity and often incompleteness of reservoir data, there is a need for reliable simulation methods. This research aims to model and analyze multiphase displacement processes in porous media to deepen the understanding of these phenomena and develop methods that will ultimately bridge the gap between microscopic and macroscopic scales. The primary objective is to compute capillary pressure and relative permeabilities and conduct an in-depth analysis of imbibition displacement modeling under different wettability conditions. The Morphological Method (MM) is particularly appropriate for this research due to its computational efficiency, allowing for simulations on large domains while accommodating uncertainty analysis. This method, which uses mathematical morphology to populate a porous medium with different phases, will be not only utilized but also further refined within this study. Traditionally, MM models quasi-static, capillary-driven processes and does not incorporate a time scale, rendering it less effective for imbibition modeling. This study introduces an enhanced version of MM by integrating forced imbibition, effectively adding a quasi-time scale to the displacement process, which improves the alignment between model predictions and experimental data. Additionally, the extended MM includes structural constraints and introduces two strategies for distributing the non-wetting material within porous structures: a stochastic approach, which involves random distribution, and a deterministic approach that orientates the distribution on the pore size distribution. Using the extended MM, capillary pressure and relative permeability saturation functions for various rock structures are modeled, and the sensitivities of these functions to different wetting states and contact angles are investigated. Minkowski functionals are employed to provide a comprehensive description and evaluation of the results, highlighting distinct topologies for wetting and non-wetting phases and illustrating the significant influence of spontaneous imbibition on topology. This research represents a major step forward in the understanding of pore-scale physics in porous media and the enhancement of multiphase flow modeling techniques. It underscores the importance of taking into account the pore structure and wettability distribution in simulations. The extended MM emerges as a robust and efficient pore-scale simulation tool with significant potential for practical applications in accurately modeling fluid displacements in porous media. This is crucial for uncertainty analysis, the proficient extraction and storage of resources, and the underground storage of CO2.