The combined use of mathematical and computational modeling has become essential for optimizing the exploration and management of oil and gas reservoirs. Various mathematical techniques are employed to develop analytical solutions, particularly in reservoir simulation, where parameters such as permeability remain unknown, requiring testing for information extraction. A classic approach to solving the diffusivity equation, which describes fluid flow in porous media, is the pseudopressure function. Its purpose is to linearize part of the equation, facilitating the solution calculation, but its application requires complementary methods to handle nonlinearities and achieve greater accuracy. This thesis proposes two analytical solutions for single-phase oil flow in two types of reservoirs: multilayer homogeneous and single-layer heterogeneous with two homogeneous regions, considering pressure-dependent permeability. The solutions utilize Green s function problem combined with the perturbation method and asymptotic expansion, enabling a detailed analysis of reservoir properties and permeability-pressure curves. The model validation was carried out through the implementation of an algorithm and comparison with a commercial finite-difference based flow simulator. Given the increasing demand for more robust techniques in the oil industry, advanced mathematical methods, such as the proposed approach, are essential for optimizing decision-making and improving production efficiency. Thus, this work contributes to the advancement of analytical tools in reservoir modeling and simulation.