The seepage mechanics model comprises multiple nonlinearly coupled partial differential equations. In various applications, seepage mechanics problems exhibit distinct characteristics and the corresponding solution methods are also very different. This paper focuses on the representative mathematical models used in oil and gas reservoir development. It introduces the mathematical formulation and application characteristics of multiphase multicomponent seepage mechanics equations within porous media, along with efficient techniques for solving their discretized linear equation systems, including commonly employed preconditioning methods. Additionally, this study appropriately modifies standard test cases and evaluates the shared-memory parallel efficiency of these preconditioning methods.