Three compositional reservoir simulators have been developed in the Department of Petroleum and Geosystems Engineering at The University of Texas at Austin (UT-Austin): UTCOMP (miscible gas flooding simulator), UTCHEM (chemical flooding simulator), and GPAS (General Purpose Adaptive Simulator). UTCOMP and UTCHEM simulators have been used by various oil companies for solving a variety of field problems. The efficiency and accuracy of each simulator becomes critically important when they are used to solve field problems. In this study, two well-developed solver packages, SAMG and HYPRE, along with existing solvers were compared. Our numerical results showed that SAMG can be an excellent solver for the usage in the three simulators for solving problems with a high accuracy requirement and long simulation times, and BoomerAMG in HYPRE package can also be a good solver for application in the UTCHEM simulator. In order to investigate the flexibility and the efficiency of a partitioned coupling method, the second part of this thesis presents a new implementation using a partition method for a thermal module in an equation-of-state (EOS) compositional simulator, the General Purpose Adaptive Simulator (GPAS) developed at The University of Texas at Austin. The finite difference method (FDM) was used for the solution of governing partial differential equations. Specifically, the new coupled implementation was based on the Schur complement method. For the partition method, two suitable acceleration techniques were constructed. One technique was the optimized choice of preconditioner for the Schur complement; the other was the optimized selection of tolerances for the two solution steps. To validate the implementation, we present simulation examples of hot water injection in an oil reservoir. The numerical comparison between the new implementation and the traditional, fully implicit method showed that the partition method is not only more flexible, but also faster than the classical, fully implicit method for the same test problems without sacrificing accuracy. In conclusion, the new implementation of the partition method is a more flexible and more efficient method for coupling a new module into an existing simulator than the classical, fully implicit method.The third part of this thesis presents another type of coupling method, iterative coupling methods, which has been implemented into GPAS with thermal module, FICM (Fully, Iterative Coupling Method) and GICM (General, Iterative Coupling Method), LICM (Loose, Iterative Coupling Method). The results show that LICM is divergent, and GICM and FICM can work normally. GICM is the fastest among the compared methods, and FICM has a similar efficiency as CFIM (Classic Fully Implicit Method). Although GICM is the fastest method, GICM is less accurate than FICM for in the test cases carried out in this study. / text