In-situ adaptive tabulation (ISAT) method, which can treat complex chemistry efficiently, has been implemented into a multiphase computational fluid dynamics (CFD) code. The numerical algorithm is improved to solve the chemical source term. Two-dimensional and three-dimensional non-isothermal detailed silane pyrolysis cases are used to test the features of ISAT, such as scale factors and multiple tables on multiple processors. ISAT can reduce the computational time for chemistry drastically. For example, a speed-up of 50 times is achieved with the non-isothermal three-dimensional case. Coal gasification with detailed chemical reactions is simulated to test the performance of ISAT with complex gas-solid reaction mechanisms. The speed-up of chemistry is around 16 times with 10% reduction in total CPU time for simulations. The elutriation phenomenon in fluidized beds is also studied in order to increase the efficiency of biomass reactors. In the simulations, fine and coarse particles are solved as two individual phases. Effects of gas velocity, and fine and coarse particle diameters are investigated for elutriation rate constants. The elutriation rate constants are proportional to approximately the 5.6th power of the gas velocity and decrease with increasing fine diameters. The diameters of coarse particles have little influence on elutriation rate constants. The simulation results are compared with experiments from the literature and performed at Iowa State University. Apart from the mainstream of this research, the effects on the use of coordinate systems and configurations to model fluidized bed reactors are tested. Three different fluidization regimes: bubbling, slugging and turbulent regimes are investigated. The results indicate that a two-dimensional Cartesian system can be used to successfully simulate and predict a bubbling regime. Caution must be exercised when using two-dimensional simulations for other fluidized regimes.