Finite element simulations of bubbling gas-solid fluidized beds were performed using the two-fluid granular temperature model. A study was carried out to establish the number of equations necessary to describe the dynamics of this fluidized bed. In order to investigate the bubbles' behaviour and shape, several simulations were performed using differing numerical resolution. The main purpose of these investigations is to analyse, through numerical simulation, the dynamics of fluidized beds and to show how the application of deterministic chaos theory may be used to obtain the real dimensionality, or the number of degrees of freedom, of a simulated fluidized bed. Moreover, this type of statistical information can be used to quantify the similarities between experiment and simulation results.