Beyond a given threshold, an upward fluid flow at constant flowrate, injected through a small size section, is able to generate a fluidization along a vertical chimney over the entire height of a granular assembly. Fluidization is first initiated in the immediate vicinity of the injection hole and then the fluidized zone grows gradually until reaching the upper surface of the granular packing. In this work, we present numerical results on the kinetics of chimney fluidization in an immersed granular bed produced with two-dimensional simulations coupling the Discrete Element and Lattice Boltzmann Methods (DEM-LBM). A parametric study is carried out with 11 different sets of physical parameters and analyzed based on spatio-temporal diagrams. Then a dimensional analysis allows finding general scaling laws for both threshold and growth rate of the fluidized zone by use of two dimensionless numbers, namely Reynolds and Archimedes numbers, while quite simple empirical relationships can also be proposed.