Direct measurements of total reaction cross sections (sigma R) have been performed in the energy range of 10-300 MeV/nucleon for heavy ion collisions. A decrease of sigma R with increasing energy was observed for a wide range of masses of the colliding systems. The data suggest that sigma R reaches a minimum located around 300 MeV/nucleon independently of the projectile target combination. A dependence of sigma R on mass asymmetry of the svstem is also demonstrated. Trends of sigma R in this energy range are well reproduced by the predictions of a simple microscopic model based on individual nucleon-nucleon collisions. Our data have been employed in this framework to derive a new semi-empirical parametrization of sigma R. Most of the experimental results in the intermediate and high energy range have been reproduced by this parametrization using a single energy-dependent parameter.