The two-dimensional multifluid code TECXY has been used to model the biasing (with respect to the first wall) of the toroidal belt limiter ALT-II on the tokamak TEXTOR-94 and of the new toroidal pump limiter being installed on Tore Supra tokamak in the framework of the CIEL project. It is well known that the edge flow pattern can be influenced by the poloidal electric drifts from imposing radial electric fields. The modelling with TECXY introduces imprinted bias currents in the scrape-off layer (SOL) for the case of negative (limiter) biasing, and imprinted bias potentials for the case of positive biasing. This allowed us to simulate sufficiently well the experimental I-V characteristics for either biasing of ALT-II and also reproduced the essential features and trends of the observed plasma profiles in the SOL of TEXTOR-94. For negative biasing a moderate improvement of the pumping exhaust efficiency can be achieved in the case of TEXTOR. For Tore Supra, however, only a negligible improvement of the limiter performance with biasing can be predicted, which is explained by the relatively weak drift flows in Tore Supra.