In this work, we introduce a simple flux-controlled compact memristor model for bipolar neuromorphic ReRAM devices. The model behaviour and accuracy have been evaluated in comprehensive investigations by using measured values of a device fabricated by the CNR-IMM, MDM Laboratory. Thereby, we developed a model parameter extraction for the considered devices. As shown in the results, the model is capable to catch the effects of width or/and height change in the pulse input signal for a train of pulses by using a technological parameter linked to the device and internal parameters related to the width or/and height of the pulse input voltage signal. This makes it specially suitable to model neuromorphic ReRAM devices.