A two-dimensional (2D) numerical model is implemented to describe the movement of ions under thermal poling for the specific case of optical fibers. Three types of cations are considered (representing Na(+), Li(+) and H3O(+)) of different mobility values. A cross-sectional map of the carrier concentration is obtained as a function of time. The role of the various cations is investigated. The assumptions of the model are validated by comparing the predictions to experimental data of the time evolution of the nonlinearity induced. A variational analysis of poling parameters including temperature, poling voltage, sign of the bias potential and initial ionic concentrations is performed for a particular fiber geometry. The analysis allows identifying the impact of these parameters on the induced second-order nonlinearity in poled fibers.