This is the first of two papers in which critical point calculations in binary systems were performed utilizing cubic equations of state (EOS) combined with excess energy models using the Wong-Sandler mixing rule. In this paper, the van der Waals equation of state is combined with the NRTL model in order to investigate the influence of the model parameters on the shapes of the calculated critical phase diagrams. Due to the large number of parameters in the model, it is not possible to obtain a two-dimensional global phase diagram, however the results indicate that many different types of critical phase diagrams can be obtained from the model. Due to the comparatively simple functional form of the van der Waals EOS, no attempt was made to compare the calculated critical phase diagrams with experimental data. Such a comparison is made on the second paper of this series, in which the Peng-Robinson EOS is combined with the NRTL model and the resulting model is used in the computation of the critical loci of several real systems.