Nickel-chromium alloys are susceptible to long-range ordering under certain thermal aging conditions, resulting in the formation of a Ni₂Cr phase. This can lead to significant changes in physical or mechanical properties compared to those of the disordered alloy. Mechanical degradation due to this ordering phenomenon is of particular concern for commercial alloys based on the Ni-Cr system, such as Alloy 690 which has been widely used in pressurized water reactors. In this research, a disorder-order phase transformation has been studied in the model alloy Ni-33 at.%Cr by a numerical approach based on a model of pair interactions depending on the temperature and local composition. These pair interactions are fitted at 0 K to existing ab initio calculations of the formation enthalpies of ordered and disordered (special quasi-random) structures. They are also systematically fitted to the Gibbs free energy of the $\gamma$ Ni-Cr solid solution as described in the available CALPHAD (CALculation of PHAse Diagrams) studies. Grand Canonical Monte Carlo simulations based on such a pair interaction database reproduce well the compositional and temperature domain for the ordered Ni₂Cr phase compared to experimental studies. We also perform kinetic Monte Carlo simulations to study the initiation of ordering transformation at temperatures and time scales relevant to nuclear power systems.