A three-dimensional simulation study is performed for investigating the hydrodynamic behaviors of a cross-flow liquid nitrogen spray injected into an air-fluidized catalytic cracking (FCC) riser of rectangular cross-section. Rectangular nozzles with a fixed aspect ratio but different fan angles are used for the spray feeding. While our numerical simulation reveals a generic three-phase flow structure with strong three-phase interactions under rapid vaporization of sprays, this paper tends to focus on the study of the effect of nozzle fan angle on the spray coverage as well as vapor flux distribution by spray vaporization inside the riser flow. The gas-solid (air-FCC) flow is simulated using the multi-fluid method while the evaporating sprays (liquid nitrogen) are calculated using the Lagrangian trajectory method, with a strong two-way coupling between the Eulerian gas-solid flow and the Lagrangian trajectories of spray. Our simulation shows that the spray coverage is basically dominated by the spray fan angle. The spray fan angle has a very minor effect on spray penetration. The spray vaporization flux per unit area of spray coverage is highly non-linearly distributed along the spray penetration. The convection of gas-solid flow in a riser leads to a significant downward deviation of vapor generated by droplet vaporization, causing a strong recirculating wake region in the immediate downstream area of the spray.