The main objective of the present paper is to propose a new model of the hydrodynamics in an air-lift internal loop reactor. The model is based on one-dimensional (1D) two-fluid mass and momentum balances. It requires closure relations for the slip velocity of the gas bubbles and both friction factors and singular pressure drop coefficients. The way to propose reliable closure relations for these terms is based on three-dimensional (3D) numerical simulations, using the Computational Fluid Dynamics software ASTRID developed by Edf (Chatou, France). The numerical simulations are first validated with experiments acquired on a laboratory pilot plant. Then the numerical simulations are used to improve a more global modeling of the air-lift internal loop reactor. In particular, one can space average the local 3D results to obtain closure relations for the simpler 1D model.