In most industrial gas-phase polyethylene reactors, heat is removed by cooling the recycle gas stream in an external heat exchanger, where a portion of the vapor is condensed. The condensate evaporates in the reactor to absorb heat released by polymerization reactions, thereby increasing the production capacity of the unit. Nonequilibrium methods of multicomponent condensation are applied to develop a 1-D model to simulate the cooling unit of an industrial polyethylene reactor system operated in partial condensing mode. Finite difference approximations are used to convert the resulting set of differential equations to algebraic equations. A practical method of solving the equations is to combine the rapid local convergence of Newton's method with a globally convergent strategy. Correlation methods for estimating local heat-transfer coefficients in the liquid film layer are discussed. Butterworth's method for shear-stress-controlled condensate flow gives reasonable agreement between simulation results and industrial data, while Chen et al.'s method can better describe the transition process of condensate flow from laminar to turbulent flow.