A complete numerical solution for a two-dimensional steady flow of a gas-solid mixture exiting a fluidized bed into a vertical standpipe is presented. The numerical solutions of the equations of motion for gas and particles, treated as inter-penetrating continua, reveal marked changes in the density of the mixture near the standpipe entrance region and inside the standpipe, depending on the boundary conditions at the inlet of the fluidized bed and standpipe exit. It is shown that the gas pressure at the standpipe exit influences primarily the overall density of the mixture inside the standpipe and fluidized bed, but it does not greatly affect gas and particle velocity profiles. On the other hand, the specified particle momentum at the bed inlet is shown to have profound effects on gas and particle profiles inside the standpipe. High particle concentration or velocity at the inlet of the fluidized bed leads to gas flow reversal inside the standpipe due to particle segregation at the standpipe entrance. The simulation results support earlier findings that used a first approximation approach to show that the gas-solid mixture flow inside the standpipe is governed primarily by the particle phase, and more specifically by particle inertia near the standpipe entrance. If the solid particles approach the standpipe entrance with a high horizontal velocity component, particle segregation will occur which could propagate inside the standpipe, triggering reversal of gas velocity in regions of lowest particle concentration, thus rendering the flow of the granular fluid erratic and difficult to control.