A coke distribution model of catalyst particles in three-dimensional space was developed based on population balance theory, and an analytic expression of coke distribution for zero-dimensional time-independent problem was deduced. The expression shows that the coke distribution is determined by the average catalyst residence time, coke deposition (or burning) rate, and coke distribution of catalyst inflow. The coke distribution model was further applied to the methanol to olefins (MTO) process. The critical factors influencing coke distribution in MTO process, as well as the effect of coke distribution on product selectivity, were investigated. Three scales of MTO fluidized bed reactor-regenerator systems, i.e., pilot-scale, demonstration-scale and commercial-scale with the reactor diameter of 0.261, 1.25, and 10.5 m, respectively, were simulated. The simulated results were in good agreement with the operation data. The model could be helpful in the operation optimization and reactor design. (c) 2018 American Institute of Chemical Engineers AIChE J, 65: 1149-1161, 2019