In a pebble bed nuclear reactor, each fuel pebble draining through the core experiences a different amount of burnup depending on the precise trajectory that it follows. Understanding the burnup profile of pebbles is essential for reactor safety, as well as for fuel economy. Here, we introduce a method for constructing the burnup profile based on performing a discrete element simulation of the pebble drainage, followed by a burnup calculation in each individual pebble. This method is more accurate than previous approaches, and in particular it captures the extremal cases of pebble burnup. We demonstrate the method using the geometry, neutron flux data, and thermal characteristics from the HTR-10 reactor being developed at Tsinghua University. We examine pebble burnup during a single drainage cycle, and over multiple drainage cycles characteristic of normal reactor operation. Our results show that the presence of slow-moving boundary layers of pebbles near the reactor wall strongly influences the burnup profile. We perform a systematic study where the pebble–pebble and pebble–wall friction coefficients are independently varied, and we show that the strength of the boundary layers is a complex interplay of these two parameters.