For partial oxidation systems, where the reaction order in oxygen of the formation rate of the target product is smaller than the reaction order in oxygen of the consecutive reaction rate toward the waste product, a packed bed membrane reactor can be applied to distributively dose oxygen along the reactor in order to improve the selectivity toward the desired intermediate product. In this paper, how the performance of a PBMR for partial oxidations is influenced by the extent of intraparticle diffusion limitations has been investigated. First, the intrinsic effects for a single catalyst particle are discussed, and subsequently the integral effects over the entire reactor on the conversion and selectivity are studied with numerical models (considering different sets of reaction orders, different ratios of reaction rates of the primary and secondary reaction, and different stoichiometric coefficients). In Part 2, the effects of radial oxygen concentration gradients from the membrane wall to the center of the packed bed are investigated. The main objective of this work is to provide guidelines to assess whether mass-transfer limitations inside the particles (Part 1) and/or from the membrane wall to the center of the catalyst bed (Part 2) affect the reactor performance and to quantify these effects.