We report a model to use to evaluate the performance of multiple quantum key distribution (QKD) channel transmission using spatial division multiplexing (SDM) in multicore (MCF) and few-mode fibers (FMF). This model is then used to analyze the feasibility of QKD transmission in 7-core MCFs in two practical scenarios involving the (1) transmission of only QKD channels and (2) simultaneous transmission of QKD and classical channels. In the first case, standard homogeneous MCFs enable transmission distances per core compatible with transmission parameters (distance and net key rate) very close to those of single-core single-mode fibers. For the second case, heterogeneous MCFs must be employed to make this option feasible.