In order to investigate the origin and the structure of the low velocity, chemically rich clumps observed along the lobes of low- and intermediate-mass outflows, we construct a detailed model of the S1 clump along the CB3 outflow. We use a time-dependent chemical model coupled with a radiative transfer model to reproduce the observed line profile for a direct comparison with previous observations of this clump. We find that the simultaneous fitting of multiple species and transitions is a powerful tool in constraining the physical parameters of the gas. Different scenarios for the clump formation have been investigated. The models that better reproduce all the observed lines are those where the clump is formed, at least partially, before the advent of the outflow; with the advent of the outflow the clump undergoes a short period of non-dissociative shock and the consequent release of the icy mantle together with the high temperature chemistry leads to the observed chemical enrichment. Our results also suggest the presence of substructure within the clump: a more extended component traced by CS, SO and the lower energy transitions (3_k-2_k and 2_k-1_k) of CH_3OH, and a more compact component traced by H_2CO, SO_2 and the higher energy transitions (5_k-4_k) of CH_3OH.