We present reactive gasdynamic, axisymmetric simulations of dense, high velocity clumps for modelling the CO streamers observed in Orion BN/KL. We have considered 15 chemical species, a cooling function for atomic and molecular gas, and heating through cosmic rays. Our numerical simulations explore different ejection velocities, interstellar medium density configurations, and CO content. Using the CO density and temperature, we have calculated the CO (J = 2 → 1) emissivity, and have built CO maps and spatially resolved line profiles, allowing us to see the CO emitting regions of the streamers and to obtain position velocity diagrams to compare with observations. We find that in order to reproduce the images and line profiles of the BN/KL CO streamers and H2 fingers, we need to have clumps that first travel within a dense cloud core, and then emerge into a lower-density environment.