  Using the observed submillimetre source counts, from 250-1200 microns
(including the most recent 250, 350 and 500 micron counts from BLAST), we
present a model capable of reproducing these results, which is used as a basis
to make predictions for upcoming surveys with the SPIRE instrument aboard the
Herschel Space Observatory. The model successfully fits both the integral and
differential source counts of submillimetre galaxies in all wavebands,
predicting that while ultra-luminous infrared galaxies dominate at the
brightest flux densities, the bulk of the infrared background is due to the
less luminous infrared galaxy population. The model also predicts confusion
limits and contributions to the cosmic infrared background that are consistent
with the BLAST results. Applying this to SPIRE gives predicted source confusion
limits of 19.4, 20.5 and 16.1mJy in the 250, 350 and 500 micron bands
respectively. This means the SPIRE surveys should achieve sensitivities 1.5
times deeper than BLAST, revealing a fainter population of infrared-luminous
galaxies, and detecting approximately 2600, 1300, and 700 sources per square
degree in the SPIRE bands (with one in three sources expected to be a high
redshift ultra-luminous source at 500 microns). The model number redshift
distributions predict a bimodal distribution of local quiescent galaxies and a
high redshift peak corresponding to strongly evolving star-forming galaxies. It
suggests the very deepest surveys with Herschel-SPIRE ought to sample the
source population responsible for the bulk of the infrared background.
