  We present an extrapolation-based semi-implicit multirate time stepping (MRT)
scheme and a compound-fast MRT scheme for a naturally partitioned,
multi-time-scale hydro-geomechanical hydrate reservoir model. We evaluate the
performance of the two MRT methods compared to an iteratively coupled solution
scheme and discuss their advantages and disadvantages. The performance of the
two MRT methods is evaluated in terms of speed-up and accuracy by comparison to
an iteratively coupled solution scheme. We observe that the extrapolation-based
semi-implicit method gives a higher speed-up but is strongly dependent on the
relative time scales of the latent (slow) and active (fast) components. On the
other hand, the compound-fast method is more robust and less sensitive to the
relative time scales, but gives lower speed up as compared to the semi-implicit
method, especially when the relative time scales of the active and latent
components are comparable.
