Multi-zone models of Type I X-ray bursts are presented that use an adaptive nuclear reaction network of unprecedented size, up to 1300 isotopes. Sequences of up to 15 bursts are followed for two choices of accretion rate and metallicity. At 0.1 Eddington (and 0.02 Eddington for low metallicity), combined hydrogen-helium flashes occur. The rise times, shapes, and tails of these light curves are sensitive to the efficiency of nuclear burning at various waiting points along the rp-process path and these sensitivities are explored. The bursts show "compositional inertia", in that their properties depend on the fact that accretion occurs onto the ashes of previous bursts which contain left-over hydrogen, helium and CNO nuclei. This acts to reduce the sensitivity of burst properties to metallicity. For the accretion rates studied, only the first anomalous burst in one model produces nuclei as heavy as A=100, other bursts make chiefly nuclei with A~64. The amount of carbon remaining after hydrogen-helium bursts is typically <1% by mass, and decreases further as the ashes are periodically heated by subsequent bursts. At the lower accretion rate of 0.02 Eddington and solar metallicity, the bursts ignite in a hydrogen-free helium layer. At the base of this layer, up to 90% of the helium has already burned to carbon prior to the unstable ignition. These helium-ignited bursts have briefer, brighter light curves with shorter tails, very rapid rise times (<0.1 s), and ashes lighter than the iron group.