  The neutron star low-mass X-ray binary SAX J1712.6-3739 is known for its very
long and hard thermonuclear bursts in past X-ray observations. Its
thermonuclear bursts are so energetic that they can even last for tens of
minutes in the hard X-ray observations of Swift/BAT (E > 15 keV). For exploring
the natures of SAX J1712.6-3739 and its thermonuclear bursts, we analyzed its
four bursts which were all captured by Swift/BAT. The peak flux and fluence for
these bursts are derived by applying the archive observation data of Swift/BAT
and Swift/XRT. Based on the peak fluxes observed by Swift, the distance of SAX
J1712.6-3739 is estimated as 4.6 kpc, which is much closer than the estimate by
the BeppoSAX observations. The corresponding absolute magnitude and average
accretion rate agree its ultra-compact X-ray binary nature. By the measurements
of effective duration, we determined that the 2010 burst corresponds to a
normal X-ray burst, the 2011 burst is consistent with an intermediate-duration
burst while the 2014 and the 2018 bursts are more energetic than common
intermediate-duration bursts but less energetic than superbursts. Since the
average mass accretion rate of SAX J1712.6-3739 was only 0.6% Eddington
accretion rate, and current theory predict no carbon production in the bursters
under very low accretion rate. Therefore, the 2014 and the 2018 bursts are very
likely to be deep helium bursts. In the Swift observations, SAX J1712.6-3739
has shown at least three different levels of duration in thermonuclear bursts.
They were possibly induced by variable accretion rates, because their ignition
column depths roughly follow the prediction of ignition models for pure helium
bursts at corresponding accretion rates.
