  The amount of H$_2$O and CO$_2$ that is carried into deep mantle by
subduction beyond subarc depths is of fundamental importance to the deep
volatile cycle but remains debated. Given the large uncertainties surrounding
the spatio-temporal pattern of fluid flow and the equilibrium state within
subducting slabs, a model of H$_2$O and CO$_2$ transport in slabs should be
balanced between model simplicity and capability. We construct such a model in
a two-part contribution. In this Part I of our contribution, thermodynamic
parameterization is performed for the devolatilization of representative
subducting materials---sediments, basalts, gabbros, peridotites. The
parameterization avoids reproducing the details of specific devolatilization
reactions, but instead captures the overall behaviors of coupled (de)hydration
and (de)carbonation. Two general, leading-order features of devolatilization
are captured: (1) the released volatiles are H$_2$O-rich near the onset of
devolatilization; (2) increase of the ratio of bulk CO$_2$ over H$_2$O inhibits
overall devolatilization and thus lessens decarbonation. These two features
play an important role in simulation of volatile fractionation and infiltration
in thermodynamically open systems. When constructing the reactive fluid flow
model of slab H$_2$O and CO$_2$ transport in the companion paper Part II, this
parameterization can be incorporated to efficiently account for the open-system
effects of H$_2$O and CO$_2$ transport.
