  This series of papers investigates the early stages of planet formation by
modeling the evolution of the gas and solid content of protostellar disks from
the early T Tauri phase until complete dispersal of the gas. In this first
paper, I present a new set of simplified equations modeling the growth and
migration of various species of grains in a gaseous protostellar disk evolving
as a result of the combined effects of viscous accretion and photo-evaporation
from the central star. Using the assumption that the grain size distribution
function always maintains a power-law structure approximating the average
outcome of the exact coagulation/shattering equation, the model focuses on the
calculation of the growth rate of the largest grains only. The coupled
evolution equations for the maximum grain size, the surface density of the gas
and the surface density of solids are then presented and solved
self-consistently using a standard 1+1 dimensional formalism. I show that the
global evolution of solids is controlled by a leaky reservoir of small grains
at large radii, and propose an empirically derived evolution equation for the
total mass of solids, which can be used to estimate the total heavy element
retention efficiency in the planet formation paradigm. Consistency with
observation of the total mass of solids in the Minimum Solar Nebula augmented
with the mass of the Oort cloud sets strong upper limit on the initial grain
size distribution, as well as on the turbulent parameter $\alphat$. Detailed
comparisons with SED observations are presented in a following paper.
