  The computational requirements posed by multi-dimensional simulations of type
Ia supernovae make it difficult to incorporate complex nuclear networks to
follow the release of nuclear energy along with the propagation of the flame.
Instead, these codes usually model the flame and use simplified nuclear
kinetics, with the goal of determining a sufficiently accurate rate of nuclear
energy generation and, afterwards, post-processing the thermodynamic
trajectories with a large nuclear network to obtain more reliable nuclear
yields. In this work, I study the performance of simplified nuclear networks
with respect to reproduction of the nuclear yields obtained with a
one-dimensional supernova code equipped with a large nuclear network. I start
by defining a strategy to follow the properties of matter in nuclear
statistical equilibrium (NSE). I propose to use published tables of NSE
properties, together with a careful interpolation routine. Short networks (iso7
and 13{\alpha}) are able to give an accurate yield of 56Ni, after
post-processing, but can fail by order of magnitude in predicting the ejected
mass of even mildly abundant species (> 0.001 solar masses). A network of 21
species reproduces the nucleosynthesis of the Chandrasekhar and
sub-Chandrasekhar explosions studied here with average errors better than 20%
for the whole set of stable elements and isotopes followed in the models.
