  We study the deeply virtual Compton scattering process with both twist-two
and twist-three Compton form factors and present our cross-sections formulas
with all polarization configurations. While the twist-three contributions are
generally assumed to be negligible in the literature due to the kinematical
suppression, we compare them with the twist-two ones at typical JLab 6 GeV and
12 GeV kinematics as well as EIC kinematics and show their kinematical
suppression explicitly, justifying the leading-twist approximation made in the
literature. In addition, we also estimate the twist-three Compton form factors
using Wandzura-Wilczek relations and inputs of twist-two generalized parton
distributions based on a reggeized spectator model. With those estimated
Compton form factors, we analyze the kinematical behavior of twist-two and
twist-three cross-sections in a wide range of kinematics, and discuss the
optimal regions for separating the leading-twist effects from the higher-twist
ones.
