  It is usually assumed that hydraulic fracture has two symmetrical wings with
respect to the fluid injection point. Hence, authors limit themselves to
modelling of one half of the fracture. In our work we demonstrate that the case
of a symmetrical fracture occurs only in a homogeneous reservoir with constant
physical parameters and confining {\it in situ} stress. Otherwise,
inhomogeneity in the stress or the rock permeability can significantly change
the dynamics of the fracture propagation. The mathematical model of the
hydraulic fracturing used in the paper is adopted from our earlier work
\cite{Golovin_Baykin_2016_Pore}. In present paper we perform numerical
experiments demonstrating that in case of non-constant confining stress or
reservoir permeability the fracture is developing non-symmetrically. An
important role is played by the action of the backstress that is formed near
the fracture due to the pore pressure. To support this observation we give a
formal definition of the backstress and compare the values of the backstress
acting on the two different fracture wings. These numerical experiments
underline the importance of the proper modelling of the interaction between
pore and fracturing fluids for the correct simulation of the hydraulic
fracturing.
