  In this paper we demonstrate the influence of the pore pressure to the
development of a hydraulically-driven fracture in a poroelastic medium. We
present a novel numerical model for propagation of a planar hydraulic fracture
and prove its correctness by demonstration of the numerical convergence and by
comparison with known solutions. The advantage of the algorithm is that it does
not require the distinguishing of the fracture's tips and reconstruction of the
numerical mesh according to the fracture propagation. Next, we perform a
thorough analysis of the interplay of fluid filtration and redistribution of
stresses near the fracture. We demonstrate that the fracture length decreases
with the increase of the Biot's number (the parameter that determines the
contribution of the pore pressure to the stress) and explain this effect by
analysing the near-fracture pore pressure, rock deformation and stresses. We
conclude, that the correct account for the fluid exchange between the fracture
and the rock should be based not only on physical parameters of the rock and
fluid, but also on the analysis of stresses near the fracture.
