We investigate the main pumping parameters that influence a fluid driven fracture in cohesive poroelastoplastic weak formation. These parameters include the fluid viscosity and the injection rate. The first parameter dominates in the mapping of the propagation regimes from toughness to viscosity while the second parameter controls the storage to leak-off dominated regime through diffusion. The fracture is driven in weak permeable formation by injecting an incompressible viscous fluid at the fracture inlet assuming plane strain conditions. Fluid flow in the fracture is modeled by lubrication theory. Irreversible rock deformation is modeled with the Mohr-Coulomb yield criterion assuming associative flow rule. Fracture propagation criterion is based on the cohesive zone approach. Leak-off is also considered. We perform numerical calculations with the finite element method to obtain the fracture opening, length and propagation pressure versus time. We demonstrate that pumping parameters influence the fracture geometry and fluid pressures in weak formations through the diffusion process that create back stresses and large plastic zones as the fracture propagates. We also show that the product of propagation velocity and fluid viscosity, (μ.v) that appears in the scaling controls the magnitude of the plastic zones and influences the net pressure and fracture geometry.
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