... of poroelasticity on the contact stress and the transient indentation force response is then discussed. The asymptotic behaviors for the normalized transient force at early and late times are derived. Though derivation of these fully coupled solutions requires the aid of a variety of mathematical techniques...

... of the stage and, more importantly, spatial variations of the entry friction due to near-wellbore fracture tortuosity have a more pronounced adverse effect on the fluid partitioning. Engineering variation MPa injection Upstream Oil & Gas stress interaction asymptote hydraulic fracture...

... initiation equation indentation numerical integration reservoir geomechanics radial stress asymptote expression material constant indenter deformation contact axis 1. INTRODUCTION The process of indentation by a rigid tool has been widely studied for its versatility as an experimental technique...

... (? 2/3 ) solutions for the fracture aperture co-exist near the fracture tip. Depending on the ratio of viscous dissipation and fracture resistance, the region for the validity of each tip asymptote varies. In this paper, we developed a 2D displacement discontinuity based hydraulic fracture propagation...

... or viscous regimes of propagation by using the corresponding asymptotic solution at the tip element. Since either the viscous or toughness asymptote is used, the intermediate regime is not described accurately. To deal with this problem, this study aims to implement the intermediate asymptotic solution...

... asymptote Newtonian fluid fracture analytical solution hydraulic fracture algorithm formulation reservoir geomechanics asymptotic behavior boundary condition Detournay finite difference scheme equation propagation self-similar solution Rock Mechanics in the National Interest, Elsworth...