An asymptotic solution for fluid production from an elliptical hydraulic fracture at early-times

• Derives short-time asymptotic solution for fluid production from a fractured well.
• Obtains the first three terms in the asymptotic solution.
• Shows fracture tip starts to influence production rate only after a finite time.
• Finds geometry induces corrections to bilinear flow before tip effect sets in.
• Corrects the erroneous claim of Riley.

The early-time transient flow during the start-up of fluid production from a porous medium by a well intersected by a vertical elliptical hydraulic fracture is studied using an asymptotic analysis. The analysis is focused on the situation of practical interest where the fracture conductivity is high so that production from the fracture dominates. The first three terms in a short-time asymptotic expansion for the production rate during constant-pressure production, and for the well-pressure during constant-rate production, are obtained. It is shown that the fracture tip starts to influence the production rate only when the dimensionless time is increased to the square of the reciprocal of the dimensionless fracture conductivity. The asymptotic results also show that geometric factors of an elliptical fracture introduce non-negligible corrections to the so-called bilinear flow in the early times, which were previously erroneously associated with the effect of the fracture tip.