Abstract
Recent diagnostic fracture injection test (DFIT) data presented on a Bourdet log-log diagnostic plot showed derivative slope of 0 in the before closure (BC) portion of the DFIT response. Some works qualitatively describe it as radial flow. This behavior has not been quantitatively analyzed, modeled and matched. The present work disagrees with the hypothesis of radial flow and successfully matches the relatively flat trend in the Bourdet derivative with a model dominated by friction dissipation coupled with tip extension.
The flat trend in Bourdet derivative occurs shortly after shut-in during the before closure period. Because a flat derivative trend suggests diffusive radial flow, our first approach was to consider the possibility that an open crack at a layer interface stopped the fracture propagation and caused the apparent radial flow behavior observed in falloff data. However, a model that coupled pressure falloff from diffusive flow into a layer interface crack with pressure falloff from closure of a fracture that propagated up to the layer interface failed to reproduce the observed response. Subsequently, we discovered that existing models could match the data without considering the layer interface crack.
We found that data processing is very important to what is observed in derivative trends and can mislead the behavior diagnosis. We succeeded to match one field DFIT case showing an obvious early flat trend. The presence and dominance of geomechanics, coupled with diffusive flow, disqualify the description of the flat trend in Bourdet derivative as radial flow. Instead, flow friction coupled with tip extension can completely match the observed behavior. Based on our model, cases with a long flat trend have large magnitude near-wellbore tortuosity friction loss and relatively long tip extension distance. Further, we match the near wellbore tortuosity behavior with rate raised to a power lower than the usually assumed 0.5.
The significance of these analyses relates to two key factors. First, large magnitude near wellbore tortuosity friction loss increases the pressure required for fracture propagation during pumping. Second, tip extension is a way to dissipate high pumping pressure when very low formation permeability impedes leakoff. Matching transient behavior subject to the presence of both of these factors requires lowering the near-wellbore tortuosity exponent.
Finite Element Analysis of the Vibration of a Rotor System with an Open Crack under the Harmonic Excitation