Analysis of pressure derivative data of hydraulically fractured wells by the Tiabʹs Direct Synthesis technique

This paper extends Tiabʹs Direct Synthesis (TDS) technique for interpreting the behavior of the pressure and pressure derivative data of a well intersected by a finite conductivity hydraulic fracture. In this technique log–log plots of pressure and pressure derivative data of a pressure drawdown or pressure buildup test are analyzed without using the type-curve matching or regression procedures. log plot of pressure and pressure derivative versus test time for a fractured well in a closed system may reveal the presence of several straight lines corresponding to different flow regimes; bilinear flow, linear flow, infinite-acting radial flow, and pseudosteady state flow. The slopes and points of intersection of these straight lines are unique and therefore can be used to calculate several well, reservoir and fracture parameters: permeability, skin factor, wellbore storage coefficient, fracture conductivity, half-fracture length, and drainage area. ons corresponding to the points of intersection are very useful in checking on the parameters obtained from the slopes, when the pressure derivative curve is not smooth. A new equation is derived for calculating (a) the half-fracture length in the absence of the linear flow regime straight line of slope 0.5 such as in the case of low conductivity fracture, (b) the fracture conductivity in the absence of the bi-linear flow line of slope 0.25, and (c) the skin factor in the absence of the infinite acting radial flow line such as in the case of a short test.