The physical process and pressure-transient analysis considering fractures excessive extension in water injection wells

Based on the proposed models, the pressure-transient behavoirs of wells with waterflood-induced fractures are obtained and type curves are plotted. The shape of these type curves is studied as a function of different relevant parameters, i.e. water injection volume, fracture area exponent, flow coefficient for main and secondary fractures, fracture surface area, secondary fracture initiation time and so on. It is concluded that the bottom-hole pressure is consisted of two parts: one is the increase of pressure caused by water injection while the other is pressure relief caused by fractures extension. Calculations indicate that the relationship between pressure logarithmic derivative and fractured injection time still meet the linearity approximately in log-log plot even considering fracture extension if constant fracture height is assumed. The slope of the curve is largely controlled by flow coefficient from fracture into matrix and fracture area exponent. Compared with the model of fixed fracture length (in the shut-in moment), the slope of pressure logarithmic derivative of this model proposed is smaller. The initiation of secondary fractures lowers the pressure derivative value. The results show pretty good agreements between our model and the fall-off analysis after shut-in period, with the relative error of 3.6%, which indicates our new models are reasonable.