Complex Fracture Depletion Model for Reserves Estimations in Shale

Reserve estimation is a subject of continuous importance in the petroleum industry; controlling field development related decisions and providing valuation of corporations. Tight formations are usually completed with multistage hydraulic fractures and horizontal wellbores. However, these completion scheme results in heterogeneous fracture lengths and spacing. Consequently, some counterparts of the reservoir would experience boundary-dominated flow, while others are still experiencing an infinite-acting linear flow which creates a composite flow regime dubbed as complex fracture depletion (CFD). It is worth noting that the CFD flow regime might be preceded by a linear flow depending on the fracture complexity. We are proposing a unified model that integrates the flow regime analysis and the well performance analysis. Our model utilizes the derivative of the cumulative production with respect to the square root of produced time where the linear flow exhibits a horizontal line and the CFD exhibits an exponential straight line. Therefore, the onset of the CFD becomes the only variable for the regression analysis. Another consequence of utilizing an exponential fit of the flow derivative is a continuous reduction in the Arps’ “b” exponent from a “b” value of two during CFD. We also validated our model estimations to the estimations of Arap’s and stretch exponential production decline (SEPD) with recent production data from the Bone Spring formation, New Mexico, and major shale/tight reservoirs.