Reserve estimation is a subject of continuous importance in the petroleum industry; controlling field development related decisions and providing valuation of corporations. For unconventional reservoirs completed with multistage fracture stimulation treatments in horizontal wellbores, these completion treatments are apt to be complex in terms of fracture lengths and distances between fractures creating a composite flow regime characterized by a continuous change in the proportional contribution from the reservoir experiencing of infinite acting linear flow and boundary dominated flow. A unified approach is presented that integrates well performance analysis of the linear flow and combination of linear and boundary dominated flow, dubbed complex fracture depletion. The approach relies on the linear flow derivative. Linear flow exhibits a straight line when cumulative production is plotted versus the square root of produced time and the derivative, the change in cumulative production with respect to the square root of produced time, is a constant. At the onset of partial boundary flow the linear derivative decreases and can be fitted with an exponential straight line. The time that identifies this juncture becomes the only variable of regression analysis. A consequence of utilizing an exponential fit of the linear flow derivative is a continuous reduction in the Arps' "b" exponent at the onset of partial boundary flow from a "b" value of two during linear flow. Other decline curve analysis methods that result in declining "b" exponents and constant "b" values are discussed. Well production performance from the Bone Springs formation located in Lea and Eddy counties, New Mexico, concentrating on completions between 2010 and 2015 are selected for presentation in this study. The applicability of the approach is further validated with examples from other major shale/tight reservoirs.
Linear Flow and its Derivative
Shown in Fig. 1 are the cumulative oil production, Np, on the primary y axis and the linear flow derivative, dNp/dt1/2, on the secondary y axis with a logarithmic scale. Early on, the derivative displays a horizontal line (which is the straight line portion of the cumulative production versus the square root of produced time - linear flow) and then becomes an exponential straight line displayed on Fig. 1 leading to rate and cumulative production equations 1 & 2 for the Complex Fracture Depletion model.