The advent of unconventional resources has radically changed the gas and oil supply landscape in North America. To a great extent, investment decisions with respect to development of unconventional resources depend on the ability to accurately forecast future recovery. Conventional forecasting methods have serious shortcomings. A class of empirical decline equations, termed stretched exponentials, was meant to address these forecasting weaknesses. These equations targeted unconventional gas and held great promise for predicting reserves from wells that were previously forecast using linked super-hyperbolic/exponential equations. Unfortunately, stretched exponentials have been underutilized, possibly because the equations are difficult to solve.
This paper will present solution algorithms for the three most popular equations proposed by Ilk (SPE116731), Valko (SPE 134231) and Duong (SPE 137748). Methods will be presented to identify which data should be rejected and which production trend should be solved when operational or reservoir changes result in multiple trends. Conditions will be described that prevent finding a solution or that will result in an inaccurate solution.
Stretched exponential equations are complex and, unlike the Arps’ equations, they cannot be readily manipulated. For example, it is not possible to use Ilk's equation to determine when a well's recovery will reach a specified amount. A formulation will be presented to make stretched exponentials calculator friendly. Regulators require that the decline factor not exceed a specified minimum and the new formulation honors this requirement.
Case studies will be shown to verify the solutions, compare the expected recovery from the three equations and demonstrate why they sometimes fail.