Transient Well Indices: A Link between Analytical Solution Accuracy and Coarse Grid Efficiency

Abstract

Abstract A new numerically derived transient well index is presented. This well index is an elegant approach that combines and compares pressure predictions from coarse grid finite difference models and analytical solutions. The ratio of the drawdowns from each solution approach is used to modify the conventional Peaceman well index to produce a new transient well index. The new well index is shown to also be accurate for constant pressure production (i.e. for rate transient behavior) and performs well for a variety of well types, e.g. wells with wellbore storage, partial penetration of hydraulic fractures. Local grid refinements around the well do not produce the same level of accuracy. The new well index can be presented in terms of an equivalent well radius. In late time this becomes the Peaceman well index. The transient behavior of the equivalent well radius is shown to be universal when it is plotted against a dimensionless time function which includes a scaling for the grid size. The new transient well index approach means that coarse grid models can accurately reproduce pressure transient behavior making them a useful tool for numerical well test interpretation.