Uncertainties in Standard Analyses of Boundary Effects in Buildup Data

Summary Boundary effects are often observed in buildup data—or at least that is the conclusion frequently drawn from an observed increase in derivative on a log-log plot or an increase in slope on a semilog plot. Furthermore, if (for instance) it is concluded that the effects of a sealing fault are seen in a given data set, then simple line methods or direct analytical-modeling efforts are normally used to determine the distance to the boundary. A sealing fault is the normal choice of boundary model if a doubling is observed in derivative or semilog slope. If a four-fold increase in derivative is observed, then a model with the well placed somewhere between two sealing faults forming a right angle would be a normal choice. But what if the two faults are not sealing? If the flow capacity on the other side of the faults is only one-third of the value on the well side, what will be the derivative characteristics? Problems like these are addressed in detail in this paper, with a series of simple rules given for possible combinations that will generate buildup data of a specific type (i.e., with specific "familiar characteristics"). The rules can be used to list alternative interpretations without running separate analyses. For instance, it is shown that the derivative characteristics of any sector model bounded by sealing faults correspond to an infinite number of two-zone sector models with an angle between the boundaries and permeability contrast satisfying a single equation. Other pairs of models with similar characteristics are models with partially sealing faults and specific three-zone sector models, and either of these types of models and radial composite models. This clearly complicates analyses. Also addressed are problems related to possible differences in the boundary effects observed in drawdown and buildup data for certain models. As one example, U-shaped and sector models can have identical buildup characteristics over a wide time range, although drawdown data from the models have distinctly different boundary characteristics. Radial composite and composite sector models are also of this type, with potentially significant differences between drawdown and buildup data. The reason for bringing up such cases is to emphasize the importance of attempting to collect high-quality drawdown data in addition to buildup data to limit the range of possible interpretation models. For completeness, effects of uncertainties in basic input parameters on the final analyses are also covered in the paper. Introduction It is well known that buildup data from a well near a sealing fault might exhibit a doubling of derivatives on a log-log diagnostic plot, as illustrated in Fig. 1. This doubling of derivatives corresponds to a doubling of slope on a semilog plot, as shown by Horner, and refers to a change between early and late data requiring storage effects to become negligible and radial flow to be reached before the onset of boundary effects. For this behavior to occur, it is also necessary for the flow period before shut-in to be long enough to be fully or almost fully affected by the boundary effect.