Limitations on the Use of Single- and Multiple-Rate Horner, Miller-Dyes-Hutchinson, and Matthews-Brons-Hazebroek Analysis

SUMMARY A major objective of this paper is to present methods to determine the range of applicability of Horner and Miller-Dyes-Hutchinson analysis for a variety of reservoir shapes, outer boundary conditions, and producing times. This concerns limitations on the end of semilog data caused by approximations of the drawdown transient, and not limitations on the beginning of such data caused by effects in or near the wellbore. The results, based on derivatives of dimensionless pressures, also have some bearing on the use of drawdown type curves to analyze buildup data. Moreover, they imply that the "producing time" used in Horner analysis, or in type-curve analysis based on Agarwal's effective drawdown time, can be limited by tDA =0.08 for closed reservoirs. This is important when use of later portions of test data are essential to obtain valid results. Limitations on the use of standard methods to determine the distance to the nearest boundary in closed reservoirs, both for short and long producing times, are also investigated. From an example presented, it is evident that exact doubling of the semilog slope is not necessary to determine this distance, but such doubling simplifies the analysis. This is important since exact doubling only occurs under favorable conditions. Both Horner and Matthews-Brons-Hazebroek analysis have natural extensions from single- to multiple-rate buildup data. This leads to a formula relating the extrapolated pressure to the average reservoir pressure through a sum of Matthews-Brons-Hazebroek functions. Using the results from the first part of the paper, it follows that a single-rate Horner plot can be used if all drawdown transients have lasted longer than tDA = 0.08, even if a longer producing time is needed to reach pseudosteady state.