ANALYSIS OF VARIABLE RATE PRESSURE DATA USING DUHAMEL'S PRINCIPLE

Three general methods have been developed for generating equivalent constant sandface rate wellbore pressure data, given simultaneously recorded measurements of variable sandface rate and bottomhole pressure. The numerical schemes for the analysis of variable rate drawdown pressure data are based on the exact Duhamel's Principle Solution for Darcy flow of a slightly compressible fluid of constant viscosity in a porous medium. Schemes for analyzing buildup pressure-rate data are based on an approximate Duhamel's Principle solution which neglects producing time effects.;We consider the conditions under which the widely used Rate Normalization procedure of Gladfelter and Tracy yields accurate results. If producing time effects are negligible, the error associated with employing Rate Normalization to analyze variable rate pressure data is dependent on the instantaneous value of the log-log slope of rate versus time, (or change in rate versus shut-in time for buildup). If the absolute value of this slope is small ((VBAR)slope(VBAR) < 0.1), Rate Normalization yields an excellent approximation to the constant rate drawdown pressure response. For larger absolute values of this slope, significant difference between the rate normalization pressure and the true constant sandface rate drawdown solution are observed.;The effect of variation in producing rate prior to shut-in on the maximum shut-in time for which pressure buildup data is analyzable using the classical analysis methods is investigated. In certain cases, rate stabilization prior to shut-in may actually decrease the maximum shut-in time for which data is analyzable.;In general, the methods based on Duhamel's Principle yield equivalent constant rate drawdown pressure data for the same maximum shut-in times as the classical MDH method. However, buildup data analyzed using these methods may exhibit pseudosteady state behavior provided the producing time error term is negligible throughout the entire shut-in period.;The numerical schemes based on Duhamel's Principle may be employed to (i) remove wellbore storage effects on well test data, (ii) analyze declining rate reservoir limit tests and (iii) decouple commingled layered systems to yield individual layer properties, provided individual layer sandface rates are measured. The methods are equally applicable to cylindrical or vertically fractured wells in homogeneous or heterogeneous reservoirs.