This paper presents a new method of estimating a constant-rate analog for a variable-rate flow period followed by a pressure-buildup test. The time and rate in the analog are used to generate a conventional Horner plot for the buildup test. The approximation is derived rigorously from the Horner buildup and variable-rate superposition equations. The major advantage of this method over other proposals is that it not only forces the production volumes to be equal (material-balance constraint) but also forces the pressures at a particular time to be equal.
Our approximate method has been verified for several variable-rate schemes with a finite-difference numerical simulator. The effect of wellbore storage was studied at both surface and sandface rates. The effects of a short shut-in time and a shut-in time equal to the duration of the production period were also investigated. The results of the new method seldom varied more than 5% from the results obtained with rigorous superposition.
The new method is not intended to replace superposition, but rather to give the best possible constant-rate analog. This method enhances our ability to use the conventional (constant-rate) Horner theory to generate accurate results. Also, our new method requires a single superposition calculation rather than a superposition calculation for each data point, as in the case of the superposition plot.