Alternative Method to Horner's Approximation for Multirate Analysis of Pressure Buildup

Abstract

This paper presents a method to calculate an equivalent production rate and time (tp), that models the transient effect of a multirate production period prior to a buildup test. The proposed solution increases the accuracy of Pressure Transient Analysis (PTA). The traditional Horner method estimates the production time (tp) using the cumulative production and the last production rate; however, this method is an intuitive but not rigorous solution that puts emphasis on the most recent nonzero production rate. There are currently commercial applications that consider the superposition effects of complex production history for PTA analysis, nevertheless, superposition can include a material balance error. The proposed technique is an alternative to superposition that uses the transient effect generated for each production period to estimate the equivalent rate and production time. A reservoir simulation model with known petrophysical parameters, fluid properties, pressure, and temperature, is used as a reference to evaluate the accuracy of the proposed method. The studied reservoir produces through a well that uses a multirate schedule that includes two different scenarios: (1) a progressive increase in each new production rate and (2) a progressive decrease in each new production rate. Then, the well is shut-in, starting a buildup pressure response. Production time and rate are estimated by applying the Horner's approximation and the proposed solution. Finally, the results from both methods are compared with the known parameters of the reference model. The proposed method provides a more accurate solution to buildup analysis compared to the Horner time approximation by using the production rate history. The approach can also be applied to drawdown analysis and pressure derivative analysis, keeping the precision of the calculations.