New Radius of Investigation Calculation Technique using Pressure Transient Analysis for Reserve Estimate & Applications in Field & Synthetic Case Studies
Authors: Cobanoglu Mustafa 
Published: November 2020

Abstract
Reserve estimate have had been a vital issue as it is being used to justify the project. Although historically different drainage area estimation methods have been developed and applied, there is no valid method accepted by the whole industry for reserve calculations. The traditional "radius of investigation" (Rinvt) is given in below;
Eq 1.0 R i n v t = 0.029 k t φ μ c
Historically, there are 3 different methods used to estimate drainage area. Those are "traditional radius of investigation formula (Rinvt)", "Pressure-rate deconvolution method" and "Shrinking Box" approach using the conventional pressure transient analysis. Principally, last two methods, if carefully used, can yield almost identical radius of investigation derived from the entire test sequence {Kui Fu (2007) }.
However, none of the previous studies have been brought an entire industry accepted solution using above three methods since Rinvt does not consider some critical parameters (i.e. rate history, gauge resolution) effecting pressure drop in reservoir as well as not able to use the entire well history.
In this paper. a new "Radius of investigation" (Rinv_new) calculation technique, which is robust with strong technical foundation and compatible with other methods (i.e. "Shrinking Box" & "pressure-rate deconvolution" method), was developed. It covers;
○ To Include the key parameters {i.e. rate, rate history and gauge resolution}, which was not part of Rinvt ○ To Able to get in line with the other two reserve calculation method (i.e. using entire history) ○ To Develop for other geometries (i.e. for rectangular geometry and various fault models) ○ To Test the validity of the method with synthetic and real well test data;

Results demonstrated that
○ Rinvt provides a conservative estimate and this method does not consider the rate & rate history ○ Synthetic data was used to test new proposed method. Results showed that: ■ Rinv could be increased by 48-142 % using new method compared to Rinvt, depending on the rate & rate history and gauge resolution. ■ Calculated error in Rinv estimate using new formula compared to exact analytical solution is 1.4-3.5 % for infinite reservoir case (i.e. no boundary has seen) ■ Rinv_new estimates are significantly improved by developed method and it is now comparable with other two methods (I.e. analytical solution considering entire well history and gauge resolution) ○ New formula could be extended to be used for other reservoir geometries. However, results showed that estimated error in Rinv calculation is increasing with number of boundaries that has already been seen. Estimated error in Rinv calculation is 1-3 % in case of no boundary has already been seen while estimated error in Rinv calculation is increasing up to 12 % in case of 2 to 3 boundaries has already been seen. ○ Actual field cases were used to test "Developed method". Results showed that Rinv was increased by 20-50 % at 0.1 psia recognizable pressure drop, compared to traditional calculation of Rinvt using the entire test period. In addition, new calculated Rinv is in line with analytical exact solution (i.e. "Shrinking Box"). Estimated error in calculation of Rinv is 1-2 % in case of no boundary has been seen while estimated error in calculation of Rinv is increasing up to 9-10 % for the case of 2 boundaries has been seen.
In this article, a new novel Rinv_new formula was developed, which is improving the Rinv estimations as well as volume estimate. A several synthetic and field case data was presented to illustrate key benefits of new method