Explicit Deconvolution of Wellbore-Storage-Distorted Well-Test Data
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 103216, "Explicit Deconvolution of Wellbore-Storage- Distorted Well-Test Data," by O. Bahabanian, SPE, D. Ilk, SPE, N. Hosseinpour-Zonoozi, SPE, and T.A. Blasingame, SPE, Texas A&M U., prepared for the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September.
The analysis and interpretation of wellbore-storage-distorted pressure-transient-test data remain significant challenges. Deconvolution (i.e., conversion of a variable-rate-distorted pressure profile into the pressure profile for an equivalent constant-rate-production sequence) has been in limited use as a conversion mechanism for the last 25 years. Unfortunately, standard deconvolution techniques require accurate measurements of flow rate and pressure at downhole (or sandface) conditions. While accurate pressure measurements are commonplace, the measurement of sandface flow rates is rare, essentially nonexistent in practice. An explicit (direct) deconvolution of wellbore-storage-distorted pressure-test data that uses only those pressure data was developed.

Introduction
To eliminate wellbore-storage effects in pressure-transient-test data, several methods have been proposed. An approximate direct method corrects the pressure-transient data distorted by wellbore storage into the equivalent-pressure function for the constant-rate case. Despite its simplicity, it has several shortcomings such as limited accuracy and erroneous skin-factor estimation.
Rate-normalization techniques have been used to correct for wellbore-storage effects, and these methods were successful in some cases. The most appropriate application of rate normalization is its use for pressure-transient data influenced by continuously varying flow rates. Application of rate normalization requires sandface-flow-rate measurements and generally yields a shifted result trend that has the correct slope but incorrect intercept on a semilog graph (i.e., incorrect skin factor).
Material-balance deconvolution has been shown to be a practical approach for the analysis of pressure-transient data distorted by wellbore-storage effects. In particular, this approach remedies the issue of a poor skin-factor estimate that typically is obtained with rate normalization. Material-balance deconvolution also is thought to require continuously varying sandface-flow-rate measurements. It is shown that sandface flow rates can be approximated from the observed pressure data.

Methodology
This work was put forth as an attempt to provide a set of simple, explicit deconvolution formulas that could be used on wellbore-storage-distorted pressure-transient-test data. The material-balance deconvolution was successful and should be considered sufficiently accurate for use as a practical tool for field applications. The other major method considered was the direct β-deconvolution algorithm modified to estimate the β-parameter from pressure rather than flow-rate data as originally proposed. The modification of the β-deconvolution algorithm, given only in terms of pressure variables, also was successful.