# title
Application of Fast Fourier Transforms to Deconvolution of Multirate Well Test Data

# abstract
<jats:title>Abstract</jats:title>                <jats:p>Deconvolution of pressure and flow rate measurements is one of the great challenges inherent in well test interpretation. Deconvolution allows the test analyst to estimate the constant-rate transient pressure response of a reservoir-well system, and assists us in system identification and parameter estimation. Unfortunately, deconvolution amplifies the noise contained in data. Often we cannot identify the reservoir system from deconvolved results owing to solution instability caused by noise in measured data.</jats:p>                <jats:p>We previously presented1 a deconvolution technique based on the fast Fourier transform that we applied to a single buildup or drawdown period. Unlike other deconvolution methods that deconvolve pressure and rate data in the time domain, our method deconvolves pressure and rate data in the frequency domain. We found that we can remove the noise transferred to deconvolved pressures in the frequency domain, and we can find a stable and interpretable deconvolution solution even when test data are noisy.</jats:p>                <jats:p>In this paper, we extend our previous work and apply the deconvolution technique based on the fast Fourier transform to arbitrarily changing rate profiles such as multi-rate tests. The deconvolution results, which represent a constant-rate pressure drawdown response spanning the entire duration of the test, can provide helpful insight into the correct reservoir description. We have improved our original deconvolution method in number of ways, particularly with the introduction of an iterative algorithm that produces stable deconvolution results. We demonstrate application of our deconvolution method to analysis of synthetic and field examples, including both flow and shut-in periods. Our deconvolution method can efficiently reproduce the characteristic responses of the reservoir-well system and increase our confidence in parameter estimates.</jats:p>