Determination of Optimal Window Size in Pressure Derivative Computation UsingFrequency-omain Constraints

摘要

Analysts commonly use the pressure derivative to identifyrnflow regimes and well-test-interpretation models in pressure-transientrntest analysis. Analysts and commercial analysisrnsoftware commonly use Bourdet's approach to calculaternderivatives from measured pressure data. Bourdet's algorithmrnincludes a weighted central-difference approximation with arncertain "window" size based on an increment in the logarithmrnof time, represented by the symbol L. Although test analystsrncommonly select L in the range of 0.1 to 0.3 log cycle, norncriterion is available for choosing the optimal value of L. Anrnunresolved issue in pressure transient test analysis is how torndetermine the optimal L based on the data for each individualrndata set such that the data are smoothed sufficiently to removernnoise that obscures the signal but not smoothed to the extentrnthat the signal itself is changed.rnThis paper presents a new approach to calculate thernpressure derivative, and improves the results compared tornthose we achieved in a previous paper, SPE 84471. Thisrnapproach determines the optimal window size to use withrnBourdet's algorithm by employing the fast Fourier transform,rnGaussian filtering, and frequency-domain constraints. Ourrnapproach denoises the data in the frequency domain,rndetermines the optimal window size, and, when coupled withrnBourdet's algorithm in the time domain using the optimalrnwindow size, provides an improved pressure derivative. Wernalso developed a novel adaptive smoothing algorithm byrnrecursive differentiation-integration to further improvernpressure derivative calculation. Our method can efficientlyrnsuppress measurement errors and produce smooth pressurernderivatives from well-test data. Equally important, it canrnprevent over-smoothing of the data by inappropriate use ofrnlarge window size, and it can preserve the characteristicrnbehavior of the pressure derivative.rnWe validate our approach with a synthetic example andrndemonstrate its applicability to actual field examples.