Analysis of Well Test Data From Permanent Downhole Gauges by Deconvolution

Abstract

Current trends towards permanent downhole instrumentation allow the acquisition of large sets of well test data ranging over much longer periods of time than previously imaginable. Such data sets can contain information about the reservoir at a substantially larger radius of investigation than that accessible to conventional derivative analysis, which is limited to the interpretation of single flow periods at constant rate. By contrast, deconvolution methods do not suffer from this constraint as they are designed to perform well test analysis at variable flow rate.Recently we presented a new method for the deconvolution of well test data in which the problem is reformulated as a separable nonlinear Total Least Squares problem which accounts for uncertainties in the measurement of both rate and pressure data.8 In this paper we report a number of improvements to our algorithm, and derive error bounds for rate and response estimates in the presence of uncertainties in the data, for which we assume simple Gaussian models. We illustrate our method by applying it to a small simulated example and two large sets of field data with up to 6000 hours of pressure data and up to 450 flow periods.