Wavelet Based Regularization of the Well Test Deconvolution Problem

Permanent downhole measurements provide "well test" data in abundance, but their behaviour often reflects the erratic environment of everyday well operations rather than the more sterile conditions typical of a traditional well test. Consequently, processing and interpretation demand an increased level of sophistication.<br><br>In reference [1] the authors make a strong case for total least squares (TLS) applied to deconvolution of well test data. Their approach includes regularization based on penalizing the total curvature of the response function.<br><br>The present effort combines a TLS approach with regularization based on a discrete wavelet transform. As indicated in reference [2], this allows a systematic approach where the regularization have a concrete interpretation in terms of resolved details of the response function. Highly contaminated data only allows the most prominent details to be determined within relevant accuracy, while improved data quality allows correspondingly more details to be revealed.<br><br>Preliminary results demonstrating feasibility, accuracy and robustness will be presented.<br><br>[1] von Schroeter,T., Hollaender,F and Gringarten,A.C. - Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem - SPEJ 9 no 4, 375-390 2004<br> <br>[2] Nikolaou,M. and Vuthandam,P. - FIR Model Identification: Achieving Parsimony through Kernel Compression with Wavelets - AIChE J. 44 no 1, 141-150 1998