The objective of the study summarized in this paper was to develop an accurate and robust method (deconvolution) to transform rate data from a well producing with variable bottom-hole pressure (BHP) into the rate data that would have resulted had the well been produced at constant bottom-hole pressure throughout its history. These ‘corrected’ rate data can then be analyzed with confidence to determine parameters in decline models or to use in more general rate-transient analysis. Current methods used in the industry to correct for the effects of variable BHP, such as pressure-normalized rates and material-balance time, lead to less accurate model-parameter determination and thus to less accurate forecasts of future production.

We propose a new methodology based on Inverse Problem Theory to accurately forecast performance of a reservoir exhibiting variable pressure and rate trends. We first apply a unique deconvolution algorithm to the observed rate and pressure data; this deconvolved rate response represents the true decline model response if the bottomhole pressure remained constant throughout the production history. We then use the deconvolved rate response to estimate decline model parameters (like Arps decline parameter "b", loss-ratio and derivative of loss ratio) using standard curve fitting techniques. We then convolve this rate decline model with the proposed future pressure decline to obtain an accurate forecast of reservoir performance.

We pose this deconvolution problem as a regularized and weighted least square problem; the novelty in our approach lies in the regularization and weighting strategy we propose. We have overcome the limitations due to the poor quality of production data (as compared to well test data) by proposing an unsupervised weighting scheme based on a local outlier factor. We validate our method with synthetic examples generated using numerical models of multi-stage hydraulically fractured wells in unconventional reservoirs. We then illustrate application of our method using field examples from four major shale plays. Our work demonstrates that this new methodology of integrating pressures into decline curve analysis is theoretically and practically more robust than the analysis of pressure normalized rate data currently used to solve the problem.

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