Rate-decline Relations for Unconventional Reservoirs and Development of Parametric Correlations for Estimation of Reservoir Properties



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Time-rate analysis and time-rate-pressure analysis methods are available to estimate reserves and study flow performance of wells in unconventional gas reservoirs. However, these tools are often incorrectly used or the analysis can become difficult because of the complex nature of the reservoir system. Conventional methods (e.g., Arps' time-rate relations) are often used incorrectly to estimate reserves from such reservoirs. It was only recently that a serious study was conducted to outline the limitations of these relations and to set guidelines for their correct application. New time-rate relations, particularly the Duong and logistic growth model, were introduced to estimate reserves and forecast production from unconventional reservoirs. These new models are being used with limited understanding of their characteristics and limitations. Moreover, well performance analyses using analytical/semi-analytical solutions (time-rate-pressure) are often complicated from non-uniqueness that arises when estimating well/formation properties.

In this work, we present a detailed study of the Duong model and logistic growth model to investigate the behaviors and limitations of these models when analyzing production data from unconventional reservoirs. We consider production data generated from numerical simulation cases and data obtained from unconventional gas reservoirs to study the quality of match to specific flow regimes and compare accuracy of the reserve estimates. We use the power-law exponential model (PLE), which has been shown to model transient, transition and boundary-dominated flow regimes reliably, as a benchmark to study performance of Duong and logistic growth models. Moreover, we use the "continuous EUR" approach to compare these models during reserve estimation. Finally, we develop four new time-rate relations, based on characteristics of the time-rate data on diagnostic plots. Using diagnostic plots we show that the new time-rate relations provide a quality match to the production data across all flow regimes, leading to a reliable reserve estimate.

In a preliminary study, we integrated time-rate model parameters with fundamental reservoir properties (i.e., fracture conductivity (Fc) and 30 year EUR (EUR30yr)), by studying 15 numerical simulation cases to yield parametric correlations. We have demonstrated a methodology to integrate time-rate model parameters and reservoir properties. This method avoids the non-uniqueness issues often associated with model-based production data analysis. This study provides theoretical basis for further demonstration of the methodology using field cases.