Accounting for exterior flow using the modified logistic growth model for unconventional geopressured shale reservoirs




Villarroel Salvatierra, Julio Cesar

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The flow of gas in shale gas wells is known to be linear from the matrix through fractures. At early times, the rate declines in proportion to the inverse of square root of time (t⁻¹/²). Once fractures start interfering each other, the rate from the stimulated reservoir volume (SRV) declines exponentially (Patzek et al, 2013). The scope of this work is to assess the flow beyond boundary-dominated flow. Defining the existence of “exterior flow” and further use of decline curve analysis in unconventional reservoirs. This regime is the linear flow of gas from the non-stimulated matrix “feeding into” the depleted stimulated reservoir volume, at late times, beyond boundary-dominated flow. Additionally, we present novel diagnostic plots on rate-time data to obtain the characteristic time of switching from boundary-dominated to exterior flow that enables the prediction of additional volumes produced under this new flow regime. These volumes could be justified as probable reserves (P2). Clark, et al. (2011) presented a decline curve model based on nature’s theory of logistic growth that enlightened the use of the carrying capacity parameter “K” as a proxy for the Estimated Ultimate Recovery (EUR). However, in geopressured shales such as the Haynesville Shale, where Arps (1945) or any of the decline curve models currently available may not fit production curves, a flow regime analysis is needed in order to characterize the entire well history data and fit a model. Since all decline curve models are empirical, after appropriate flow regime identification, the modified logistic growth model (m-LGM) provides some physical meaning about the EUR. The logistic growth model fits all periods in a typical shale gas well: ramp-up, plateau, sharp decline; and the period described as exterior flow, which is evident as a kink in the slope of the logarithm of rate vs. time plot, is characterized by using an exponential decline tail (b-factor = 0). Moreover, for all the wells observed, the characteristic time of switching from boundary-dominated to exterior flow is between 4.5-5.0 years independent of well completion schemes and/or location. When volumes obtained from exterior flow are forecasted to economic limit rate, an additional 10-20% is observed compared to the EUR forecasted using classic decline curve analysis. As the Pareto Principle states: 80% of production comes from the most important 20% of the resource (ideally, the depleted stimulated reservoir volume, in this case). Thus, the remaining 20% from exterior flow. This could be a significant volume if hundreds or thousands of wells are accounted for in the basin. Finally, we present new diagnostic plots using rate-time data to better understand the flow regimes existing in a geopressured shale production curve that enables estimates of the volumes beyond boundary-dominated flow. This method accounts for an additional recovery that could be justified and categorized as probable reserves


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