Exact Analytical Solution of the Telegraphic Warren and Root Model

González-Calderón, Alfredo; Vivas-Cruz, Luis X.; Salmeron-Rodriguez, Uriel

doi:10.1007/s11242-017-0932-y

Cited by 4 publications

(1 citation statement)

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“…Many fluid flow models have exact solutions in Laplace space, but their inverse transforms can be quite complex to obtain by means of contour integration in the complex plane (González-Calderón et al, 2017;Yao et al, 2012). Remarkably, the Hankel transform provides a simple way to treat radially symmetric problems, since their inverse transform formulas are the solutions of the models (Cinelli, 1965;Jiang and Gao, 2010;Sneddon, 1946).…”

Section: Introductionmentioning

confidence: 99%

Solutions and Type Curves of a Fluid Flow Model for Naturally Fractured Reservoirs With Influx Recharge

Vivas-Cruz

Perera-Burgos²,

Taneco-Hernández

et al. 2020

J Por Media

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Modeling of fluid flow considering radially symmetric reservoirs is common in groundwater science and petroleum engineering. The Hankel transform is suitable for solving boundary value problems, considering this flow geometry. However, there are few applications of this transform for reservoirs with a finite wellbore radius, although there are formulas of the finite Hankel transform for homogeneous boundary conditions. In this work, we refer to them as the Cinelli formulas, which are used to obtain novel solutions for transient fluid flow in bounded naturally fractured reservoirs with time-varying influx at the outer boundary, i.e., a technique to incorporate inhomogeneous boundary conditions based on the Cinelli formulas is developed. An analysis shows that the results of the solutions are highly oscillating and slowly convergent. Nevertheless, we show that this problem is largely overcome when the long-time solution is expressed as a closed relationship. Accordingly, we present the characteristic drawdown pressure curves and its Bourdet derivatives for a double-porosity reservoir with influx recharge. These curves allow us to distinguish between the pressure drops of a single-porosity reservoir with influx recharge from that of a double-porosity closed reservoir, which have been stated in the literature to resemble one another. Similarly, double-and triple-porosity reservoirs are analyzed.

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