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Journal of Porous Media
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ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.2020033939
pages 1015-1041


Luis Xavier Vivas-Cruz
Centro de Ingeniería y Desarrollo Industrial (CIDESI), Av. Playa Pie de la Cuesta 702, Desarrollo San Pablo, Querétaro, Qro, 76125, México
Jorge Adrián Perera-Burgos
CONACYT – Unidad de Ciencias del Agua, Centro de Investigación Científica de Yucatán A.C., Calle 8, No. 39, Mz. 29, S.M. 64, Cancún, Quintana Roo, 77524, México
M. A. Taneco-Hernández
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas, Cd. Universitaria Sur, Chilpancingo, Guerrero, 39087, México
Alfredo González-Calderón
CONACYT – CIDESI sede Campeche, Ctra. Carmen Puerto Real km 7.5, Mundo Maya, Cd. del Carmen, Campeche 24153, México


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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