Transp Porous Med DOI 10.1007/s11242-017-0932-y Exact Analytical Solution of the Telegraphic Warren and Root Model Alfredo González-Calderón 1 · Luis X. Vivas-Cruz 1 · Uriel Salmerón-Rodríguez 1 Received: 9 March 2017 / Accepted: 18 September 2017 © Springer Science+Business Media B.V. 2017 Abstract We exactly solved a Warren and Root-like model that considers telegraphic fluid flow, a constant hydraulic head at the bottomhole, and an infinite Euclidean reservoir with radial flux. Complex integrals on the Bromwich contour are used to obtain the exact solutions of the hydraulic head and flux. Given that the behavior of the propagation of the hydraulic head has a discontinuous front, this system is appropriate for evaluating numerical methods that have difficulties with discontinuities. To this end, the results from the Stehfest method and Iseger method are analyzed. Keywords Inversion Laplace transform · Telegraphic fluid flow · Double-porosity model 1 Introduction Fluid flow through a porous medium is usually modeled using Darcy’s law. As a consequence of this law, the partial differential equations (PDEs) used are diffusive type, i.e., parabolic type, which implies that the disturbances in the pressure at the bottomhole are transmitted at infinite velocity (Rehbinder 1989). With the goal of considering finite velocity pressure propagation, Darcy’s law is modified in such a way that it looks similar to the Cattaneo equation (Cattaneo 1958). This extended formulation gives rise to hyperbolic PDEs, i.e., second-order wave-like equations, which describe anomalous transport at short times Compte and Metzler (1997) and ordinary diffusion at times greater than the relaxation time. It is noteworthy that these hyperbolic models are usually known as telegraphic models. It has been observed that this description has applications in petroleum engineering and groundwater sciences because anomalous fluxes are associated with carbonate reservoirs (Wang 2013). According to Economides and Nolte (2000), the equation for a single-phase radial flow at the bottomhole of a single porosity medium “is perhaps the most important relationship in B Alfredo González-Calderón alfredo.gonzalez@cidesi.edu.mx 1 CONACyT - Centro de Ingeniería y Desarrollo Industrial (CIDESI), Av. Playa Pie de la cuesta 702, Desarrollo San Pablo, 76125 Querétaro, QRO, Mexico 123