Exact Analytical Solution of the Telegraphic Warren and Root Model

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.