Spontaneous imbibition in a porous medium is known to have two macroscopic fronts, the leading one in narrow pores and the lagging front in the wider pores. This behavior contradicts the behavior predicted by Washburn law due to interaction of the pores in the porous medium. In this work, we investigate the spontaneous imbibition behavior in a randomly arranged interacting capillaries system and propose a one dimensional Washburn like model which can be used to upscale the porous medium properties. We first use Volume of Fluid (VOF) simulations, which tracks the fluid-fluid interface in the multiphase flow, and show several approximations that can be used to develop a quasi one-dimensional Washburn like model for interacting capillaries. Using these approximations, we build a model for two and three capillary systems, which is able to mimic the spontaneous imbibition in a three-dimensional interacting capillary system simulated using VOF. The one-dimensional model for three capillaries shows a strong dependence of the spontaneous imbibition behavior on the arrangement of the interacting capillaries and their relative radii. We show using the one-dimensional model, that the meniscus does not always lead in the smallest radius capillary in the interacting system. We also show that the spontaneous imbibition in the whole system also deviates from the Washburn like diffusive behavior. (C) 2018 Elsevier Ltd. All rights reserved.