Accurate acid placement constitutes a major concern in matrix stimulation because the acid tends to penetrate the zones of least resistance while leaving the low-permeability regions of the formation untreated. Degradable materials (fibers and solid particles) have recently shown a good capability as fluid diversion to overcome the issues related to matrix stimulation. Despite the success achieved in the recent acid stimulation jobs stemming from the use of some products that rely on fiber flocculation as the main diverting mechanism, it was observed that the volume of the base fluid and the loading of the particles are not optimized. The current industry lacks a scientific design guideline because the used methodology is based on experience or empirical studies in a particular area with a particular product. It is important then to understand the fundamentals of how acid diversion works in carbonates with different diverting mechanisms and diverters. Mathematical modeling and computer simulations are effective tools to develop this understanding and are efficiently applied to new product development, new applications of existing products or usage optimization. In this work, we develop a numerical model to study fiber dynamics in fluid flow. We employ a discrete element method in which the fibers are represented by multi-rigid-body systems of interconnected spheres. The discrete fiber model is coupled with a fluid flow solver to account for the inherent simultaneous interactions. The focus of the study is on the tendency for fibers to flocculate and bridge when interacting with suspending fluids and encountering restrictions that can be representative of fractures or wormholes in carbonates. The trends of the dynamic fiber behavior under various operating conditions including fiber loading, flow rate and fluid viscosity obtained from the numerical model show consistency with experimental observations. The present numerical investigation reveals that the bridging capability of the fiber–fluid system can be enhanced by increasing the fiber loading, selecting fibers with higher stiffness, reducing the injection flow rate, reducing the suspending fluid viscosity or increasing the attractive cohesive forces among fibers by using sticky fibers.