Although increasing superwetting membranes have been developed for separating oil-water emulsions based on the "size-sieving" mechanism, their pores are easily blocked and fouled by the intercepted emulsified droplets, which would result in a severe membrane fouling issue and a sharp decline in flux. Instead of droplet interception, a fiber-based coalescer separates oil/water emulsions by inducing the emulsified droplets to coalesce and transform into layered oil/water mixtures, exhibiting an ability to work continuously for a long time with high throughput, which makes it a promising technology for emulsion treatment. However, the underlying mechanism of the separation process is not well understood, which makes it difficult to further improve the separation performance. Hence, in this work, the dynamic behaviors of water-in-oil emulsified droplets on the surface of the coalescing fiber were numerically investigated based on the phase-field model. The attachment, transport, and detachment behaviors of droplets on fibers were directly observed, and the effects of fiber wettability, orientation, arrangement, and fluid speed were studied in detail. First, it was observed that the droplets will move downstream along the fiber surface under the effect of fluid shear, and the large droplets tend to coalesce with their downstream small droplets on the same fiber surface because they move faster compared to the small droplets. Second, it was found that the emulsified droplet will spontaneously transport to the intersection of two angled fibers under the drive of asymmetric Laplace pressure, which demonstrated that the emulsified droplets tend to gather at the intersection of fibers when permeating through a coalescing medium. Third, it was found that the detachment behaviors of droplets from the fiber surface are strongly affected by their size, fiber wettability, and fluid velocity. In addition, the results of our simulation show that the backside of two closely attached fibers can further inhibit the detachment of droplets. We truly believe that our research results are of significance to optimize the parameters of a fiber-based coalescer for separating oil-water emulsions and to develop novel oil/water separators.