The three-dimensional connectivity of the fluid phases in porous media plays a crucial role in governing the fluid transport, displacement, and recovery. Accurate three-dimensional quantification of the fluid phase connectivity following each fluid injection stage will lead to better understanding of the efficacy and efficiency of the fluid injection strategies. Two metrics for measuring the connectivity in 3D show robust performance; one uses fast marching method to quantify average time required for a monotonically advancing wave to travel between any two pixels and the other uses two-point probability function to approximate the average distance between any two connected pixels belonging to the same fluid phase. The two connectivity metrics are applied on the three-dimensional (3D) CT scans of one water-wet Ketton whole-core sample subjected to five stages of multiphase fluid injection to quantify the evolution of the three-dimensional connectivity of the three fluid phases (oil, water, and gas). The water-wet Ketton carbonate sample (4.9 mm in diameter and 19.5 mm in length) is subjected to five sequential stages of fluid injection: 100%-brine-saturated sample, oil injection, water-flooding #1, gas injection, and water-flooding #2. CT-scan of the core sample was acquired after each injection stage. The metric response for oil phase connectivity drops after each injection process, denoting a reduction in oil connectivity after each fluid injection. The spatiotemporal variations in the connectivity of a fluid phase help understand the fluid displacement across pores of varying sizes depending on the wettability.