This paper uses the Volume of Fluid (VOF) method to simulate a double Co-Flow microfluidic device that can produce double emulsions in both Newtonian (water) and non-Newtonian fluids. The simulation is 2D axisymmetric and involves three phases. A model is evaluated in this study to examine how the size and double emulsion’s generation rate are impacted by factors such as phase velocity, viscosities, interfacial tension, and the rheological properties of non-Newtonian fluids. The model predicted the process of emulsification successfully in dripping and jetting regimes and predicted the impacts of phase velocity on the dimension and frequency of compound droplets. Increasing the flow rate of the inner phase causes the inner droplets to grow, while the outer droplet dimensions remain mostly unchanged. Vice versa, an increase in outer phase flow rate reduces compound droplet size. However, when the middle phase's flow rate is enhanced, the size of detached droplets in the inner and outer phases undergoes opposite changes, i.e., decreasing and increasing, respectively. The results showed that in non-Newtonian fluids, smaller droplets are formed compared to water, and the diameter of the double emulsions formed decreases with the rise in the viscosity at zero shear rate of the non-Newtonian fluid.