Oil-water separation is a very important process in petroleum engineering, as well as in industries that produces oily wastewater and other oil-water pollution. The basic process of oil-water separation is illustrated in the figures below. From left to right, the figures show a simple emulsion in which dispersed (Dutch: verspreidt) oil droplets in water coalesce (come together to form one mass) as time passes. Assume that the number of oil droplets decreases with time (in minutes) following the equation: ൌ െ0.02 a) Calculate how long it takes for half of the oil droplets to coalesce. (3p) b) How long will it take for practically all the oil droplets to coalesce? (2p) c) Provide a sketch of the number of oil droplets as function of time in the oily water. Add relevant values along the axis. (1p) To speed up the process of coalescence, a chemical component (surfactant) is added to the oily water. Assume that now the number of oil droplets decreases with time following the equation: ൌ െ0.02ଶ d) After adding the surfactant to the mixture, can the process still be considered a natural process? Explain. (1p) e) Show that, after adding the surfactant to the oil-water mixture, less time is needed for half of the oil droplets to coalesce. (