Hi i need help with the following problem regarding drilling fluids :

In this task we assume that our rig has a relatively small maximum drilling fluid handling capacity of only 40 m, or 335.5 bbl. Our current water-based mud is made up of 6 % volume fraction bentonite, 10% volume fraction baryte and the rest water. Using the ingredient mass densities in table 1, this results in a mud density of 1429 kg/m, or 11.9 lb/gal. Ingredient Water Bentonite Baryte Mass density 1000 kg/m3 (8.3 lb/gal) 2350 kg/m3 (19.6 lb/gal) 4480 kg/m3 (37.4 lb/gal) Table 1: Mass density of drilling fluid components. a) We have a full mud system, corresponding to 40 m of the 1429 kg/m mud. We are now notified that the drilling fluid is too thick and not sufficiently heavy. So we need to thin the bentonite volume fraction to 4 % and increase the mass density to 1500 kg/m?. We must do this without exceeding the volume capacity of our mud system. How much of the current mud should be discarded? b) How much baryte and how much water do we need to add to get back to a total of 40 m drilling fluid, that now has the correct bentonite volume fraction and the correct mass density? c) The drilling fluid with mass density 1500 kg/m3 has been used to drill a vertical 12 1/4-in hole section to a depth of 2000 m. After tripping the drill string out of the well, the mud or drilling fluid has been left static in the hole for an extended period of time, and we are worried that the baryte particles have fallen out of suspension and generated a baryte plug in the bottom of the well. Assume that baryte particles can achieve a close-packing in the bottom of the well corresponding to a volume fraction of 60 % baryte within this plug, and estimate the height of the baryte plug