Forty-eight cubic meters of sewage sludge containing 3.5% solids by mass is fed daily into an anaerobic digester. The solids in the sludge are 68% organic and 32% inert by mass. Some of the organic material is converted to CO2 and CH4 and some of it is converted into stable biosolids. The sludge density is 1.15 kg/L. In the digester the sludge stratifies into two layers and material leaves the digester as stabilized sludge, clear supernatant and gas. The stabilised sludge is withdrawn at 8% solids by mass of which 45% is organic and 55% is inert. Only 85% of the digestable component is converted to biogas with approximate proportions of 65% CH4 and 33% CO2, and 2% other gases. Assume steady state conditions and that a negligible amount of solids leaves the digester in the supernatant. (a) Compile a water and solids mass balance over the digester and calculate: (ii) The volume of water (supernatant) that leaves the digester daily (iii) The percentage reduction of the organic material in the sludge (iv) Calculate the mass of CH4 produced daily