Produced waters generated during shale gas production typically have high salinities and are often stored in lined impoundments on site. Compared to other formations, brines produced from the Fayetteville shale have one of the lowest concentrations of total dissolved solids (TDS) and are thus highly suited to reuse in subsequent hydraulic fracturing operations with minimal treatment. a. An oil operator stores produced water containing 10,000 ppm TDS in an impoundment. One day the liner tears and the water begins leaking into an adjacent lake, which has a volume of 18,000 m3 and is perfectly mixed. The stream feeding the lake flows into and out of the lake at 0.2 m3/s. Following the impoundment leak, the TDS level in the lake rises from an initial concentration of 100 mg/L to a new steady-state concentration of 300 mg/L. What is the rate (in m3/s) at which TDS from the produced water is flowing into the lake? b. The operator finds and remediates the leak such that no more produced water is entering the lake How long will it take for TDS levels in the lake to drop to 200 mg/L? c. Reverse Osmosis (RO) is a water purification technology that uses a semipermeable membrane to remove ions, molecules, and other larger particles from water. A portion of the RO feedwater is rejected as waste while the rest exits as filtered water known as permeate. The typical recovery rate for high TDS water is approximately 50% (ie, 2 liters of feed water will produce 1 liter of permeate and 1 liter of reject water). The operator decides to treat some of the produced water with RO. If the feed water is flowing at 10 m/h and a typical RO membrane can reject 99% of the dissolved salt mass in the influent, what will be the TDS concentration in the permeate and rejected water streams? Consider all TDS as salt