The SO₂ scrubbing tower described in Problem 4.26 is to be used to reduce the SO₂ mole fraction in the waste gas to a level that meets air quality control regulations. The solvent feed rate must be large enough to keep the SO₂ mass fraction in the exit liquid below a specified maximum value.

(a) Draw and label a flowchart of the tower. Along with the molar flow rates and SO₂ mole fractions of the four process streams, label the feed gas temperature and pressure [T₁ (°F), P₁ (psig)], the feed gas orifice meter reading [h₁ (mm), the SO₂ analyzer reading for the feed gas (R₁), the volumetric feed rate of solvent to the column [V₂ (m³/min)], and the SO₂ analyzer reading for the exit gas (R₃). (The temperature and pressure Units are taken from the calibration curves for the gauges used to measure these variables.)

(b) Derive a series of equations relating all of the Labeled variables on the flowchart. The equations should include the calibration formulas calculated in part (b) of Problem 4.26. Determine the number of degrees of freedom for the process system. In the remainder of the problem, you will be given values of measured feed gas stream variables [T₁ (°F). P1(psig), hi(mm), and Ru, the maximum allowed SO₂ mole fraction in the exit solution [x₄], and the specified SO₂ mole fraction in the exit gas (y), and asked to calculate the expected SO₂ analyzer reading for the exit gas (R³) and the minimum volumetric flow rate of solvent (V₂). Part (c) involves using a spreadsheet for the calculation, and part (d) calls for an independent calculation using an equation-solving program.

(c) Create a spreadsheet to store input values of T₁, P₁, h₁, R₁, x₄, and y and to calculate R₃ and V₂. In the first five rows, insert the values T₁ 75, P₁ = 150. h₁ 210, R₁ 82.4 x₄ = 0.10 and y₃ = 0.05, 0.025, 0.01, 0.005, and 0.001. In the next five rows, insert the same input values except make x₄ = 0.02. On a single graph draw plots of V₂ versus y₃ for each of the two given values of x4 (preferably using the spreadsheet program to generate the graph). Briefly explain the shape of the curves and their position relative to each other.

(d) Enter the equations of part (b) into an equation-solving program. Use the program to calculate R₃ and V₂ corresponding to T₁ = 75. P₁ = 150. h₁ = 210, R₁ = 82.4, x₄. = 0.10 and v₃ = 0.05, 0.025, 0.01, 0.005, and 0.001, and then T₁ = 75, P₁ = 150, h₁ = 210, R₁ = 82.4, x₄ = 0.02 and = 0.05, 0.025, 0.01, 0.005 and 0.001. If you did not already do so in part (c), draw on a single graph plots of V₂ versus y₃ for each of the two given values of x₄ and briefly explain the shape of the curves and their position relative to each other.