Q1. [50 pt] Consider the process shown below. VA = F Process characteristics: A liquid stream enters tank at a volumetric flow rate F (cfm) and contains reactant A at a concentration of co mole A ft. Reactant A decomposes in the tanks according to the irreversible chemical reaction: AB. The reaction rate is: Ak where FA is the rate of A consumption in(mole/fi.min k is the reaction rate constant in 17min F.C e is the concentration of component infmole/f VTC. V.Tk The reaction takes place in two CSTR in series with temperature being constant. The outlet concentration of component 4 is controlled by manipulating the feed concentration, co. The feed flow rate F is considered constant. The controller has a simple proportional element. Controter Control valve characteristics: The flow of A through the valve varies linearly from 9 to 4 cfm as the valve-top pressure varies from 3 to 19 psia. The time constant 1, of the valve is so negligible. Measuring device characteristics: the output of the measuring element varies from 4 to 20 mA as the concentration of A varies from 0.01 to 0.09 lbmole A ft. We will assume that the concentration measuring device is linear and has negligible lag. (a) [22pt] Develop the transfer function for the process, control valve, measuring device and controller. Assume constant holdup. (b) [8pt] Comment on the effect of reaction rate constant on time constant. (c) [6pt] Calculate the numerical values for all parameters using the table and define the overall gain between c2 and co. Comment on its effect on offset. (d) [14pt] Draw the block diagram for the feed-back control system. MW 100 lb/lbmole PA 0.8 lbmole/ft k₁ 1/6 min 2/3 min F 100 cfm Co 0.1 lbmole/ft V 300 ft