A continuously stirred tank reactor with constant liquid volume V is fed by an inlet stream...

 

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A continuously stirred tank reactor with constant liquid volume V is fed by an inlet stream with volumetric flowrate F(t) [l/min] and solute concentration Ci(t) [mol/l]. An outlet stream leaves the reactor with the same flowrate and at concentration C(t) [mol/l]. Within the reactor, the solute dissociates irreversibly with the reaction rate r(t) = -k C(t). If the inlet and outlet concentrations and flowrates are the only variables in the system, answer the following questions: Derive an ODE for the state variable and use this to solve the steady-state outlet concentration Derive a linear ODE for the deviation of the state variable Derive the transfer functions that link the state and input deviations Draw the block diagram for the system Use these transfer functions to solve: (i) determine an expression for the outlet concentration when the inlet flowrate jumps to 5 [1/min] with all else constant (ii) determine an expression for the outlet concentration when the inlet concentration increases at the rate of 0.01 [mol/(1-min)] with all else constant Steady state values: F =4 1/min V =1001 C = 0.5 mol/l k = 0.01 1/(mol-min) A continuously stirred tank reactor with constant liquid volume V is fed by an inlet stream with volumetric flowrate F(t) [l/min] and solute concentration Ci(t) [mol/l]. An outlet stream leaves the reactor with the same flowrate and at concentration C(t) [mol/l]. Within the reactor, the solute dissociates irreversibly with the reaction rate r(t) = -k C(t). If the inlet and outlet concentrations and flowrates are the only variables in the system, answer the following questions: Derive an ODE for the state variable and use this to solve the steady-state outlet concentration Derive a linear ODE for the deviation of the state variable Derive the transfer functions that link the state and input deviations Draw the block diagram for the system Use these transfer functions to solve: (i) determine an expression for the outlet concentration when the inlet flowrate jumps to 5 [1/min] with all else constant (ii) determine an expression for the outlet concentration when the inlet concentration increases at the rate of 0.01 [mol/(1-min)] with all else constant Steady state values: F =4 1/min V =1001 C = 0.5 mol/l k = 0.01 1/(mol-min)