You are to simulate a single-phase adiabatic reactor in which a single gas-phase reaction takes place. The reaction has the general form

In this equation A_i is the ith reactant or product and v_i is the stoichiometric coefficient of this species; is negative for reactants and positive for products. It is also convenient to define v_i for each inert species in the feed to the reactor, assigning it a value of 0. The inputs to the program are the stoichiometric coefficients, feed stream flow rate, composition, and temperature, and the fractional conversion of one of the reactants. The program is to calculate the product stream component flow rates and temperature.

The program equations should be written in terms of the following variables:

(a) Write the equations you would use to calculate the attributes of SP from specified values of all the other listed variables. The last equation you derive should be a fourth-order equation for the reactor temperature,

where α, β, γ, δ and ε involve most of the system variables.

Write a spreadsheet to perform the calculations of part (a) for a reactor in which carbon monoxide is oxidized with 25% excess air at 1 atm to form carbon dioxide. The combined feed stream enters the reactor at 650°C at a rate of 23.0 kmol/h, and a CO conversion of 45% is obtained. Use the goalseek tool to solve the fourth-order energy balance equation. After you have performed the calculations and recorded the output variable values, use the spreadsheet to generate a plot of product gas temperature versus percentage CO conversion and briefly explain why the plot looks the way it does.

(c) Use an equation-solving program to perform the calculations outlined in part (b).

(d) Write a computer subprogram REACTAD to implement the procedure of part (a). The subprogram arguments should be SF, SP, NU, N, X, and IX. The arrays ACP, BCP, CCP, DCP, and DHF should either be transmitted as additional arguments or via COMMON or GLOBAL. All arguments but the attributes of SP should be considered input variables. Use Newton's rule (Appendix A.2) to solve the fourth-order energy balance equation. Write and run a calling program that defines the input variables, calls the subprogram, and prints out the required output variables for the test case of part (b). Number the species involved in the process as follows: 1—CO, 2-O₂, 3—N₂, 4—CO₂. For example, NU(1) = —1, NU(2) = —1/2, SF(1) = 1.607, and SF(3) = 3.777. (Verify these values as part of your problem solution.)

v A1 + v2A2 + V3A3 + + vm Am = 0 %3D