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problem_set3

# problem_set3 - 10.34 Fall 2006 Homework#3 Due Date...

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10.34 – Fall 2006 Homework #3 Due Date: Wednesday, Sept. 27 th , 2006 – 9 AM Problem 1: Peak Temperature For safety reasons, it is useful to be able to bound the peak temperature which could be realized in an exothermic reaction. An overestimate can be computed by assuming the limiting reactant is 100% converted to products, and the process is adiabatic (no heat losses). A more accurate bound can be computed by considering the fact that the reaction will reach equilibrium before the limiting reactants is 100% consumed. In an adiabatic process, enthalpy is conserved, so for an ideal mixture m H T T ( ) = m H ( ) i i in k k out in out For many common molecules, expressions for H(T) are presented in the NIST Webbook http://webbook.nist.gov . Usually these are given as coefficients for a Shomate functional form. A program Shomate.m is provided on the 10.34 Web page which can read these coefficients and compute H(T) (and other thermodynamic properties) for these molecules. Note that Shomate.m only takes in coefficients A – G, T min , and T max ; you will need to read the file to determine the format for the inputs. In this problem, we will investigate the peak temperature which could be reached in an adiabatic reactor for the Water-Gas Shift reaction. In this case, the flow rates (in millimoles/second ) into the reactor are: [H 2 ] = 2, [H 2 O] = 5, [CO] = 1, and [CO 2 ] = 0.1. Part A: Generate a plot showing the temperature dependence of the Hrxn, T* Srxn, and Grxn over the range of 500 – 1500 K. Part B: For the worst case scenario (100% conversion), generate a plot showing the peak temperatures as a function of the inlet temperature to the system over the range. Cite as: William Green, Jr., course materials for 10.34 Numerical Methods Applied to Chemical Engineering, Fall 2006. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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Part C: You know that the system cannot proceed beyond equilibrium under steady state conditions; therefore, solve for the realistic outlet temperature and CO conversion for the given range of inlet temperatures, and plot the results. Part D: You found the equilibrium boundary in the previous part, but this does not represent the entire range of accessible operating conditions. Generate a surface or mesh plot of the reactor temperature using Matlab that displays ONLY the valid parameter space which is accessible experimentally. (i.e. do not plot any points that are non-feasible based on equilibrium considerations). The figure should have x- and y-axes as the conversion and inlet temperature, and the z-axis should be the reactor temperature. You may find it
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