10 34 Quiz 1 October 4 2006 A perfectly stirred reactor a CSTR is loaded with cells which multiply at a rate k1 N cells Nutrients Cell Multiplication 1 c1 Nutrients 1 d P So the net balance on cells in the CSTR is dN cells Cell Multiplication Rate at which cells flowout of reactor dt A nutrient water mixture with Nutrients in 0 2 M is flowed into the 150 liter CSTR at a rate of 2 3 liter min The cells in the CSTR eat some of the nutrients Nutrient Consumption Rate k2 N cells c2 Cell Multiplication and produce a desired pharmaceutical product P k3 N cells exp d P 2 Nutrients 0 01 P production rate 1 c1 Nutrients The parameters are k1 0 5 M 1 s 1 c1 0 1 M 1 k2 1 10 7 moles cell 1 s 1 c2 1 10 5 moles cell 1 k3 1 10 6 moles cell 1 s 1 M 1 d 0 01 M 1 a Write a couple of Matlab functions that together compute the concentrations P and Nutrients units M moles liter as well as the number of cells per liter in the output stream when the system is operated at steady state Give numerical values for all the inputs Do you think that scaling will be a problem Explain and give an appropriate scaling factor if necessary b If your program from part a works correctly how would you test whether the solution found is physical and achievable i e stable Explain in words bonuses for giving correct relevant equations and or Matlab functions c If your program from part a converges to an unphysical or unstable solution what would you do next to try to find an experimentally relevant steady state solution Explain in words bonuses for giving correct relevant equations and or Matlab functions For your convenience on the next page we have supplied the Matlab functions Cell Multiplication m Nutrient Consumption m P production m and param set m which you can call with the functions you write yourself You can also call any built in functions in Matlab and any functions presented as examples in class 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 function CMrate Cell Multiplication Ncells Nutrients P params computes the Cell Multiplication rate cells s in the CSTR inputs Ncells number of cells in the CSTR Nutrients concentration of Nutrients in the CSTR moles liter P concentration of Product in CSTR moles liter params values of k1 k2 k3 c1 c2 d as listed in problem statement k1 params 1 c1 params 4 d params 6 CMrate k1 Ncells Nutrients 1 c1 Nutrients 1 d P function NCrate Nutrient Consumption Ncells Nutrients P params computes the nutrient consumption rate in the CSTR moles s inputs Ncells number of cells in the CSTR Nutrients concentration of Nutrients in the CSTR moles liter P concentration of Product in CSTR moles liter params values of k1 k2 k3 c1 c2 d as listed in problem statement k2 params 2 c2 params 5 NCrate k2 Ncells c2 Cell Multiplication Ncells Nutrients P params function Prate P production Ncells Nutrients P params computes the product production rate in the CSTR moles s inputs Ncells number of cells in the CSTR Nutrients concentration of Nutrients in the CSTR moles liter P concentration of Product in CSTR moles liter params values of k1 k2 k3 c1 c2 d as listed in problem statement k3 params 3 d params 6 c1 params 4 Prate k3 Ncells exp d P Nutrients 0 01 2 1 c1 Nutrients function params param set sets params as in the problem statement k1 k2 k3 c1 c2 d params 0 5 1e 7 1e 6 0 1 1e 5 0 01 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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