(e) i - (part 2) What fractions of this concentration come from reactor 1 and re

Question

(e) i - (part 2) What fractions of this concentration come from reactor 1 and reactor 2?

11.15 A chemical constituent flows between three reactors as depicted in Fig. P11.15. Steady-state mass balances can be written for a substance that reacts with first-order kinetics. For example the mass balance for reactor 1 is Where Q1,in = the volumetric inflow to reactor 1 (m^3/min). c1,in = the inflow concentration to reactor 1 (g/m^3), Qi,j = the flow from reactor i to reactor j (m^3/min), ci = the concentration of reactor i (g/ m^3), k = a first-other decay rate (/min), and Vi = the volume of reactor i (m^3). (a) Write the mass balances for reactors 2 and 3. (b) If k = 0.1/min. write the mass balances for all three reactors as a system of linear algebraic equations. (e) Compute the LU decomposition for this system. (d) Use the LU decomposition to compute the matrix inverse. (e) Use the matrix inverse to answer the following questions: (1) What are the steady-state concentrations for the three reactors? (ii) If the inflow concentration to the second reactor is set to zero, what is the resulting reduction in concentration of reactor 1? (iii) If the inflow concentration to reactor 1 is doubled, and the

Explanation / Answer

a.) for reaction 2

10*200-Q21*c1+Q12c2+ Q32c2-k(V2-50)

for reaction 3

Q3c3+Q13c1-Q32c3-k(V3-150)

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