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 kinet- ics. For example, the mass balance for reactor 1 is 21,incl.in 21,201 - Q1.301 + Q2.102-kVic = 0 (P11.15) where in the volumetric inflow to reactor 1 (m/min), Cin the inflow concentration to reactor 1 (g/m), Q = the flow from reactor i to reactor j (m/min), c = the concentra- tion of reactor i (g/m), k = a first-order decay rate (/min), and V, the volume of reactor i (m). (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. (c) 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 ques- tions: (i) 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 in- flow concentration to reactor 1 is doubled, and the 22in10 2.in 200 V = 50 22.1=22 23,2=7 Q12=5 V = 100 V=150 2in100 13-117 23,out = 110 1.in 10 FIGURE P11.15