Page - 13 - in Advanced Chemical Kinetics

5.Themeasuringmethods Thekineticequationsof theabovereactionmechanism(R-1)canbemeasuredbyusingEq. (13) d dt cA2 cB cAB cZ cAZ 26666664 37777775¼ �kþ1 c1c22�k�1 c23 kþ2 c3c4�k�2 c2c5�2kþ1 c1c22þ2k�1 c23 �kþ2 c3c4þk�2 c2c5þ2kþ1 c1c22�2k�1 c23 �kþ2 c3c4þk�2 c2c5 kþ2 c3c4�k�2 c2c5 266666664 377777775 whileNs=2,Nint=2(Z,AZ),Nas=1(Z), andareaction routeNrr is 1. A reduced form of the system (R-1) can be achieved by using the Eqs. (12) and (13).While initialparametersaredefinedas ceq1 ¼0:5,ceq2 ¼0:1,ceq3 ¼0:1,ceq4 ¼0:4,ceq5 ¼0:1,kþ1 ¼1,kþ2 ¼0:5. Similarly, (R-2) implies thatwe can reduce this system into three components,whileNs = 3, Nint =3(Z,ZO,ZCO),Nas=1(Z), andNrr=1. Thus, a single reaction route is available. The kinetic equations for the involved species are givenbyEq. (13) d dt cA2 cB cAB cZ cAZ cBZ 26666666664 37777777775 ¼ �kþ1 c1c22�k�1 c23 2kþ3 c3c4�2k�3 c22c6�kþ2 c2c5þk�2 c4�2kþ1 c1c22þ2k�1 c23 �kþ3 c3c4þk�3 c22c6þ2kþ1 c1c22�2k�1 c23 �kþ3 c3c4þk�3 c22c6þkþ2 c2c5�k�2 c4 �kþ2 c2c5þk�2 c4 kþ3 c3c4�k�3 c22c6 26666666664 37777777775 ByusingEqs. (12) and (13), a systemcanbe reduced into three numbers of species and their initialparametersaredefinedas ceq2 ¼0:1,ceq3 ¼0:1,ceq5 ¼ :4, ceq1 ¼0:500000000ceq3 ceq3=ceq2 ceq2 , ceq4 ¼0:25000000000ceq2 ceq5 , ceq6 ¼0:2500000000ceq3 ceq5=ceq2 : kþ1 ¼1,kþ2 ¼0:5,kþ3 ¼0:5: Figures 6 and 7 clear the idea of the slow invariant manifold (SIM), i.e., decomposing the systemintotheir fastandslowmotion.Theirsolutiontrajectories (duringtheirrelaxationtime) quickly move toward the low-dimensional manifold and after that start moving along it [4–13]. That is the easyway of getting an idea of the SIM.Otherwise, by using the different availablemethods of SIM, i.e., [14–27]wewill get their initial approximations lying on it or near to it. Forcomparison,werefer the readers to [28]. Complex Reactions and Dynamics http://dx.doi.org/10.5772/intechopen.70502 13