A new analytical solution technique for networks of irreversible chemical reactions in batch reactors with first-order kinetics is presented. The solution technique involves the iterative calculation of a coefficient matrix that is then applied for direct calculation of species concentrations at any time. The derivation, which is based on Laplace transforms of an arbitrary network, is presented in the appendix. Several examples and extensions to the solution are discussed. Extensions made to the solution include the consideration of phase equilibria, first-order and zero-order sources and sinks, common reaction products outside the network, and combined networks of reactions and CSTRs. Rate-limited mass transfer effects and reversible reactions were not considered. The solution is general, compact, easy to use, and allows several extensions that will likely aid scientists and engineers in solving problems related to the dynamics of these networks.
Eykholt, G. R. (1999). Analytical solution for networks of irreversible first-order reactions. Water Research, 33(3), 814–826. https://doi.org/10.1016/S0043-1354(98)00273-5