Application of Graph Theory to Nonsteady State Processes

7 Application of Graph Theory to Nonsteady State Processes 

Vorkenshtein and Gordshtein were the first to apply graph theory to investigation of the kinetics of nonsteady state processes (3,31). We present here a short summary of their method. 

In nonsteady state reactions, the concentration derivatives with respect to time are not equal to zero and. instead of stationary conditions (12). a system of differential equations is obtained  

System (50) is nonlinear and cannot be solved exactly if a,r and a,t are functions of the time r. If we assume that the concentrations of the reagents are much larger than those of the ISCs. then a, and QrrS can be taken as independent of time. 

Let the integral transformation of Laplace-Carson be applied to system (50). The functions of time x t) can then be substituted by the x (q) transformation functions, and the time derivatives by the qx (g) — f/xlO) values, where q represents reciprocal time and the x(0) are the initial concentrations of the intermediates. The Laplace-Carson procedure transforms the system of differential equations (50) into a system of algebric equations with respect to X (q) thus  

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