The Non-competitive or Direct Method

Conceptually, the simplest way to measure a kinetic isotope effect (KIE) is to use a non-competitive method, in which two separate kinetic runs are carried out, each starting with a different isotopomer of the reactant. The rate constants for both species are determined and the kinetic isotope effect (KIE) is the ratio of the two rate constants. This procedure is frequently referred to as the direct method . 

Wolfsberg et al., Isotope Effects in the Chemical, Geological, and Bio Sciences, DOI 10.1007/978-90-481-2265-3 7, Springer Science+Business Media B.V. 2009 

The time dependence of accumulation of product P ([P]) depends on the initial concentration of substrate (reactant), S ([So])  

The subscript indicates the beginning concentration (t = 0), k is the rate constant, and t is time. Introducing the fraction of reaction f, 

Taking logarithms and dividing, we obtain an expression for KIE in terms of the ratios of concentrations of product to substrate  

---