Disequilibrium chemical processes significantly affect the spectra of substellar objects. To study these effects, dynamical disequilibrium has been parameterized using the quench and eddy diffusion approximations, but little work has been done to explore how these approximations perform under realistic planetary conditions in different dynamical regimes. As a first step toward addressing this problem, we study the localized, small-scale convective dynamics of planetary atmospheres by direct numerical simulation of fully compressible hydrodynamics with reactive tracers using the Dedalus code. Using polytropically stratified, plane-parallel atmospheres in 2D and 3D, we explore the quenching behavior of different abstract chemical species as a function of the dynamical conditions of the atmosphere as parameterized by the Rayleigh number. We find that in both 2D and 3D, chemical species quench deeper than would be predicted based on simple mixing-length arguments. Instead, it is necessary to employ length scales based on the chemical equilibrium profile of the reacting species in order to predict quench points and perform chemical kinetics modeling in 1D. Based on the results of our simulations, we provide a new length scale, derived from the chemical scale height, that can be used to perform these calculations. This length scale is simple to calculate from known chemical data and makes reasonable predictions for our dynamical simulations.