Dispersion models containing a single effective dispersion coefficient have been extensively used in the literature to predict the performance of chemical reactors. In recent years, there is considerable debate on whether the effective dispersion relations determined in the absence of reaction are also valid in the presence of a reaction, especially for the case of bulk reactions. We examine this problem in some detail and show that for the two most commonly used effective dispersion models (axial dispersion and tanks-in-series or cell model), the widely used relationship N = Pe/2, (Pe>> I, N = number of cells and Pe = Peclet number), derived in the absence of a reaction, also holds for all slow reactions characterized by 0 less than or equal to Da\f'(cN)\ < Pe(2/3). Here, Da is the Damkohler number and f'(c(N)) is the derivative of the normalized reaction rate at the exit concentration c(N) of the cell model. For Da values exceeding this upper bound (fast reaction regime), the model predictions diverge, or equivalently, the effective dispersion coefficient concept is not valid. We show that the same result applies for transient behavior of the discrete and continuous (PDE) models provided Da is replaced by Da(2) + omega (2), where omega is the dimensionless forcing frequency. We also derive similar bounds for two other commonly used dispersion models, namely, the recycle and interphase resistance models. A formula for choosing the mesh size for fast reactions so that the discrete and continuous models have the same qualitative features is also presented. The analytical results derived for linear reactions are validated for nonlinear kinetics using numerical simulations. Some new results and comparisons are also presented at the other extreme of near perfect mixing.