In this paper we report on a numerical study of wave propagation and its failure in a one-dimensional array of coupled chemical cells and irreversible thermodynamics of the array. The Oregonator model for the Belousov-Zhabotinsky reaction is used to model the chemical reactions. In particular, we investigate the dependence of wave front propagation failure on the mass exchange rate for the Ce4+ component between cells and on the amplitude of a perturbation employed to trigger a propagation of transition from an initially homogeneous state to final stationary patterns reached by the system. In the case of the Oregonator, there appear two critical mass transfer rates at which propagation failure occurs, in contrast to the cases of the cubic model or the sine-Gordon model reported in the literature. By following the evolution of the calortropy production accompanying wave propagation, we construct phase diagrams that provide valuable insights into the propagation failure phenomenon. The global calortropy production is shown to exhibit discontinuous changes with respect to the transfer rate when propagation failure occurs. When a complete propagation failure occurs, the global calortropy flux through the array vanishes, whereas it is nonvanishing when there is a partial or complete propagation of the wave front. When the calortropy flux vanishes, the wave front speed and the net mass flux between the cells also vanish.