Towards a better understanding of high rate biological film flow reactor theory

On the assumption that performance of biological film flow reactors is independent of oxygen transfer, a theoretical extension of a mathematical model (after Ames) is described. This predictive and interpretive model incorporates both mass transfer-limitations between biomass and liquid film, and kinetic biological reaction rate of organic “food” utilization.Given general boundary conditions for the differential equations describing the mass transfer process, it is shown that: C_e = C_r + (C_l − C_r.exp(−K_m D/Q) where by definition: C_t = α C_s + C_r1/K_m = 1/K_LA_γ + α/Kx.For an influent concentration biochemical oxygen demand (C_i) and resultant effluent concentration (C_e) obtained during film flow through a packed media depth (D), the Model proposes that the residual concentration (C_r) is a function of surface irrigation rate (Q) and biomass activity. If this term is negative, adsorption occurs; while if positive, desorption from the biomass film at concentration (C_s) takes place.An overall mass transfer coefficient (K_m) is defined by a series equation where the usual mass transfer coefficient (K_L) is primarily a function of Reynolds Number surface irrigation rate (Q) and specific surface area (A_V)], Schmidt Number (diffusivity of organic “Food”) and concentration. “Food” utilization at active sites on the biological film is governed by a specific adsorption coefficient (α) and explained by a Langmuir analogy. Biological conversion of “food” is described by a kinetic rate constant (K), while the necessary oxygen is defined by (X).This predictive model was developed from a wide range of pilot plant data, successfully tested further on a variety of published results and on actual full scale operating plants.Parameters derived from this Model, in terms of Height of Transfer Unit and Kinetic Reaction coefficient, characterize organic “treatability” for a variety of wastes.