Modeling hexavalent chromium removal in a Bacillus sp. fixed-film bioreactor

A one-dimensional diffusion-reaction model was developed to simulate Cr(VI) reduction in a Bacillus sp. pure culture biofilm reactor with glucose as a sole supplied carbon and energy source. Substrate utilization and Cr(VI) reduction in the biofilm was best represented by a system of (second-order) partial differential equations (PDEs). The PDE system was solved by the (fourth-order) Runge-Kutta method adjusted for mass transport resistance using the (second-order) Crank-Nicholson and Backward Euler finite difference methods. A heuristic procedure (genetic search algorithm) was used to find global optimum values of Cr(VI) reduction and substrate utilization rate kinetic parameters. The fixed-film bioreactor system yielded higher values of the maximum specific Cr(VI) reduction rate coefficient and Cr(VI) reduction capacity (k_mc = 0.062 1/h, and R_c = 0.13 mg/mg, respectively) than previously determined in batch reactors (k_mc = 0.022 1/h and R_c = 0.012 mg/mg). The model predicted effluent Cr(VI) concentration well with 98.9% confidence (σ_y² = 2.37 mg²/L², N = 119) and effluent glucose with 96.4% confidence (σ _y(w)² = 5402 mg²/L², N = 121, w = 100) over a wide range of Cr(VI) loadings (10-498 mg Cr(VI)/L/d).