Environmental Modeling & Assessment

, Volume 16, Issue 2, pp 213–225 | Cite as

Sensitivity Analysis of Phenol Degradation with Sulfate Reduction Under Anaerobic Conditions



This study derives a mathematical description of the kinetics of phenol degradation with sulfate reduction by an anaerobic mixed-culture biofilm on an inert medium. The model incorporates the mechanisms of diffusive mass transport and Monod kinetics. It is solved using both the orthogonal collocation method and Gear’s method. Sensitivity studies were performed to investigate the dependence of process dynamics on the model parameters pertaining to biokinetic parameters, liquid film mass transport, and the biofilm and reactor operational parameters. Sensitivity analysis quantifies the magnitude of the effect of each variable on the simulated results using the least-square method. The transient-state process dynamics are sensitive to the biokinetic parameters including yield coefficient of phenol-utilizing bacteria, Monod maximum specific utilization rate of phenol, and the decay coefficient of phenol-utilizing bacteria. The process efficiency is also sensitive to biofilm parameters such as biofilm density of phenol-utilizing bacteria and initial biofilm thickness , and to such operational parameters as the influent phenol concentration and the hydraulic retention time of the system. The process dynamics are relatively insensitive to mass transport parameters, including the film transfer coefficient of phenol and the diffusion coefficient of phenol. Sensitivity analysis of the process dynamics to model parameters helps determine how to alter process conditions to enhance removal efficiency.


Sensitivity analysis Phenol degradation Sulfate reduction Model Least-square method 


The following symbols are used in this paper


total surface area of the media (L 2)


decay coefficient of SRB (1/T)


decay coefficient of PUB (1/T)


shear-loss coefficient of SRB (1/T)


shear-loss coefficient of PUB (1/T)


diffusion coefficient of acetate in the biofilm (L 2/T)


diffusion coefficient of phenol in the biofilm (L 2/T)


diffusion coefficient of sulfate in the biofilm (L 2/T)


conversion efficiency of phenol to acetate (M s /M s )


hydraulic retention time


Monod maximum specific utilization rate of acetate by SRB (1/T)


liquid film transfer coefficient of acetate (L/T)


liquid film transfer coefficient of phenol (L/T)


liquid film transfer coefficient of sulfate (L/T)


inhibition constant of phenol (M s/L 3)


Monod maximum specific utilization rate of phenol by PUB (1/T)


Monod half-velocity coefficient of acetate (M s /L 3)


Monod half-velocity coefficient of phenol (M s/L 3)


Monod half-velocity coefficient of sulfate (M s /L 3)


phenol-utilizing bacteria


flow rate of the influent (L 3/T)


utilization rate of acetate by SRB in biofilm (M s /L 3 − T)


net generation rate of acetate (M s /L 3 − T)


utilization rate of phenol by PUB in biofilm (M s /L 3 − T)


concentration of acetate in the bulk liquid (M s /L 3)


concentration of acetate in the influent (M s /L 3)


concentration of phenol in the bulk liquid (M s /L 3)


concentration of phenol in the influent (M s /L 3)


concentration of sulfate in the bulk liquid (M s /L 3)


concentration of sulfate in the influent (M s /L 3)


concentration of acetate in the biofilm (M s /L 3)


concentration of phenol in the biofilm (M s /L 3)


concentration of sulfate in the biofilm (M s /L 3)


concentration of sulfide in the effluent (M s /L 3)


sulfate-reducing bacteria


phenol concentration at liquid/biofilm interface (M s /L 3)


sulfate concentration at liquid/biofilm interface (M s /L 3)


time (T)


volume of the reactor (L 3)


concentration of SRB in the bulk liquid (M x /L 3)


concentration of PUB in the bulk liquid (M x /L 3)


biofilm density of SRB (M x /L 3)


biofilm density of PUB (M x /L 3)


yield coefficient of SRB (M x /M s )


yield coefficient of PUB (M x /M s )


radial distance in biofilm (L)


conversion factor for reduction of sulfate to sulfide (M s /M s )


stoichiometric coefficient for sulfate utilization (M s /M s )


porosity of the reactor (dimensionless)



This research was supported in part by a grant from National Science Council of the Republic of China (Taiwan) under Contract No. NSC 98-2221-E-166-001-MY2. Ted Knoy is appreciated for his editorial assistance.


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of Safety, Health and Environmental EngineeringCentral Taiwan University of Science and TechnologyTaichungTaiwan

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