Bioprocess and Biosystems Engineering

, Volume 42, Issue 1, pp 17–27 | Cite as

Simulation and experimental validation of a gradient feeding system for fast assessment of the kinetic behavior of a microbial consortium in a tubular biofilm reactor

  • Merlyn Alejandra Salazar-Huerta
  • Nora Ruiz-OrdazEmail author
  • Juvencio Galíndez-MayerEmail author
  • Jaime García-Mena
  • Cleotilde Juárez-Ramírez
Research Paper


This study deals with the mathematical simulation and experimental validation of a gradient system for the gradual change of the imidacloprid loading rate to a tubular biofilm reactor (TBR). The strategy was used for fast studies of the kinetic and stoichiometric impact caused by the increase in the pesticide loading rate in a TBR, running in plug flow regime. Seemingly, this strategy has never been used for biokinetic and stoichiometric studies in biofilm reactors. For this purpose, a mathematical model describing the substrate transient behavior Sg(t) in a concentration gradient generator system using variable volume tanks is proposed. A second model, representing the temporary variation in the loading rate of imidacloprid to an aerated equalizer tank preceding the packed zone of the TBR, is also presented. Both models were experimentally confirmed. After the treatment of the experimental data, the kinetic and stoichiometric changes occurring in the TBR, caused by the gradual increase in the imidacloprid loading rate, were readily evaluated. Although the structure of the microbial community, at the phylum level, showed similar behavior along the tubular reactor, the stress produced by the gradual increase in imidacloprid concentration had functional consequences on the mixed microbial populations which were reflected on the stoichiometric and kinetic parameters. After increasing more than five times the imidacloprid loading rate to the TBR, the imidacloprid removal efficiency decayed about 40%, and the microbial-specific removal rate of the insecticide showed a decrease of about 30%.


Tubular reactor Biofilm Microbial consortium Gradient feeding Simulation 



Sectional area of gradient tank G (cm2)


Sectional area of tank R (cm2)

BV = FSeq/VL

Volumetric loading rate of imidacloprid (mg L−1 h−1)


Chemical oxygen demand (mg L−1)




Diameter of gradient tank G (cm)


Diameter of reservoir tank R (cm)


Aerated compartment operating as equalizer


Exponential integral \(\int_{1}^{\infty } {\frac{{e^{ - mt} }}{{t^{n} }}}\) in Eq. (9)


Liquid flow rate (L h−1)

MS medium

Mineral salts medium


Specific degradation rate of imidacloprid (mg CFU−1 h−1)

\(q_{{{\text{s}}_{\text{i}} }}\)

Overall initial specific removal rate of imidacloprid (mg CFU−1 h−1)

\(q_{{{\text{s}}_{\text{f}} }}\)

Overall final specific removal rate of imidacloprid (mg CFU−1 h−1)

RV= F(Seq − s)/VL

Volumetric loading rate of imidacloprid (mg L−1 h−1)


Imidacloprid concentration in equalizer (mg L−1)


Imidacloprid concentration in G tank (mg L−1)


Imidacloprid concentration in reservoir tank (mg L−1)


Imidacloprid concentration in the TBR packed zone (mg L−1)


Time (h)


Tubular biofilm reactor


Liquid volume of equalizer (L)


Liquid volume of gradient tank G (L)


Interstitial liquid volume in the TBR packed zone (L)


Liquid volume of reservoir tank (L)


Volume of the support material in the TBR packed zone (L)


Weight of porous fragments in TBR


Suspended cells in equalizer (CFU L−1)


Initial total viable cells in the reactor (CFU/reactor)


Final total viable cells in the reactor (CFU/reactor)


Length of the packed zone of the tubular biofilm reactor (cm)









Final condition






Initial condition


Porous support





Intraparticle porosity (non-dimensional)


Interparticle porosity (non-dimensional)

\(\varepsilon_{\text{T}} \, = \,\varepsilon_{\text{P}} \, + \,\varepsilon_{\text{E}}\)

Total bed porosity (non-dimensional)


Imidacloprid removal efficiency (%)

\(\varphi_{\text{g}} \, = \, 1\, - \,\varphi_{\text{r}}\)

Relative area of gradient tank (non-dimensional)


Relative area of reservoir tank (non-dimensional)


Density of porous rock (g cm−3)



This investigation was supported by a Grant obtained from SIP, Instituto Politécnico Nacional (SIP-IPN 20170884). The authors wish to thanks to COFAA-IPN and SNI-Conacyt for the fellowships to N. Ruiz-Ordaz, and J. Galindez-Mayer; SNI-Conacyt for fellowships to J. García-Mena; and Conacyt for the financial support of MA Salazar-Huerta.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Ingeniería Bioquímica ENCB-ZacatencoInstituto Politécnico NacionalMexico CityMexico
  2. 2.Departamento de Genética y Biología Molecular, CinvestavInstituto Politécnico NacionalMexico CityMexico

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