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Model-based scale-up methodology for aerobic fed-batch bioprocesses: application to polyhydroxybutyrate (PHB) production

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Abstract

This work presents a general model-based methodology to scale-up fed-batch bioprocesses. The idea behind this approach is to establish a dynamics hierarchy, based on a model of the process, that allows the designer to determine the proper scale factors as well as at which point of the fed-batch the process should be scaled up. Here, concepts and tools of linear control theory, such as the singular value decomposition of the Hankel matrix, are exploited in the context of process design. The proposed scale-up methodology is first described in a bioprocesses general framework highlighting its main features, key variables and parameters. Then, it is applied to a polyhydroxybutyrate (PHB) fed-batch bioreactor and compared with three empirical criteria, that are traditionally employed to determine the scale factors of these processes, showing the usefulness and distinctive features of this proposal. Moreover, this methodology provides theoretical support to a frequently used empirical rule: scale-up aerobic bioreactors at constant volumetric oxygen transfer coefficient. Finally, similar process dynamic behavior and PHB production set at the laboratory scale are predicted at the new operating scale, while it is also determined that is rarely possible to reproduce similar dynamic behavior of the bioreactor using empirical scale-up criteria.

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Abbreviations

\(A_x\) :

Cross-sectional flow area \(\left({\rm m}^2\right)\)

\(a_1,a_2, a_3\) :

Empirical coefficients for \(P_{g}\) calculation \(\left({\rm dimensionless}\right)\)

\(c_1, c_2, c_3\) :

Empirical coefficients for \(K_{\rm L}{a}\) calculation \(\left({\rm dimensionless}\right)\)

\(D_{i}\) :

Impeller diameter \(\left({\rm m}\right)\)

\(f_{\rm P}\) :

PHB to active biomass ratio \(\left({\rm dimensionless}\right)\)

\(f_{\rm P,m}\) :

PHB to active biomass ratio \(\left({\rm dimensionless}\right)\)

\(F_{\rm N}\) :

Nitrogen flow rate \(\left(\frac{\rm L}{\rm h}\right)\)

\(F_{\rm O}\) :

Air flow rate \(\left(\frac{\rm L}{\rm h}\right)\)

\(F_{{\rm O}_{\rm Bias}}\) :

Nominal air flow rate \(\left(\frac{\rm L}{\rm h}\right)\)

\(F_{\rm O,m}\) :

Maximum air flow rate \(\left(\frac{\rm L}{\rm h}\right)\)

\(F_{\rm S}\) :

Substrate flow rate \(\left(\frac{\rm L}{\rm h}\right)\)

\(k_{\rm P}\) :

Controller proportional gain \(\left( \frac{\rm L}{\rm gs}\right)\)

\(K_{i{\rm N}}\) :

Nitrogen inhibition constant for growth \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{i{\rm S}}\) :

Substrate inhibition constant for growth \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{i{\rm PN}}\) :

Nitrogen inhibition constant for PHB production \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{i{\rm PS}}\) :

Substrate inhibition constant for PHB production \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{{\rm L}}a\) :

Volumetric oxygen transfer coefficient \(\left( \frac{1}{\rm h}\right)\)

\(K_{\rm N}\) :

Saturation constant for nitrogen in growth \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{\rm O}\) :

Saturation constant for oxygen in growth \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{\rm P}\) :

Saturation constant for PHB in growth \(\left( {\rm dimensionless}\right)\)

\(K_{\rm PS}\) :

Saturation constant for substrate in PHB production \(\left( \frac{\rm g}{\rm L}\right)\)

\(K_{\rm S}\) :

Saturation constant for substrate in growth \(\left( \frac{\rm g}{\rm L}\right)\)

\(m_{\rm O}\) :

Specific oxygen consumption for maintenance \(\left( \frac{1}{\rm h}\right)\)

\(m_{\rm S}\) :

Specific glucose consumption for maintenance \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm PS}\) :

Specific PHB production rate \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm PS}^{\rm max}\) :

Maximum specific PHB production rate over substrate \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm XP}\) :

Specific biomass growth rate over PHB \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm XP}^{\rm max}\) :

Maximum specific biomass growth rate over PHB \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm XS}\) :

Specific biomass growth rate over substrate \(\left( \frac{1}{\rm h}\right)\)

\(\mu _{\rm XS}^{\rm max}\) :

Maximum specific biomass growth rate over substrate \(\left( \frac{1}{\rm h}\right)\)

\(N\) :

Nitrogen concentration in culture broth \(\left( \frac{\rm g}{\rm L}\right)\)

\(N_{i}\) :

Impeller speed \(\left( {\rm rpm}\right)\)

\(N_{\rm F}\) :

Nitrogen concentration in feeding solution \(\left( \frac{\rm g}{\rm L}\right)\)

\(N_{\rm p}\) :

Power number \(\left( {\rm dimensionless}\right)\)

\({O}_{\rm G}\) :

Oxygen concentration in the gaseous phase \(\left( \frac{\rm g}{\rm L}\right)\)

\({O}_{{\rm G,F}}\) :

Oxygen concentration in the feeding stream \(\left( \frac{\rm g}{\rm L}\right)\)

\({O}_{\rm L}\) :

Dissolved oxygen concentration \(\left( \frac{\rm g}{\rm L}\right)\)

\({O}_{\rm L,sp}\) :

Dissolved oxygen concentration set point \(\left( \frac{\rm g}{\rm L}\right)\)

\({O}_{\rm L}^{\star }\) :

Saturation concentration of dissolved oxygen \(\left( \frac{\rm g}{\rm L}\right)\)

\({\rm OTR}\) :

Oxygen transfer rate \(\left( \frac{\rm g}{\rm Lh}\right)\)

\({P}\) :

PHB concentration \(\left( \frac{\rm g}{\rm L}\right)\)

\({P}_{\rm g}\) :

Aerated input power \(\left( {\rm W}\right)\)

\(r_{\rm N}\) :

Rate of reaction of nitrogen \(\left( \frac{\rm g}{\rm Lh}\right)\)

\(r_{\rm O}\) :

Rate of reaction of oxygen \(\left( \frac{\rm g}{\rm Lh}\right)\)

\(r_{\rm P}\) :

Rate of reaction of PHB \(\left( \frac{\rm g}{\rm Lh}\right)\)

\(r_{\rm S}\) :

Rate of reaction of substrate \(\left( \frac{\rm g}{\rm Lh}\right)\)

\(r_{\rm X}\) :

Rate of reaction of active biomass \(\left( \frac{\rm g}{\rm Lh}\right)\)

\({S}\) :

Substrate concentration in culture broth \(\left( \frac{\rm g}{\rm L}\right)\)

\({S}_{\rm F}\) :

Substrate concentration in feeding solution \(\left( \frac{\rm g}{\rm L}\right)\)

\({T}\) :

Inner diameter of the reactor \(\left( {\rm m}\right)\)

\(t_{\rm D}\) :

Derivative time for controller gain \(\left( {\rm s}\right)\)

\(t_{\rm I}\) :

Integral time for controller gain \(\left( {\rm s}\right)\)

\(V_{\rm G}\) :

Gas volume \(\left( {\rm L}\right)\)

\(V_{\rm L}\) :

Liquid volume \(\left( {\rm L}\right)\)

\(V_{{\rm t}}\) :

Impeller tip speed \(\left( \frac{\rm m}{\rm s}\right)\)

\(V_{\rm T}\) :

Total fermenter volume \(\left( {\rm L}\right)\)

\(V_{\rm L,0}\) :

Initial fermenter volume \(\left( {\rm L}\right)\)

\(X\) :

Active biomass concentration \(\left( \frac{\rm g}{\rm L}\right)\)

\(X_{\rm m}\) :

Maximum residual cell concentration \(\left( \frac{\rm g}{\rm L}\right)\)

\(X_{\rm t}\) :

Total biomass concentration (\({\rm P}+{\rm X}\)) \(\left( \frac{\rm g}{\rm L}\right)\)

\(X_{\rm t}^{\rm phase}\) :

Total biomass concentration (\({\rm P}+{\rm X}\)) for changing the phase \(\left( \frac{\rm g}{\rm L}\right)\)

\(Y_{\rm PO}\) :

PHB yield over oxygen \(\left( {\rm dimensionless}\right)\)

\(Y_{\rm PS}\) :

PHB yield over substrate \(\left( {\rm dimensionless}\right)\)

\(Y_{\rm XN}\) :

Biomass yield over nitrogen \(\left( {\rm dimensionless}\right)\)

\(Y_{\rm XO}\) :

Biomass yield over oxygen \(\left( {\rm dimensionless}\right)\)

\(Y_{\rm XP}\) :

Biomass yield over PHB \(\left( {\rm dimensionless}\right)\)

\(Y_{\rm XS}\) :

Biomass yield over substrate \(\left( {\rm dimensionless}\right)\)

\(Z\) :

Liquid reactor height \(\left( {\rm dimensionless}\right)\)

\(\alpha\) :

Cell density inhibition coefficient \(\left( {\rm dimensionless}\right)\)

\(\beta\) :

PHB saturation power coefficient \(\left( {\rm dimensionless}\right)\)

\(\rho _{\rm FN}\) :

Density of the nitrogen source stream \(\left( \frac{\rm g}{\rm L}\right)\)

\(\rho _{\rm FS}\) :

Density of the substrate stream \(\left( \frac{\rm g}{\rm L}\right)\)

\(\rho _{\rm W}\) :

Water density \(\left( \frac{\rm g}{\rm L}\right)\)

\(\mu _{\rm W}\) :

Water viscosity \(\left( {\rm Pa\;s}\right)\)

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Acknowledgments

This work was supported in part by ANPCyT (PICT 2011-0888 and PICT 2012-0037), CONICET (PIP 112-2011-01-0361), UNLP (Project 11/I164) of Argentina and Red de Macrouniversidades Públicas de America Latina y el Caribe through the program “Movilidad en el Posgrado de la RED MACRO”.

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Authors and Affiliations

  1. Departamento de Procesos y Energía, Facultad de Minas, Universidad Nacional de Colombia-Sede Medellín, Medellín, Colombia

    Gloria Milena Monsalve-Bravo & Hernan Alvarez

  2. Grupo de Control Aplicado, Laboratorio de Electrónica Industrial, Control e Instrumentación (LEICI), Facultad de Ingeniería, Universidad Nacional de La Plata, La Plata, Argentina

    Gloria Milena Monsalve-Bravo, Fabricio Garelli & Hernan De Battista

  3. Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina

    Fabricio Garelli & Hernan De Battista

  4. Business Unit Separation and Conversion Technology, Flemish Institute for Technological Research (VITO), Boeretang 200, 2400, Mol, Belgium

    Md. Salatul Islam Mozumder

  5. Department of Biosystems Engineering, Ghent University, Coupure Links 653, 9000, Ghent, Belgium

    Md. Salatul Islam Mozumder

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  1. Gloria Milena Monsalve-Bravo
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Correspondence to Gloria Milena Monsalve-Bravo.

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Monsalve-Bravo, G.M., Garelli, F., Mozumder, M.S.I. et al. Model-based scale-up methodology for aerobic fed-batch bioprocesses: application to polyhydroxybutyrate (PHB) production. Bioprocess Biosyst Eng 38, 1179–1190 (2015). https://doi.org/10.1007/s00449-015-1360-4

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