Mathematical Model for Scaling up Bioprocesses Using Experiment Design Combined with Buckingham Pi Theorem

Abstract

Scaling up bioprocesses from the experimental to the pilot or industrial scale involves heuristics and scale relationships that are far from the specific phenomena and are usually not connected to the experimental data. In complex systems, the scaling-up methodology must connect the experimental data with the tools of engineering design. In this work, a two-stage gold bioleaching process was used as a case study to develop a mathematical model of bioprocess scaling that combines the design of experiments with dimensional analysis using the Buckingham Pi theorem to formulate a predictive model that allows scaling up bioprocesses. It was found that the C/N, C/K, and T/C ratios are dimensionless factors that can explain the behavior of a system. Using the Pearson Product–Moment bivariate analysis, it was found that the dimensionless factors C/N and C/K were correlated with the leaching potential of the fermented broth at 1060 cm−1. With these results, a non-linear logarithmic model based on dimensionless parameters was proposed to explain the behavior of the system with a correlation coefficient of R2 = 0.9889, showing that the optimal conditions to produce fermented broth comprised a C/N ratio close to 50 and a C/K ratio close to 800, which allows predicting the scaling of the bioprocess.

Effects of Oxygen Transference on Protease Production by Rhodotorula mucilaginosa CBMAI 1528 in a Stirred Tank Bioreactor

“…The selection of design conditions and operational procedures is very important to expand the process and to ensure that the effect of the variables on the process are the same [ 40 ]. The scaling up of the fermentation processes from the laboratory-scale to commercial units is challenging due to the difficulty in assessing the factors of influence during cultivation [ 49 ]. It is well known that microorganisms are more susceptible to large-scale environmental variables.…”

Scale-Up of Capsular Polysaccharide Production Process by Haemophilus influenzae Type b Using kLa Criterion

“…Fermentation carried out in the 75 L pilot-scale bioreactor showed a higher yield profile in the production of PRP and DCW in comparison with 1.5 L and 15 L bioreactors ( Table 3 ), although, commonly during scaling-up, a 10–30% of reduction in performance associated with heat and mass transfer issues was observed [ 14 ]. On the other hand, differences in PRP production in fermentations could be explain by a spontaneous loss of capsular expression; this phenomenon occurs in several H. influenzae type b strains with a rate of 0.1–0.3% per generation [ 44 ].…”

“…Vaccines and several products with therapeutical applications are part of the global bioprocess market to be valued at USD 360 million by 2024 [ 14 ]. Due to great demand, this bioprocess should reach industrial scale under three development stages (laboratory or bench scale, pilot scale and full-scale manufacturing) [ 15 , 16 ].…”

“…In the case of PRP production for vaccine manufacturing, it requires a bioprocess developed to achieve a desirable productivity into a bioreactor of high operation volume. However, the bioprocesses are difficult to standardize and commonly limited by the scaling process because they did not reach the required efficacy [ 14 ]. Moreover, the large-scale process faces technical challenges correlated with the cell source, culture media, use of pure reagents as precursors, sterilization step, type of product and unit operations [ 14 , 17 , 18 ].…”

“…However, the bioprocesses are difficult to standardize and commonly limited by the scaling process because they did not reach the required efficacy [ 14 ]. Moreover, the large-scale process faces technical challenges correlated with the cell source, culture media, use of pure reagents as precursors, sterilization step, type of product and unit operations [ 14 , 17 , 18 ]. In this sense, H. influenzae requires a complex culture medium containing Hemin and NAD used as growth factors for aerobic conditions, which impact the process costs and product recovery [ 12 , 19 ].…”