CFD simulation of non-Newtonian fluid flow in anaerobic digesters

A general mathematical model that predicts the flow fields in a mixed-flow anaerobic digester was developed. In this model, the liquid manure was assumed to be a non-Newtonian fluid, and the flow governed by the continuity, momentum, and k-epsilon standard turbulence equations, and non-Newtonian power law model. The commercial computational fluid dynamics (CFD) software, Fluent, was applied to simulate the flow fields of lab-scale, scale-up, and pilot-scale anaerobic digesters. The simulation results were validated against the experimental data from literature. The flow patterns were qualitatively compared for Newtonian and non-Newtonian fluids flow in a lab-scale digester. Numerical simulations were performed to predict the flow fields in scale-up and pilot-scale anaerobic digesters with different water pump power inputs and different total solid concentration (TS) in the liquid manure. The optimal power inputs were determined for the pilot-scale anaerobic digester. Some measures for reducing dead and low velocity zones were proposed based upon the CFD simulation results.     

Application of Modeling to Scale-up Dissolution in Pharmaceutical Manufacturing

Liquid mixing scale-up in pharmaceutical industry has often been based on empirical approach in spite of tremendous understanding of liquid mixing scale-up in engineering fields. In this work, we attempt to provide a model-based approach to scale-up dissolution process from a 2 l lab-scale vessel to a 4,000 l scale vessel used in manufacturing. Propylparaben was used as a model compound to verify the model predictions for operating conditions at commercial scale that would result in similar dissolution profile as observed in lab scale. Geometric similarity was maintained between both of the scales to ensure similar mixing characteristics. We utilized computational fluid dynamics (CFD) to ensure that the operating conditions at laboratory and commercial scale will result in similar power per unit volume (P/V). Utilizing this simple scale-up criterion of similar P/V across different scales, results obtained indicate fairly good reproducibility of the dissolution profiles between the two scales. Utilization of concepts of design of experiments enabled summarizing scale-up results in statistically meaningful parameters, for example −90% dissolution in lab scale at a given time under certain operating conditions will result in 75–88% at commercial scale with 95% confidence interval when P/V is maintained constant across the two scales. In this work, we have successfully demonstrated that scale-up of solid dissolution can be done using a systematic process of lab-scale experiments followed by simple CFD modeling to predict commercial-scale experimental conditions.     

Scaling-up of a batch whey fermentation by Kluyveromyces fragilis

Summary A whey fermentation by Kluyveromyces fragilis was scaled-up to a 1000-dm³ stirred fermentor, by varying the stirrer speed, the air-flow rate and the initial concentration of lactose. Its evolution was simulated by applying the same unstructured model (consisting of a microbial specific growth rate of pseudo-first order with respect to the COD concentration and constant biomass yield per unit COD removed) set up in previous experiments using 8- to 80-dm³ fermentors. Despite the great scale-up ratios, very different operating conditions, and geometric dissimilarity, a series of empirical regressions previously developed allowed approximate, but acceptable prediction of the stoichiometric and kinetic coefficients of the above mathematical model, thus confirming the capability of this model to provide a reliable basis for further scale-up of this fermentation process to a production scale.     

New developments in solid-state fermentation: II. Rational approaches to the design, operation and scale-up of bioreactors

Over the last decade there has been a significant improvement in understanding how to design, operate and scale-up solid-state fermentation bioreactors. The key to these advances has been the application of mathematical modeling techniques to describe the biological and transport phenomena within the system. This review focuses on the advances in understanding that have come from this modeling work, and the insights it has given us into bioreactor design, operation and scale-up. It also highlights two promising bioreactor designs that have emerged over the last decade or so. For processes in which the substrate bed must remain static throughout the fermentation, the most promising design is the Zymotis design of ORSTOM at Montpellier, France, which involves closely spaced internal heat transfer plates within a packed-bed bioreactor. For those processes in which mixing can be tolerated, the stirred bioreactor developed at INRA, in Dijon, France, has been successfully demonstrated at scales of 1–25 t of substrate. Theoretical work suggests that mathematical models will be useful tools in the scale-up process, however, there are no reports that they have been used in the development of any current large-scale process. Rather, the models have been validated against data obtained from laboratory-scale bioreactors. There is an urgent need to test the accuracy and robustness of the models by applying them within real process development.     

Heat transfer simulation in solid substrate fermentation

A mathematical model was developed and tested to simulate the generation and transfer of heat in solid substrate fermentation (SSF). The experimental studies were realized in a 1-L static bioreactor packed with cassava wet meal and inoculated with Aspergillus niger. A simplified pseudohomogeneous monodimensional dynamic model was used for the energy balance. Kinetic equations taking into account biomass formation (logistic), sugar consumption (with maintenance), and carbon dioxide formation were used. Model verification was achieved by comparison of calculated and experimental temperatures. Heat transfer was evaluated by the estimation of Biot and Peclet heat dimensionless numbers 5-10 and 2550-2750, respectively. It was shown that conduction through the fermentation fixed bed was the main heat transfer resistance. This model intends to reach a better understanding of transport phenomena in SSF, a fact which could be used to evaluate various alternatives for temperature control of SSF, i.e., changing air flow rates and increasing water content. Dimensionless numbers could be used as scale-up criteria of large fermentors, since in those ratios are described the operating conditions, geometry, and size of the bioreactor. It could lead to improved solid reactor systems. The model can be used as a basis for automatic control of SSF for the production of valuable metabolites in static fermentors.     

Spatial Variation of Pressure in the Lyophilization Product Chamber Part 2: Experimental Measurements and Implications for Scale-up and Batch Uniformity

Product temperature during the primary drying step of freeze-drying is controlled by a set point chamber pressure and shelf temperature. However, recent computational modeling suggests a possible variation in local chamber pressure. The current work presents an experimental verification of the local chamber pressure gradients in a lab-scale freeze-dryer. Pressure differences between the center and the edges of a lab-scale freeze-dryer shelf were measured as a function of sublimation flux and clearance between the sublimation front and the shelf above. A modest 3-mTorr difference in pressure was observed as the sublimation flux was doubled from 0.5 to 1.0 kg·h^?1·m^?2 at a clearance of 2.6 cm. Further, at a constant sublimation flux of 1.0 kg·h^?1·m^?2, an 8-fold increase in the pressure drop was observed across the shelf as the clearance was decreased from 4 to 1.6 cm. Scale-up of the pressure variation from lab- to a manufacturing-scale freeze-dryer predicted an increased uniformity in drying rates across the batch for two frequently used pharmaceutical excipients (mannitol and sucrose at 5% w/w). However, at an atypical condition of shelf temperature of +10°C and chamber pressure of 50 mTorr, the product temperature in the center vials was calculated to be a degree higher than the edge vial for a low resistance product, thus reversing the typical edge and center vial behavior. Thus, the effect of local pressure variation is more significant at the manufacturing-scale than at a lab-scale and accounting for the contribution of variations in the local chamber pressures can improve success in scale-up.     

Heat and mass transfer scale-up issues during freeze-drying, III: Control and characterization of dryer differences via operational qualification tests

The objective of this research was to estimate differences in heat and mass transfer between freeze dryers due to inherent design characteristics using data obtained from sublimation tests. This study also aimed to provide guidelines for convenient scale-up of the freeze-drying process. Data obtained from sublimation tests performed on laboratory-scale, pilot, and production freeze dryers were used to evaluate various heat and mass transfer parameters: nonuniformity in shelf surface temperatures, resistance of pipe, refrigeration system, and condenser. Emissivity measurements of relevant surfaces such as the chamber wall and the freeze dryer door were taken to evaluate the impact of atypical radiation heat transfer during scale-up. “Hot” and “cold” spots were identified on the shelf surface of different freeze dryers, and the impact of variation in shelf surface temperatures on the primary drying time and the product temperature during primary drying was studied. Calculations performed using emissivity measurements on different freeze dryers suggest that a front vial in the laboratory lyophilizer received 1.8 times more heat than a front vial in a manufacturing freeze dryer operating at a shelf temperature of −25°C and a chamber pressure of 150 mTorr during primary drying. Therefore, front vials in the laboratory are much more atypical than front vials in manufacturing. Steady-state heat and mass transfer equations were used to study a combination of different scaleup issues pertinent during lyophilization cycles commonly used for the freeze-drying of pharmaceuticals.     

Studies on the modeling and simulation of a sequential bienzymatic reaction system immobilized in emulsion liquid membrane

Experiments have been carried out to study the reaction engineering behavior of the liquid membrane-encapsulated, sequential bienzymatic reaction system, n 2n glucose. A dynamic mathematical model, free from adjustable parameters, has been developed taking into account peri-emulsion mass transfer, intra-emulsion diffusion, membrane-related mass transfer limitations and substrate and product inhibitions. A finite difference-based, user-friendly software has been developed to solve the model equations. Experimental data satisfactorily correlate with the model. While it is understood that study of sequential bienzymatic reaction system immobilized in emulsion liquid is essential for their industrial exploitation, reaction engineering behavior of such a system in presence of both substrate and product inhibitions has not yet been reported in the literature. Therefore, the model predictions of the present investigations are expected to pave the way for scale-up and design of industrial bioreactors in this field.     

Robust scale-up of dead end filtration: impact of filter fouling mechanisms and flow distribution

Robust design of a dead end filtration step and the resulting performance at manufacturing scale relies on laboratory data collected with small filter units. During process development it is important to characterize and understand the filter fouling mechanisms of the process streams so that an accurate assessment can be made of the filter area required at manufacturing scale. Successful scale-up also requires integration of the lab-scale filtration data with an understanding of flow characteristics in the full-scale filtration equipment. A case study is presented on the development and scale-up of a depth filtration step used in a 2nd generation polysaccharide vaccine manufacturing process. The effect of operating parameters on filter performance was experimentally characterized for a diverse set of process streams. Filter capacity was significantly reduced when operating at low fluxes, caused by both low filtration pressure and high stream viscosity. The effect of flux on filter capacity could be explained for a variety of diverse streams by a single mechanistic model of filter fouling. To complement the laboratory filtration data, the fluid flow and distribution characteristics in manufacturing-scale filtration equipment were carefully evaluated. This analysis identified the need for additional scale-up factors to account for non-uniform filter area usage in large-scale filter housings. This understanding proved critical to the final equipment design and depth filtration step definition, resulting in robust process performance at manufacturing scale.     

Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection

Several mathematical models have been developed in anaerobic digestion systems and a variety of methods have been used for parameter estimation and model validation. However, structural and parametric identifiability questions are relatively seldom addressed in the reported AD modeling studies. This paper presents a 3-step procedure for the reliable estimation of a set of kinetic and stoichiometric parameters in a simplified model of the anaerobic digestion process. This procedure includes the application of global sensitivity analysis, which allows to evaluate the interaction among the identified parameters, multi-start strategy that gives a picture of the possible local minima and the selection of optimization criteria or cost functions. This procedure is applied to the experimental data collected from a lab-scale sequencing batch reactor. Two kinetic parameters and two stoichiometric coefficients are estimated and their accuracy was also determined. The classical least-squares cost function appears to be the best choice in this case study.     

微藻培养系统内光现象的研究进展

分析了微藻培养系统内光传递过程的数学模型和光分布影响因素,重点综述了光暗循环对微藻生长影响的实验研究和CFD技术应用研究进展,展望了微藻培养系统内光现象的发展方向,以期为规模化、高效微藻培养光生物反应器的设计、优化和放大提供参考。     

Finite Element Method (FEM) Modeling of Freeze-drying: Monitoring Pharmaceutical Product Robustness During Lyophilization

Lyophilization is an approach commonly undertaken to formulate drugs that are unstable to be commercialized as ready to use (RTU) solutions. One of the important aspects of commercializing a lyophilized product is to transfer the process parameters that are developed in lab scale lyophilizer to commercial scale without a loss in product quality. This process is often accomplished by costly engineering runs or through an iterative process at the commercial scale. Here, we are highlighting a combination of computational and experimental approach to predict commercial process parameters for the primary drying phase of lyophilization. Heat and mass transfer coefficients are determined experimentally either by manometric temperature measurement (MTM) or sublimation tests and used as inputs for the finite element model (FEM)-based software called PASSAGE, which computes various primary drying parameters such as primary drying time and product temperature. The heat and mass transfer coefficients will vary at different lyophilization scales; hence, we present an approach to use appropriate factors while scaling-up from lab scale to commercial scale. As a result, one can predict commercial scale primary drying time based on these parameters. Additionally, the model-based approach presented in this study provides a process to monitor pharmaceutical product robustness and accidental process deviations during Lyophilization to support commercial supply chain continuity. The approach presented here provides a robust lyophilization scale-up strategy; and because of the simple and minimalistic approach, it will also be less capital intensive path with minimal use of expensive drug substance/active material.     

Semi-continuous scale-down models for clone and operating parameter screening in perfusion bioreactors

Perfusion cell culture, confined traditionally to the production of fragile molecules, is currently gaining broader attention in the biomanufacturing of therapeutic proteins. The development of these processes is made difficult by the limited availability of appropriate scale-down models. This is due to the continuous operation that requires complex control and cell retention capacity. For example, the determination of an optimal perfusion and bleed rate for continuous cell culture is often performed in scale-down bioreactors and requires a substantial amount of time and effort. To increase the experimental throughput and decrease the required workload, a semi-continuous procedure, referred to as the VCD_max (viable cell density) approach, has been developed on the basis of shake tubes (ST) and deepwell plates (96-DWP). Its effectiveness has been demonstrated for 12 different CHO-K1-SV cell lines expressing an IgG1. Further, its reliability has been investigated through proper comparisons with perfusion runs in lab-scale bioreactors. It was found that the volumetric productivity and the CSPR_min (cell specific perfusion rate) determined using the ST and 96-DWP models were successfully (mostly within the experimental error) confirmed in lab-scale bioreactors, which then covered a significant scale-up from the half milliliter to the liter scale. These scale-down models are very useful to design and scale-up optimal bioreactor operating conditions as well as screening for different media and cell lines.     

Model-based workflow for scale-up of process strategies developed in miniaturized bioreactor systems

Miniaturized bioreactor (MBR) systems are routinely used in the development of mammalian cell culture processes. However, scale-up of process strategies obtained in MBR- to larger scale is challenging due to mainly non-holistic scale-up approaches. In this study, a model-based workflow is introduced to quantify differences in the process dynamics between bioreactor scales and thus enable a more knowledge-driven scale-up. The workflow is applied to two case studies with antibody-producing Chinese hamster ovary cell lines. With the workflow, model parameter distributions are estimated first under consideration of experimental variability for different scales. Second, the obtained individual model parameter distributions are tested for statistical differences. In case of significant differences, model parametric distributions are transferred between the scales. In case study I, a fed-batch process in a microtiter plate (4 ml working volume) and lab-scale bioreactor (3750 ml working volume) was mathematically modeled and evaluated. No significant differences were identified for model parameter distributions reflecting process dynamics. Therefore, the microtiter plate can be applied as scale-down tool for the lab-scale bioreactor. In case study II, a fed-batch process in a 24-Deep-Well-Plate (2 ml working volume) and shake flask (40 ml working volume) with two feed media was investigated. Model parameter distributions showed significant differences. Thus, process strategies were mathematically transferred, and model predictions were simulated for a new shake flask culture setup and confirmed in validation experiments. Overall, the workflow enables a knowledge-driven evaluation of scale-up for a more efficient bioprocess design and optimization.     

Mathematical modeling of ethanol production in solid-state fermentation based on solid medium’ dry weight variation

In this work, mathematical modeling of ethanol production in solid-state fermentation (SSF) has been done based on the variation in the dry weight of solid medium. This method was previously used for mathematical modeling of enzyme production; however, the model should be modified to predict the production of a volatile compound like ethanol. The experimental results of bioethanol production from the mixture of carob pods and wheat bran by Zymomonas mobilis in SSF were used for the model validation. Exponential and logistic kinetic models were used for modeling the growth of microorganism. In both cases, the model predictions matched well with the experimental results during the exponential growth phase, indicating the good ability of solid medium weight variation method for modeling a volatile product formation in solid-state fermentation. In addition, using logistic model, better predictions were obtained.     

Development of a fed-batch fermentation process to overproduce phosphoenolpyruvate carboxykinase using an expression vector with promoter and plasmid copy number controllable by heat

To effectively achieve tight regulation and high-level expression of cloned genes, a novel expression plasmid has been developed to contain the promoter and allow the plasmid copy number to be controlled by heat. The feasibility of the plasmid was tested by overproducing the pck gene product (Pck), a protein responsible for cell growth on gluconeogenic carbons and with potential toxicity. By fusing the pck gene with the promoter on the plasmid, the Escherichia coli strain harboring the composite vector was shown to produce various amounts of Pck in response to different degrees of heat shock. With the use of a 30 degrees -->41 degrees C stepwise upshift, the shake-flask culture of recombinant cells enabled production of maximal Pck in soluble form accounting for 20% of total cell protein. In sharp contrast, Pck production was undetectable in the uninduced cell, and this was further confirmed by the failed growth of strain JCL1305, defective in the essential genes for gluconeogenesis, carrying the composite vector on succinate at 30 degrees C. By exploiting the fed-batch fermentation approach, the recombinant cell batch initially kept at 30 degrees C in a lab-scale fermentor was exposed to 41 degrees C for 2 h at the batch fermentation stage, followed by a reduction in temperature to 37 degrees C throughout the remainder of the culturing process. Consequently, this resulted in Pck production equivalent to 15% of total cell protein. The total Pck yield thus calculated was amplified 1880-fold over that obtained at the shake-flask scale. Overall, there is great promise for this expression system due to its tight control, high production, simple thermomodulation, and feasible scale-up of recombinant proteins.     

Dynamics and modeling on fermentative production of poly (β-hydroxybutyric acid) from sugars via lactate by a mixed culture of Lactobacillus delbrueckii and Alcaligenes eutrophus

The mixed culture system was considered in the present research where sugars such as glucose were converted to lactate by Lactobacillus delbrueckii and the lactate was converted to poly β-hydroxybutyrate (PHB) by Alcaligenes eutrophus in one fermentor. For the modeling of the effect of NH₃ concentration on the cell growth of A. eutrophus and PHB production rates, metabolic flux distributions were computed at two culture phases of cell growth and PHB production periods. It was found that the NADPH, generated through isocitrate dehydrogenate in TCA cycle, was predominantly utilized for the reaction from α-ketoglutalate to glutamate when NH₃ was abundant, while it tended to be utilized for the PHB production through acetoacetyl CoA reductase as NH₃ concentration decreased. This phenomenon was reflected in the development of mathematical model. In the mixed culture experiments, the two phases were observed, namely the lactate production phase due to L. delbrueckii and the lactate consumption phase due to A. eutrophus. The lactate concentration could be estimated on-line by the amount of NaOH solution and HCl solution supplied to keep the culture pH at constant level. Several mixed culture experiments were conducted to see the dynamics of the system. Finally, a mathematical model which can describe the dynamic behavior of the present mixed culture was developed and the model parameters were tuned for fitting the experimental data. The model may be used for several purposes such as control, optimization, and understanding process dynamics etc.