Dynamic mathematical modeling of sulfate reducing gas-lift reactors

This paper presents a mathematical model able to simulate under dynamic conditions the physical, chemical and biological processes prevailing in a biological sulfate reducing gas-lift reactor. The proposed model is based on differential mass balance equations for substrates, products and bacterial groups involved in a sulfate reduction process. Heterotrophic sulfate reducing bacteria (HSRB), autotrophic sulfate reducing bacteria (ASRB), homoacetogenic bacteria (HB), methanogenic archaea (MA) and acetate degraders (AD) are the microbial groups taken into account in the model. The model is also used to validate a steady-state design model previously proposed by Esposito et al. [1].The proposed model is able to simulate the competition between the biological bacteria growing in the reactor, and predict the performance of a gas-lift reactor. The model includes two main parts: (1) a kinetic part including growth, metabolism and competition of SRB, HB, MA and AD in the system and (2) a mass-transfer part describing the thermodynamic concentration equilibria of gaseous components in the liquid and gas phase. The model has been validated using experimental data obtained by operating a laboratory-scale gas-lift reactor as described in Esposito et al. [2].The model can be applied to simulate the sulfate reduction process in a gas-lift reactor for several purposes, such as the evaluation of the optimal process conditions in terms of COD:SO₄^2? ratio, hydraulic retention time and gas input flow. In particular, model simulations reported in this paper show the model capability to predict the prevailing bacterial species and concentrations in the reactor as a function of the hydraulic retention time.     

Determination of carbon dioxide evolution rate using on-line gas analysis during dynamic biodegradation experiments

Respirometry is a precious tool for determining the activity of microbial populations. The measurement of oxygen uptake rate is commonly used but cannot be applied in anoxic or anaerobic conditions or for insoluble substrate. Carbon dioxide production can be measured accurately by gas balance techniques, especially with an on-line infrared analyzer. Unfortunately, in dynamic systems, and hence in the case of short-term batch experiments, chemical and physical transfer limitations for carbon dioxide can be sufficient to make the observed carbon dioxide evolution rate (OCER) deduced from direct gas analysis very different from the biological carbon dioxide evolution rate (CER).To take these transfer phenomena into account and calculate the real CER, a mathematical model based on mass balance equations is proposed. In this work, the chemical equilibrium involving carbon dioxide and the measured pH evolution of the liquid medium are considered. The mass transfer from the liquid to the gas phase is described, and the response time of the analysis system is evaluated.Global mass transfer coefficients (K(L)a) for carbon dioxide and oxygen are determined and compared to one another, improving the choice of hydrodynamic hypotheses. The equations presented are found to give good predictions of the disturbance of gaseous responses during pH changes.Finally, the mathematical model developed associated with a laboratory-scale reactor, is used successfully to determine the CER in nonstationary conditions, during batch experiments performed with microorganisms coming from an activated sludge system. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 53: 243-252, 1997.     

Kinetic modeling of cellulosic biomass to ethanol via simultaneous saccharification and fermentation: Part I. Accommodation of intermittent feeding and analysis of staged reactors

The model of South et al. [South et al. (1995) Enzyme Microb Technol 17(9): 797-803] for simultaneous saccharification of fermentation of cellulosic biomass is extended and modified to accommodate intermittent feeding of substrate and enzyme, cascade reactor configurations, and to be more computationally efficient. A dynamic enzyme adsorption model is found to be much more computationally efficient than the equilibrium model used previously, thus increasing the feasibility of incorporating the kinetic model in a computational fluid dynamic framework in the future. For continuous or discretely fed reactors, it is necessary to use particle conversion in conversion-dependent hydrolysis rate laws rather than reactor conversion. Whereas reactor conversion decreases due to both reaction and exit of particles from the reactor, particle conversion decreases due to reaction only. Using the modified models, it is predicted that cellulose conversion increases with decreasing feeding frequency (feedings per residence time, f). A computationally efficient strategy for modeling cascade reactors involving a modified rate constant is shown to give equivalent results relative to an exhaustive approach considering the distribution of particles in each successive fermenter.     

Modeling of an aerobic biofilm reactor with double-limiting substrate kinetics: bifurcational and dynamical analysis

A mathematical model of an aerobic biofilm reactor is presented to investigate the bifurcational patterns and the dynamical behavior of the reactor as a function of different key operating parameters. Suspended cells and biofilm are assumed to grow according to double limiting kinetics with phenol inhibition (carbon source) and oxygen limitation. The model presented by Russo et al. is extended to embody key features of the phenomenology of the granular‐supported biofilm: biofilm growth and detachment, gas–liquid oxygen transport, phenol, and oxygen uptake by both suspended and immobilized cells, and substrate diffusion into the biofilm. Steady‐state conditions and stability, and local dynamic behavior have been characterized. The multiplicity of steady states and their stability depend on key operating parameter values (dilution rate, gas–liquid mass transfer coefficient, biofilm detachment rate, and inlet substrate concentration). Small changes in the operating conditions may be coupled with a drastic change of the steady‐state scenario with transcritical and saddle‐node bifurcations. The relevance of concentration profiles establishing within the biofilm is also addressed. When the oxygen level in the liquid phase is <10% of the saturation level, the biofilm undergoes oxygen starvation and the active biofilm fraction becomes independent of the dilution rate. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2011     

Modeling of the pyruvate production with Escherichia coli: comparison of mechanistic and neural networks-based models

Three different models: the unstructured mechanistic black-box model, the input–output neural network-based model and the externally recurrent neural network model were used to describe the pyruvate production process from glucose and acetate using the genetically modified Escherichia coli YYC202 ldhA::Kan strain. The experimental data were used from the recently described batch and fed-batch experiments [ Zelić B, Study of the process development for Escherichia coli-based pyruvate production. PhD Thesis, University of Zagreb, Faculty of Chemical Engineering and Technology, Zagreb, Croatia, July 2003. (In English); Zelić et al. Bioproc Biosyst Eng 26:249–258 (2004); Zelić et al. Eng Life Sci 3:299–305 (2003); Zelić et al Biotechnol Bioeng 85:638–646 (2004)]. The neural networks were built out of the experimental data obtained in the fed-batch pyruvate production experiments with the constant glucose feed rate. The model validation was performed using the experimental results obtained from the batch and fed-batch pyruvate production experiments with the constant acetate feed rate. Dynamics of the substrate and product concentration changes was estimated using two neural network-based models for biomass and pyruvate. It was shown that neural networks could be used for the modeling of complex microbial fermentation processes, even in conditions in which mechanistic unstructured models cannot be applied.     

On several conjectures from evolution of dispersal

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17-36 [ 9 ]] concerning the dynamics of a diffusion-advection-competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [ 9 ]. It was shown in [ 9 ] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [ 9 ] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [ 9 ], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.     

Methane production from acetamide in an upflow anaerobic sludge-blanket reactor based on a synergistic association between an aerobic rod and methanogens

Acetamide degradation was investigated in a bench-scale upflow anaerobic sludge-blanket (UASB) reactor, successively fed with acetamide, acetate and acetamide, over a period of 343 days, at different hydraulic retention times (t _HR). The reactor was seeded with the sludge previously described [Guyot et al. (1994) Appl Microbiol Biotechnol, 42:452-456], in which methanogenesis from acetamide was performed through a synergistic relationship between an acetamide-degrading, aerobic rod and methanogens. When the reactor was fed acetamide, the chemical oxygen demand (COD) removal efficiency was 86% at volumetric loads less than 1.18 kg COD m^–3 day ^–1. At higher volumetric loads, the efficiency decreased markedly, e.g. 50.9% at a volumetric organic load of 3.39 kg COD m^–3 day^–1 (1 day t _HR) with an accumulation of both acetamide and acetate. The same reactor, when fed with acetate at t _HR 1 day, reached a high COD removal (99%). Evidence of the inhibition of acetate degradation by acetamide is presented. After a long period (135 days) without feeding the reactor with acetamide, the sludge reactor was still capable of degrading acetamide when this substrate was supplied again. It seems that the synergistic degradation of acetamide by aerobes and methanogens present in the UASB reactor sludge is stable over a long period (343 days), in spite of limiting concentrations of dissolved oxygen in the feed.     

Mathematical modeling of non-ideal mixing continuous flow reactors for anaerobic digestion of cattle manure

Most conventional digesters used for animal wastewater treatment include continuously stirred-tank reactors. While imperfect mixing patterns are more common than ideal ones in real reactors, anaerobic digestion models often assume complete mixing conditions. Therefore, their applicability appears to be limited. In this study, a mathematical model for anaerobic digestion of cattle manure was developed to describe the dynamic behavior of non-ideal mixing continuous flow reactors. The microbial kinetic model includes an enzymatic hydrolysis step and four microbial growth steps, together with the effects of substrate inhibition, pH and thermodynamic considerations. The biokinetic expressions were linked to a simple two-region liquid mixing model, which considered the reactor volume in two separate sections, the flow-through and the retention regions. Deviations from an ideal completely mixed regime were represented by changing the relative volume of the flow-through region (a) and the ratio of the internal exchange flow rate to the feed flow rate (b). The effects of the hydraulic retention time, the composition of feed, the initial conditions of the reactor and the degree of mixing on process performance can be evaluated by the dynamic model. The simulation results under different conditions showed that deviations from the ideal mixing regime decreased the methane yield and resulted in a reduced performance of the anaerobic reactors. The evaluation of the impact of the characteristic mixing parameters (a) and (b) on the anaerobic digestion of cattle manure showed that both liquid mixing parameters had significant effects on reactor performance.     

High solid fed‐batch butanol fermentation with simultaneous product recovery: Part II—process integration

In these studies, liquid hot water (LHW) pretreated and enzymatically hydrolyzed Sweet Sorghum Bagasse (SSB) hydrolyzates were fermented in a fed‐batch reactor. As reported in the preceding paper, the culture was not able to ferment the hydrolyzate I in a batch process due to presence of high level of toxic chemicals, in particular acetic acid released from SSB during the hydrolytic process. To be able to ferment the hydrolyzate I obtained from 250 g L^?1 SSB hydrolysis, a fed‐batch reactor with in situ butanol recovery was devised. The process was started with the hydrolyzate II and when good cell growth and vigorous fermentation were observed, the hydrolyzate I was slowly fed to the reactor. In this manner the culture was able to ferment all the sugars present in both the hydrolyzates to acetone butanol ethanol (ABE). In a control batch reactor in which ABE was produced from glucose, ABE productivity and yield of 0.42 g L^?1 h^?1 and 0.36 were obtained, respectively. In the fed‐batch reactor fed with SSB hydrolyzates, these productivity and yield values were 0.44 g L^?1 h^?1 and 0.45, respectively. ABE yield in the integrated system was high due to utilization of acetic acid to convert to ABE. In summary we were able to utilize both the hydrolyzates obtained from LHW pretreated and enzymatically hydrolyzed SSB (250 g L^?1) and convert them to ABE. Complete fermentation was possible due to simultaneous recovery of ABE by vacuum. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:967–972, 2018     

Mathematical analysis of solid-liquid mass transfer in a batch reactor for the enzymatic transformation of testosterone to 4AD

A previous mathematical analysis of mass transfer in a two-phase (solid-liquid) batch reactor for enzymatic transformation of testosterone to 4AD (Pereira et al., 1987) is extended to incorporate the effect of convective mixing. The results of the analysis showed that for a given enzyme loading, the mass transfer resistance in the solid (a function of the bead size) and the intensity of convective mixing (as embodied in the mass transfer coefficient) are two parameters that can be varied such that the overall mass transfer rate from the solid to the liquid phase ensures optimal reactor performance.     

Parametric sensitivity analysis and reduction of a detailed nutritional model of plant cell cultures

A kinetic model of plant nutrition described by Cloutier et al. (Cloutier et al., 2008. Biotechnol Bioeng 99:189-200) is progressively simplified so as to obtain a predictive model that describes the evolution of the biomass and the extracellular and intracellular concentrations of three determining nutrients, that is, free intracellular nitrogen, phosphate, and carbohydrate compounds. Three techniques of global sensitivity analysis are successively applied to assess the model parameter influence and potential correlation. The resulting dynamic model is able to predict plant growth for the two most encountered plant bioprocesses, namely suspension cells and hairy roots.     

An unstructured kinetic model of macromolecular metabolism in batch and fed-batch cultures of hybridoma cells producing monoclonal antibody

Growth profiles of the batch and fed-batch culture of hybridoma cells producing monoclonal antibody were simulated using an unstructured model. The model describes the production of cellular macromolecules and monoclonal antibody, the metabolism of glucose and glutamine with the production of lactate and ammonia, and the profiles of cell growth in batch and fed-batch culture. Equations describing the cells arrested in G1 phase [T.I. Linardos, N. Kalogerakis, L.A. Behie, Biotechnol. Bioeng. 40 (1992) 359–368; E. Suzuki, D.F. Ollis, Biotechnol. Bioeng. 34 (1989) 1398–1402] were included in this model to describe the increase of the specific antibody productivity in the near-zero specific growth rate, which was observed in the recent experiments in fed-batch cultures of this study and the semi-continuous culture of hybridoma cells [S. Reuveny, D. Velez, L. Miller, J.D. Macmillan, J. Immnol. Methods 86 (1986) 61–69]. This model predicted the increase of specific antibody production rate and the decline of the specific production rate of cellular macromolecules such as DNA, RNA, protein, and polysaccharide in the late exponential and decline phase of batch culture and at lower specific growth rates in the fed-batch culture.     

Dynamic model of a nitrifying fixed bed column: Simulation of the biomass distribution of Nitrosomonas and Nitrobacter and of transient behaviour of the column

A dynamic model for a fixed bed nitrifying column with recirculation of the liquid and gas phases was developed. Liquid RTD experiments demonstrated that the liquid phase was perfectly mixed inside the column. Hete- rogeneity of biomass distribution on the solid phase (beads) was represented by an N-tanks in series model, and a back-mixing term was set to account for the well-mixed liquid phase throughout the column. In autotrophic conditions, competition for oxygen is the cause of the spatial segregation of the two species. Nitrosomonas is concentrated on beads at the bottom of the bed whereas Nitrobacter is more widely distributed. This is consistent with biomass distribution results reported by Cox et al. [17] in a nitrifying fixed bed column. Nitrification takes place at the bottom of the column, always in oxygen gas-liquid mass transfer limiting conditions. Nevertheless, considering the whole process, nitrification is complete (>98% of NH₃ oxidised) and there is no oxygen limitation (the outlet dissolved oxygen concentration is not limiting). The dynamic behaviour of the column, in conditions set up to avoid biofilm diffusion limitation, was simulated for different NH₃-load variations and oxygen shutdowns. The simulated behaviour of the column can be compared to results reported by Bazin et al. [16]. This confirms that the output transient nitrite peaks are higher when changes in the process conditions produce a rearrangement of biomass distribution in the fixed bed.     

A special reactor design for investigations of mixing time effects in a scaled‐down industrial L‐lysine fed‐batch fermentation process

A specially designed model reactor based on a 42‐L laboratory fermentor was equipped with six stirrers (Rushton turbines) and five cylindrical disks. In this model reactor, the mixing time, Θ₉₀, turned out to be 13 times longer compared with the 42‐L standard laboratory fermentor fitted with two Rushton turbines and four wall‐fixed longitudinal baffles. To prove the suitability of the model reactor for scaledown studies of mixing‐time‐dependent processes, parallel exponential fed‐batch cultivations were carried out with the leucine‐auxotrophic strain, Corynebacterium glutamicum DSM 5715, serving as a microbial test system. L‐ Leucine, the process‐limiting substrate, was fed onto the liquid surface of both reactors. Cultivations were conducted using the same inoculum material and equal oxygen supply. The model reactor showed reduced sugar consumption (−14%), reduced ammonium consumption (−19%), and reduced biomass formation (−7%), which resulted in a decrease in L ‐lysine formation (−12%). These findings were reflected in less specific enzyme activity, which was determined for citrate synthase (CS), phosphoenolpyruvate carboxylase (PEP‐C), and aspartate kinase (AK). The reduced specific activity of CS correlated with lower CO₂ evolution (−36%) during cultivation. The model reactor represents a valuable tool to simulate the conditions of poor mixing and inhomogeneous substrate distribution in bioreactors of industrial scale. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 64: 599–606, 1999.     

Dynamic flux balance analysis of the metabolism of Saccharomyces cerevisiae during the shift from fully respirative or respirofermentative metabolic states to anaerobiosis

Dynamic flux balance analysis was utilized to simulate the metabolic behaviour of initially fully respirative and respirofermentative steady-state cultures of Saccharomyces?cerevisiae during sudden oxygen depletion. The hybrid model for the dynamic flux balance analysis included a stoichiometric genome-scale metabolic model as a static part and dynamic equations for the uptake of glucose and the cessation of respirative metabolism. The yeast consensus genome-scale metabolic model [Herrg?rd MJ et?al. (2008) Nat Biotechnol26, 1155-1160; Dobson PD et?al. (2010) BMC Syst Biol4, 145] was refined with respect to oxygen-dependent energy metabolism and further modified to reflect S.?cerevisiae anabolism in the absence of oxygen. Dynamic flux balance analysis captured well the essential features of the dynamic metabolic behaviour of S.?cerevisiae during adaptation to anaerobiosis. Modelling and simulation enabled the identification of short time-scale flux distribution dynamics under the transition to anaerobic metabolism, during which the specific growth rate was reduced, as well as longer time-scale process dynamics when the specific growth rate recovered. Expression of the metabolic genes was set into the context of the identified dynamics. Metabolic gene expression responses associated with the specific growth rate and with the cessation of respirative metabolism were distinguished.     

A note on an interaction between Rhinopithecus bieti and a buzzard at Baima Snow Moutain

Predation avoidance relies primarily on behavioural mechanisms [van Schaik and van Hooff, 1983]. Primates alarm call at predators, including most birds and mammals [Cheney and Wrangham, 1987]. Alarm calls could be used to signal to the predator that it has been spotted [Zuberbühler et al., 1999], thereby probably decreasing the likelihood of an attack [Schultz, 2001], and they also inform prey of the presence of the predator, thereby increasing overall attention levels [Schülke, 2001]. Although eagles are reported to be one of the predators of Rhinopithecus bieti [Bai et al., 1987], few interactions between these monkeys and raptors have been documented to date. Here I document an interaction witnessed between R. bieti and a buzzard [Buteo sp., Yang X-J, pers. comm.].     

Effects of tension-compression nonlinearity on solute transport in charged hydrated fibrous tissues under dynamic unconfined compression

Cartilage is a charged hydrated fibrous tissue exhibiting a high degree of tension-compression nonlinearity (i.e., tissue anisotropy). The effect of tension-compression nonlinearity on solute transport has not been investigated in cartilaginous tissue under dynamic loading conditions. In this study, a new model was developed based on the mechano-electrochemical mixture model [Yao and Gu, 2007, J. Biomech. Model Mechanobiol., 6, pp. 63-72, Lai et al., 1991, J. Biomech. Eng., 113, pp. 245-258], and conewise linear elasticity model [Soltz and Ateshian, 2000, J. Biomech. Eng., 122, pp. 576-586; Curnier et al., 1995, J. Elasticity, 37, pp. 1-38]. The solute desorption in cartilage under unconfined dynamic compression was investigated numerically using this new model. Analyses and results demonstrated that a high degree of tissue tension-compression nonlinearity could enhance the transport of large solutes considerably in the cartilage sample under dynamic unconfined compression, whereas it had little effect on the transport of small solutes (at 5% dynamic strain level). The loading-induced convection is an important mechanism for enhancing the transport of large solutes in the cartilage sample with tension-compression nonlinearity. The dynamic compression also promoted diffusion of large solutes in both tissues with and without tension-compression nonlinearity. These findings provide a new insight into the mechanisms of solute transport in hydrated, fibrous soft tissues.