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Concept# Sensitivity analysis

Summary

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem.
The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes, including:

- Testing the robustness of the results of a model or system in the presence of uncertainty.
- Increased understanding of the relationships between input and output variables in a system or model.
- Uncertainty reduction, through the identification of model input that cause significant uncertainty in the output and should therefore be the focus of attention in order to increase robustness (perhaps by

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This work demonstrated that consolidated bioprocessing is a promising concept for conversion of lignocellulose to ethanol at industrial scale. CBP offers great cost saving potential, is feasible to be operated continuously and may be scaled up due to extensive knowledge of the process from a chemical engineering point of view.Cost savings of up to 27.5% of the total costs compared to conventional bioethanol production from lignocellulose, as stated by a techno-economic assessment, make continuous CBP the strongest lever to reduce processing costs of lignocellulosic ethanol. A cost sensitivity analysis identified scale and yield as the main cost-pushers from a process point of view, whereas the price level of the plant location has the highest impact on the investment conditions.To prove the feasibility of continuous CBP, and therefore the mentioned cost savings, experiments with a maximum titer of 3.258±0.007 g/L, a productivity of 0.025 g/(L*h) and constant enzyme production over 750h were conducted. Furthermore, the continuous experiments showed that experiments with identical volumetric oxygen transfer rate k_L a, but different oxygen fluxes per membrane area, showed titer differences of ca. 80% (1.83 g/L vs 3.26 g/L) in favor of setups with the large membrane surface. A rigorous process model was developed for continuously operated CBP. 9 species were considered (oxygen, glucose, total concentration Trichoderma reesei, secondary mycelia concentration of T. reesei, enzymes, cellulose, cellobiose, yeast density and ethanol). 8 of these 9 species needed to be modelled spatially resolved to account properly for mass transfer limitations. The fungal biofilm thickness d_f was found to be a critical parameter with an optimum for every membrane configuration. Smaller d_f reduced the fungal biofilm volume and thus, the enzyme production and larger d_f increased the diffusion path length causing shortage in nutrient supply as well as lower enzyme concentrations in the bulk. The enzyme synthesis rate of the secondary mycelia was fitted by reducing it by ca. 40% (0.67 FPU/(mL*d) vs 1.152 (FPU/(mL*d) compared to batch models.With the process model as centerpiece, a scale-up framework consisting of the model and a set of non-dimensional parameters was developed to scale CBP from 2.7L laboratory scale to 130L pilot scale. The majority of the non-dimensional parameters could be kept constant during scale-up as requested by the similarity paradigm. Necessary changes were simulated with the model. Again, the fungal biofilm thickness d_f proved to be a relevant parameter for scale-up considerations. In general, the relative loss of biofilm volume is compensated by longer residence times since the residence time has by far the least impact on the process economics.Finally, popular rate-controlled separation techniques were investigated regarding their potential with CBP, since they offer the potential to reduce yeast inhibition, to avoid separation limitations by the azeotrope and they are not bound to the vapor-liquid-equilibrium of highly diluted ethanol-water mixtures. However, most of the mechanisms fail to handle the solids of the fermentation broth. Pervaporation, being the most promising concept for in-situ product removal, would be a cost-saving alternative to distillation for batch operation, but is limited by an unfavorable vapor-liquid equilibrium due to low bulk concentrations during continuous operation.

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2010Aim of this diploma thesis is to approach to kinetic modelling of subsurface hydrochemistry with the program code phreeqc. The reaction considered is the degradation of organic mass and its concomitant reactions. Phreeqc is a program for thermodynamical based equilibrium calculations of geo- and hydrochemistry. Although the degradation of organic matter, and the associated reduction reactions due to the oxidation of organic matter, can be modelled with phreeqc, it does not account for kinetically controlled reactions, whose characteristic feature is the dependency of time. This study focuses on the state of the art of environmental modelling, the thermodynamical based calculation of the degradation of organic matter and on two mathematical approaches to model bacterial degradation of a contaminant, the Monod equation and the Michaelis-Menten approach. Sensitivity analyses of the respective models runs were done. As a result one can see, that the redox chemistry of a natural water depends strongly on the abundance of oxygen and nitrate and, as a matter of course, on the abundance of organic matter. Considering bacterial activity within the degradation process, two basic mathematical formulations have been stated. The Monod equation and the Michaelis-Menten formulation were implemented in a BASIC interpreter in PHREEQC. The sensitivity analyses show, that that a accurate determination of the parameters in laboratory or field is essential. The coupling of kinetically controlled reactions and thermodynamical based equilibrium calculations might lead to auspicious hydrochemical modelling capabilities.

2008