Selective catalytic reduction of nitrogen oxides with ammonia in forced unsteady state reactors - Case based reasoning and mathematical model simulation reasoning

The application of forced unsteady-state reactors in case of selective catalytic reduction of nitrogen oxides (NOx) with ammonia (NH3) is sustained by the fact that favorable temperature and composition distributions which cannot be achieved in any steady-state regime can be obtained by means of unsteady-state operations. In a normal way of operation the low exothermicity of the selective catalytic reduction (SCR) reaction (usually carried out in the range of 280-350°C) is not enough to maintain by itself the chemical reaction. A normal mode of operation usually requires supply of supplementary heat increasing in this way the overall process operation cost. Through forced unsteady-state operation, the main advantage that can be obtained when exothermic reactions take place is the possibility of trapping, beside the ammonia, the moving heat wave inside the catalytic bed. The unsteady state-operation enables the exploitation of the thermal storage capacity of the catalyticbed. The catalytic bed acts as a regenerative heat exchanger allowing auto-thermal behaviour when the adiabatic temperature rise is low. Finding the optimum reactor configuration, employing the most suitable operation model and identifying the reactor behavior are highly important steps in order to configure a proper device for industrial applications. The Reverse Flow Reactor (RFR) - a forced unsteady state reactor - corresponds to the above mentioned characteristics and may be employed as an efficient device for the treatment of dilute pollutant mixtures. As a main disadvantage, beside its advantages, the RFR presents the 'wash out' phenomena. This phenomenon represents emissions of unconverted reactants at every switch of the flow direction. As a consequence our attention was focused on finding an alternative reactor configuration for RFR which is not affected by the incontrollable emissions of unconverted reactants. In this respect the Reactor Network (RN) was investigated. Its configuration consists of several reactors connected in a closed sequence, simulating a moving bed by changing the reactants feeding position. In the RN the flow direction is maintained in the same way ensuring uniformcatalyst exploitation and in the same time the 'wash out' phenomena is annulated. The simulated moving bed (SMB) can operate in transient mode giving practically constant exit concentration and high conversion levels. The main advantage of the reactor network operation is emphasizedby the possibility to obtain auto-thermal behavior with nearly uniformcatalyst utilization. However, the reactor network presents only a small range of switching times which allow to reach and to maintain an ignited state. Even so a proper study of the complex behavior of the RN may give the necessary information to overcome all the difficulties that can appear in the RN operation. The unsteady-state reactors complexity arises from the fact that these reactor types are characterized by short contact times and complex interaction between heat and mass transportphenomena. Such complex interactions can give rise to a remarkable complex dynamic behavior characterized by a set of spatial-temporal patterns, chaotic changes in concentration and traveling waves of heat or chemical reactivity. The main efforts of the current research studies concern the improvement of contact modalities between reactants, the possibility of thermal wave storage inside the reactor and the improvement of the kinetic activity of the catalyst used. Paying attention to the above mentioned aspects is important when higher activity even at low feeding temperatures and low emissions of unconverted reactants are the main operation concerns. Also, the prediction of the reactor pseudo or steady-state performance (regarding the conversion, selectivity and thermal behavior) and the dynamicreactor response during exploitation are important aspects in finding the optimal control strategy for the forced unsteady state catalytic tubular reactors. The design of an adapted reactor requires knowledge about the influence of its operating conditions on the overall process performance and a precise evaluation of the operating parameters rage for which a sustained dynamic behavior is obtained. An apriori estimation of the system parameters result in diminution of the computational efforts. Usually the convergence of unsteady state reactor systems requires integration over hundreds of cycles depending on the initial guess of the parameter values. The investigation of various operation models and thermal transfer strategies give reliable means to obtain recuperative and regenerative devices which are capable to maintain an auto-thermal behavior in case of low exothermic reactions. In the present research work a gradual analysis of the SCR of NOx with ammonia process in forced unsteady-state reactors was realized. The investigation covers the presentationof the general problematic related to the effect of noxious emissions in the environment, the analysis of the suitable catalysts types for the process, the mathematical analysis approach for modeling and finding the system solutions and the experimental investigation of the device found to be more suitable for the present process. In order to gain information about the forced unsteady state reactor design, operation, important system parameters and their values, mathematical description, mathematicalmethod for solving systems of partial differential equations and other specific aspects, in a fast and easy way, and a case based reasoning (CBR) approach has been used. This approach, using the experience of past similarproblems and their adapted solutions, may provide a method for gaining informations and solutions for new problems related to the forced unsteady state reactors technology. As a consequence a CBR system was implemented and a corresponding tool was developed. Further on, grooving up the hypothesis of isothermal operation, the investigation by means of numerical simulation of the feasibility of the SCR of NOx with ammonia in the RFRand in the RN with variable feeding position was realized. The hypothesis of non-isothermal operation was taken into account because in our opinion ifa commercial catalyst is considered, is not possible to modify the chemical activity and its adsorptive capacity to improve the operation butis possible to change the operation regime. In order to identify the most suitable device for the unsteady state reduction of NOx with ammonia, considering the perspective of recuperative and regenerative devices, a comparative analysis of the above mentioned two devices performance was realized. The assumption of isothermal conditions in the beginningof the forced unsteadystate investigation allowed the simplification of the analysis enabling to focus on the impact of the conditions and mode of operation on the dynamic features caused by the trapping of one reactant in the reactor, without considering the impact of thermal effect on overall reactor performance. The non-isothermal system approach has been investigated in order to point out the important influence of the thermal effect on overall reactor performance, studying the possibility of RFR and RN utilization as recuperative and regenerative devices and the possibility of achieving a sustained auto-thermal behavior in case of lowexothermic reaction of SCR of NOx with ammonia and low temperature gasfeeding. Beside the influence of the thermal effect, the influence of the principal operating parameters, as switching time, inlet flow rate and initial catalyst temperature have been stressed. This analysis is important not only because it allows a comparison between the two devices and optimisation of the operation, but also the switching time is the main operating parameter. An appropriate choice of this parameter enables the fulfilment of the process constraints. The level of the conversions achieved, the more uniform temperature profiles, the uniformity ofcatalyst exploitation and the much simpler mode of operation imposed the RN as a much more suitable device for SCR of NOx with ammonia, in usual operation and also in the perspective of control strategy implementation. Theoretical simplified models have also been proposed in order to describe the forced unsteady state reactors performance and to estimate their internal temperature and concentration profiles. The general idea was to extend the study of catalytic reactor dynamics taking into account the perspectives that haven't been analyzed yet. The experimental investigation ofRN revealed a good agreement between the data obtained by model simulation and the ones obtained experimentally.

Mathematical model to estimate of the deterioration of wooden poles in contact with soil used in rural areas

In São Paulo State, mainly in rural areas, the utilization of wooden poles is observed for different purposes. In this context, wood in contact with the ground presents faster deterioration, which is generally associated to environmental factors and, especially to the presence of fungi and insects. With the use of mathematical models, the useful life of wooden structures can be predicted by obtaining "climatic indexes" to indicate, comparatively among the areas studied, which have more or less tendency to fungi and insects attacks. In this work, by using climatological data of several cities at São Paulo State, a simplified mathematical model was obtained to measure the aggressiveness of the wood in contact with the soil.

Evaluation of a new mathematical model to describe Clostridium perfringens growth during the cooling of cooked ground beef

A mathematical model previously developed to study microbial growth in food products under an isothermal environment was adapted to a time-varying temperature regime. The resulting model was applied to study the growth of Clostridium perfringens in meat products. This micro-organism is of particular relevance to public health and economy due to the loss of productivity caused by it. Results showed a similar performance of the model used compared to the Baranyi model under an isothermal situation and a slightly better performance under a non-isothermal temperature profile.

Modelling oil absorption during post-frying cooling - II: solution of the mathematical model, model testing and simulations

The mathematical models that describe the immersion-frying period and the post-frying cooling period of an infinite slab or an infinite cylinder were solved and tested. Results were successfully compared with those found in the literature or obtained experimentally, and were discussed in terms of the hypotheses and simplifications made. The models were used as the basis of a sensitivity analysis. Simulations showed that a decrease in slab thickness and core heat capacity resulted in faster crust development. On the other hand, an increase in oil temperature and boiling heat transfer coefficient between the oil and the surface of the food accelerated crust formation. The model for oil absorption during cooling was analysed using the tested post-frying cooling equation to determine the moment in which a positive pressure driving force, allowing oil suction within the pore, originated. It was found that as crust layer thickness, pore radius and ambient temperature decreased so did the time needed to start the absorption. On the other hand, as the effective convective heat transfer coefficient between the air and the surface of the slab increased the required cooling time decreased. In addition, it was found that the time needed to allow oil absorption during cooling was extremely sensitive to pore radius, indicating the importance of an accurate pore size determination in future studies.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: a mathematical model

In this paper we have proposed and analyzed a simple mathematical model consisting of four variables, viz., nutrient concentration, toxin producing phytoplankton (TPP), non-toxic phytoplankton (NTP), and toxin concentration. Limitation in the concentration of the extracellular nutrient has been incorporated as an environmental stress condition for the plankton population, and the liberation of toxic chemicals has been described by a monotonic function of extracellular nutrient. The model is analyzed and simulated to reproduce the experimental findings of Graneli and Johansson [Graneli, E., Johansson, N., 2003. Increase in the production of allelopathic Prymnesium parvum cells grown under N- or P-deficient conditions. Harmful Algae 2, 135–145]. The robustness of the numerical experiments are tested by a formal parameter sensitivity analysis. As the first theoretical model consistent with the experiment of Graneli and Johansson (2003), our results demonstrate that, when nutrient-deficient conditions are favorable for the TPP population to release toxic chemicals, the TPP species control the bloom of other phytoplankton species which are non-toxic. Consistent with the observations made by Graneli and Johansson (2003), our model overcomes the limitation of not incorporating the effect of nutrient-limited toxic production in several other models developed on plankton dynamics.

Mathematical model for NF-kappaB-driven proliferation of adult neural stem cells

Neural stem cells (NSCs) are early precursors of neuronal and glial cells. NSCs are capable of generating identical progeny through virtually unlimited numbers of cell divisions (cell proliferation), producing daughter cells committed to differentiation. Nuclear factor kappa B (NF-kappaB) is an inducible, ubiquitous transcription factor also expressed in neurones, glia and neural stem cells. Recently, several pieces of evidence have been provided for a central role of NF-kappaB in NSC proliferation control. Here, we propose a novel mathematical model for NF-kappaB-driven proliferation of NSCs. We have been able to reconstruct the molecular pathway of activation and inactivation of NF-kappaB and its influence on cell proliferation by a system of nonlinear ordinary differential equations. Then we use a combination of analytical and numerical techniques to study the model dynamics. The results obtained are illustrated by computer simulations and are, in general, in accordance with biological findings reported by several independent laboratories. The model is able to both explain and predict experimental data. Understanding of proliferation mechanisms in NSCs may provide a novel outlook in both potential use in therapeutic approaches, and basic research as well.

A mathematical model for the dynamics of Banana Xanthomonas Wilt with vertical transmission and inflorescence infection

A mathematical model for Banana Xanthomonas Wilt (BXW) spread by insect is presented. The model incorporates inflorescence infection and vertical transmission from the mother corm to attached suckers, but not tool-based transmission by humans. Expressions for the basic reproduction number R0 are obtained and it is verified that disease persists, at a unique endemic level, when R0 > 1. From sensitivity analysis, inflorescence infection rate and roguing rate were the parameters with most influence on disease persistence and equilibrium level. Vertical transmission parameters had less effect on persistence threshold values. Parameters were approximately estimated from field data. The model indicates that single stem removal is a feasible approach to eradication if spread is mainly via inflorescence infection. This requires continuous surveillance and debudding such that a 50% reduction in inflorescence infection and 2–3 weeks interval of surveillance would eventually lead to full recovery of banana plantations and hence improved production.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Drying of persimmon: Mathematical model for diffusivity as a simultaneous function of moisture content and shrinkage

Fresh persimmon has a high moisture content (about 85% wet basis) making it highly perishable and requiring adequate drying conditions to obtain an acceptable dehydrated product. Drying kinetics of persimmon cv. Rama Forte was studied in a fixed bed dryer at temperatures ranging from 50 to 80 degreesC and air velocity of 0.8 m/s. Shrinkage during drying was described by a linear correlation with respect to water content. Evaluation of effective diffusivity as a function of moisture content, with undergoing shrinkage during drying was based on Fourier series solution of Fick's diffusion equation. Effective diffusivity values at moisture contents between 0.09 - 4.23 kg water/kg dry matter were found to be in the range of 2.6 x 10(-10) m(2)/s to 5.4 x 10(-10) m(2)/s, and its dependence on air drying temperature was represented by an Arrhenius type equation. Activation energy increased with decreasing water content in persimmons.

The influence of floc size and hydraulic detention time on the performance of a dissolved air flotation (DAF) pilot unit in the light of a mathematical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A mathematical model for optimizing the indications of liver transplantation in patients with hepatocellular carcinoma

Abstract Background The criteria for organ sharing has developed a system that prioritizes liver transplantation (LT) for patients with hepatocellular carcinoma (HCC) who have the highest risk of wait-list mortality. In some countries this model allows patients only within the Milan Criteria (MC, defined by the presence of a single nodule up to 5 cm, up to three nodules none larger than 3 cm, with no evidence of extrahepatic spread or macrovascular invasion) to be evaluated for liver transplantation. This police implies that some patients with HCC slightly more advanced than those allowed by the current strict selection criteria will be excluded, even though LT for these patients might be associated with acceptable long-term outcomes. Methods We propose a mathematical approach to study the consequences of relaxing the MC for patients with HCC that do not comply with the current rules for inclusion in the transplantation candidate list. We consider overall 5-years survival rates compatible with the ones reported in the literature. We calculate the best strategy that would minimize the total mortality of the affected population, that is, the total number of people in both groups of HCC patients that die after 5 years of the implementation of the strategy, either by post-transplantation death or by death due to the basic HCC. We illustrate the above analysis with a simulation of a theoretical population of 1,500 HCC patients with tumor size exponentially. The parameter λ obtained from the literature was equal to 0.3. As the total number of patients in these real samples was 327 patients, this implied in an average size of 3.3 cm and a 95% confidence interval of [2.9; 3.7]. The total number of available livers to be grafted was assumed to be 500. Results With 1500 patients in the waiting list and 500 grafts available we simulated the total number of deaths in both transplanted and non-transplanted HCC patients after 5 years as a function of the tumor size of transplanted patients. The total number of deaths drops down monotonically with tumor size, reaching a minimum at size equals to 7 cm, increasing from thereafter. With tumor size equals to 10 cm the total mortality is equal to the 5 cm threshold of the Milan criteria. Conclusion We concluded that it is possible to include patients with tumor size up to 10 cm without increasing the total mortality of this population.