Mathematical Modeling of a Biomass Steam Gasifier—A Modified Equilibrium Approach

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Gröbl ◽  
Heimo Walter

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.

Author(s):  
Lawrence A. Boland

Equilibrium models used in beginning economics classes are based on the equilibrium concept developed by Alfred Marshall, but that concept of an equilibrium does not correspond to the equilibrium concept recognized in modern formal mathematical models taught to graduate students. In both cases, the assumptions needed to produce explanations of economic events are open to question. The assumptions needed to prove the existence of an equilibrium in formal mathematical models are often questioned not only by older model builders but also by today’s formal model builders. This book critically examines both model building cultures by examining the major problematic assumptions employed building equilibrium models with particular attention to the assumptions used to characterize learning, knowledge, and expectations. These assumptions are recognized as essential in any equilibrium model that claims to address the dynamics of decision making. These assumptions are also the object of the critiques provided by those developing evolutionary models and by those promoting the development of complexity economics. Attention is also given to the inadequacies of what is taught to beginning students when it comes to the question of whether equilibrium models can provide a realistic explanation of economic events and objects such as prices, market demands, and market supplies.


Energies ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 160 ◽  
Author(s):  
Sérgio Ferreira ◽  
Eliseu Monteiro ◽  
Paulo Brito ◽  
Cândida Vilarinho

Biomass gasification is realized as a settled process to produce energy in a sustainable form, between all the biomass-based energy generation routes. Consequently, there are a renewed interest in biomass gasification promoting the research of different mathematical models to enlighten and comprehend gasification process complexities. This review is focused on the thermodynamic equilibrium models, which is the class of models that seems to be more developed. It is verified that the review articles available in the literature do not address non-stoichiometric methods, as well as an ambiguous categorization of stoichiometric and non-stoichiometric methods. Therefore, the main purpose of this article is to review the non-stoichiometric equilibrium models and categorize them, and review the different stoichiometric equilibrium model’s categorization available in the literature. The modeling procedures adopted for the different modeling categories are compared. Conclusion can be drawn that almost all equilibrium models are modified by the inclusion of empirical correction factors that improves the model prediction capabilities but with loss of generality.


Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5668
Author(s):  
Hafiz Muhammad Uzair Ayub ◽  
Sang Jin Park ◽  
Michael Binns

Biomass gasification is the most reliable thermochemical conversion technology for the conversion of biomass into gaseous fuels such as H2, CO, and CH4. The performance of a gasification process can be estimated using thermodynamic equilibrium models. This type of model generally assumes the system reaches equilibrium, while in reality the system may only approach equilibrium leading to some errors between experimental and model results. In this study non-stoichiometric equilibrium models are modified and improved with correction factors inserted into the design equations so that when the Gibbs free energy is minimized model predictions will more closely match experimental values. The equilibrium models are implemented in MatLab and optimized based on experimental values from the literature using the optimization toolbox. The modified non-stoichiometric models are shown to be more accurate than unmodified models based on the calculated root mean square error values. These models can be applied for various types of solid biomass for the production of syngas through biomass gasification processes such as wood, agricultural, and crop residues.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1569
Author(s):  
Jesús Montejo-Gámez ◽  
Elvira Fernández-Ahumada ◽  
Natividad Adamuz-Povedano

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to the evidence that characterizes a school model. The discussion leads to the consideration of three components, which constitute the main categories of the proposed tool: the real system to be modeled, its mathematization and the representations used to express both. These categories and the corresponding analysis procedure are explained and illustrated through two working examples, which expose the value of the tool in establishing the foci of analysis when investigating school models, and thus, suggest modeling skills. The connection of this tool with other approaches to educational research on mathematical modeling is also discussed.


2013 ◽  
Vol 18 (9) ◽  
pp. 571

This call for manuscripts is requesting articles that address how to use mathematical models to analyze, predict, and resolve issues arising in the real world.


Author(s):  
Terrence Fine

This chapter challenges the nearly universal reliance upon standard mathematical probability for mathematical modeling of chance and uncertain phenomena, and offers four alternatives. In standard practice, precise assignments are made inappropriately, even to the occurrences of events that may be unobservable in principle. Four familiar examples of chance or uncertain phenomena are discussed, about which this is true. The theory of measurement provides an understanding of the relationship between the accuracy of information and the precision with which the phenomenon under examination should be modeled mathematically. The model of modal or classificatory probability offers the least precision. Comparative probability, plausibility/belief functions and upper/lower probabilities are carefully considered. The selectable precision of these alternative mathematical models of chance and uncertainty makes for an improved range of levels of accuracy in modeling the empirical domain phenomena of chance, uncertainty, and indeterminacy. Knowledge of such models encourages further thought in this direction.


2021 ◽  
Author(s):  
◽  
Adolf Hermanus Stroombergen

<p>Whether a country gains or loses from dismantling protection is a question which has received much attention in overseas studies; studies which deal both with the relevant theory and with actual measurement. The topic has not been well analysed in the New Zealand context. Discussion amongst economists and other interested parties has certainly occurred but this has been based more on philosophical and political considerations than on applied economic research. Since questions of protection reform affect the whole economy it is inappropriate to study such problems in a partial or selective framework which cannot capture the interdependencies between each and every sector in the economy. A multi-sectoral general equilibrium model overcomes this deficiency. This thesis is concerned with the development and application of such a model. The model (named JULIANNE) is a medium term policy model designed to answer 'what if' type questions, particularly questions about trade and structure. It is not a forecasting model. Its role is rather like that of a laboratory in the natural sciences, where experiments can be conducted in a situation where certain aspects of the (economic) environment can be controlled by the researcher so that it is possible to measure the relationships between the variables of interest. The closer the environment is to the 'real world' the easier it is to apply deductions from the experiment to reality. But even quite artificial experiments can yield useful insights. The thesis comprises eleven chapters, the first three of which introduce and develop the model, examining some of the overseas general equilibrium models and assessing some of the problems which need to be addressed when constructing such a model for New Zealand; a model with an emphasis on trade and structure. The following three chapters present the JULIANNE model including its equations, a detailed explanation of its features and routines, and its method of solution, which for general equilibrium models is a most important consideration as it distinguishes the purely abstract Walrasian model from a model which is actually computable. Chapters 7 and 8 apply the model to various problems, especially to protection reform, but also to other interesting topics such as export subsidisation, relative occupational wage rates and medium term projections. The issue of model validation (in a general sense) is also covered. In Chapter 9 the model is extended from a single period snapshot model into a multi-period dynamic model, essentially introducing another variable; time, that can be controlled by the experimenter. Some of the results from Chapters 7 and 8 are then reassessed with the extended model, as described in Chapter 10. Results from the application of the model to questions about the effects of changes in protection enabled one to conclude that under flexible factor prices with fixed factor employment, the gains from freer trade vary directly with the values of the export price elasticities of demand, with the potential for economies of scale arising from specialization, and with the time horizon under consideration. They vary inversely with the values of the elasticities of substitution both between domestic and imported goods of a given type, and between goods of different types. Under a different labour market asumption, namely fixed real wage rates and flexible employment, the case for free trade is much stronger (that is, for a given set of parameter values). The profile of protection across sectors can also be important with the not improbable chance that a low uniform level of protection is superior to complete free trade, again depending on parameter values and the characteristics of the labour market. In this connection the observed uniformity of the current protection regime is very dependent on the degree of sectoral disaggregation identified in the model. As the degree of disaggregation increases, the potential for specialization also increases, as does the potential for substitution between different commodity types. Just how important these issues are, is a question for future research.</p>


2021 ◽  
Author(s):  
◽  
Adolf Hermanus Stroombergen

<p>Whether a country gains or loses from dismantling protection is a question which has received much attention in overseas studies; studies which deal both with the relevant theory and with actual measurement. The topic has not been well analysed in the New Zealand context. Discussion amongst economists and other interested parties has certainly occurred but this has been based more on philosophical and political considerations than on applied economic research. Since questions of protection reform affect the whole economy it is inappropriate to study such problems in a partial or selective framework which cannot capture the interdependencies between each and every sector in the economy. A multi-sectoral general equilibrium model overcomes this deficiency. This thesis is concerned with the development and application of such a model. The model (named JULIANNE) is a medium term policy model designed to answer 'what if' type questions, particularly questions about trade and structure. It is not a forecasting model. Its role is rather like that of a laboratory in the natural sciences, where experiments can be conducted in a situation where certain aspects of the (economic) environment can be controlled by the researcher so that it is possible to measure the relationships between the variables of interest. The closer the environment is to the 'real world' the easier it is to apply deductions from the experiment to reality. But even quite artificial experiments can yield useful insights. The thesis comprises eleven chapters, the first three of which introduce and develop the model, examining some of the overseas general equilibrium models and assessing some of the problems which need to be addressed when constructing such a model for New Zealand; a model with an emphasis on trade and structure. The following three chapters present the JULIANNE model including its equations, a detailed explanation of its features and routines, and its method of solution, which for general equilibrium models is a most important consideration as it distinguishes the purely abstract Walrasian model from a model which is actually computable. Chapters 7 and 8 apply the model to various problems, especially to protection reform, but also to other interesting topics such as export subsidisation, relative occupational wage rates and medium term projections. The issue of model validation (in a general sense) is also covered. In Chapter 9 the model is extended from a single period snapshot model into a multi-period dynamic model, essentially introducing another variable; time, that can be controlled by the experimenter. Some of the results from Chapters 7 and 8 are then reassessed with the extended model, as described in Chapter 10. Results from the application of the model to questions about the effects of changes in protection enabled one to conclude that under flexible factor prices with fixed factor employment, the gains from freer trade vary directly with the values of the export price elasticities of demand, with the potential for economies of scale arising from specialization, and with the time horizon under consideration. They vary inversely with the values of the elasticities of substitution both between domestic and imported goods of a given type, and between goods of different types. Under a different labour market asumption, namely fixed real wage rates and flexible employment, the case for free trade is much stronger (that is, for a given set of parameter values). The profile of protection across sectors can also be important with the not improbable chance that a low uniform level of protection is superior to complete free trade, again depending on parameter values and the characteristics of the labour market. In this connection the observed uniformity of the current protection regime is very dependent on the degree of sectoral disaggregation identified in the model. As the degree of disaggregation increases, the potential for specialization also increases, as does the potential for substitution between different commodity types. Just how important these issues are, is a question for future research.</p>


2016 ◽  
Vol 19 (3) ◽  
pp. 96-109
Author(s):  
Phung Thi Kim Le ◽  
Viet Tan Tran ◽  
Thien Luu Minh Nguyen ◽  
Viet Vuong Pham ◽  
Truc Thanh Nguyen ◽  
...  

Finding alternative energy sources for fossil fuels was a global matter of concern, especially in developing countries. Rice husk, an abundant biomass in Viet Nam, was used to partially replace fossil fuels by gasification process. The study was conducted on the pilot plant fixed bed up-draft gasifier with two kind of gasification agents, pure air and air-steam mixture. Mathematical modeling and computer simulations were also used to describe and optimize the gasification processes. Mathematical modeling was based on Computational Fluid Dynamics method and simulation was carried by using Ansys Fluent software. Changes in outlet composition of syngas components (CO, CO2, CH4, H2O, H2) and temperature of process, in relation with ratio of steam in gasification agents, were presented. Obtained results indicated concentration of CH4, H2 in outlet was increased significantly when using air-steam gasification agents than pure air. The discrepancies among the gasification agents were determined to improve the actual process.


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