Three-step model

The formation of a phenolic resin is often formally separated into two steps, though it probably should be three. If we use a three-step model, the first step is activation of the phenol or aldehyde. The second step is methylolation, and the third is condensation or chain extension. In addition to the clarity provided by the formalism, these steps are also generally separated in practice to provide maximum control of exothermic behavior, with the strategy being to separate the exotherm from each step from that of the others as much as possible. As there are significant differences in the activation step and in the details of the methylolation and condensations steps of novolacs and resoles, we will treat the two types separately. 

A recent discovery that RNA will act as a self-catalyst, called a ribozyme, leads to a simple three-step model for self-replication - this might include a surface. In the model (Figure 8.18), the template molecule T is self-complementary and is able to act as an autocatalyst. In the first step, it reversibly binds with its constituents A and B, forming the termolecular complex M. The termolecular complex undergoes irreversible polymerisation and becomes the duplex molecule D. Reversible dissociation of D gives two template molecules T, which can initiate new replication. The model preserves the order of the moieties on the template (the direction of the arrow) and the backbone, which may be on the surface... 

The interaction of even simple diatomic molecules with strong laser fields is considerably more complicated than the interaction with atoms. In atoms, nearly all of the observed phenomena can be explained with a simple three-step model [1], at least in the tunneling regime (1) The laser field releases the least bound electron through tunneling ionization (2) the free electron evolves in the laser field and (3) under certain conditions, the electron can return to the vicinity of the ion core, and either collisionally ionize a second electron [2], scatter off the core and gain additional kinetic energy [3], or recombine with the core and produce a harmonic photon [4]. 

Teramobile, 112 Thomson scattering, 168, 179 Three-level system, 11 Three-step model, 65 Time-resolved second harmonic generation, 29 TOF spectroscopy, 5 Transient depletion field screening (TDFS), 28... 

I. Friberg R. and Blasiak W., Part I - A Mass Flow Analysis of Packed-Bed Combustion Systems in the Context of the Three-step Model - A New System Theory , accepted for publication in the journal Archivum Combustionis... 

The objectives of this project are consistent with the objectives (1) and (4) above. The general objective of this project has been to verify a new measurement method to analyse the thermochemical conversion of biofuels in the context of PBC, which is based on the three-step model mentioned above. The sought quantities of the method are the mass flow and stoichiometry of conversion gas, as well as air factors of conversion and combustion system. One of the specific aims of this project is to find a physical explanation why it is more difficult to obtain acceptable emissions from combustion of fuel wood than from for example wood pellets for the same conditions in a given PBC system. This project includes the following stages ... 

Mathematical formulation of a new system theory - the three-step model -applicable to PBC. 

Mathematical model and uncertainty propagation analysis of a hypothetical measurement method in the context of the three-step model. 

Firstly, it is this author s hope that the three-step model should be regarded as a fast and simple theory in the analysis of PBC systems. It can also be the natural starting point for more advanced theoretical approaches, such as partial differential theories. 

First the three-step model is presented, which is the backbone of the thesis. Secondly, the review and classification attached as Appendix B is summarized. Finally, Paper I-IV are outlined. 

Below is a brief description of the three-step model, outlining the most important concepts, without any mathematical analysis. 

According to the three-step model (Figure 4), PBC system can ideally be defined as a complex process consisting of three consecutive subsystems (unit operations, functions) the conversion system (furthest upstream), the combustion (chamber) system, and the heat exchanger system (boiler system). The conversion system... 

Figure 5 The classification of solid fuel in the three-step model...

Finally, the novel part of the three-step model is the identification of a separate unit operation (subsystem) in a PBC system, that is, the thermochemical conversion of the fuel bed, which by logical consequence requires the introduction of a third subsystem referred to as the conversion system. Commonly, PBC systems are modelled with two steps, that is, a two-step model [3,15], see Figure 7. In the two-step model the thermochemical conversion of solid fuels and the gas-phase combustion are lumped together. Several new concepts are deduced in the scope of the three-step model in general and the conversion system in particular, for example the conversion gas, conversion concept, conversion zone, conversion efficiency, which are all explained later in this summary. 

Appendix B consists of a systematic classification and review of conceptual models (physical models) in the context of PBC technology and the three-step model. The overall aim is to present a systematic overview of the complex and the interdisciplinary physical models in the field of PBC. A second objective is to point out the practicability of developing an all-round bed model or CFSD (computational fluid-solid dynamics) code that can simulate thermochemical conversion process of an arbitrary conversion system. The idea of a CFSD code is analogue to the user-friendly CFD (computational fluid dynamics) codes on the market, which are very all-round and successful in simulating different kinds of fluid mechanic processes. A third objective of this appendix is to present interesting research topics in the field of packed-bed combustion in general and thermochemical conversion of biofuels in particular. 

This review defines the thermochemical conversion processes of solid fuels in general and biofuels in particular that is, what they are (drying, pyrolysis, char combustion and char gasification) and where they take place (in the conversion zone of the packed bed) in the context of the three-step model. 

Huge resources are required to develop an all-round and predictive bed model of an arbitrary conversion system. Based on this conclusion, this thesis presents a simplified approach to obtain useful knowledge about PBC in general and the small scale combustion of biofuels in particular. This method of attack is presented in paper I-IV and is based on a steady-state approach in the context of the three-step model. 

Paper I presents a mathematical analysis of the three-step model with a focus on the mass flow of a PBC system, see Figure 11. The mathematical approach is based on a steady-state mass balance, which is also referred to as the simple three-step model. 

What the three-step model really points out is that it is theoretically correct to carry out basic combustion calculations for a PBC system based on the mass flow and stoichiometry of the conversion gas from the conversion system and not based on the mass flow of solid fuel entering the conversion system. The two-step model approach applied on a PBC system, which is equivalent to assuming that the conversion efficiency is 100 %, is a functional engineering approach, because the conversion efficiency is in many cases very close to unity. However, there are cases where the two-step model approach results in a physical conflict, for example the mass flows in PBC sysfem of batch type cannot be theoretically analysed with a two-step model. 

Two new efficiencies are deduced in the context of the three-step model that is, conversion efficiency and combustion efficiency, which can be very useful in the optimization of existing PBC system and in the design of new advanced environmental-friendly PBC systems. However, to be able to quantify these new parameters, the mass flow and stoichiometry of the conversion gas need to be measured. 

The three-step model states that a PBC system which performs ideally with respect to the mass flow should operate in a mode of complete combustion and complete conversion, that is, conversion efficiency and combustion efficiency equal to one. In practice, a PBC system in general and a small-scale PBC system in particular, operate in different ranges of incomplete conversion and combustion that is, the ash flow contains fuel and the flue gas contains unbumt compounds, such as VOC, tar and CO. 

The system consists of the conversion and combustion system, according to the three-step model. A system boundary is put around the combustion system. In other words, a mass-balance is carried out over the combustion system. 

Based on the three-step model, a hypothetical mathematical model has been formulated to measure the mass flow and stoichiometry of conversion gas as well as the air factors of conversion and combustion system. 

The experimental system consists of a PBC system and a measurement system. The PBC system consists of a conversion system and a combustion system, according to the three-step model, and primary and secondary air lines. A boiler system is not required to realise the measurement method. The measurement system consists of twelve measuring devices (sensors) and a data acquisition system. 

The three-step model was developed as a consequence of the extreme complexity of a PBC system. This author had a wish to describe the PBC-process as simple as possible and to define the main objectives of a PBC system. The main objectives of a PBC system are indicated by the efficiencies of each unit operation, that is, the conversion efficiency, the combustion efficiency, and the boiler efficiency. The advantage of the three-step model, as with any steady-state system theory, is that it presents a clear overview of the major objectives and relationships between main process flows of a PBC system. The disadvantage of a system theory is the low resolution, that is, the physical quantity of interest cannot be differentiated with respect to time and space. A partial differential theory of each subsystem is required to obtain higher resolution. However, a steady-state approach is often good enough. 

A new system theory - the three-step model - of packed-bed combustion is formulated. Some new quantities and efficiencies are deduced in the context of the three-step model, such as the conversion gas, the solid-fuel convertibles, the conversion efficiency and the combustion efficiency. Mathematical models to determine the efficiencies are formulated. 

The three-step model, which is a new system theory, identifies the least common functions (unit operations) of a packed-bed combustion system. The three steps are referred to as the conversion system, the combustion system, and the boiler system. Previously, PBC has been modelled in two steps [3,15]. The novel approach with the three-step model is the splitting of the combustion chamber (furnace) into a combustion system and a conversion system. The simple three-step model is a steady-state approach together with some other simplifications applied to the general three-step model. The simple three-step model implies a simplified approach to the mathematical analysis of the extremely differentiated and complex PBC process. 

Some new concepts have been deduced in the context of the three-step model, for example, the conversion system, the conversion gas, the conversion efficiency, and the combustion efficiency. Two new physical quantities have been associated with the conversion gas. The physical quantities are referred to as the mass flow and the stoichiometry of the conversion gas. The conversion efficiency is a measure of how well the conversion system performs, that is, the degree of solid-fuel convertibles that are converted from the conversion system to the combustion system. The combustion efficiency is defined as the degree of carbon atoms being oxidised to carbon dioxide in the combustion system. In other words, the combustion efficiency is a measure of the combustion system performance. 

A new mesurement method, based on the three-step model, has been verified. It is based on a mass-balance approach similar to the work carried out by Rogers (see Appendix A) [18]. Besides information about the mass flow and the stoichiometry of the conversion gas, this method also determines the air factors of the conversion system and the combustion system, which Rogers method did not. 

The hardware of the method is a newly constructed experimental PBC system. It is designed according to the three-step model. The object (variable) of the measurement method is the conversion system, which can be varied that is, different conversion systems in small-scale range (<300 kW) can be studied by this method. The method works well on both continuous and batch conversion systems. However, the primary and secondary air flow need to be constant during the test. 

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