Heat and mass balances

Thermochemistry. From an overall heat and mass balance point of view, the main chemical reactions of the blast furnace include oxidation of carbon in the zone in front of the tuyeres (raceway) to give CO plus heat. 

To model this highly complex and nonlinear dynamics properly, we need the heat and mass balances. In classical control, however, we would replace them with a linearized model that is the sum of two functions in parallel ... 

In Section 10.1, the fuel gas flow rate is the manipulated variable (M) and cascade control is used to handle its fluctuations. Now, we consider also changes in the cold process stream flow rate as another disturbance (L). Let s presume further that we have derived diligently from heat and mass balances the corresponding transfer functions, GL and Gp, and we have the process model... 

Several excellent reviews of fluid bed granulation were published by Nienow and coworkers (Nienow, 1983, Nienow and Rowe, 1985 and Nie-now, 1994) in which the operation is described in detail. Heat and mass balances on the system are presented and a granule growth model is proposed. The advantages and disadvantages of the operation are discussed. The present approach differs from the above work by looking at the microscale... 

Heat and Mass Balance Analysis of the Process Flow Sheet..141... 

Some early calorimeters use thermal methods based on principles of heat and mass balance (12) and temperature rise of a constant flow of air through the combustion chamber (13). These calorimeters suffer from many drawbacks associated with their design. Heat and mass balance requires numerous measurements to account for all heat and mass flows. In most cases, thermal lag and losses in the equipment occur, which are not easily calculated. 

In this problem, the temperature varies throughout the column and the tower will be divided into increments so that by heat and mass balances the terminal conditions over each section may be found. Knowing the compositions and the temperature, the data given may be used in conjunction with the mass coefficient to calculate the height of the chosen increment. Adiabatic conditions will be assumed and, as the sensible heat change of the gas is small, the heat of solution will be used only to raise the temperature of the liquid. The gas temperature will therefore remain constant at 295 K. 

In Chapter 3, the reaction system is discussed using the heat and mass balances, and interaction with the equipment. Scale-up affects both temperature and pressure profiles, which vary with types of reactor systems and sizes. Relevant test methods for scale-up and for process design are covered, including discussions on the methods as well as the relative advantages and disadvantages. Typical approaches for safe design and for defensive measures are presented. The theoretical and experimental subjects in Chapters 2 and 3 are illustrated by the use of examples. 

Heat and Mass Balances, Kinetics, and Reaction Stability... 

At the heart of the model are the heat and mass balance equations governing the chlorine gas, brine and amalgam layers within the cell as illustrated by Fig. 20.3. At a more detailed level each cell is divided into eight zones. Conditions within each zone are assumed to be constant and there is a trade-off between model accuracy and execution time associated with the number of zones. Typically eight zones have been found to be a good compromise. 

Heat and mass balance equations are used in all aspects of process modelling however, what is key to this model is an understanding of the electrolytic process behind the cell. For example, the model must be able to predict current efficiency and k-factor if it is to predict electricity consumption. Most of these electrolytic parameters are calculated using empirical relationships derived from experimental data both from test cells and the full-scale plant. Considering k-factor, this is primarily a function of brine strength and temperature. Figure 20.5 illustrates the experimentally derived function used in the model. 

Fig. 20.4 Each zone has heat and mass balance equations and empirical relationships to describe the electrolysis.

The model of a mercury cell described in this chapter represents an effective combination of empirical data accumulated over several years of operation and theoretical heat and mass balance equations. Modern software tools and fast desk-top computers make the task of implementing the model relatively straightforward and of low cost so that it can be exploited for plant optimisation. 

Heat- and mass-balance table relative to the flow diagram reported in Figure 8.3-2, with the... 

Experiments with the system H2-02 were performed also by Horak et al. (21-23) who observed pronounced ignition-extinction phenomena. They were able to construct a reliable mathematical model based on the heat and mass balances describing the gas-to-solid heat and mass transfer. Their general conclusion is that the multiplicity phenomena may be explained in terms of thermokinetic theory. However, on the other hand, because of the high thermal capacity of the pellet, the oscillations cannot be described by this mechanism (72). Obviously we should examine a more detailed kinetic mechanism to be able to analyze successfully this phenomenon (25). 

The reaction is also influenced by the heat of reaction developing during the conversion of the reactants, which is a problem in tubular screening reactors. In microstructures, the heat transport through the walls of the channels is facilitated by their small dimensions, which allows the development of isothermal reaction conditions. Thus, by decoupling the heat and mass balance, an analytical description of the flow in the screening reactor is achievable. 

Figure 8.3 Adiabatic CSTR Working point as intercept of heat and mass balances. Point A is the working point for an exothermal reaction. Point B is the working point for an endothermal reaction.

Heat and mass balances, reaction kinetics, heal nad mass transfer Equation of state and phase equilibrium calculations ... 

It should be understood that this rate expression may in fact represent a set of diffusion and mass transfer equations with their associated boundary conditions, rather than a simple explicit expression. In addition one may write a differential heat balance for a column element, which has the same general form as Eq. (17), and a heat balance for heat transfer between particle and fluid. In a nonisothermal system the heat and mass balance equations are therefore coupled through the temperature dependence of the rate of adsorption and the adsorption equilibrium, as expressed in Eq. (18). 

Additional information on the plug flow fixed bed reactors and on the heat and mass balance equations can be found in the Handbook of Heterogeneous Catalysis[15] and in the classical books devoted to chemical engineering kinetics.113,141... 

For the same type of catalyst we have observed in a recirculation laboratory reactor multiplicity, periodic and chaotic behavior. Unfortunately, so far we are not able to suggest such a reaction rate expression which would be capable of predicting all three regimes [8]. However, there is a number of complex kinetic expressions which can describe periodic activity. One can expect that such kinetic expressions combined with heat and mass balances of a tubular nonadiabatic reactor may give rise to oscillatory behavior. Detailed calculations of oscillatory behavior of singularly perturbed parabolic systems describing heat and mass transfer and exothermic reaction are apparently beyond, the capability of both standard current computers and mathematical software. 

SO2, NOx, and total hydrocarbons. The mass spectrometric gas analysis is on a wet basis, as water vapor is not condensed out of the gas, while the analyzers at the sample port measure a gas stream dried using a permeation tube and refrigeration-type dryers in series. In addition to the measurements described above, surface temperature measurements of the boiler skin are made to estimate radiation losses, using the skin temperature, the room temperature and tabulated heat loss factors based on the temperature difference. Particulate mass emission rate and carbon content are measured for heat and mass balance purposes. At present, material deposited within the boiler during a test is collected but not factored into the heat or mass balances, because this deposition is considered to be negligible. Data taken are used to examine the heat balance for the 20-hp system. 

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