Chemical species enthalpy

The rate constants (/c[and k]) and the stoichiometric coefficients (t and 1/ ) are all assumed to be known. Likewise, the reaction rate functions Rt for each reaction step, the equation of state for the density p, the specific enthalpies for the chemical species Hk, as well as the expression for the specific heat of the fluid cp must be provided. In most commercial CFD codes, user interfaces are available to simplify the input of these data. For example, for a combusting system with gas-phase chemistry, chemical databases such as Chemkin-II greatly simplify the process of supplying the detailed chemistry to a CFD code. 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

A theoretical framework based on the one-point, one-time joint probability density function (PDF) is developed. It is shown that all commonly employed models for turbulent reacting flows can be formulated in terms of the joint PDF of the chemical species and enthalpy. Models based on direct closures for the chemical source term as well as transported PDF methods, are covered in detail. An introduction to the theory of turbulence and turbulent scalar transport is provided for completeness. 

If one of the scalars is enthalpy, the Schmidt number is replaced by the Prandtl number. The ratio of the Schmidt number to the Prandtl number is the Lewis number - a measure of the relative diffusivity of chemical species and enthalpy. Non-unity Lewis number effects can be important in combustion. 

Our major concern is the heat generated or absorbed by the chemical reactions that occur in the reactor. If Hy is the molar enthalpy of a chemical species, then the heat of a chemical reaction is defined as... 

An indication of the degree of exothermicity of sulphide oxidation reactions can be gained by comparing the enthalpy of formation (A//f), that is, a measure of the energy locked up in each chemical species, relative to native elements. The difference in enthalpies of formation of all reactants and all products defines the enthalpy (heat released or absorbed) of the reaction. Thermodynamic data on sulphide minerals, such as pyrite, are notoriously varied and disputed, and the values in Table 4 must be treated with caution. Nevertheless, depending on whether one defines the reaction as ending in an aqueous solution (equation 5), an intermediate secondary sulphate (e.g., melanterite - equation 6) or in complete oxidation to an oxyhydroxide (equation 7), the calculated reaction enthalpy (AH°) released is of the order of at least 1000 kJ/mol. 

The example illustrates that enthalpy can be gained when nonpolar bonds, as commonly encountered in organic molecules, are broken and polar bonds, such as those in carbon dioxide and water, are formed. Reactions which involve the transfer of electrons between different chemical species are generally referred to as redox reactions. Such reactions form the basis for the energy production of all organisms. From this point of view we can consider organic compounds as energy sources. 

This equation shows that the rate of change of species in the mixture contributes directly to the enthalpy change. Recall from the species continuity equation, Eq. 3.124, that there are two principal contributions to the rate of change of chemical species molecular diffusion across the control surfaces and homogeneous chemical reaction within the control volume. Substituting the species continuity equation, Eq. 3.124, yields... 

It is readily apparent that the system of equations is a coupled system of nonlinear partial differential equations. The independent variables are time t and the spatial coordinates (e.g., z, r, 0). For the fluid mechanics alone, the dependent variables are mass density, p, pressure p, and V. In addition the energy equation adds either enthalpy h or temperature T. Finally the mass fractions of chemical species are also dependent variables. 

This chapter gives an overview of the fundamental physical basis for the thermodynamic (enthalpy, entropy and heat capacity) properties of chemical species. Other chapters discuss chemical kinetics and transport properties (viscosity, thermal conductivity, and diffusion coefficients) in a similar spirit. 

The energies in Table 2.1 are listed as enthalpies (AH), but the driving forces in the chemical species/sensor interactions are really the changes of free energy (AG), which include the change of entropy (A5). At constant temperature, the two are related by (2.1). 

Exciplexes and excimers have their own structure and properties (e.g. multiplicity, absorption and emission spectra, lifetime, stability constant, enthalpy and entropy content, pathways of deactivation) and can be regarded thus as new chemical species. 

Chemical species Phase Temperature (K) Gibbs free energy (G ) (kj mol-1) Enthalpy (Hi) (kj mol-1) Entropy (5)) (J mol-1-K-1) Heat Capacity (Cpi) (J mol-1-K-1) Reference... 

Table 5.5 Enthalpy and Gibbs free energy of formation of chemical species.

When chemical equations are combined by addition, the standard heats of reaction may also be added to give, the standard heat of the resulting reaction. This is possible because enthalpy is a property, and changes in it are independent of path. In particular, formation equations and standard heats of formation may always be combined to produce any desired equation (not itself a formation equation) and its accompanying standard heat of reaction. Equations written for this purpose often include an indication of the physical state of each reactant and product, i.e., the letter g, l, or s is placed in parentheses after the chemical formula to show whether it is a gas, a liquid, or a solid. This might seem unnecessary since a pure chemical species at a particular temperature and 1 bar or l(atm) can usually exist only in one physical state. However, fictitious states are often assumed as a matter of convenience. 

We need enthalpy of formation data, since some fuels are normally composed of several chemical species. The heating value of a fuel is the enthalpy of combustion a lower heating value occurs when all the water is in vapor state. The entropy balance for the combustion cell is... 

Formulation of the left-hand side of Eq. (5-180) requires representative thermodynamic data and information on the combustion stoichiometry. In particular, the former includes the lower heating value of the fuel, the temperature-dependent molal heat capacity of the inlet and outlet streams, and the air preheat temperature T . It proves especially convenient now to introduce the definition of a pseudoadiabatic flame temperature Tt, which is not the true adiabatic flame temperature, but rather is an adiabatic flame temperature based on the average heat capacity of the combustion products over the temperature interval T < T < 7), The calculation of Tf does not allow for dissociation of chemical species and is a surrogate for the total enthalpy content of the input fuel-air mixture. It also proves to be an especially convenient system reference temperature. Details for the calculation of 7 are illustrated in Example 13. 

Number of chemical species Distillate flow rate Diffusion coefficient Efficiency Energy flux Energy transfer rate Eeed flow rate Column height Enthalpy Liquid holdup Height of a transfer unit Vapor-liquid equilibrium ratio (K value)... 

Approximately three hundred dimensionless groups [6.23] are used to describe the most important problems that characterize chemical engineering processes. Out of these, only a limited number is frequently used and can be classified according to the flow involved in the investigated process, the transport and interface transfer of one property (species, enthalpy, pressure) and the interactions of the transport mechanisms of the properties. In order to be considered in this anal-... 

The class composite-operator contains procedures that transform a set of chemical species of predisposed behaviors into a set of products, provided that an optional set of prespecified conditions is satisfied. These conditions can be specified by the user or imposed by the system. They may encompass virtually any symbolically encodable concept structural character, chemical behavior, spatial orientation, reaction conditions, free-energy requirements, enthalpy considerations, toxicity, etc. An instance of the composite-operator (e.g., k) calls on the following procedures to carry out the corresponding tasks ... 

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