Reaction heat term energy balance

For a complete description of the temperature and degree conversion fields throughout the volume of an article it is necessary to add a term for the heat of chemical reaction to the energy balance equation ... 

An abuse model requires (i) materials (mass) balance for the exothermic side reactions, (ii) estimation of the reaction parameters (e.g., heat of reaction) from experimental measurements such as differential scanning calorimetry (DSC) and accelerated rate calorimetry (ARC), (iii) devising the kinetic expressions of the reactions, and (iv) incorporation of the thermal behavior due to these reactions in the energy balance equation (e.g., in terms of volumetric source terms). Specifically, the thermal energy conservation equation is duly modified to include the additional heat generation effects to reflect the specific abuse behavior in terms of heat generation due to side reaction kinetics and/or joule heating. The thermal boundary condition may also include radiative heat transfer to the ambient air. 

Finally, the energy available from the above reaction might be used to operate a fuel cell such as those involved in the space program. In that case, as much as 818 kj/mol of useful electrical work could be obtained relatively litde heat is evolved. Summarizing this discussion in terms of an energy balance (per mole of methane reacting) ... 

The RNG model provides its own energy balance, which is based on the energy balance of the standard k-e model with similar changes as for the k and e balances. The RNG k-e model energy balance is defined as a transport equation for enthalpy. There are four contributions to the total change in enthalpy the temperature gradient, the total pressure differential, the internal stress, and the source term, including contributions from reaction, etc. In the traditional turbulent heat transfer model, the Prandtl number is fixed and user-defined the RNG model treats it as a variable dependent on the turbulent viscosity. It was found experimentally that the turbulent Prandtl number is indeed a function of the molecular Prandtl number and the viscosity (Kays, 1994). 

The input and output terms of equation 1.5-1 may each have more than one contribution. The input of a species may be by convective (bulk) flow, by diffusion of some kind across the entry point(s), and by formation by chemical reaction(s) within the control volume. The output of a species may include consumption by reaction(s) within the control volume. There are also corresponding terms in the energy balance (e.g., generation or consumption of enthalpy by reaction), and in addition there is heat transfer (2), which does not involve material flow. The accumulation term on the right side of equation 1.5-1 is the net result of the inputs and outputs for steady-state operation, it is zero, and for unsteady-state operation, it is nonzero. 

Equations similar to 12.3-10 to -15 may be written in terms of internal energy, U, with Cv, the heat capacity at constant volume, replacing CP. For liquid-phase reactions, the difference between the two treatments is small. Since most single-phase reactions carried out in a BR involve liquids, we continue to write the energy balance in terms of H, but, if required, it can be written in terms of U. In the latter case, it is usually necessary to calculate AU from AH and Cv from CP, since AH and CP are the quantities listed in a database. Furthermore, regardless of which treatment is used, it may be necessary to take into account the dependence of AH (or AU) and CP (or C,) on T ... 

Equation 12.3-16 is valid whether heat is transferred to or from the system, and whether the reaction is exothermic or endothermic. Note that each term on the left side of equation 12.3-16 may be an input or an output. Furthermore, CP is the molar heat capacity of the system, and is given by equation 12.3-13 as such, it may depend on both T and composition (through /A). The right side of equation 12.3-16 may also be expressed on a specific-mass basis (12.3-11). This does not affect the consistency of the units of the terms in the energy balance, which are usually J s-1. 

For nonadiabatic operation and an exothermic reaction, the overall situation is similar, but is complicated by the inclusion of the heat transfer term for Q in the energy balance in equation 14.3-10. 

For reactions involving heat effects, the total and component material balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by where each term has units of kj/s. For steady-state operation the accumulation... 

In this work, the goal is to design a control function in such a manner that neither the reaction heat nor kinetic nor mass transfer terms are required for stabilizing temperature. The scheme provides an estimated value of the heat generation from energy balance. Alkylation isobutane/propylene using sulfuric... 

The material balance of Eq. 1 and the energy balance of Eq. 2 are tied together by their third terms because the heat effect is produced by the reaction itself. 

The mass- and ener -balance equations must be solved numerically in the general situation where heat is transferred to or from walls. There are three terms on the right side of the energy equation, heat flow with reactants and products, reaction heat, and heat transfer through walls. Flowever, the adiabatic reactor is a special case where we need to solve only one equation for a single reaction. 

For R simultaneous reactions we have R different Xj values and R simultaneous maSS-balance equations to solve along with the energy-balance equation. In the energy-balance equation the flow and heat removal terms are identical, but the energy generation has terms for each of the R reactions,... 

These configurations are essentially two reactors connected by the heat exchange area A, and we will consider this in more detail in a later chapter in connection with multiphase reactors. We do not need to write a species balance on the coolant, but the energy balance in the jacket or cooling coil is exactly the same as for the reactor except that we omit the reaction generation term. 

The reaction chamber energy balance is written in terms of the total internal energy, U. In each reaction chamber, reactant with a given energy is added, reactant with a given energy leaves, and heat is added via the intermediate heat exchanger. Thus ... 

On the right-hand side of the solids energy balance, the first term represents the gas-solids heat transfer, and the second term is the heat gain and loss from the solids reactions. Exothermic reactions have a negative heat of reaction and endothermic reactions have a positive heat of reaction. The local gas-solids heat transfer coefficient is indicated by hGS, AGS is the local gas-solids heat transfer area, TG is the gas stream absolute temperature, and AHi are the heats of reaction. 

The energy balance in the fixed bed includes convective, conductive and radiative heat transfer and heats of reactions terms. The equation is described below ... 

If a mixture enters and leaves a system without a reaction taking place, we would find that the same species entered and left so that the enthalpy change in Eq. (4724a) would not be any different-with the-modification-described above than what we have used before, because the terms that account for the heat of formation in the energy balance would cancel. For example, for the case of two species in a flow system, the output enthalpy would be... 

The interconnections between the unit modules may represent information flow as well as material and energy flow. In the mathematical representation of the plant, the interconnection equations are the material and energy balance flows between model subsystems. Equations for models such as mixing, reaction, heat exchange, and so on, must also be listed so that they can be entered into the computer code used to solve the equation. Table 5.1 lists the common type of equations that might be used for a single subsystem. In general, similar process units repeatedly occur in a plant and can be represented by the same set of equations, which differ only in the names of variables, the number of terms in the summations, and the values of any coefficients in the equations. 

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