Conversion energy balance equation

In the case of isothermal operation the material and energy balance equations are not coupled, and design equations like 10.2.1 can be solved readily, since the reaction rate can be expressed directly as a function of the fraction conversion. For operation in this mode, an energy balance can be used to determine how the heat transfer rate should be programmed to keep the system isothermal. For this case equation 10.2.12 simplifies to the following expression for the heat transfer rate... 

Equation 10.3.6, the reaction rate expression, and the design equation are sufficient to determine the temperature and composition of the fluid leaving the reactor if the heat transfer characteristics of the system are known. If it is necessary to know the reactor volume needed to obtain a specified conversion at a fixed input flow rate and specified heat transfer conditions, the energy balance equation can be solved to determine the temperature of the reactor contents. When this temperature is substituted into the rate expression, one can readily solve the design equation for the reactor volume. On the other hand, if a reactor of known volume is to be used, a determination of the exit conversion and temperature will require a simultaneous trial and error solution of the energy balance, the rate expression, and the design equation. 

In order to provide a periodic check on the energy balance equation, one may use the form of equation 13.1.18, which results from integration between the reactor inlet and a distance L downstream where the fraction conversion is... 

For exothermic reactions in mixed flow (or close to mixed flow) an interesting situation may develop in that more than one reactor composition may satisfy the governing material and energy balance equations. This means that we may not know which conversion level to expect, van Heerden (1953, 1958) was the first to treat this problem. Let us examine it. 

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 ... 

Determining the conversion of monomer can only be as accurate as the method of quantifying the heat liberated from the reaction. The usual method is to take the difference between the inlet and outlet jacket water temperatures multiplied by the specific heat and flow rate of the water. This steady-state energy balance equation is ... 

Beginning with -G8h + 8Q = 0, the energy balance equation in terms of the fractional conversion XA gives... 

Consider an exothermic irreversible reaction with first order kinetics in an adiabatic continuous flow stirred tank reactor. It is possible to determine the stable operating temperatures and conversions by combining both the mass and energy balance equations. For the mass balance equation at constant density and steady state condition,... 

For a 10x10 array of unit cells, there is a total of 601 e-quations 200 mass balances (Equations 10 and 12), 300 energy balances (Equations 17, 21, 28), 100 electron balances (Equation 40) and one voltage equation (41). The corresponding 601 unknowns are 200 local fuel and oxidant conversions, 300 local fuel, oxidant and solid temperatures, 100 local current densities, and the dimensionless operating voltage. 

Figure 8-7 Graphical solution of equilibrium and energy balance equations to obtain adiabatic temperature and equilibrium conversion.

Note that Eq. 7.5.16 was derived from the energy balance equation (first law of thermodynamics), and it does not impose a limit on the value of 0. However, the second law of thermodynamics imposes a restriction on the conversion of thermal energy to kinetic energy. For compressible fluids in tubes with uniform cross-sectional area, the velocity cannot exceed the sound velocity hence. 

For the purpose of comparison, it is useful to express the simplified TAC model in terms of process variables, e.g., conversion, reactant distribution, relative volatilities, and reaction rate constant. This can be done by substituting relevant process variables for the equipment sizes, tray numbers, and vapor rates in Eq.(2). From the mass and energy balance equations, the total amount of catalyst (implying reactor size, Fji) can be expressed as ... 

Figure 11-4 Graphical solution of equitibrium and energy balance equations to obtain the adiabatic temperature and the adiabatic equilibrium conversion X,.

Solve the energy balance equation for temperature and find the steady-state operating temperatures of the reactor and the conversions corresponding to these temperatures. Additional data are ... 

When the flow pattern is known, conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first-order irreversible isothermal reactions, the conversion equation can be obtained from the R sfer function by replacing. s with the specific rate k. Thus, if G(.s) = C/Cq = 1/(1 -i- t.s), then C/Cq = 1/(1 -i-kt). Complete knowledge of a network enables incorporation of energy balances into the solution, whereas the RTD approach cannot do that. 

The temperature may be related to the fraction conversion by means of an energy balance such as equation 10.4.7. 

In order to determine the required reactor volume one must relate the temperature (and thus k) and the local pressure P to the fraction conversion using an energy balance and conventional fluid flow equations. 

Conversion in a known network and flow pattern is evaluated from appropriate material and energy balances. For first order irreversible isothermal reactions, the conversion equation can be obtained from the transfer function if that is known by replacing the parameter s by the... 

These equations must be supplemented by a kinetic equation for the time dependence of the degree of conversion P(t), and the dependence of the viscosity of a reactive mass on (3, temperature, and (perhaps) shear rate, if the reactive mass is a non-Newtonian liquid. The last two terms in the right-hand side of Eq. (2.89) are specific to a rheokinetic liquid. The first reflects the input of the enthalpy of polymerization into the energy balance, and the second represents heat dissipation due to shear deformation of a highly viscous liquid (reactive mass). 

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