Energy balance around reactor

To implement the GMC, an energy balance around the reactor is required it gives the relation between the reactor temperature (controlled variable) and the jacket temperature (manipulated variable). Based on the assumption that the amount of the heat accumulated in the walls of the reactor... 

The flowrate of the vapor to the condenser V (and the liquid returned to the reactor) is calculated by first using an overall energy balance around the entire system to find the condenser heat removal Qc... 

An energy balance around the reactor at 333 K shows that this small reactor (jacket area = 21.6 m2) with a heat removal rate of 1.04 x 106 J/s requires a jacket temperature of 276 K This is impossible if 294 K cooling water is the cooling medium. 

One important physical property assumption is made about heat capacities. The mass heat capacities of all components are assumed to be the same (2kJkg-1 K-1). This means that the product of the mass flowrate and the mass heat capacity is constant for any stream and equal to the sum of the product of the component molar flowrates times the corresponding molar heat capacities. Thus, despite the fact that molar flowrates of individual components vary down the length of the reactor, the term F Ylf=A yjcpj is constant, where F is the total molar flowrate, y - is the mole fraction of component j, and cpj is the molar heat capacity of component j. This relationship is used in the design procedures discussed below to calculate the inlet flowrate from an energy balance around the reactor. 

Calculate the molar flowrate Fjn of the gas entering the reactor using an energy balance around the reactor given as follows ... 

Equation (5.15) gives the energy balance around each reactor ... 

Fixing ATR sets the reactor inlet temperature Tm and the recycle flowrate FR because of the energy balance around the reactor with the fixed conversion. The larger is ATR, the lower is Tm and the smaller the recycle flowrate required to give the 500 K exit temperature. Thus increasing ATR, reduces compression costs. However, the lower 7jn results in a... 

The latter will be a major part of the operating costs and will be reflected in the sales price. Material and energy balances around the reactor or burner will be necessary. However, complete kinetic data for these complex reactions will probably not be available. In e case of these well-known processes, the information needed would be available from the licensor. 

Component A balance around reactor Energy balance on reacting mixture Energy balance on the coolant in the jacket... 

Figure 3. Mass and Energy balance around the Reactor...

The differential PEM fuel cell reactor is motivated by considering a small element in the serpentine flow channel fuel cell as shown in Figure 3.1 [12]. Mathematical models of fuel cells use differential mass, momentum and energy balances around the differential element as the defining equations for modeling larger and more complex flow fields [12]. In the differential element the only compositional variations are transverse to the membrane. The key element of a differential fuel cell is that the compositions in the gas phases in the flow channels at the anode and cathode are uniform. 

The steady-state energy balance around the reactor is... 

We will assume that a feed containing pure A is available, so that Cf = [x, y]T = [1,0]. Isothermal operation is no longer assumed. Rather, we will use an expression to describe an adiabatic energy balance around the reactor network. 

FIGURE 10.2.1. Material and energy balance around a reactor. 

FIGURE 10.2.2. Energy balance around a continuous reactor. Q = Heat W — Work n = Number of electrons during charge transfer F — Faraday s constant E = Electrical potential p = Pressure V — Volume U = Internal energy m = Mass u = Velocity. 

The conversion of the monomer into the polymer and the energy balance around the reactor can be described by the following system of ordinary differential equations for the mass thm [kg] of monomer and the mass mp [kg] of polymer in the reactor, and for the reactor temperature T [K] ... 

An overall mass balance on the reactor shows that the inlet mass flow rate, wi, is equal to the outlet mass flow rate, W2- A total energy balance around the system gives... 

Set up and solve energy balances around an ideal chemical reactor. 

If the enthalpy of reaction is not negligible, or if it is required to supply or remove thermal energy in the form of heat from the reactor, an energy balance around the system must be obtained in order to determine the temperature within the reactor. This is addressed later in the text (Part III, Chapter 12). 

The correct choice of the state of the compounds is crucial to obtain a correct enthalpy balance [6]. For the energy balance around the reactor depicted in Figure 5, the following state of the carrier flow of each species must be as listed in Table 2 and the modified enthalpy of combustion is listed for some compounds in Table 3. 

The model is able to predict the influence of mixing on particle properties and kinetic rates on different scales for a continuously operated reactor and a semibatch reactor with different types of impellers and under a wide range of operational conditions. From laboratory-scale experiments, the precipitation kinetics for nucleation, growth, agglomeration and disruption have to be determined (Zauner and Jones, 2000a). The fluid dynamic parameters, i.e. the local specific energy dissipation around the feed point, can be obtained either from CFD or from FDA measurements. In the compartmental SFM, the population balance is solved and the particle properties of the final product are predicted. As the model contains only physical and no phenomenological parameters, it can be used for scale-up. 

UN-SS Energy Balance. To predict the outlet temperature, an unsteady-state (UN-SS), energy balance (1) must be written around the reactor jacket. That balance is ... 

Biomass combustion occurs mostly at a temperature around 850°C. Heat is produced by the combustion reaction (17.5 MJ/kg) while part of it is consumed by heating the biomass and the air to the reactor temperature. A heat balance around the combustor results in the net energy of 11 MJ/kg biomass. Burning 2500 kg/hr biomass... 

Material Balance and Heat Balance, Required heat was mainly supplied by incineration of char, and some amount of produced combustible gas was fed as auxiliary fuel to the regenerator, as the amount of char was not sufficient for continuous thermal cracking. The material balance around the reactors is shown in Table-Ill and heat balance in Table-IV. Radiation and convection loss in Table-IV is larger than that of usual incinerators because of the thin refractory. It can be decreased in case of commercial plants. Energy balance of the total plant is shown in Fig-3. 

Steady-state component balances around the whole system and around each of the units are used to solve for the conditions throughout the plant for a given recycle flow rate D. The reactor holdup Vr and the reactor temperature Tr necessary to achieve a specified Qm JQ ratio are calculated as part of the design procedure. The other fixed design parameters are the kinetic constants (preexponential factors, activation energies, and heats of reaction for both reactions), the fresh feed flow rate and composition, the overall heat transfer coefficient in the reactor, the inlet coolant... 

Often, in engineering analysis, there will be a theoretical value of a parameter (for example, the outlet temperature of a reactor calculated from an energy balance), and there will be an actually-measured value. It is often desirable to compare them. One easy graphical way to do this is with a parity plot. In a parity plot, one plots the measured values against the experimental values (for the same trial). The y=x line is also plotted as a reference. If the theoretical and experimental values agree, they should lie close to the y=x line and be randomly scattered around it. If they do not (due to either a problematic assumption in the theory, errors in measurement, or both), then the data will be skewed away from the y=x line. This is also useful for identifying outlying measurements. 

Liquid circulation is developed in a bubble column or airlift reactors because of the introduction of gas, and it affects the performance of the reactor. As shown in Figure 2, if a gas is injected in the center of the bubble column, in the core region (r < R ) the liquid rises with the bubbles and the liquid velocity decreases with distance from the column center. In the outer annular region (r > R ), liquid flows downward [16]. Between these two sections there is a transition point (r = R ) at which the velocity is zero. In the case of high flow rate condition, the transition point occurs at around R = 0.7R. It is important to estimate the extent of the induced liquid phase mixing. While experimental study of the liquid circulation has been carried out by a number of investigators, theoretical analysis of this problem is rather limited. Some models based on the pressure balance or the energy balance have been proposed for the liquid phase flow patterns [1]. 

As pointed out earlier, for adiabatic reactor, the temperatures (T, and r ,) play significant role in operability and energy balance has to be taken into consideration. Without loss of generality, let us use one-lump adiabatic tubular reactor to illustrate the derivation. The relationship between heat generation and the production rate can be found from the energy balance equation around the reactor [10] ... 

Perform energy balance analyses around isothermal and adiabatic ideal reactors... 

Discussion of Resuits The mole and energy balance equations are solved by three different methods of different order of error Euler [0 h )], second-order Runge-Kutta [0(/j )], and Adams [0 h ). Graphical results are given in Figs. E5.3h and b. At the beginning the temperature of the reactor decreases because the reaction is endothermic. However, it starts to increase steadily at about 10% of the length of the reactor, due to the heat transfer from the hot gas circulation around the reactor. 

Gross measurement errors are easier to detect when several elemental balances (for carbon, nitrogen, degree of reduction) can be checked. Because heat (enthalpy) is an extensive variable, an energy balance can be set-up around the reactor boundary considered as an open system. Therefore heat can be used to check that no major substrate or product has been neglected. 

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