Reactor outlet composition

The modeling of real industrial reactors is usually the most difficult step in process simulation. It is usually easy to construct a model that gives a reasonable prediction of the yield of main product, but the simulator library models are not sophisticated enough to fully capture all the details of hydraulics, mixing, mass transfer, catalyst and enzyme inhibition, cell metabolism, and other effects that often play a critical role in determining the reactor outlet composition, energy consumption, rate of catalyst deactivation, and other important design parameters. 

Table 5.13 Comparison of the reactor outlet composition as calculated for a diesel autothermal reformer (ATR) and a diesel steam reformer (STR) [443],...

Carbon Laydown. The potential for carbon laydown is readily estimated from the thermodynamics of Reactions 4 and 5. The areas where carbon laydown, according to these reactions, is thermodynamically possible were developed by Gruber (36). It is readily seen that carbon laydown via Reaction 4 is thermodynamically favorable at the reactor inlet for practically any commercially conceivable feed gas composition. As noted by Gruber (36), carbon laydown is thermodynamically unfavorable at the reactor outlet for practically all commercially conceivable methanator conditions. The methanation reactor will therefore, in practice, have two zones—the first is a finite zone between the inlet and some way down the catalyst bed where carbon laydown is thermodynamically possible, and the second zone is the balance of the reactor. 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

Equations (4.1) or (4.2) are a set of N simultaneous equations in iV+1 unknowns, the unknowns being the N outlet concentrations aout,bout, , and the one volumetric flow rate Qout- Note that Qom is evaluated at the conditions within the reactor. If the mass density of the fluid is constant, as is approximately true for liquid systems, then Qout=Qm- This allows Equations (4.1) to be solved for the outlet compositions. If Qout is unknown, then the component balances must be supplemented by an equation of state for the system. Perhaps surprisingly, the algebraic equations governing the steady-state performance of a CSTR are usually more difficult to solve than the sets of simultaneous, first-order ODEs encountered in Chapters 2 and 3. We start with an example that is easy but important. 

Consider a transition from Product I to Product II. The simplest case is just to add component C to the feed at the required steady-state concentration of c,>, = 9mol/m. The governing ODEs are solved subject to the initial condition that the reactor initially contains the steady-state composition corre-sponding to Product I. Figure 14.3 shows the leisurely response toward the new steady state. The dotted lines represent the specification limits for Product II. They allow any Q concentration between 7 and 9mol/m. The outlet composition enters the limits after 2.3 h. The specification for Product I allows 1 mol/m of Q to be present, but the rapid initial increase in the concentration of Q means that the limit is quickly exceeded. The total transition time is about 2h, during which some 1001 of off-specification material would be produced. 

The molecules in the system are carried along by the balls and will also have an exponential distribution of residence time, but they are far from perfectly mixed. Molecules that entered together stay together, and the only time they mix with other molecules is at the reactor outlet. The composition within each ball evolves with time spent in the system as though the ball was a small batch reactor. The exit concentration within a ball is the same as that in a batch reactor after reaction time tf,. 

Kinetic analysis of the data obtained in differential reactors is straightforward. One may assume that rates arc directly measured for average concentrations between the inlet and the outlet composition. Kinetic analysis of the data produced in integral reactors is more difficult, as balance equations can rarely be solved analytically. The kinetic analysis requires numerical integration of balance equations in combination with non-linear regression techniques and thus it requires the use of computers. 

The inlet stream (5) will be taken as having the same composition as the reactor outlet stream (4). 

If no NO is oxidised the composition of the outlet gas will be the same as the inlet. The inlet gas has the same composition as the reactor outlet, which is summarised above. Summarised below are the flow changes if the NO is oxidised ... 

In principle one can treat the thermodynamics of chemical reactions on a kinetic basis by recognizing that the equilibrium condition corresponds to the case where the rates of the forward and reverse reactions are identical. In this sense kinetics is the more fundamental science. Nonetheless, thermodynamics provides much vital information to the kineticist and to the reactor designer. In particular, the first step in determining the economic feasibility of producing a given material from a given reactant feed stock should be the determination of the product yield at equilibrium at the conditions of the reactor outlet. Since this composition represents the goal toward which the kinetic... 

The ideal continuous stirred tank reactor is the easiest type of continuous flow reactor to analyze in design calculations because the temperature and composition of the reactor contents are homogeneous throughout the reactor volume. Consequently, material and energy balances can be written over the entire reactor and the outlet composition and temperature can be taken as representative of the reactor contents. In general the temperatures of the feed and effluent streams will not be equal, and it will be necessary to use both material and energy balances and the temperature-dependent form of the reaction rate expression to determine the conditions at which the reactor operates. 

For fixed initial conditions, the solution to this expression is uniquely defined in terms of the age, i.e., 0batch(oO. The joint composition PDF ftime-dependent RTD distribution 14... 

Finding the Conversion in a Given System A graphical procedure for finding the outlet composition from a series of mixed flow reactors of various sizes for reactions with negligible density change has been presented by Jones (1951). All that is needed is an r versus C curve for component A to represent the reaction rate at various concentrations. 

For fast or moderately fast liquid phase reactions, the stirred-tank reactor can be very useful for establishing kinetic data in the laboratory. When a steady state has been reached, the composition of the reaction mixture may be determined by a physical method using a flow cell attached to the reactor outlet, as in the case of a tubular reactor. The stirred-tank reactor, however, has a number of further advantages in comparison with a tubular reactor. With an appropriate ratio of... 

The performance of this control structure, which does not use the furnace, is shown in Figure 7.31. At 0.1 hours, the feed composition is changed from 5 to 7.5 mol% chlorine. The reactor outlet temperature climbs because of the increase in reaction heat generation. The hotter gas entering the FEHE raises the temperature of exit stream, which raises the temperature of the mixture. The temperature controller increases the bypass flow to hold the reactor inlet temperature at 400 K. 

At 4 h, the feed composition is dropped to 2.5 mol% chlorine. Temperatures decrease sharply. The valve in the bypass line is driven completely shut at about 5.7 h, but the reactor inlet temperature cannot be maintained at the desired 400 K and drops to 393 K. The reactor outlet temperature drops from 500 to 438 K because of the reduction in reactant in the feed. Figure 7.32 shows the temperature profile at this new steady state. 

In the simplest case, only the stoichiometry of chemical reactions is known, but no kinetic information is available. This allows designing the control structure, which is choosing the controlled and manipulated variables and their pairing. Note that the knowledge of stoichiometry is also necessary for designing the structure of the separation system, which is determined by the composition and the thermodynamic properties of the reactor-outlet mixture. 

Then, the flow rate and composition of the reactor-outlet and the recycle flow rate are given by ... 

At the reactor outlet the reaction mixture has a temperature of 230 °C and a pressure of 34 bar, the molar composition being 86.6% benzene, 12.6% cumene and 0.8% DIPB. Other components are lights, in this case the propane entered with the feed, and heavies, lumped as tri-propylbenzene. 

The final composition of the SGP reactor product gas is established by the water-gas shift equilibrium at the reactor outlet/waste-heat exchanger inlet where rapid cooling begins. 

The conversion can be determined by a measurement of the flow rates, Eqn. 7.24. This usually involves a chromatographic analysis of the reactor outlet stream. A complete kinetic analysis requires the determination of versus W/FA0 curves over the range of temperatures, total pressures and inlet compositions jfo, of interest. The production rates obtained after differentiation are then regressed by a postulated rate equation on featuring parameters, such as preexponential factors, Aq, and activation energies, Ea ... 

Figure 2. Product composition at the reactor outlet as a function of the amount of FAME processed and the amount of Pd in the reactor.

This last item is important because it leads to an easy way to accommodate the molar contraction of the gas as the reaction proceeds. The program calculates steady-state profiles of each of these down the length of the tubular reactor, given the reaction kinetics models, a description of the reactor and catalyst geometries, and suitable inlet gas flow-rate, pressure and composition information. Reactor performance is calculated from the flow-rate and composition data at the reactor outlet. Other data, such as the calculated pressure drop across the reactor and the heat of reaction recovered as steam, are used in economic calculations. The methods of Dixon and Cresswell (7) are recommended for heat-transfer calculations. 

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