Model reactor

Reactor designs for AOP depend on the mode of operation (a) homogeneous or heterogeneous operation, (b) radiation source used, and (c) addition of chemical. AOP reactors are operated in either batch or flow-through mode with or without recycle. For homogeneous AOP, tank type batch reactors are often used. The flow-through mode is used in radiation-based AOP for water with low contaminant concentration (less than 10 ppm). 

At low water flow rates, a batch mode of operation can be used for greater treatment efficiency. 

The hydraufic residence time can be calculated if the AOP reaction kinetics and reaction rate constants are available. Typically, many AOP exhibit first order kinetics with respect to the contaminant concentration and the hydraulic detention time can be calculated as  

For batch and plug flow flow-through reactors  

Radiation model involving multi-lamp reactors is provided by Yokota and Suzuki (22). Based on a diffused line source emission model, the light absorption rate in any geometrical photoreactor with multiple lamps was assessed, and the work reveals the existence of optimum light arrangement. 

First we will describe the model of a fed-batch reactor. The purpose of this model is to describe the penicillin production as a function of the feed rate and substrate feed concentration. The reactor is usually operated in such a way that the first period is a batch phase or growing period dnring which the feed is zero. The second phase is the production phase, during which a specific feeding strategy is used. In this case, the feed is increase to an initial value and ramped subsequently to a find value. 

Assuming that no density changes take place, the volumetric flow balance can be written 

A mass balance for an arbitrary liquid-phase component in the stirred tank reactor is thus written as follows dci 

The initial condition is c = cfO) at t = 0. The flux at the particle surface is obtained from the solution of Eq. (8.1) and the gas-liquid flux can be estimated from the film theory. 

In this section, an attempt is made to define the mathematical models of reactors encountered both in the laboratory and in industrial practice. Theoretical and practical considerations about reactors can be found in books on chemical kinetics [1—13], chemical reaction engineering [20— 31], or specialized books (see, for example, refs. 35—37 for pyrolysis reactors). 

After studying this chapter, the reader should 

Be familiar with the types of reactor models available in the simulators and their use in 

Be able to design a system for heat transfer in association with the reactor, to sustain an exothermic or endothermic reaction at its desired temperature level, and study the design using simulation. 

Be able to determine if a reactor network should be considered and, if so, design it using the concept of the attainable region. 

Chemical reactors, particularly for continuous processes, are often custom designed to involve multiple phases (e.g., vapor, liquid, reacting solid, and solid catalyst), different geometries (e.g., stirred tanks, tubular flows, converging and diverging nozzles, spiral flows, and membrane transport), and various regimes of momentum, heat, and mass transfer (e.g., viscous flow, turbulent flow, conduction, radiation, di sion, and dispersion). There 

The complicated interactions between the chemical reaction and the transport processes for mass, energy and momentum, which occur simultaneously, are described by the corresponding laws of conservation. We have [4] 

Equation (3.4) expresses that the variation with time of the concentration of substance i (left hand side of the equation) is caused by forced convection (for example by stirring) (first term on the right hand side), the effective diffusion (second term on the right hand side) and the chemical transformation (third term on the right hand side). D is the effective diffusion coefficient in m s of substance i and Vj j the stoichiometric coefficient of substance i in reaction j (negative sign for feed materials and positive sign for products) u is the velocity vector of the flow in ms .  

For process safety problems normally space-independent solutions of Eq. (3.4) are used. However, for some cases, for example stirrer failure or the correct placing of measuring sensors, accounting for space dependence is desirable. Space independence leads to the concept of ideal stirring , i.e. at any point inside the reactor we have the same temperature and concentrations (ideal reactor). This is assumed in subsequent sections. 

---

Fig. 8. Combined flow reactor models (a) parallel flow reactors with longitudinal diffusion (diffusivities can differ), (b) internal recycle—cross-flow reactor (the recycle can be in either direction), comprising two countercurrent plug-flow reactors with intercormecting distributed flows, (c) plug-flow and weU-mixed reactors in series, and (d) 2ero-interniixing model, in which plug-flow reactors are parallel and a distribution of residence times dupHcates that...

Analytical solutions also are possible when T is constant and m = 0, V2, or 2. More complex chemical rate equations will require numerical solutions. Such rate equations are apphed to the sizing of plug flow, CSTR, and dispersion reactor models by Ramachandran and Chaud-hari (Three-Pha.se Chemical Reactors, Gordon and Breach, 1983). 

Atwood et al, (1989) developed a reactor model that included axial and radial mass and heat dispersions to compare the performance of laboratory... 

The effectiveness of a fluidized bed as a ehemical reactor depends to a large extent on the amount of convective and diffusive transfer between bubble gas and emulsion phase, since reaction usually occurs only when gas and solids are in contact. Often gas in the bubble cloud complex passes through the reactor in plug flow with little back mixing, while the solids are assumed to be well mixed. Actual reactor models depend greatly on kinetics and fluidization characteristics and become too complex to treat here. 

Figure 12-31. Block flow diagram showing the reaction kinetics and thermodynamics needed to create a reactor model. (Source Reproduced with permission of the AlChE. Copyright 1996 AlChE. All rights reserved.)...

Figure 8.12 Gas-liquid reactor model (Yagi, 19H6) where...

Donnet, M., Jongen, N., Lemaitre, J., Bowen, P. and Hofmann, H., 1999. Better control of nucleation and phase purity using a new segmented flow tubular reactor Model system Precipitation of calcium oxalate. In 14th International Symposium on Industrial Crystallization. Cambridge, U.K., September 12-16, Institution of Chemical Engineers, CD ROM, pp. 1-13. 

Since it is a conceptual study employing a theoretical reactor model, it is also important to appreciate the limits of this type of investigation. The advantage of the computer investigation over a pilot or production reactor investigation is the obvious cost and time saving over the real reactor experiment. 

A theoretical polymerization tubular reactor model was used to study the effects of reactor operating parameters on conversion... 

Mixing Models. The assumption of perfect or micro-mixing is frequently made for continuous stirred tank reactors and the ensuing reactor model used for design and optimization studies. For well-agitated reactors with moderate reaction rates and for reaction media which are not too viscous, this model is often justified. Micro-mixed reactors are characterized by uniform concentrations throughout the reactor and an exponential residence time distribution function. 

To differentiate between the micro-mixed reactor with dead-polymer and the by-pass reactor models in this investigation, the effect of mixing speed on the value of "( )" was observed. As illustrated in Table V, the value (j>" is not observed to increase with decreasing mixing speed as would be expected for a by-pass reactor. This rules out the possibility of a by-pass model and further substantiates the dead-polymer model. 

Deposition of TiN by the thermal decomposition of tetrakis(dimethylamido)titanium (TDMAT) in a nitrogen atmosphere (as opposed to ammonia) was characterized by a simple Arrhenius rate expression. Adequate deposition rates and good step coverage were achieved for 3/1 aspect ratio holes, 0.40 micron in size. A reactor model was designed,... 

The selectivity is 100% in this simple example, but do not believe it. Many things happen at 625°C, and the actual effluent contains substantial amounts of carbon dioxide, benzene, toluene, methane, and ethylene in addition to styrene, ethylbenzene, and hydrogen. It contains small but troublesome amounts of diethyl benzene, divinyl benzene, and phenyl acetylene. The actual selectivity is about 90%. A good kinetic model would account for aU the important by-products and would even reflect the age of the catalyst. A good reactor model would, at a minimum, include the temperature change due to reaction. 

Reactor models consisting of series and parallel combinations of ideal reactors... 

McLaughlin, H. S., Mallikarjun, R., and Nauman, E. B., The Effect of Radial Velocities on Laminar Flow, Tubular Reactor Models, AIChE J., 32, 419-425 (1986). 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

The completely segregated stirred tank can be modeled as a set of piston flow reactors in parallel, with the lengths of the individual piston flow elements being distributed exponentially. Any residence time distribution can be modeled as piston flow elements in parallel. Simply divide the flow evenly between the elements and then cut the tubes so that they match the shape of the washout function. See Figure 15.12. A reactor modeled in this way is said to be completely segregated. Its outlet concentration is found by averaging the concentrations of the individual PFRs ... 

Two reactors were built and put into operation. The design of the first reactor was based on minimal intermediate reactor modeling and subsequently operated for less than 4 h in the laboratory. From the pictures of the reactor after operation, shown in Figure 11.9, and operational pressure-drop data, shown in Figure 11.10, it was readily concluded that carbon deposition was a problem. A second reactor was designed with the full use of an intermediate model to overcome initially unrecognized limitations in the first reactor. 

Steady performance data from the second reactor are shown in Figure 11.10, where the pressure drop did not rise exponentially and the conversion and selectivity remained at 75 and 83%, respectively. The reactor was further analyzed after operation, shown in Figure 11.11, to confirm the lack of carbon deposition. Reactor models were pivotal to developing a robust design for this high-temperature and... 

---