Example Chemical Reactor

It is easy to model the microfluidic device as a chemical reactor. You prepare the flow problem as illustrated in Chapter 10, add the convective diffusion equation, and enter the reaction rate. Suppose the rate of reaction is 

Step 1 Under Multiphysics, select the Convection and Diffusion option. 

Step 2 Under Physics/Subdomain Settings, select the domain and enter the reaction rate in the window for R, the reaction rate. The equation listed at the top is 

---

Very often the choice is not available. For example, if reactor temperature is above the critical temperature of the chemical species, then the reactor must be gas phase. Even if the temperature can be lowered below critical, an extremely high pressure may be required to operate in the liquid phase. 

Ratio and Multiplicative Feedforward Control. In many physical and chemical processes and portions thereof, it is important to maintain a desired ratio between certain input (independent) variables in order to control certain output (dependent) variables (1,3,6). For example, it is important to maintain the ratio of reactants in certain chemical reactors to control conversion and selectivity the ratio of energy input to material input in a distillation column to control separation the ratio of energy input to material flow in a process heater to control the outlet temperature the fuel—air ratio to ensure proper combustion in a furnace and the ratio of blending components in a blending process. Indeed, the value of maintaining the ratio of independent variables in order more easily to control an output variable occurs in virtually every class of unit operation. 

Next consider the case that uses randomized blocking to eliminate the effect of some variable whose effect is of no interest, such as the batch-to-batch variation of the catalysts in the chemical reactor example. Suppose there are k treatments and n experiments in each treatment. The results from nk experiments can be arranged as shown in the block design table within each block, the various treatments are applied in a random order. Compute the block average, the treatment average, as well as the grand average as before. 

Other types of selective systems employ multiple final control elements or multiple controllers. In some applications, several manipulated variables are used to control a single process variable (also called split-range control). Typical examples include the adjustment of both inflow and outflow from a chemic reactor in order to control reactor pressure or the use of both acid and base to control pH in waste-water treatment. In this approach, the selector chooses from several controller outputs which final control element should be adjusted (Marlin, Process Control, McGraw-Hill, New York, 1995). 

An industrial chemical reacdor is a complex device in which heat transfer, mass transfer, diffusion, and friction may occur along with chemical reaction, and it must be safe and controllable. In large vessels, questions of mixing of reactants, flow distribution, residence time distribution, and efficient utilization of the surface of porous catalysts also arise. A particular process can be dominated by one of these factors or by several of them for example, a reactor may on occasion be predominantly a heat exchanger or a mass-transfer device. A successful commercial unit is an economic balance of all these factors. 

A number of successful devices have been in use for finding mass-transfer coefficients, some of which are sketched in Fig. 23-29, and all of which have known or adjustable interfacial areas. Such laboratoiy testing is reviewed, for example, by Danckwerts (Ga.s-Liquid Reac-tion.s, McGraw-Hih, 1970) and Charpentier (in Ginetto and Silveston, eds., Multiphase Chemical Reactor Theory, De.sign, Scaleup, Hemisphere, 1986). 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Once a decision to use QRA has been made, you must decide whether frequency and/or consequence information is required (Steps 6 and 7). In some cases you may simply need frequency information to make your decision. For example, suppose you wish to evaluate the adequacy of operating procedures and safety systems associated with a chemical reactor. The main hazard of concern is that the reactor could experience a violent runaway exothermic reaction. You believe that you know enough about the severe consequences of a runaway and nothing more will be gained by quantifying the consequences of potential run-... 

In a chemical production process at least one of the unit operations (the chemical reactor) is the place in which chemical conversion takes place. However, the chemical upstream reactor is proceeded by a series of unit operations in which the new materials are downstream prepared (the upstream operations). After conversion has taken place, the products are operations subjected to a further series of unit operations (the downstream operations). These downstream operations include product recovery and purification steps. A typical example of a production process is illustrated in Figure 1.1. 

Chemical engineers of the future will be integrating a wider range of scales than at r other branch of engineering. For example, some may work to relate the macroscale of the environment to the mesoscale of combustion systems and the microscale of molecular reactions and transport (see Chapter 7). Others may work to relate the macroscale performance of a composite aircraft to the mesoscale chemical reactor in which the wing was formed, the design of the reactor perhaps having been influenced by studies of the microscale dynamics of complex liquids (see Chapter 5). 

Why are the CSTRs worth considering at all They are more expensive per unit volume and less efficient as chemical reactors (except for autocatalysis). In fact, CSTRs are useful for some multiphase reactions, but that is not the situation here. Their potential justification in this example is temperature control. BoiUng (autorefrigerated) reactors can be kept precisely at the desired temperature. The shell-and-tube reactors cost less but offer less effective temperature control. Adiabatic reactors have no control at all, except that can be set. 

Other model representations of flow mixing cases in chemical reactors are described by Levenspiel (1972), Fogler (1992) and Szekely and Themelis (1971). Simulation tank examples demonstrating non-ideal mixing phenomena are CSTR, NOSTR, TUBMIX, MIXFLO, GASLIQ and SPBEDRTD. 

Where heat is generated in the system for example, in a chemical reactor ... 

This section is a review of the properties of a first order differential equation model. Our Chapter 2 examples of mixed vessels, stined-tank heater, and homework problems of isothermal stirred-tank chemical reactors all fall into this category. Furthermore, the differential equation may represent either a process or a control system. What we cover here applies to any problem or situation as long as it can be described by a linear first order differential equation. 

We use this example to illustrate how state space representation can handle complex models. First, we make use of the solution to Review Problem 2 in Chapter 3 (p. 3-18) and write the mass balances of reactant A in chemical reactors 1 and 2 ... 

Once the product specifications have been fixed, some decisions need to be made regarding the reaction path. There are sometimes different paths to the same product. For example, suppose ethanol is to be manufactured. Ethylene could be used as a raw material and reacted with water to produce ethanol. An alternative would be to start with methanol as a raw material and react it with synthesis gas (a mixture of carbon monoxide and hydrogen) to produce the same product. These two paths employ chemical reactor technology. A third path could employ a biochemical reaction (or fermentation) that exploits the metabolic processes of microorganisms in a biochemical reactor. Ethanol could therefore also be manufactured by fermentation of a carbohydrate. 

At the first level of detail, it is not necessary to know the internal parameters for all the units, since what is desired is just the overall performance. For example, in a heat exchanger design, it suffices to know the heat duty, the total area, and the temperatures of the output streams the details such as the percentage baffle cut, tube layout, or baffle spacing can be specified later when the details of the proposed plant are better defined. It is important to realize the level of detail modeled by a commercial computer program. For example, a chemical reactor could be modeled as an equilibrium reactor, in which the input stream is brought to a new temperature and pressure and the... 

---