Example Continuous Stirred Tank Reactor

Another type of reactor is known as a continuous, stirred-tank reactor (CSTR). This reactor is a vessel with an inlet stream and an outlet stream, and the contents are constantly being stirred. Engineers often assume that this reactor is so well mixed that the concentration is the same everywhere. The mole balance on this reactor is 

When the volumetric flow rates are constant, Eq. (8.13) becomes 

In a well-mixed reactor (CSTR), the concentration going out of the reactor is the same as the concentration in the reactor. Since the rate expression is a function of c, it is a function of Cou,. Then Eq. (8.15) becomes an algebraic equation in one variable (here) for Cq,. You can solve this using either Excel or MATLAB. 

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The nonlinearity of chemical processes received considerable attention in the chemical engineering literature. A large number of articles deal with stand-alone chemical reactors, as for example continuously stirred tank reactor (CSTR), tubular reactor with axial dispersion, and packed-bed reactor. The steady state and dynamic behaviour of these systems includes state multiplicity, isolated solutions, instability, sustained oscillations, and exotic phenomena as strange attractors and chaos. In all cases, the main source of nonlinearity is the positive feedback due to the recycle of heat, coupled with the dependence of the reaction rate versus temperature. 

Cooking extmders have been studied for the Uquefaction of starch, but the high temperature inactivation of the enzymes in the extmder demands doses 5—10 times higher than under conditions in a jet cooker (69). Eor example, continuous nonpressure cooking of wheat for the production of ethanol is carried out at 85°C in two continuous stirred tank reactors (CSTR) connected in series plug-fiow tube reactors may be included if only one CSTR is used (70). 

Over 25 years ago the coking factor of the radiant coil was empirically correlated to operating conditions (48). It has been assumed that the mass transfer of coke precursors from the bulk of the gas to the walls was controlling the rate of deposition (39). Kinetic models (24,49,50) were developed based on the chemical reaction at the wall as a controlling step. Bench-scale data (51—53) appear to indicate that a chemical reaction controls. However, flow regimes of bench-scale reactors are so different from the commercial furnaces that scale-up of bench-scale results caimot be confidently appHed to commercial furnaces. For example. Figure 3 shows the coke deposited on a controlled cylindrical specimen in a continuous stirred tank reactor (CSTR) and the rate of coke deposition. The deposition rate decreases with time and attains a pseudo steady value. Though this is achieved in a matter of rninutes in bench-scale reactors, it takes a few days in a commercial furnace. 

A continuous stirred tank reactor (CSTR) is usually much smaller than a batch reactor for a specific production rate. In addition to reduced inventory, using a CSTR usually results in other benefits which enhance safety, reduce costs, and improve the product quality. For example ... 

There are a variety of ways of accomplishing a particular unit operation. Alternative types of process equipment have different inherently safer characteristics such as inventory, operating conditions, operating techniques, mechanical complexity, and forgiveness (i.e., the process/unit operation is inclined to move itself toward a safe region, rather than unsafe). For example, to complete a reaction step, the designer could select a continuous stirred tank reactor (CSTR), a small tubular reactor, or a distillation tower to process the reaction. 

Various reactor combinations are used. For example, the product from a relatively low solids batch-mass reactor may be transferred to a suspension reactor (for HIPS), press (for PS), or unagitated batch tower (for PS) for finishing. In a similar fashion, the effluent from a continuous stirred tank reactor (CSTR) may be transferred to a tubular reactor or an unagitated or agitated tower for further polymerization before devolatilization. 

Establish ideal flow patterns This is usually assumed to be the case for plug-flow and continuously stirred tank reactors, but are all conditions for ideal mixing fulfilled For example, a rule of thumb is that the diameter d of the PFR should be at least lOx the diameter of the catalyst particles to eliminate the influence of the reactor wall. Also, the amount of catalyst should be sufficient to avoid axial gradients. Another rule is that the ratio of the bed length L to the reactor diameter d, i.e. L/d, should be >5-10. Higher values are preferable, but these may cause other problems such as temperature gradients and pressure drops. 

An nth-order reaction is run in a continuous stirred-tank reactor. The model and program are written in both dimensional and dimensionless forms. This example provides experience in the use of dimensionless equations. 

A cascade of three continuous stirred-tank reactors arranged in series, is used to carry out an exothermic, first-order chemical reaction. The reactors are jacketed for cooling water, and the flow of water through the cooling jackets is countercurrent to that of the reaction. A variety of control schemes can be employed and are of great importance, since the reactor scheme shows a multiplicity of possible stable operating points. This example is taken from the paper of Mukesh and Rao (1977). 

Continuous reactor a reactor characterized by a continuous flow of reactants into and a continuous flow of products from the reaction system examples are the plug flow reactor (PFR) and the continuous stirred tank reactor (CSTR). 

Example 2.3. Consider the same tank of perfectly mixed Hquid that we used in Example 2.1 except that a chemical reaction takes place in the liquid in the tank. The system is now a CSTR (continuous stirred-tank reactor) as shown in Fig. 2.3. Component A reacts irreversibly and at a specific reaction rate k to form product, component B. 

The catalyst components are generally dissolved in methyl acetate which acts as both reactant and solvent. Other solvents may be used and in fact, upon several batch recycles where lower boiling products are distilled off, the solvent is an ethylidene diacetate-acetic acid mixture. Any water introduced in the reaction mixture will be consumed via ester and anhydride hydrolysis, therefore anhydrous conditions are warranted. Typical batch reaction examples are presented in Table 1. There is generally sufficient reactivity when carbon monoxide and hydrogen are present at 200-500 psi. Similar results were obtained from the pilot plant using a continuous stirred tank reactor (CSTR). The reaction can also be run continuously over a supported catalyst with a feed of methyl acetate, methyl iodide, CO, and hydrogen. 

Pertinent examples of the value of dimensional analysis have been reported in a series of papers by Maa and Hsu (19,37,63). In their first report, they successfully established the scale-up requirements for microspheres produced by an emulsification process in continuously stirred tank reactors (CSTRs) (63). Their initial assumption was that the diameter of the microspheres, <7ms, is a function of phase quantities, physical properties of the dispersion and dispersed phases, and processing equipment parameters ... 

A continuous bulk polymerization process with three reaction zones in series has been developed. The degree of polymerization increases from the first reactor to the third reactor. Examples of suitable reactors include continuous stirred tank reactors, stirred tower reactors, axially segregated horizontal reactors, and pipe reactors with static mixers. The continuous stirred tank reactor type is advantageous, because it allows for precise independent control of the residence time in a given reactor by adjusting the level in a given reactor. Thus, the residence time of the polymer mixtures can be independently adjusted and optimized in each of the reactors in series (8). 

For a given load and conversion, the total volume of a CSTR (continuous stirred tank reactor) battery decreases with the number of stages, sharply at first and then more slowly. When the reaction is first order, for example, r = kC, the ratio of total reactor volume Vr of n stages to the volumetric feed rate Vq is represented by... 

An example of didactic distortion is the drawing of the phase-planes in Fig. 6, taken from A. Uppal, W. H. Ray, and A. B. Poore. On the dynamic behavior of continuous stirred tank reactors. Chem. Eng. Set 29, 967 (1974). 

Fig. 1.18. Continuous stirred-tank reactor worked example...

One of the simplest practical examples is the homogeneous nonisothermal and adiabatic continuous stirred tank reactor (CSTR), whose steady state is described by nonlinear transcendental equations and whose unsteady state is described by nonlinear ordinary differential equations. 

A number of innovative polymerization reactors using loop reactors, plug-flow and static mixer reactors, and continuous stirred-tank reactors have been reported. For example, Wilkinson and Geddes (15) describe a 50-liter reactor that has the same capacity as a 5000-gallon batch reactor. Extruders, thin-film evaporators, and other devices designed to provide intense mixing for viscous or unstable materials have also been used as reactors. 

The production of substances that preserve the food from contamination or from oxidation is another important field of membrane bioreactor. For example, the production of high amounts of propionic acid, commonly used as antifungal substance, was carried out by a continuous stirred-tank reactor associated with ultrafiltration cell recycle and a nanofiltration membrane [51] or the production of gluconic acid by the use of glucose oxidase in a bioreactor using P E S membranes [52]. Lactic acid is widely used as an acidulant, flavor additive, and preservative in the food, pharmaceutical, leather, and textile industries. As an intermediate product in mammalian metabolism, L( +) lactic acid is more important in the food industry than the D(—) isomer. The performance of an improved fermentation system, that is, a membrane cell-recycle bioreactors MCRB was studied [53, 54], the maximum productivity of 31.5 g/Lh was recorded, 10 times greater than the counterpart of the batch-fed fermentation [54]. 

Emulsion polymerization is usually carried out isothermally in batch or continuous stirred-tank reactors. Temperature control is much easier than for bulk or solution polymerization because the small ( 0.5 fim) polymer particles, which are the locus of the reaction, are suspended in a continuous aqueous medium. This complex, multiphase reactor also shows multiple steady states under isothermal conditions. In industrial practice, such a reactor often shows sustained oscillations. Solid-catalyzed olefin polymerization in a slurry batch reactor is a classic example of a slurry reactor where the solid particles change size and characteristics with time during the reaction process. 

Example 4.8 Chemical reactions and reacting flows The extension of the theory of linear nonequilibrium thermodynamics to nonlinear systems can describe systems far from equilibrium, such as open chemical reactions. Some chemical reactions may include multiple stationary states, periodic and nonperiodic oscillations, chemical waves, and spatial patterns. The determination of entropy of stationary states in a continuously stirred tank reactor may provide insight into the thermodynamics of open nonlinear systems and the optimum operating conditions of multiphase combustion. These conditions may be achieved by minimizing entropy production and the lost available work, which may lead to the maximum net energy output per unit mass of the flow at the reactor exit. 

An ideally mixed continuous stirred-tank reactor at steady state may serve as an example. The process rate —rA of consumption of a reactant A is finite, but is compensated by the inequality of the reactant mass-transfer rates into and out of the reactor. The result is a zero rate of change of the reactant concentration, dCA Idt, in the reactor and its effluent. 

Continuous stirred-tank reactors (CSTRs, see Figure 3.4) have the advantage over batch reactors that they are easier to keep at constant temperature. This is because they do not see the high initial reaction rate of batch reactors, and because continuous flow into and out of the reactor helps to consume or supply heat. For example, if the reaction is highly exothermic, the entering fluid may be introduced at a temperature below that of the reactor, so that it consumes heat as it is heated up. Another advantage is that samples can be taken from the effluent rather than... 

Example 2—Unstable CSTR with bounded output. Consider the reaction R P occurring in a nonisothermal jacket-cooled continuous stirred tank reactor (CSTR) with three steady states. A, B, C, corresponding to the intersection points of the two lines shown in Fig. 3 (Stephanopoulos,... 

Example 5—Stability dependence on the set of inputs. Consider a continuous stirred-tank reactor modeled by the following equations, in continuous time ... 

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