Reactors Continuous-stirred tank

Assume perfect or ideal mixing, the steady-state material balance for the CSTR reactor 

The second-order reaction rate with respect to component A, 

The CSTR reactor volume a function of fractional conversion, 

Find the reactor volume that achieves 94% conversion of ethanol, for the following liquid-phase reaction in an isothermal CSTR. The inlet molar flow rate is 50 kgmol/h ethanol, 50 kmol/h diethylamine, and 100 kgmol/h water. The reaction is in second order with respect to ethanol 

The steady-state material balance on the CSTR reactor 

we can develop the material balance equation starting from the general balance eqnation given earlier, noting that there is no accumulation within the reactor (this system operates at steady state). 

Since the composition of the fluid inside the reactor is identical everywhere, the reaction rate must be the same everywhere. We replace the integral with a simple multiplication, which provides 

We frequently prefer to define reaction rates in terms of concentration. In order to make this transformation, we need to define the mean residence time, which is the average length of time that an element of fluid remains within the reactor. The residence time can be calculated from the volumetric flow rate and the volume of the reactor. 

we write the molar flow rate as F.= C. Vj, and the volume as V= Ty, which provides the required residence time as a function of concentration 

Finally, we can rewrite the equation in terms of the reactant conversion 

FIGURE 6.23 Schematic representatian of a continuous stirred tank reactor. 

The birth and death functions are assumed for simplidly to be zero. The solution to this differential equation is given by 

The size distribution is solely determined by the mean residence time and the rates of nucleation and growth. In general, the total number of particles present in the system can be calculated by the following integral  

1 Continuous Stirred Tank Reactor with Recycle 

Continuous flow reactors are almost always operated at steady state. We will consider three types the continuous stirred tank reactor (CSTR). the plug flow reactor (PFR). and the packed bed reactor (PBR). Detailed descriptions of these reactors can be found in both the Professional Reference Shelf (PRS) for Chapter 1 and in the Visual Encyclopedia of Equipinent on the CD-ROM, 

F ijtiire l 7ta) CSTR/batch reactor, [Courtesy of Pfaudter, tnc.l 

The CSTR design equation gives the reactor volume V necessary to reduce the entering flow rate of species j, from to the exit flow rate Fj, when species j is di.sappearing at a rate of -r. We note that the CSTR is modeled such that the conditions in the exit stream (e.g.. concentration, temperature) are iden-lical to those in the tank. The molar flow rate Ff is just the product of the concentration of species j and the volumetric flow rate v  

Consequently, we could combine Equations (1-7) and f 1-8) to write a balance on species A as 

When is [ubular reactor mosi often used  

In this section we discuss in a qualitative way the classical types of reactors batch, continuous stirred-tank reactor (CSTR), and plug flow reactor (PFR). Our purpose is to point out the features of each that impact the ease or difficulty of their temperature control. 

This characteristic of a CSTR immediately generates an inherent weakness of the CSTR type of reactor, that is, the concentration of reactant in the vessel is the same as the concentration of reactant in the product. The concentration of reactant is inversely related to conversion. 

If a high conversion is desired, the reactant concentration must be small. But the reaction rate depends directly on the reactant concentration. It also depends on the reactor volume. So, if a high conversion desired, the reactor must be large to compensate for the small reactant concentration. Thus a single CSTR is seldom used if high conversion is desired. Of course, using several CSTRs in series is one way to reduce the total reactor volume because only the last vessel will have the small reactant concentration. 

We will develop detailed steady-state and dynamic mathematical models of CSTRs in Chapters 2 and 3 with several types of reactions and quantitatively explore the effect of kinetic and design parameters on controllability. For the moment, let us just make some qualitative observations. There are several features of a CSTR that impact controllability  

A variety of methods and configurations can be used for heat transfer. These are described in Section 1.5. Since heat transfer is one of the key issues in reactor control, the CSTR is usually more easily controlled than a tubular reactor. It is physically difficult to adjust the heat removal down the length of a tubular reactor. 

In order to model a continuously operating reactor a feed and a removal term with a volumetric flow of V m s are added to Eq. (3.6). It is supposed that the volume of the reactor contents does not change. Differences in composition are expressed via the concentrations Cj,in and Cj in mol m . In line with the assumption of an ideally stirred reactor, the composition of the substances flowing out of the reactor is the same as that inside the reactor. We obtain 

The heat balance is treated analogously. Equation (3.16) is extended by a term representing enthalpy feed (V Cp,in Tin) and one for enthalpy removal 

Example 3.6 Determination of material concentrations for the stationary operation of a reactor 

The nitration of hexamethylenetetramine (hexamine) takes place in a continuous stirred tank reactor (CSTR). The following data apply 

Feed and removal volumetric flow Concentration of hexamine in feed Molar mass of hexamine Concentration of nitric acid in feed Molar mass of nitric acid Pre-exponential factor Apparent energy of activation Order of the reaction Thermal capacity of hexamine Feed temperature of hexamine Thermal capacity of nitric acid Feed temperature of nitric acid Overall coefficient of heat transfer Area for heat transfer (jacket + coU) Enthalpy of reaction Reaction temperature 

The plot of (Cs0 - Cs) /ln(CSo/Cs) versus t/ln(CsJCs) may yield a straight line with a slope of rmax and an intercept of -Kh 

A continuous stirred-tank reactor (CSTR) is an ideal reactor which is based on the assumption that the reactor contents are well mixed. Therefore, the concentrations of the various components of the outlet stream are assumed to be the same as the concentrations of these components in the reactor. Continuous operation of the enzyme reactor can increase the productivity of the reactor significantly by eliminating the downtime. It is also easy to automate in order to reduce labor costs. 

For the steady-state CSTR, the substrate concentration of the reactor should be constant. Therefore, dCs/dt is equal to zero. If the Michaelis-Menten equation can be used for the rate of substrate consumption (rs), Eq. (2.39) can be rearranged as  

Michaelis-Menten kinetic parameters can also be estimated by running a series of steady-state CSTR runs with various flow rates and plotting Cs versus (Cst)/(CSq- Cs). Another approach is to use the Langmuir plot (Csr vs Cs) after calculating the reaction rate at different flow rates. The reaction rate can be calculated from the relationship r = F (CSq - Cs)/V. However, the initial rate approach described in Section 2.2.4 is a better way to estimate the kinetic parameters than this method because steady-state CSTR runs are much more difficult to make than batch runs. 

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Some slurry processes use continuous stirred tank reactors and relatively heavy solvents (57) these ate employed by such companies as Hoechst, Montedison, Mitsubishi, Dow, and Nissan. In the Hoechst process (Eig. 4), hexane is used as the diluent. Reactors usually operate at 80—90°C and a total pressure of 1—3 MPa (10—30 psi). The solvent, ethylene, catalyst components, and hydrogen are all continuously fed into the reactor. The residence time of catalyst particles in the reactor is two to three hours. The polymer slurry may be transferred into a smaller reactor for post-polymerization. In most cases, molecular weight of polymer is controlled by the addition of hydrogen to both reactors. After the slurry exits the second reactor, the total charge is separated by a centrifuge into a Hquid stream and soHd polymer. The solvent is then steam-stripped from wet polymer, purified, and returned to the main reactor the wet polymer is dried and pelletized. Variations of this process are widely used throughout the world. 

Third-generation high yield supported catalysts are also used in processes in which Hquid monomer is polymerized in continuous stirred tank reactors. The Hypol process (Mitsui Petrochemical), utilizes the same supported catalyst technology as the Spheripol process (133). Rexene has converted the hquid monomer process to the newer high yield catalysts. Shell uses its high yield (SHAC) catalysts to produce homopolymers and random copolymers in the Lippshac process (130). 

Processes. Toluene is nitrated ia two stages. Mononitration occurs ia mixed acid, 30% HNO and 55% H2SO4, at 30—70°C ia a series of continuous stirred-tank reactors. Heat is Hberated and must be removed. The isomer distribution is approximately 58% o-nitrotoluene 38% -nitrotoluene, and 4% y -nitrotoluene (Fig. 1). 

A process based on a nickel catalyst, either supported or Raney type, is described ia Olin Mathieson patents (26,27). The reduction is carried out ia a continuous stirred tank reactor with a concentric filter element built iato the reactor so that the catalyst remains ia the reaction 2one. Methanol is used as a solvent. Reaction conditions are 2.4—3.5 MPa (350—500 psi), 120—140°C. Keeping the catalyst iaside the reactor iacreases catalyst lifetime by maintaining a hydrogen atmosphere on its surface at all times and minimises handling losses. Periodic cleaning of the filter element is required. 

Copolymers are typically manufactured using weU-mixed continuous-stirred tank reactor (cstr) processes, where the lack of composition drift does not cause loss of transparency. SAN copolymers prepared in batch or continuous plug-flow processes, on the other hand, are typically hazy on account of composition drift. SAN copolymers with as Httle as 4% by wt difference in acrylonitrile composition are immiscible (44). SAN is extremely incompatible with PS as Httle as 50 ppm of PS contamination in SAN causes haze. Copolymers with over 30 wt % acrylonitrile are available and have good barrier properties. If the acrylonitrile content of the copolymer is increased to >40 wt %, the copolymer becomes ductile. These copolymers also constitute the rigid matrix phase of the ABS engineering plastics. 

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). 

Despite the higher cost compared with ordinary catalysts, such as sulfuric or hydrochloric acid, the cation exchangers present several features that make their use economical. The abiHty to use these agents in a fixed-bed reactor operation makes them attractive for a continuous process (50,51). Cation-exchange catalysts can be used also in continuous stirred tank reactor (CSTR) operation. 

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. 

Continuous stirred tank reactor Dispersion coefficient Effective diffusivity Knudsen diffusivity Residence time distribution Normalized residence time distribution... 

Experimental data that are most easily obtained are of (C, t), (p, t), (/ t), or (C, T, t). Values of the rate are obtainable directly from measurements on a continuous stirred tank reactor (CSTR), or they may be obtained from (C, t) data by numerical means, usually by first curve fitting and then differentiating. When other properties are measured to follow the course of reaction—say, conductivity—those measurements are best converted to concentrations before kinetic analysis is started. 

Continuous stirred tank reactors (CSTRs) are frequently employed multiply and in series. Reactants are continuously fed to the first vessel they overflow through the others in succession, while being thor-... 

Continuous. stirred tank reactor (CSTR), with the effluent concentration the same as the uniform vessel concentration. With a mean residence time t = V /V, the material balance is... 

The experimental unit, shown on the previous page, is the simplest assembly that can be used for high-pressure kinetic studies and catalyst testing. The experimental method is measurement of the rate of reaction in a CSTR (Continuous Stirred Tank Reactor) by a steady-state method. 

In previous studies, the main tool for process improvement was the tubular reactor. This small version of an industrial reactor tube had to be operated at less severe conditions than the industrial-size reactor. Even then, isothermal conditions could never be achieved and kinetic interpretation was ambiguous. Obviously, better tools and techniques were needed for every part of the project. In particular, a better experimental reactor had to be developed that could produce more precise results at well defined conditions. By that time many home-built recycle reactors (RRs), spinning basket reactors and other laboratory continuous stirred tank reactors (CSTRs) were in use and the subject of publications. Most of these served the original author and his reaction well but few could generate the mass velocities used in actual production units. 

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. 

If the mixing is "perfect," tlie estuary behavior may be approximated by what chemical engineers define as a continuous stirred tank reactor (CSTR) (5). However, accurately estimating the time and spatial beliavior of water quality in estuaries is complicated by the effects of tidal motion as just described. The upstream and downstream currents produce substantial variations of water quality at certain points in the estuary, and tlie calculation of such variation is indeed a complicated problem. How ei er, the following simplifications provide some reiiitirkably useful results in estimating the distribution of estuarine water quality. 

During the manufacturing process, if the grafting increases during early stages of the reaction, the phase volume will also increase, but the size of the particles will remain constant [146-148]. Furthermore, reactor choice plays a decisive role. If the continuous stirred tank reactor (CSTR) is used, little grafting takes place and the occlusion is poor and, consequently, the rubber efficiency is poor. However, in processes akin to the discontinuous system(e.g., tower/cascade reactors), the dispersed phase contains a large number of big inclusions. 

Frequently, stirred tanks are used with a continuous flow of material in on one side of the tank and with a continuous outflow from the other. A particular application is the use of the tank as a continuous stirred-tank reactor (CSTR). Inevitably, there will be a vety wide range of residence times for elements of fluid in the tank. Even if the mixing is so rapid that the contents of the tank are always virtually uniform in composition, some elements of fluid will almost immediately flow to the outlet point and others will continue circulating in the tank for a very long period before leaving. The mean residence time of fluid in the tank is given by ... 

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