The Ideal Well-Stirred Batch Reactor

The rate at which heat is transferred to a system can be expressed in terms of an overall heat transfer coefficient U, the area through which the heat exchange occurs and on which U is based, and the difference between the temperature of the heat source (or sink) and that of the reactor contents T  

This expression may be combined with equations (10.1.4) and (10.1.8) in order to analyze the different situations that may arise in operating the various types of ideal reactors. These analyses are the subject of Sections 10.2 to 10.4. 

The key assumption on which the design analysis of a batch reactor is based is that the degree of agitation is sufficient to ensure that the composition and temperature of the contents are uniform throughout the reaction vessel. Under these conditions one may write the material and energy balances on the entire contents of the reaction vessel. 

If one considers a batch reactor in which the chemistiy is characterized by a single extent of reaction, the material balance analysis presented in Section 8.1 indicates that the holding time necessary to change the fraction conversion from/ i to/A2 is given by 

For operation in a constant pressure nonisothermal mode with a relatively low pressure gas phase reaction, it is convenient to approximate the reactor volume by 

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The above equations were already encountered in Section 1.1.2 of Chapter 1. The equations defining reaction rates were written there for a point , a volume in which the composition is uniform. This is also assumed here for the ideal, well stirred batch reactor, whatever its volume. 

Three ideal reactor types are relevant from reactor theory [15], the two continuous flow types, the plug flow reactor (PFR) and continuous flow stirred tank reactor (CSTR), and the well-stirred batch reactor. The... 

The reactor in which chemical reactions lake place is fhe mosl imporlanl piece of equipmenl in each chemical planl. A variety of reactors are used in induslry, bul all of Ihem can be assigned to cerlain basic types or a combination of fhese ideal reactors [53] (1) bafch slirred-lank reactor, (2) continuous slirred-lank reactor, and (3) lubular reactor. The ideal slirred-lank bafch reactor is characterized by complete mixing, while in the ideal tubular reactor, plug flow is assumed. In contrast to the stirred-tank batch reactor with well-defined residence time, the continuous stirred-tank reactor has a very broad residence-time distribution. In... 

In the analysis of batch reactors, the two flow terms in equation (8.0.1) are omitted. For continuous flow reactors operating at steady state, the accumulation term is omitted. However, for the analysis of continuous flow reactors under transient conditions and for semibatch reactors, it may be necessary to retain all four terms. For ideal well-stirred reactors, the composition and temperature are uniform throughout the reactor and all volume elements are identical. Hence, the material balance may be written over the entire reactor in the analysis of an individual stirred tank. For tubular flow reactors the composition is not independent of position and the balance must be written on a differential element of reactor volume and then integrated over the entire reactor using appropriate flow conditions and concentration and temperature profiles. When non-steady-state conditions are involved, it will be necessary to integrate over time as well as over volume to determine the performance characteristics of the reactor. 

Chapter 2 treated multiple and complex reactions in an ideal batch reactor. The reactor was ideal in the sense that mixing was assumed to be instantaneous and complete throughout the vessel. Real batch reactors will approximate ideal behavior when the characteristic time for mixing is short compared with the reaction half-life. Industrial batch reactors have inlet and outlet ports and an agitation system. The same hardware can be converted to continuous operation. To do this, just feed and discharge continuously. If the reactor is well mixed in the batch mode, it is likely to remain so in the continuous mode, as least for the same reaction. The assumption of instantaneous and perfect mixing remains a reasonable approximation, but the batch reactor has become a continuous-flow stirred tank. 

Ideal mixing and plug flow. The batch, contlnuous-stirred-tank, and plug-flow reactors are defined by certain idealized assumptions on the fluid flow. The batch and continuous-stirred-tank reactors are assumed to be ideally well mixed, which means that the temperature, pressure and species concentrations are independent of spatial position within the reactor. The plug-flow reactor describes a special type of flow in a itube in which the fluid.is well.mixed in the radial direction and varies... 

In a batch reactor, there is no inflow or outflow of reactants. It is a commonly used apparatus in the fine and pharmaceutical industry as well as in laboratories because of its flexibility and multifunctionality. The ideal stirred tank reactor is characterized by complete mixing down to the molecular level. Therefore, no concentration or temperature gradients exist. The system volume (Figure 2.1) corresponds to the volume occupied by the reaction mixture as indicated in Figure 2.3. As reactants are neither added nor removed during the reaction time (batch time), the mass balance Equation 2.1 simplifies to... 

Hot spring pools are usually well stirred by thermal convection and rising gas bubbles, so they can be modeled as ideal batch reactors and the volume of water in the pool can be determined using a tracer spike. 

In addition to processes involving gas-liquid reactions, stirred-tank reactors can also be used for single (liquid)-phase reactions. Moreover, their operation is not limited to the continuous mode, and they can be easily adapted for use in semibatch and batch modes. The absence of a gas phase does not pose important structural and operational differences from those stated earlier for multiphase systems. However, in the case of single-phase operation, the aspect ratio is usually kept lower ( 1) to ensure well mixing of the reactive liquid. Regardless of the number of phases involved, stirred-tank reactors can approach their ideal states if perfect mixing is established. Under such conditions, it is assumed that reaction takes place immediately just... 

There are three idealized flow reactors fed-batch or semibatch, continuously stirred tank, and the plug flow tubular. Each of these is pictured in Figure 1. The fed-batch and continuously stirred reactors are both taken as being well mixed. This means that there is no spatial dependence in the concentration variables for each of the components. At any point within the reactor, each component has the same concentration as it does anywhere else. The consequence... 

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