Reactor volume variable

Solution The obvious way to solve this problem is to choose a pressure, calculate Oq using the ideal gas law, and then conduct a batch reaction at constant T and P. Equation (7.38) gives the reaction rate. Any reasonable values for n and kfCm. be used. Since there is a change in the number of moles upon reaction, a variable-volume reactor is needed. A straightforward but messy approach uses the methodology of Section 2.6 and solves component balances in terms of the number of moles, Na, Nb, and Nc-... 

The component balances with second-order kinetics for the variable volume reactor are as follows... 

A gas-phase reaction, A —> 2B, is conducted at 300 K (constant) in a variable-volume reactor equipped with a piston to maintain a constant pressure of 150 kPa. Initially, 8 mol of A are present in the reactor. The reaction is second-order with respect to A, with the following rate expression ... 

Figure 1-3 shows two different types of batch reactors used for gas-phase reactions. Reactor A is a constant-volume (variable-pressure) reactor and Reactor B is a constant-pressure (variable-volume) reactor. At time r = 0, the reactants are injected into the reactor and the reaction is initiated. To see clearly the different forms the mole balance will take for eadi type of reactor, consider the follovring examples, in which the gas-phase decomposition of dimethyl ether is taking place to form methane, hydrogen, and carbon monoxide ... 

The implementation of a variable-volume reactor could be seen as not practical, because the reactor is an expensive equipment item whose volume should be effectively used. In fact, sizing properly the reactor should ensure by design the required flexibility to large variations in throughput. However, the rule of limiting the variation of recycles... 

Variable Volume Reactor with Constant Rate of Inflow Scheme 2... 

In these definitions, Qr and Kr have been used as arbitrary normalizing parameters. They can be readily identified for a constant volume reactor Qr = Qo = Qf = Q< 3nd Vr = y = Vm where represents the maximum volume of the reactor (in other words, the volume at which the reactor would function as a constant volume CSTR). Clearly, in this case f = F/Q = Fq/Qo is the true residence time. However, for the variable volume reactor, Qr and Fr have to be selected carefully on a case by case basis, and the residence time r= Fr/Qr should be regarded as no more than a parameter whose dimension is time or simply as pseudoresidence time. Using these dimensionless parameters (with normalizing variables different from those for an MFR), the general material balance of Equation 10.22 can be expressed as... 

MEASURES OF MIXING COMPARISON OF THE SERIES. RECYCLE, AND VARIABLE VOLUME REACTORS... 

Arbitrarily chosen volume parameter of the variable volume reactor, m. Reactor volume, often referred to merely as F, m. ... 

Variable-volume reactor with constant rate of inflow Scheme 2... 

Variable-volume reactor with constant rate of outflow of one of the products Scheme 3 In this scheme [Figure 2.10(3)], ... 

Solution. Note that this is a variable volume reactor since it operates at a constant temperature and pressure. The rate expression for the reaction, r, is... 

As pointed out in the introduction to this section, the assumptions on which the classical RTD theory are based, are restrictive. However, it is still possible to use concepts like RTD or lAD when these assumptions are no longer valid - i.e. at unsteady state, in a compressible fluid, or in a variable volume reactor having large inlet and outlet ports - by using the population balance method. 

In order to integrate Eqn. (4-6), Na and each of the three concentrations on the right-hand side must be expressed as functions of a single variable that measures the progress of the reaction, i.e., that defines the composition of the reactor contents at any time. Moreover, if the volume V is not constant (independent of time and composition), we will need to express V as a function of either time or composition. First, we will revisit the constant-volume case. Then we will extend our analysis to the case of a variable-volume reactor. 

Apparatus description diagram. 1. Gas cylinder. 2. Valve. 3. Syringe pump. 4. Vent. 5. Variable-volume reactor with view windows. 6. Sample. 7. Temperature circulator. 8. Pressure gauge. 

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