Reactions at variable volume

Increasing ba (when sa 0, expansion), the ratio between the reactors volume, 

Butanol and monobutylphthalate (MBF) react in the presence of H2SO4 forming dibutylphthalate and water. Reaction can be carried out in CSTR or PFR reactor. The reactants are placed in two separate tanks containing 0.2mol/L of MBF and 1 mol/L of butanol and fed to the reactor under lOL/h and 30L/h, respectively. The reactants are mixed before entering the reactor. The reaction rate constant is k = 7.4 X 10 L/(mol min). Calculate the CSTR and PFR volume separately and show the relation between the volumes when conversion is 70%. 

Reaction rate expression -ya = CaCb, where A = Butanol and B = MBF (reactants). Total volumetric flow in the reactor entrance  

Therefore, the CSTR volume, with = 40 L/h is Vcsto = 520L In the PFR  

the ratio between CSTR and PFR volumes will be VcSTR 

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The typical reaction at variable volume can be represented as follows ... 

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 molar flows of the other components can be determined as a function of the conversion. We then obtain the following relations, which are valid for the reactions at variable or constant volume ... 

If the reaction occurs at variable volume or variation in the number of moles, the volumetric flow will be v = vo(l + baXa). Substituting this expression Equation 14.46, we have ... 

The kinetics of the reactions is known. The acetaldehyde decomposition is of second order at variable volume and the ethane decomposition is of first order according to the unit of the rate constants. 

PFR. If the reaction takes place at variable volume, then the average residence times are different from the space times and as a consequence, the volumes are not proportional. 

Thus the rate of reaction at constant volume is seen to be equal to the derivative of the conversion variable x with respect to time. 

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 ... 

The plot of residuals versus some measure of the time at which experiments were run can also be informative. If the number of hours on stream or the cumulative volume of feed passed through the reactor is used, nonrandom residuals could indicate improper treatment of catalyst-activity decay. In the same fashion that residuals can indicate variables not taken into account in predicting reaction rates, variables not taken into account as affecting activity decay can thus be ascertained. 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

It is evident that for multiple reactions with variable density, we rapidly arrive at rather complex expressions that require considerable manipulation even to formulate the expressions, which can be used to calculate numerical values of the reactor volume required for a given conversion and selectivity to a desired product. 

In a system in which there are P pure condensed phases and one chemical reaction at equilibrium, there are (P —1) components. The system is thus univariant and hence indifferent. The state of the system is defined by assigning a value to at least one extensive variable in addition to the mole numbers of the species. The extent of the reaction taking place within the system is dependent upon the value of the additional extensive variable. A simple example is a phase transition of a pure compound when the change of phase is considered as a reaction. We consider the two phases as two species in the one-component system. In order to define the state of the system, we assign values to the volume of the system in addition to the temperature and mole number of the component. For the given temperature and mole number, the number of moles of the component in each phase is determined by the assigned volume. 

One important issue of the fed-batch operation is the variable volume of material in the reactor and its effect on heat transfer area. If jacket cooling is used, the heat transfer area covered by the liquid in the reactor will be proportional to the volume of the liquid at any point in time. However, if the reaction liquid is circulated through an external heat exchanger, the full heat transfer area is available throughout the batch cycle. 

Batch Reactor. In a batch reactor there are no inlet or outlet streams In = Out = 0. The total feed is charged into the reactor at the beginning and no withdrawal is made until the desired conversion level has been reached. Hence a reaction process occurring in a batch reactor is an unsteady one. All variables change with time. In addition, we assume that it is a perfectly mixed batch reactor, so that the concentrations of the reaction components, reactants or products are the same over the whole reactor volume. This assumption allows us to consider applying the mole balance equation across the whole reactor. With the term reactor we mean the space where the reaction(s) take place. For liquid phase reactions the reactor volume is smaller than the size of the physical reactor. It is the volume of the liquid phase, where the reaction ) take(s) place. 

Here, the temperature, pressure, and chemical potential are estimated at ambient conditions. For an optimal control problem, one must specify (i) control variables, volume, rate, voltage, and limits on the variables, (ii) equations that show the time evolution of the system which are usually differential equations describing heat transfer and chemical reactions, (iii) constraints imposed on the system such as conservation equations, and (iv) objective function, which is usually in integral form for the required quantity to be optimized. The value of process time may be fixed or may be part of the optimization. 

B. Pressure and Volume. Two of the other important system variables which are usually at our disposal experimentally are volume and pressure. In the study of reactions between gases it is possible to keep either the pressure or the volume of the system fixed. The simplest procedure is to maintain a gas system in a vessel at fixed volume. For reactions in liquid and solid systems, the pressure is most conveniently controlled, volume control being either unimportant or unattainable owing to the small coefficient of compressibility of liquids. ... 

As an extension of Exercise 15, consider the reversible, elementary, gas phase reaction of A and B to form C occurring at 300 K in a variable volume (constant pressure) reactor with an initial volume of 1.0 L. For a reactant charge to the reactor of 1.0 mol of A, 2.0 mol of B, and no C, find the equilibrium conversion of A. Plot the composition in the reactor and the reactor volume as a function of time. 

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 ... 

For reactions at constant pressure, a thermodynamic variable called enthalpy H) eliminates the need to consider PV work separately. The enthalpy of a system is defined as the internal energy plus the product of the pressure and volume ... 

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