Constant density reactions

Also, from the definition of reactor conversion, for the special case of a constant density reaction mixture ... 

Thus, for a constant-density reaction in a BR, rA may be interpreted as the slope of the cA-t relation. This is illustrated in Figure 2.2, which also shows that rA itself depends on t, usually decreasing in nicgnitudc as the rcahon proceeds, with increasing t. ... 

If we combine this with the material-balance equation 2.2-10 for a constant-density reaction,... 

Consider a constant-density reaction with one reactant, A - products, as illustrated for a liquid-phase reaction in a CSTR in Figure 3.6. One experiment at steady-state generates one point value of (—rA) for the conditions (cA, q, T) chosen. This value is given by the material balance obtained in Section 2.3.2 ... 

For an nth-order isothermal, constant-density reaction in a BR or PFR (n 1), equa-... 

For a second-order, constant-density reaction, A - products, carried out in the vessel in... 

When we mention the constant-volume batch reactor we are really referring to the volume of reaction mixture, and not the volume of reactor. Thus, this term actually means a constant-density reaction system. Most liquid-phase reactions as well as all gas-phase reactions occurring in a constant-volume bomb fall in this class. 

Such processes are frequently bimolecular, irreversible, hence second-order ki-netically. When occurring in the liquid phase they are also essentially constant-density reactions. 

Solution Since this is a first-order constant-density reaction, Eqs. (4-7) and (4-8) give the conversions for single-stirred-tank and ideal tubular-flow reactors in terms of residence time VjQ. For multiple-stirred-tank reactors Eq. (A) of Example (4-9) is applicable. 

Consider a volume element of the reaction mixture in which the concentrations have unique values. For an irreversible first-order constant density reaction, Eqs. (1.1-6) and (l.M) lead to... 

We generally do not conduct gas-phase reactions in batch reactors. For a constant liquid volume, constant density reaction or process, the component balance for a laboratory batch reactor is... 

Many batch reactors deal with constant-density reaction systems. This includes most liquid-phase reactions as well as all gas phase reactions occuring in a constant-volume bomb. This is a constant volume batch reactor and is the focus of this chapter. Much of this chapter is derived from Levenspiel[24]. 

In a closed system the rate of reaction is properly defined by a total time derivative of the concentration, if concentration is based on the closed total volume of the system or on a volume liquid of constant density. 

Consider tlie ntli-order irreversible reaction of the form A —> products, (-r ) = kC, in a constant density single-stage CESTR. If n = 1, Equation 5-158 becomes... 

The following details mathematical expressions for instantaneous (point or local) or overall (integral) selectivity in series and parallel reactions at constant density and isotliermal conditions. An instantaneous selectivity is defined as the ratio of the rate of formation of one product relative to the rate of formation of another product at any point in the system. The overall selectivity is the ratio of the amount of one product formed to the amount of some other product formed in the same period of time. 

For a constant density system, the concentration of any species, K, Cp, during the course of reaction is given by... 

A j, = Model constant for reaction n C = Concentration of species i (mole m ) k = Turbulent kinetic energy density (m s )... 

Example 1.4 Determine the reactor design equations for the various elementary reactions in a piston flow reactor. Assume constant temperature, constant density, and constant reactor cross section. (Whether or not all these assumptions are needed will be explored in subsequent chapters.)... 

This result assumes constant density and is most useful when the reaction rate depends on a single concentration, SS-a = A(ciout)-... 

Example 2.2 Derive the batch reactor design equations for the reaction set in Example 2.1. Assume a liquid-phase system with constant density. 

Example 2.5 Consider the following competitive reactions in a constant-density batch reactor ... 

The feed is charged all at once to a batch reactor, and the products are removed together, with the mass in the system being held constant during the reaction step. Such reactors usually operate at nearly constant volume. The reason for this is that most batch reactors are liquid-phase reactors, and liquid densities tend to be insensitive to composition. The ideal batch reactor considered so far is perfectly mixed, isothermal, and operates at constant density. We now relax the assumption of constant density but retain the other simplifying assumptions of perfect mixing and isothermal operation. 

This contains the dimensionless rate constant, K = aokthatch, plus the initial and final densities. The comparable equation for reaction at constant density is... 

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

All the results obtained for isothermal, constant-density batch reactors apply to isothermal, constant-density (and constant cross-section) piston flow reactors. Just replace t with z/u, and evaluate the outlet concentration at z = L. Equivalently, leave the result in the time domain and evaluate the outlet composition t = L/u. For example, the solution for component B in the competitive reaction sequence of... 

The emphasis in this chapter is on the generalization of piston flow to situations other than constant velocity down the tube. Real reactors can closely approximate piston flow reactors, yet they show many complications compared with the constant-density and constant-cross-section case considered in Chapter 1. Gas-phase tubular reactors may have appreciable density differences between the inlet and outlet. The mass density and thus the velocity down the tube can vary at constant pressure if there is a change in the number of moles upon reaction, but the pressure drop due to skin friction usually causes a larger change in the density and velocity of the gas. Reactors are sometimes designed to have variable cross sections, and this too will change the density and velocity. Despite these complications, piston flow reactors remain closely akin to batch reactors. There is a one-to-one correspondence between time in a batch and position in a tube, but the relationship is no longer as simple as z = ut. 

The fraction unreacted is /< > . Set z = L to obtain it at the reactor outlet. Suppose = 1 and that kai /Ui = 1 in some system of units. Then the variable-density case gives z = 0.3608 at = 0.5. The velocity at this point is 0.75m . The constant density case gives z = 0.5 at a = 0-5 and the velocity at the outlet is unchanged from The constant-density case fails to account for the reduction in u as the reaction proceeds and thus underestimates the residence time. 

Example 4.13 Determine the outlet concentration from a loop reactor as a function of Qi and q for the case where the reactor element is a PFR and the reaction is first order. Assume constant density and isothermal operation. 

Suppose the following reaction network is occurring in a constant-density CSTR ... 

Suppose you have two identical PFRs and you want to use them to make as much product as possible. The reaction is pseudo-first-order and the product recovery system requires a minimum conversion of 93.75%. Assume constant density. Do you install the reactors in series or parallel Would it affect your decision if the minimum conversion could be lowered ... 

Example 4.13 treated the case of a piston flow reactor inside a recycle loop. Replace the PER with two equal-volume stirred tanks in series. The reaction remains first order, irreversible, and at constant density. 

Solution The component balance for component A (styrene) for a first-order reaction in a constant-volume, constant-density CSTR is... 

Most kinetic experiments are run in batch reactors for the simple reason that they are the easiest reactor to operate on a small, laboratory scale. Piston flow reactors are essentially equivalent and are implicitly included in the present treatment. This treatment is confined to constant-density, isothermal reactions, with nonisothermal and other more complicated cases being treated in Section 7.1.4. The batch equation for component A is... 

---