Mole balances tubular reactors

The basic equation for a tubular reactor is obtained by applying the general material balance, equation 1.12, with the plug flow assumptions. In steady state operation, which is usually the aim, the Rate of accumulation term (4) is zero. The material balance is taken with respect to a reactant A over a differential element of volume 8V, (Fig. 1.14). The fractional conversion of A in the mixture entering the element is aA and leaving it is (aA + SaA). If FA is the feed rate of A into the reactor (moles per unit time) the material balance over 8V, gives ... 

In this section we apply die general energy balance [Equation (8-22)] to the CSTR and to the tubular reactor operated at steady state. We then present example problems showing how the mole and energy balances are combined to size reactors operating adiabadcally. 

In die tubular reactor, the reactants are continually consumed as they flow down the length of the reactor, In modeling the tubular reactor, we assume that the concentration varies continuously in the axial direction through the reactor. Consequently, the reaction rate, which is a function of concentration for all but zero-order reactions, will also vary axially. The general mole balance equation is given by Equation (1-4) ... 

Dibular Flow Reactor (PFR). After multiplying both sides of the tubular reactor design equation (1-10) by -1, we express the mole balance equation for species A in the reaction given by Equation (2-2) as... 

Though in later applications we may return to the concentration unit of moles per unit volume, let us take the opportunity, in discussing the tubular reactor, to use the unit of moles per unit mass. In this we follow Amundson (1958), whose work has done so much to set chemical reactor design on a sound analytical basis. We shall still assume that the flow is uniform and that there is no longitudinal diffusion. Thus G, the flow rate in mass per unit area per unit time, is constant throughout the reactor under all circumstances. The linear velocity v and the density p may vary, but their product is constant, pv = G. Then a mass balance of A, over an element of length yields the differential equation... 

Flow, Reaction, and Dispersion Having discussed how to determine the dispersion coefficient we now return to the case where we have both dispersion and reaction in a tubular reactor. A mole balance is taken on a particular component of the mixture (say, species A) over a short length Ac of a tubular reactor in a maimer identical to that in Chapter I, to arrive at... 

Consider an adiabatic tubular reactor (Davis, 1984)[15] with the following data length L = 2 m, radius Rp = 0.1 m, inlet reactant concentration cO = 30 moles/m3, inlet temperature TO = 700K, enthalpy AH = -10000 J/mole, specific heat capacity Cp = 1000 J/kg/K, activation energy Ea = 100 J/mole, p = 1200 kg/m3, velocity uO = 3 m/s, and rate constant kO = 5 s-1. Dimensionless concentration (y) and dimensionless temperature (9) are governed by material and energy balances as ... 

In ihe three idealized types of reactors just discussed (the perfectly mixed batch reactor, the plug-fiow tubular reactor (PFR). and the perfectly mixed con-tinuous-siirred tank reactor (CSTR), the design equations (i.e.. mole balances) were dei doped based on reactor volume. The deris ation of the design equation for a packed-bed catalytic reactor (PBR) will be carried out in a manner analogous to the development of the tubular design equation. To accomplish this derivation. we simply replace the volume coordinate in Equation (MO) with (he catalyst weight coordinate H (Figure - 4). 

For a tubular reactor, the mole balance on species A (j = A) was shown to be given by Equation (1-11). Then for species A (j = A) results... 

The first step in our CRE algorithm is the mole balance, which we now need to extend to include the molar fiux, and diffusional effects. The molar flow rate of A in a given direction, such as the z direction down the length of a tubular reactor, is just the product of the flux. (mol/m s), and the cross-sectional area. Ac (nt ), that is. 

We will now use this form of the molar flow rate in our mole balance in the z direction of a tubular flow reactor... 

Isothermal reactor. This example concerns an elementary, exothermic, second-order reversible liquid-phase reaction in a tubular reactor with a parabolic velocity distribution. Only the mole, rate law, and stoichiometry balance in the tubular reactor are required in ihi.s FEMLAB chemical engineering module. 

The solution to this problem requires an analysis of multiple gas-phase reactions in a differential plug-flow tubular reactor. Two different solution strategies are described here. In both cases, it is important to write mass balances in terms of molar flow rates and reactor volume. Molar densities and residence time are not appropriate for the convective mass-transfer-rate process because one cannot assume that the total volumetric flow rate is constant in the gas phase, particularly when the total number of moles is not conserved. In each reaction, 2 mol of reactants generates 1 mol of product. Furthermore, an overall mass balance suggests that the volumetric flow rate is constant only when the overall mass density does not change. This is a reasonable assumption for liquid-phase reactors but not for gas-phase problems when the total volume is not restricted. The exception is a constant-volume batch reactor. 

When multiple reactions occur in the gas phase, the mass balance for component i is written for an ideal tubular reactor at high mass transfer Peclet numbers in the following form, and each term has units of moles per volume per time ... 

This problem requires an analysis of coupled thermal energy and mass transport in a differential tubular reactor. In other words, the mass and energy balances should be expressed as coupled ordinary differential equations (ODEs). Since 3 mol of reactants produces 1 mol of product, the total number of moles is not conserved. Hence, this problem corresponds to a variable-volume gas-phase flow reactor and it is important to use reactor volume as the independent variable. Don t introduce average residence time because the gas-phase volumetric flow rate is not constant. If heat transfer across the wall of the reactor is neglected in the thermal energy balance for adiabatic operation, it... 

At high-mass-transfer Peclet numbers, the steady-state mass balance for component i, with units of moles per time, is expressed in terms of its molar flow rate Fi and differential volume dV = ttR dz for a tubular reactor. If species i... 

Measure the incremental conversion of ethanol per mass of catalyst and calculate the initial reactant product conversion rate with units of moles per area per time as a function of total pressure at the reactor inlet. One calculates this initial rate of conversion of ethanol to products via a differential material balance, unique to gas-phase packed catalytic tubular reactors that operate under plug-flow conditions at high-mass-transfer Peclet numbers. Since axial dispersion in the packed bed is insignificant. 

Conditions 2 and 3 are discussed further in Chapters 22 and 30 that focus on packed catalytic tubular reactors. Condition 1 is addressed by defining the effectiveness factor and using basic information from the mass balance to develop a correlation between the effectiveness factor and the intrapellet Damkohler number. The ratio of reaction rates described below in (a) and (b), with units of moles per time, is defined as the effectiveness factor. 

Notice that the molar density of key-limiting reactant A on the external surface of the catalytic pellet is always used as the characteristic quantity to make the molar density of component i dimensionless in all the component mass balances. This chapter focuses on explicit numerical calculations for the effective diffusion coefficient of species i within the internal pores of a catalytic pellet. This information is required before one can evaluate the intrapellet Damkohler number and calculate a numerical value for the effectiveness factor. Hence, 50, effective is called the effective intrapellet diffusion coefficient for species i. When 50, effective appears in the denominator of Ajj, the dimensionless scaling factor is called the intrapellet Damkohler number for species i in reaction j. When the reactor design focuses on the entire packed catalytic tubular reactor in Chapter 22, it will be necessary to calcnlate interpellet axial dispersion coefficients and interpellet Damkohler nnmbers. When there is only one chemical reaction that is characterized by nth-order irreversible kinetics and subscript j is not required, the rate constant in the nnmerator of equation (21-2) is written as instead of kj, which signifies that k has nnits of (volume/mole)"" per time for pseudo-volumetric kinetics. Recall from equation (19-6) on page 493 that second-order kinetic rate constants for a volnmetric rate law based on molar densities in the gas phase adjacent to the internal catalytic surface can be written as... 

Table 6.1 Mole and Energy Balance Relations for Species in Batch (or Tubular) Reactors Used for Carr3ting out Radical Polymerization...

The mole balances for radical and dead polymers for batch (or tubular) reactors are given in Table 6.1. We define concentration of polymer radicals, Apo, as... 

The reversible reaction A 2B is conducted at 540°F and 3 atma in a tubular-flow reactor. The feed contains 30 mole % A and the balance inert material, the total being at the rate of 75 lb moles/hr. The rate equation is... 

---