Tubular flow reactors material balances

Tubular flow reactors usually operate at nearly constant pressure. For a reactant A, the differential material balance is ... 

There are a variety of limiting forms of equation 8.0.3 that are appropriate for use with different types of reactors and different modes of operation. For stirred tanks the reactor contents are uniform in temperature and composition throughout, and it is possible to write the energy balance over the entire reactor. In the case of a batch reactor, only the first two terms need be retained. For continuous flow systems operating at steady state, the accumulation term disappears. For adiabatic operation in the absence of shaft work effects the energy transfer term is omitted. For the case of semibatch operation it may be necessary to retain all four terms. For tubular flow reactors neither the composition nor the temperature need be independent of position, and the energy balance must be written on a differential element of reactor volume. The resultant differential equation must then be solved in conjunction with the differential equation describing the material balance on the differential element. 

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... 

Let us consider unit volume of the reaction mixture in which concentrations are changing with time this unit volume may be situated in a batch reactor or moving in plug flow in a tubular reactor. Material balances on this volume give the following equations ... 

Related Calculations. (1) Integral analysis may be used on data from any reactor from which integral reaction rate data have been obtained. The preceding procedure applies equally well to data from an integral tubular-flow reactor, if the tube-flow material balance... 

Tubular flow reactors operate at nearly constant pressure. How the differential material balance is integrated for a number of second-order reactions will be explained. When n is the molal flow rate of reactant A the flow reactor equation is... 

The pyrolysis experiments were conducted in an electrically heated, once-through tubular flow reactor, designed to simulate the time-temperature history experienced in commercial steam-cracking operations. Reactor effluent compositions were ascertained by gas chromatograph and mass spectrometer analyses. Material and hydrogen balances could always be effected, with typical closures of 98 2 wt %. 

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. 

Fig. 3.6 Schematic for deriving the material balance of a tubular flow reactor...

Consider a first-order chemical reaction being carried out under isothermal steady-state conditions in a tubular-flow reactor. On the assumptions of laminar flow and negligible axial diffusion, the material balance equation is... 

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

In Section 11.1.3.1 we considered the longitudinal dispersion model for flow in tubular reactors and indicated how one may employ tracer measurements to determine the magnitude of the dispersion parameter used in the model. In this section we will consider the problem of determining the conversion that will be attained when the model reactor operates at steady state. We will proceed by writing a material balance on a reactant species A using a tubular reactor. The mass balance over a reactor element of length AZ becomes ... 

A laminar-flow reactor (LFR) is rarely used for kinetic studies, since it involves a flow pattern that is relatively difficult to attain experimentally. However, the model based on laminar flow, a type of tubular flow, may be useful in certain situations, both in the laboratory and on a large scale, in which flow approaches this extreme (at low Re). Such a situation would involve low fluid flow rate, small tube size, and high fluid viscosity, either separately or in combination, as, for example, in the extrusion of high-molecular-weight polymers. Nevertheless, we consider the general features of an LFR at this stage for comparison with features of the other models introduced above. We defer more detailed discussion, including applications of the material balance, to Chapter 16. 

In this liquid phase reaction, it may be assumed that the mass density of the liquid is unaffected by the reaction, allowing the material balance for the tubular reactor to be applied on a volume basis (Section 1.7.1, Volume 3) with plug flow. 

The component material balance equation, combined with the reactor energy balance equation and the kinetic rate equation, provide the basic model for the ideal plug-flow tubular reactor. 

In a tubular reactor the concentration varies from point to point along a flow-path, as shown by the solid curve in Fig. 3.3-2, right. The material balance... 

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 ... 

Consider a steady flow of reactant A to products at constant density through an element of radius r, width 8r, and height 81 in a tubular reactor at isothermal condition. Suppose that radial and axial mass transfer is expressed by Fick s law, with (D and (De)r as effective diffusivities. The rate at which A reacts is (-rA), mol/m3 sec. A material balance on a tubular element of radii r and r + 8r and height 81 is carried out from... 

These basic rate models were Incorporated Into a differential mass balance In a tubular, plug-flow reaction. This gives a set of coupled, non-llnear differential equations which, when Integrated, will provide a simulation model. This model corresponds to the Integral reactor data provided by experimentation. A material balance Is written for each of the four components In our system ... 

The analysis presented in this chapter can be used to describe reaction containers of any type—they need not be tubular reactors. For example, consider the situation where blood is flowing in a vessel and antibodies are binding to cells on the vessel wall. The situation can be described by the following material balance ... 

Write down in dimensionless form the material balance equation for a laminar flow tubular reactor accomplishing a first-order reaction and having both axial and radial diffusion. State the necessary conditions for solution. 

Reactions orders and rate coefficients can be established with methods that use either rate or concentration data. Batch, tubular plug-flow, and differential recycle reactors yield concentrations as directly measured quantities, and calculation of rates requires finite-difference approximations. To avoid these, concentration methods should be used. In contrast, continuous stirred-tank reactors allow rates to be calculated from material balances without approximation. Here, evaluation based on rates is equally suited. 

The analysis and rational design of reactors requires the simultaneous solution of material and energ> balances. For a steady-state, tubular, plug-flow reactor, we showed in Chapter 6 that the molar flows and temperature are governed by the following differential equations... 

In a tubular reactor, the concentration and temperature may vary both in time and space. One speaks about a distributed system. The ideal plug flow reactor (PFR) model is the most used. Because of the flat velocity profile, the concentrations and temperature varies only along the length. Consider for simplification a homogeneous reaction. The unsteady state material balance of the reactive species leads to the following equation ... 

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. 

For this case it will be necessary to calculate the steady-state temperature and fractional conversion profiles along the length of the tubular reactor. For a plug flow reactor the appropriate differential material balance for the reaction at hand is... 

The design of plug flow reactors (tubular and tower devices) does not assume mixing in the direction of flow (axial turbulence), therefore the chemical processes within a blend of reactants occurs in laminar flow conditions. A combination of the displacement and plug flow reactors, with consideration of their material and thermal balances, makes it possible to calculate the optimal design of a device for any chemical process. 

In contrast to the ideal CSTR, backmbdng is excluded in an ideal tubular reactor, characterized by a plug flow pattern of the fluid, with uniform radial composition and temperature. The material balance for a small volume system element (AV) shown in Figure 2.9 at the reactor steady state is written as... 

On the other hand, for the ideal tubular reactor with a plug-flow-like profile (PER), the material balance has to be made over a differential element of volume, dV = Adz, where A is the cross-sectional area of the bioreactor and dz is a differential thickness of the bioreactor (Figure 7.4). The material balance thus becomes... 

---