Mole balances isothermal reactors

For isothermal, first-order chemical reactions, the mole balances form a system of linear equations. A non-ideal reactor can then be modeled as a collection of Lagrangian fluid elements moving independe n tly through the system. When parameterized by the amount of time it has spent in the system (i.e., its residence time), each fluid element behaves as abatch reactor. The species concentrations for such a system can be completely characterized by the inlet concentrations, the chemical rate constants, and the residence time distribution (RTD) of the reactor. The latter can be found from simple tracer experiments carried out under identical flow conditions. A brief overview of RTD theory is given below. 

Stoichacmetry and reaction equilibria. Homogeneous reactions kinetics. Mole balances batch, continuous-shn-ed tank and plug flow reactors. Collection and analysis of rate data. Catalytic reaction kinetics and isothermal catalytic radar desttpi. Diffusion effects. 

It is useful to examine the consequences of a closed ion source on kinetics measurements. We approach this with a simple mathematical model from which it is possible to make quantitative estimates of the distortion of concentration-time curves due to the ion source residence time. The ion source pressure is normally low enough that flow through it is in the Knudsen regime where all collisions are with the walls, backmixing is complete, and the source can be treated as a continuous stirred tank reactor (CSTR). The isothermal mole balance with a first-order reaction occurring in the source can be written as... 

To outline the procedure used in the differential method of analysis, we consider a reaction carded out isothermally in a constant-volume batch reactor and the concentration recorded as a function of time. By combining the mole balance with the rate law given by Equation (5-1), we obtain... 

A number of fluidized bed reactor model versions are based on the cross sectional averaged two-phase transport equations as presented in sect 3.4.7. Bue to the vigorous particle flow the fluidized beds are essentially isothermal, so no energy balance is generally required . In addition, the necessary species mass (mole) balance can be deduced from (3.498). The solids are considered... 

Mass and energy balances may be written either in terms of mass or moles as long as all quantities are on the same basis. For example, if mass units are used, both the rate and the feed rate must be in mass units. For isothermal reactors molal units are more convenient, and the examples in Chap. 4 are solved using these units. Mass units may be more suitable for energy balances so that some examples in Chap. 5 are treated on a mass basis. In this chapter all the equations are written with the supposition that mass units are employed. Also note that the conversion x refers to the fraction of the reactant feed rate F that is converted, not to the fraction of the total feed rate /J. 

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. 

Analytical solution of the mole balance equations is only likely to be possible when a number of simplifying assumptions can be made such as those adopted previously where we assumed a single irreversible first-order reaction, no change in molar flow due to reaction, isothermal reactor, negligible variation in pressure, plug flow of gas in the bubble phase, and either perfect mixing or plug flow in the dense phase (see Ref. [46]). Assumptions must also be made with respect to the respective... 

In this chapter we use the mole balances with the terms of conversion. Chapter 2, Thble 2S, Eo study isothermal reactor designs. Conversion is the preferred parameter to measure progress for single reactions occurring in batch reactors. CSTRs and PFRs. Both batch reactor times and flow reactor volumes to achieve a given conversion will he calculated. 

Isothermal Reactor Design Conversion Chapter 5 4. Combining the rate law and the mole balance, we have... 

When using an ordinary differential equation (ODE) solver such as Polymath or MATLAB, it is usually easier to leave the mole balances, rate laws, and concentrations as separate equations, rather than combining them into a single equation as we did to obtain an analytical solution. Writing the equations separately leaves it to the computer to combine them and produce a solution. The fonnulations for a packed-bed reactor with pressure drop and a semibatch teactor are given below for two elementary reactions carried out isothermally. 

We conduct the reaction in a packed bed reactor, assuming that the heat transfer is sufficiently fast for the reactor to be isothermal. The mass W of catalyst in a region of volume V in the reactor is W = ps — solid catalyst and void fraction of the bed. Let T a(IT) be the flow rate (moles per unit time) of A passing through the particular surface in the reactor for which the mass of catalyst in the region between this surface and the inlet is W. The mole balance on A for the region between Wand W + SW is... 

The combined feed to the reactor contains 53.7 moIe% C2H4, 36.7% H2O and the balance nitrogen which enters the reactor at SIO C. The reactor operates isothermally at 310°C An ethylene conversion of 5% is achieved, and the yield of ethanol (moles ethanol produced/mole ethylene consumed)... 

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