Fraction conversion definition

If one combines the definition of the reaction rate in variable volume systems with a general nth-order rate expression, he finds that the time necessary to achieve a specified fraction conversion is given by... 

For semibatch operation, the term fraction conversion is somewhat ambiguous for many of the cases of interest. If reactant is present initially in the reactor and is added or removed in feed and effluent streams, the question arises as to the proper basis for the definition of /. In such cases it is best to work either in terms of the weight fraction of a particular component present in the fluid of interest or in terms of concentrations when constant density systems are under consideration. In terms of the symbols shown in Figure 8.20 the fundamental material balance relation becomes ... 

The fraction conversion in the effluent from the first reactor can be determined from equation C and the definition of the fraction conversion. 

The first column lists all the species involved (including inert species, if present). The second column lists the basis amount of each substance (in the feed, say) this is an arbitrary choice. The third column lists the change in the amount of each species from the basis or initial state to some final state in which the fractional conversion is fA. Each change is in terms of fA, based on the definition in equation 2.2-3, and takes the stoichiometry into account. The last column lists the amounts in the final state as the sum of the second and third columns. The total amount is given at the bottom of each column. 

Fractional conversion of a reactant, /A for reactant A, say, is the ratio of the amount of A reacted at some point (time or position) to the amount introduced into the system, and is a measure of consumption of the reactant. It is defined in equation 2.2-3 for a batch system, and in equation 2.3-5 for a flow system. The definition is the same whether the system is simple or complex. 

Solve for reaction time. The total molar conversion of acetylene at 90% fractional conversion may be found by direct application of the definitions for fractional and total molar conversion. Thus, let Xc2h2 stand for the fractional conversion of acetylene, which is defined as... 

Fractional conversion of a reactant is defined as the ratio of the amount consumed to that charged. In this book, the following definitions of yield, yield ratio, and selectivity are used The yield of a product is the ratio of the amount of reactant (or reactants) converted to the product to the total amount of reactant (or reactants) charged. The cumulative yield ratio of two products is the ratios of their yields. The instantaneous yield ratio is the ratio of the momentary rates of conversion to these products. The cumulative selectivity to a product is the ratio of the amount of reactant (or reactants) converted to that product to the amount consumed. The instantaneous selectivity is the ratio of the momentary rate of reactant conversion to the product to that of reactant consumption. Not used in this book is the extent of reaction, defined as the number of moles consumed or formed, divided by the stoichiometric coefficient of the respective participant. 

For the simple network 5.26 and a reaction with no fluid-density variation, the magnitude of the effect is easily calculated The cumulative selectivity of conversion to P (moles of A converted to P per mole of A consumed, see definition 1.11) in batch and continuous stirred-tank reactors as a function of fractional conversion,/A, is... 

All the above equations, written in terms of 8, hold regardless of the network of reactions present, including consecutive reactions or selectivity changes due to temperature ramping. They follow simply from the definitions of fractional conversion and stream composition. 

Because of the definition of space time, the rates of conversion to CO and CO2 are reported in (mol g.cat"1 sec 1). The conversion from partial pressures in the mechanistic rate expressions to mol fractions and hence to fractional conversions that finally result... 

Equation (1-47) is one of the few that should be committed to memory immediately. There are, of course, corresponding definitions of conversion on the basis of mass units, and in some cases fractional conversion to product (mols product made per mol reactant fed or reacted) is a useful measure. The important thing is always to be sure how the term conversion is defined. The integrated forms of simple irreversible rate laws written with conversion, x, from equation (1-47) are ... 

During emulsion polymoization proccesses crosslinking can occur due to the presence of radicals and unsaturation in the polymer chain. Chain transfer agents are often used to decrease the level of crosslinking during polymerization. The gel content of a crosslinkable polymo is d ned as the fraction of material of infinite MM experimental criteria are usually more aibitraiy, and strongly depend on the experimental procedure. The same holds for the gel point, Le. the conversion at which the first insoluble polymer network makes its appearance. For example, in ABS gel content can be based on the toluene extraction of the soluble fraction of the polybutadioie. Hie insoluble residue is the gel fraction by definition. 

Taking into consideration the definition of fractional conversion, A(-), as... 

How far a reaction goes to completion is measured for each reactant, i, can also be specified by fractional conversion, fr the definition of which is... 

From the definition of fractional conversion, Fjo — Ft = Ftoxt. Therefore, all of the parameters on the right-hand side of the above equation are known and — rr can be calculated. 

It is very important to be consistent in defining the fractional conversions for a series of reactors. The easiest definition, which will be followed in this book, is to base the conversion on the molar flow rate to the first reactor, i.e., Fao- Let Fa,i be the molar flow rate of A out of the first reactor. Fa,2 be the molar flow rate out of the second reactor, and Fa,3 be the molar flow rate out of the third reactor. Then... 

The conversion a a,i is the fractional conversion of A in the stream leaving the first reactor. This is the same definition that is used for a single reactor. The conversion xp is the overall conversion of A in the stream leaving the second reactor. In other words, jca,2 is the conversion for the first and second reactors combined. Finally, jca3 is the conversion of A in the stream leaving the third (last) reactor. It is the overall conversion for the series of three reactors. 

Equation (6-1) shows that the reaction rate can be obtained directly in a CSTR if the fractional conversion jca is measured, and if the molar feed rate Fao and the reactor volume V (or the catalyst weight W) are known. However, it is good practice to measure the complete composition of the effluent stream, even though the concentration of every species can be calculated from xa- Measuring every concentration provides a check on the quality of the data, and allows the Law of definite proportions to be used to ensure that only one reaction takes place at the conditions of the experiment. The temperature of the reactor must also be measured and carefully controlled. 

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