Gay-Lussac, J. L., gas-law

While much attention has been given to the development of computer techniques for design of distillation and absorption columns, much less attention has been devoted to the development of such techniques for equipment using liquid-liquid extraction. However, regardless of the nature of the operation, few systematic attempts have been made to organize phase-equilibrium information for direct use in chemical process design. This monograph presents a systematic procedure for calculating multi-component vapor-liquid and liquid-liquid equilibria for mixtures commonly encountered in the chemical process industries. Attention is limited to systems at low or moderate pressures. Pertinent references to previous work are given at the end of this chapter.  [c.1]

At pressures to a few bars, the vapor phase is at a relatively low density, i.e., on the average, the molecules interact with one another less strongly than do the molecules in the much denser liquid phase. It is therefore a common simplification to assume that all the nonideality in vapor-liquid systems exist in the liquid phase and that the vapor phase can be treated as an ideal gas. This leads to the simple result that the fugacity of component i is given by its partial pressure, i.e. the product of y, the mole fraction of i in the vapor, and P, the total pressure. A somewhat less restrictive simplification is the Lewis fugacity rule which sets the fugacity of i in the vapor mixture proportional to its mole fraction in the vapor phase the constant of proportionality is the fugacity of pure i vapor at the temperature and pressure of the mixture. These simplifications are attractive because they make the calculation of vapor-liquid equilibria much easier the K factors = i i  [c.25]

If the vapor mixture contains only ideal gases, the integrals in Equations (3) and (6) are zero, z is unity for all compositions, and ()i equals 1 for each component i. At low pressures, typically less than 1 bar, it is frequently a good assumption to set ( ) = 1, but even at moderately low pressures, say in the vicinity of 1 to 10 bars, (f) is often significantly different from unity, especially if i is a polar component.  [c.27]

At moderate densities. Equation (3-lOb) provides a very good approximation. This approximation should be used only for densities less than (about) one half the critical density. As a rough rule, the virial equation truncated after the second term is valid for the present range  [c.29]

Bfi and 022- However, in the second binary, intermolecular forces between unlike molecules are much stronger than those between like molecules chloroform and ethyl acetate can strongly hydrogen bond with each other but only very weakly with them-  [c.31]

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the  [c.68]

The continuous line in Figure 16 shows results from fitting a single tie line in addition to the binary data. Only slight improvement is obtained in prediction of the two-phase region more important, however, prediction of solute distribution is improved. Incorporation of the single ternary tie line into the method of data reduction produces only a small loss of accuracy in the representation of VLE for the two binary systems.  [c.69]

Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary Figure 4-16. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows small loss of accuracy. ---- Binary
Figure 4-17. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows some loss of accuracy. Figure 4-17. Representation of ternary liquid-liquid equilibria using the UNIQUAC equation is improved by incorporating ternary tie-line data into binary-parameter estimation. Representation of binary VLB shows some loss of accuracy.
For each experiment, the true values of the measured variables are related by one or more constraints. Because the number of data points exceeds the number of parameters to be estimated, all constraint equations are not exactly satisfied for all experimental measurements. Exact agreement between theory and experiment is not achieved due to random and systematic errors in the data and to "lack of fit" of the model to the data. Optimum parameters and true values corresponding to the experimental measurements must be found by satisfaction of an appropriate statistical criterion.  [c.98]

In the maximum-likelihood method used here, the "true" value of each measured variable is also found in the course of parameter estimation. The differences between these "true" values and the corresponding experimentally measured values are the residuals (also called deviations). When there are many data points, the residuals can be analyzed by standard statistical methods (Draper and Smith, 1966). If, however, there are only a few data points, examination of the residuals for trends, when plotted versus other system variables, may provide valuable information. Often these plots can indicate at a glance excessive experimental error, systematic error, or "lack of fit." Data points which are obviously bad can also be readily detected. If the model is suitable and if there are no systematic errors, such a plot shows the residuals randomly distributed with zero means. This behavior is shown in Figure 3 for the ethyl-acetate-n-propanol data of Murti and Van Winkle (1958), fitted with the van Laar equation.  [c.105]

The maximum-likelihood method, like any statistical tool, is useful for correlating and critically examining experimental information. However, it can never be a substitute for that information. While a statistical tool is useful for minimizing the required experimental effort, reliable calculated phase equilibria can only be obtained if at least some pertinent and reliable experimental data are at hand.  [c.108]

Equations (7-8) and (7-9) are then used to calculate the compositions, which are normalized and used in the thermodynamic subroutines to find new equilibrium ratios,. These values are then used in the next Newton-Raphson iteration. The iterative process continues until the magnitude of the objective function 1g is less than a convergence criterion, e. If initial estimates of x, y, and a are not provided externally (for instance from previous calculations of the same separation under slightly different conditions), they are taken to be  [c.121]

Convergence of the iteration requires the norm of the objective vector 1g to be less than the convergence criterion, e. The initial estimates used, if not provided externally, are, in addition to Equation (7-28)  [c.122]

The criterion used for "too near the plait point" is that ratio of K s for the two "solvent" components is less than seven with the feed composition in the two-phase region.  [c.127]

The subsequent representations are probably reliable within the range of data used (always less broad than 200° to 600°K), but they are only approximations outside that range. The functions are, however, always monotonic in temperature, to provide appropriate corrections when iterative programs choose temperature excursions outside the range of data.  [c.138]

Sage, B. H., Lacey, W. N., "Thermodynamic Properties of Higher Paraffin Hydrocarbons and Nitrogen," Am. Petr. Inst., New York, N.Y. (1950).  [c.210]

ERF error flag, integer variable normally zero ERF= 1 indicates parameters are not available for one or more binary pairs in the mixture ERF = 2 indicates no solution was obtained ERF = 3 or 4 indicates the specified flash temperature is less than the bubble-point temperature or greater than the dew-point temperature respectively ERF = 5 indicates bad input arguments.  [c.320]

PARCH reads update information from formatted cards, or other input file containing card images. Input having existing component indices replace old data with those indices. Otherwise the new component data is added to the library, with the restriction that the total number of components is always less than or equal to 100.  [c.344]

The program storage requirements will depend somewhat on the computer and FORTRAN compiler involved. The execution times can be corrected approximately to those for other computer systems by use of factors based upon bench-mark programs representative of floating point manipulations. For example, execution times on a CDC 6600 would be less by a factor of roughly 4 than those given in the tcible and on a CDC 7600 less by a factor of roughly 24.  [c.352]

Building an irreducible structure. The first approach follows the onion logic, starting the design by choosing a reactor and then moving outward by adding a separation and recycle system, and so on. At each layer we must make decisions based on the information available at that stage. The ability to look ahead to the completed design might lead to different decisions. Unfortunately, this is not possible, and instead, decisions must be based on an incomplete picture.  [c.8]

The lack of suitable catalysts is the most common reason preventing the exploitation of novel reaction paths. At the first stage of design, it is impossible to look ahead and see all the consequences of choosing one reaction path or another, but some things are clear even at this stage. Consider the following example.  [c.16]

Example 2.2 Devise a process from the three reaction paths in Example 2.1 which uses ethylene and chlorine as raw materials and produces no byproducts other than water. Does the process look attractive economically  [c.17]

If a reaction is reversible, there is a maximum conversion that can be achieved, the equilibrium conversion, which is less than 1.0. Fixing the mole ratio of reactants, temperature, and pressure fixes the equilibrium conversion.  [c.25]

In the third model (Fig. 2.1c), the plug-flow model, a steady uniform movement of the reactants is assumed, with no attempt to induce mixing along the direction of flow. Like the ideal batch reactor, the residence time in a plug-flow reactor is the same for all fluid elements. Plug-flow operation can be approached by using a number of continuous well-mixed reactors in series (Fig. 2.Id). The greater the number of well-mixed reactors in series, the closer is the approach to plug-flow operation.  [c.29]

For liquid-phase reactions, the effect of pressure on the selectivity and reactor volume is less pronounced, and the pressure is likely to be chosen to  [c.45]

In general, heterogeneous catalysts are preferred to homogeneous catalysts because the separation and recycling of homogeneous catalysts often can be very difficult. Loss of homogeneous catalyst not only creates a direct expense through loss of material but also creates an environmental problem.  [c.46]

Catalytic degradation. The performance of most catalysts deteriorates with time. The rate at which the deterioration takes place is another important factor in the choice of catalyst and the choice of reactor conditions. Deterioration in performance lowers the rate of reaction, which, for a given reactor design, manifests itself as a lowering of the conversion. This often can be compensated by increasing the temperature of the reactor. However, significant increases in temperature can degrade selectivity considerably and often accelerate the mechanisms that cause catalyst degradation. Loss of catalyst performance can occur in a number of ways a. Physical loss. Physical loss is particularly important with homogeneous catalysts, which need to be separated from reaction products and recycled. Unless this can be done with high efficiency, it leads to physical loss (and subsequent environmental problems). However, physical loss as a problem is not restricted to homogeneous catalysts. It also can be a problem with heterogeneous catalysts. This is particularly the case when catalytic fluidized-bed reactors are employed. Attrition of the particles causes the catalyst particles to be broken down in size. Particles which are carried over from the fluidized bed are normally separated from  [c.48]

If the mixture to be separated is homogeneous, a separation can only be performed by the addition or creation of another phase within the system. For example, if a gaseous mixture is leaving the reactor, another phase could be created by partial condensation. The vapor resulting from the partial condensation will be rich in the more volatile components and the liquid will be rich in the less volatile components, achieving a separation. Alternatively, rather than creating another phase, one can be added to the gaseous mixture, such as a solvent which would preferentially dissolve one or more of the components from the mixture. Further separation is required to separate the solvent from the process materials allowing recycle of the solvent, etc. A number of physical properties can be exploited to achieve the separation of homogeneous mixtures.If a heterogeneous or multiphase mixture leaves the reactor, then separation can be done physically by exploiting differences in density between the phases.  [c.67]

Figure 3.1a shows a flash drum used to separate by gravity a vapor-liquid mixture. The velocity of the vapor through the flash drum must be less than the settling velocity of the liquid drops. Figure 3.11) shows a simple gravity settler for removing a  [c.68]

Figure 3.1c is a schematic diagram of gravity settling chamber. A mixture of vapor or liquid and solid particles enters at one end of a large chamber. Particles settle toward the fioor. The vertical height of the chamber divided by the settling velocity of the particles must give a time less than the residence time of the air.  [c.69]

The accuracy of our calculations is strongly dependent on the accuracy of the experimental data used to obtain the necessary parameters. While we cannot make any general quantitative statement about the accuracy of our calculations for multicomponent vapor-liquid equilibria, our experience leads us to believe that the calculated results for ternary or quarternary mixtures have an accuracy only slightly less than that of the binary data upon which the calculations are based. For multicomponent liquid-liquid equilibria, the accuracy of prediction is dependent not only upon the accuracy of the binary data, but also on the method used to obtain binary parameters. While there are always exceptions, in typical cases the technique used for binary-data reduction is of some, but not major, importance for vapor-liquid equilibria. However, for liquid-liquid equilibria, the method of data reduction plays a crucial role, as discussed in Chapters 4 and 6.  [c.5]

However, if the liquid solution contains a noncondensable component, the normalization shown in Equation (13) cannot be applied to that component since a pure, supercritical liquid is a physical impossibility. Sometimes it is convenient to introduce the concept of a pure, hypothetical supercritical liquid and to evaluate its properties by extrapolation provided that the component in question is not excessively above its critical temperature, this concept is useful, as discussed later. We refer to those hypothetical liquids as condensable components whenever they follow the convention of Equation (13). However, for a highly supercritical component (e.g., H2 or N2 at room temperature) the concept of a hypothetical liquid is of little use since the extrapolation of pure-liquid properties in this case is so excessive as to lose physical significance.  [c.18]

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture.  [c.25]

Figure 17 shows results for the acetonitrile-n-heptane-benzene system. Here, however, the two-phase region is somewhat smaller ternary equilibrium calculations using binary data alone considerably overestimate the two-phase region. Upon including a single ternary tie line, satisfactory ternary representation is obtained. Unfortunately, there is some loss of accuracy in the representation of the binary VLB (particularly for the acetonitrile-benzene system where the shift of the aceotrope is evident) but the loss is not severe.  [c.71]

King, 1971 Naphtali and Sandholm, 1971 Newman, 1963 and Tomich, 1970). Moreover the choice of appropriate computation procedures for distillation, absorption, and extraction is highly dependent on the system being separated, the conditions of separation, and the specifications to be satisfied (Friday and Smith, 1964 Seppala and Luus, 1972). The thermodynamic methods presented in Chapters 3, 4, and 5, particularly when combined to  [c.110]



The flowsheets shown in Fig. 1.3 feature the same reactor design. It could be useful to explore changes in reactor design. For example, the size of the reactor could be increased to increase the aunount of FEED which reacts (Fig. 1.4a). Now there is not only much less FEED in the reactor effiuent but more PRODUCT and BYPRODUCT. However, the increase in BYPRODUCT is larger than the increase in PRODUCT. Thus, although the reactor in Fig. 1.4a has the same three components in its effiuent as the reactor in Fig. 1.2a, there is less FEED, more PRODUCT, and significantly more BYPRODUCT. This change in reactor design generates a different task for the separation system, and it is possible that a separation system different from that shown in Figs. 1.2 and 1.3 is now appropriate. Figure 1.46 shows a possible alternative. This also uses two distillation columns, but the separations are carried out in a different order.  [c.4]

See pages that mention the term Gay-Lussac, J. L., gas-law : [c.31]    [c.38]    [c.125]    [c.129]    [c.141]    [c.179]    [c.223]    [c.264]    [c.266]    [c.325]    [c.329]    [c.11]   
A life of magic chemistry (2001) -- [ c.29 ]