# Application

The calculation of vapor and liquid fugacities in multi-component systems has been implemented by a set of computer programs in the form of FORTRAN IV subroutines. These are applicable to systems of up to twenty components, and operate on a thermodynamic data base including parameters for 92 compounds. The set includes subroutines for evaluation of vapor-phase fugacity [c.5]

Detailed and extensive information on the UNIFAC method for estimating activity coefficients with application to vapor-liquid equilibria at moderate pressures. [c.8]

Early chapters give good review of classical thermodynamics for liquid-liquid systems with engineering applications. [c.12]

Equation (12), applicable at low or moderate pressures, is used in this monograph for typical vapor mixtures. However, when the vapor phase contains a strongly dimerizing component such as carboxylic acid. Equation (7) is not applicable and [c.16]

This chapter uses an equation of state which is applicable only at low or moderate pressures. Serious error may result when the truncated virial equation is used at high pressures. [c.38]

Equations (4) and (5) are not limited to binary systems they are applicable to systems containing any number of components. [c.51]

For liquid mixtures containing both condensable and noncondensable components. Equation (15) is applicable. However it is now convenient to rewrite that equation. Neglecting, as before, the last term in Equation (15), we obtain [c.88]

The method used here is based on a general application of the maximum-likelihood principle. A rigorous discussion is given by Bard (1974) on nonlinear-parameter estimation based on the maximum-likelihood principle. The most important feature of this method is that it attempts properly to account for all measurement errors. A discussion of the background of this method and details of its implementation are given by Anderson et al. (1978). [c.97]

Application to Parameter Estimation from VLE Data [c.99]

Application of the algorithm for analysis of vapor-liquid equilibrium data can be illustrated with the isobaric data of 0th-mer (1928) for the system acetone(1)-methanol(2). For simplicity, the van Laar equations are used here to express the activity coefficients. [c.99]

At low pressures, it is often permissible to neglect nonidealities of the vapor phase. If these nonidealities are not negligible, they can have the effect of introducing a nonrandom trend into the plotted residuals similar to that introduced by systematic error. Experience here has shown that application of vapor-phase corrections for nonidealities gives a better representation of the data by the model, oven when these corrections [c.106]

The maximum-likelihood method is not limited to phase equilibrium data. It is applicable to any type of data for which a model can be postulated and for which there are known random measurement errors in the variables. P-V-T data, enthalpy data, solid-liquid adsorption data, etc., can all be reduced by this method. The advantages indicated here for vapor-liquid equilibrium data apply also to other data. [c.108]

The most frequent application of phase-equilibrium calculations in chemical process design and analysis is probably in treatment of equilibrium separations. In these operations, often called flash processes, a feed stream (or several feed streams) enters a separation stage where it is split into two streams of different composition that are in equilibrium with each other. [c.110]

There is justification for allowing t to increase beyond 1, and in many particular applications this may be desirable. Here a more conservative approach is used to reduce the chance of unstable iterations. [c.116]

The procedure would then require calculation of (2m+2) partial derivatives per iteration, requiring 2m+2 evaluations of the thermodynamic functions per iteration. Since the computation effort is essentially proportional to the number of evaluations, this form of iteration is excessively expensive, even if it converges rapidly. Fortunately, simpler forms exist that are almost always much more efficient in application. [c.117]

In application of the Newton-Raphson iteration to these objective functions [Equations (7-23) through (7-26)], the near linear nature of the functions makes the use of step-limiting unnecessary. [c.119]

In the case of the adiabatic flash, application of a two-dimensional Newton-Raphson iteration to the objective functions represented by Equations (7-13) and (7-14), with Q/F = 0, is used to provide new estimates of a and T simultaneously. The derivatives with respect to a in the Jacobian matrix are found analytically while those with respect to T are found by finite-difference approximation [c.121]

As an example of the application of a fixed-bed tubular reactor, consider the production of methanol. Synthesis gas (a mixture of hydrogen, carbon monoxide, and carbon dioxide) is reacted over a copper-based cat dyst. The main reactions are [c.56]

Flotation is also used in applications such as the separation of oil [c.71]

These heuristics are based on observations made in many practical applications. In addition to being restricted to simple columns, the observations are based on no heat integration (i.e., all reboilers and condensers are serviced by utilities). Difficulties can arise when the heuristics are in conflict with each other, as the following example illustrates. [c.133]

Although side-stripper arrangements are common in the petroleum industry, designers have been reluctant to use the fully thermally coupled arrangements in practical applications until recently. [c.154]

Nk is given by the application of Eqs. (7.14) to (7.16) to interval k. [c.228]

N = number of units or shells, whichever is applicable [c.230]

Growl, D. A., and Louvar, J. F., Chemical Process Safety Fundamentals with Applications, Prentice-Hall, Englewood Cliffs, N.J., 1990. [c.272]

Condensation. Condensation can be accomplished by increasing pressure or decreasing temperature. Generally, decreasing temperature is preferred, which usually means the use of refrigeration. Condensation is preferred when treating high concentrations. In many applications, recovered materials can be recycled. [c.304]

CHjSH CHSH-CHjOH. Usually obtained as an oil, m.p. 77 C. Developed as an antidote to poisoning by organic arsenicals by external application, it is of use in poisoning by Hg, Cu, Zn, Cd but not Pb. It acts by forming a chelate with the metal and so removing it from the system. [c.50]

Born-Haber cycle A thermodynamic cycle derived by application of Hess s law. Commonly used to calculate lattice energies of ionic solids and average bond energies of covalent compounds. E.g. NaCl [c.64]

Such step-limiting is often helpful because the direction of correction provided by the Newton-Raphson procedure, that is, the relative magnitudes of the elements of the vector J G, is very frequently more reliable than the magnitude of the correction (Naphtali, 1964). In application, t is initially set to 1, and remains at this value as long as the Newton-Raphson correotions serve to decrease the norm (magnitude) of G, that is, for [c.116]

The subroutine is well suited to the typical problems of liquid-liquid separation calculations wehre good estimates of equilibrium phase compositions are not available. However, if very good initial estimates of conjugate-phase compositions are available h. priori, more effective procedures, with second-order convergence, can probably be developed for special applications such as tracing the entire boundary of a two-phase region. [c.128]

As an example, consider ammonia synthesis. In an ammonia synthesis loop, hydrogen and nitrogen are reacted to ammonia. The reactor effluent is partially condensed to separate ammonia as a liquid. Unreacted gaseous hydrogen and nitrogen are recycled to the reactor. A purge on the recycle prevents the buildup of argon and methane, which enter the system as feed impurities. The purge can be burnt as fuel. Considerable quantities of hydrogen are lost in the purge, and recovery of this hydrogen is often economic. For such hydrogen recovery applications, only two processes are usually viable, cryogenic condensation and membranes. Separation by condensation relies on differences in volatility between the components. Separation of gases in a membrane unit is achieved due to the differences in the rates at which different gases permeate through the membrane. The membrane allows fast gases, such as hydrogen, to be separated from slow gases, such as methanfe. A fractional recovery of around 90 percent is possible with a single membrane, giving better than 90 percent hydrogen purity. [c.109]

As discussed earlier, the application of such techniques should be restricted until later in the design when the full heat-integration context both within and outside the disjtillation system has been established. [c.155]

Catalytic incinerators. Cataljdic incinerators allow oxidation of wastes at lower temperatures than conventional thermal incinerators. Operating temperatures are less than 550" C. Their advantages are lower fuel consumption if auxiliary fuel is required and less severe operating conditions for materials of construction. However, catalytic incinerators cannot handle solid waste, and catalyst fouling and aging are a problem. Catalysts are usually noble metals (such as platinum or rhodium) finely divided on a support such as alumina. Both fixed and fluidized beds are used. The most common applications for catalytic incinerators are dedicated devices to treat gaseous process vents, particularly purges. [c.300]

Bucherer reaction Bucherer discovered that the interconversion of 2-naphthol and 2-naphthylamine through the action of alkali and ammonia could be facilitated if the reaction was carried out in the presence of (HSO3]" at about 150 C. This reaction is exceptional for the ease with which an aromatic C —OH bond is broken. It is not of general application, it is probable that the reaction depends upon the addition of [HSO3]" to the normally unstable keto-form of 2-naphthol, and subsequent displacement of —OH by —NH2. [c.69]

See pages that mention the term

**Application**:

**[c.89] [c.117] [c.227] [c.53] [c.71] [c.148] [c.197] [c.205] [c.312] [c.313] [c.12] [c.13] [c.15] [c.24] [c.33] [c.40] [c.57] [c.74]**

See chapters in:

** Hazardous waste compliance
-> Application
**

Chemoinformatics (2003) -- [ c.146 , c.155 , c.487 ]

Surface and thin films analysis (2002) -- [ c.0 ]

Hazardous waste compliance (2001) -- [ c.17 ]

Thin-layer chromatography Reagents and detection methods (1990) -- [ c.0 ]

Advances in heterocyclic chemistry Vol.80 (2001) -- [ c.66 , c.285 ]

Advances in heterocyclic chemistry Vol.85 (2003) -- [ c.66 , c.285 ]