Measurement, multicomponent mass

Vaclavek, V., and Loucka, M. (1976). Selection of measurements necessary to achieve multicomponent mass balances in chemical plants. Chem. Eng. Sci. 31,1199-1205. 

Inadequate knowledge of the process models and poor estimation of process parameters (physical properties, processing constants, etc.) mean that any technique for correcting the measurements should rely on simple, well-known, and indubitable process relationships, which should be satisfied independent of the measurements accuracy. Such relationships are the multicomponent mass and energy balances. 

Mass spectrometers measure the masses of positively charged ions striking a detector. This allows quantification of the sample by comparison with standard calibration gases for multicomponent mixtures. Mass spectrometers can analyze a sample point in less than 10 seconds. 

Working with multicomponent mixtures requires quantifying the amounts of various chemical constituents that comprise the mixture. In the conservation equations a mass fraction will be the most appropriate measure, since mass is a conserved quantity. By definition, the mass fraction is... 

In the present work we will deal with all the above problems and provide a unified framework to deal with the error correction for static or dynamic systems using multicomponent mass and energy balances. The topological character of the complex process is exploited for an easy classification of the measured and unmeasured variable independently of the linearity or nonlinearity of the balance equations. 

Complex polymer topologies, polymer blends, and multicomponent formulations require a different approach to perform a proper molecular characterization. In two-dimensional (2D) chromatography, different separation techniques are used to avoid co-elution of species and to measure molar mass and chemical composition in a truly independent way [5]. 

Diffusion is the mass transfer caused by molecular movement, while convection is the mass transfer caused by bulk movement of mass. Large diffusion rates often cause convection. Because mass transfer can become intricate, at least five different analysis techniques have been developed to analyze it. Since they all look at the same phenomena, their ultimate predictions of the mass-transfer rates and the concentration profiles should be similar. However, each of the five has its place they are useful in different situations and for different purposes. We start in Section 15.1 with a nonmathematical molecular picture of mass transfer (the first model) that is useful to understand the basic concepts, and a more detailed model based on the kinetic theory of gases is presented in Section 15.7.1. For robust correlation of mass-transfer rates with different materials, we need a parameter, the diffusivity that is a fundamental measure of the ability of solutes to transfer in different fluids or solids. To define and measure this parameter, we need a model for mass transfer. In Section 15.2. we discuss the second model, the Fickian model, which is the most common diffusion model. This is the diffusivity model usually discussed in chemical engineering courses. Typical values and correlations for the Fickian diffusivity are discussed in Section 15.3. Fickian diffusivity is convenient for binary mass transfer but has limitations for nonideal systems and for multicomponent mass transfer. 

The standard method to measure pure gas adsorption equilibria most often used today is the volumetric or manometric method. Chap. 2. Basically it is the mass balance of a certain amount of gas partly adsorbed on the sorbent material. This method can be realized in either open or closed systems, the former ones often using a carrier gas, the adsorption of which normally being neglected. Complemented by a gas analyzer (chromatograph, mass spectrometer) this method also can be used to measure multicomponent or coadsorption equilibria. 

Figure 3.25. Schematic of a gravimetric instrument to measure multicomponent gas adsorption equilibria. Concentrations of the sorptive gas mixture supplied are assumed to be known. After equilibration, concentrations of the sorptive gas components are determined in a gas chromatograph or mass spectrometer [3.16, 3.20, 3.41],...

Mass spectrometers have been used at some level in all of these types of investigations because of their unsurpassed sensitivity and specificity, their multicomponent analytical capability and, in some cases, their ability to provide precise and accurate isotope ratios. Traditional methods of analysis typically involve the collection of water and sediment samples, or biological specimens, during field expeditions and cmises on research vessels (R/Vs), and subsequent delivery of samples to a shore-based laboratory for mass spectrometric analyses. The recent development of field-portable mass spectrometers, however, has greatly facilitated prompt shipboard analyses. Further adaptation of portable mass spectrometer technology has also led to construction of submersible instruments that can be deployed at depth for in situ measurements. 

It has been pointed out that routine accurate mass measurements are conducted at resolutions which are too low to separate isobaric isotopic compositions in most cases. Unfortunately, coverage of multiple isotopic compositions under the same signal distort the peak shape. This effect causes a loss of mass accuracy when elemental compositions have to be determined from such multicomponent peaks, e.g., if the monoisotopic peak is too weak as the case with many transition metals. The observed decrease in mass accuracy is not dramatic and the loss of mass accuracy is counterbalanced by the information derived from the isotopic pattern. However, it can be observed that mass accuracy decreases, e.g., from 2-3 mmu on monoisotopic peaks to about 4—7 mmu on multicomponent signals. 

It was found that the requirements were satisfied for application of the linear regression technique to species mass concentrations in a multicomponent aerosol. The results of 254 particle size distributions measured at China Lake in 1979 indicate that the normalized fine aerosol volume distribution remained approximately constant. The agreement between the calculated and measrued fine particle scattering coefficients was excellent. The measured aerosol sulfur mass distribution usually followed the total distribution for particles less than 1 ym. It was assumed that organic aerosol also followed the total submicron distribution. 

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

Sedimentation velocity. Tire relative molecular mass Mr can also be measured from observation of the velocity of movement of the boundary (or boundaries for multicomponent systems) between solution and solvent from which the macromolecules have sedi-... 

First, we measured thermodynamic and mass transfer data of the multicomponent system olive 0U/CO2 (3,4). The phase equilibria was modulated by correlating the partition coefficients (Kj = y /x ) of each component present in the mixture as a function of the mole fraction of the FFA fraction in the liquid phase (3). Mass transfer studies were performed in a lab-scale countercurrent packed column. The experimental measured mass transfer coefficients were... 

Mass and molar diffusion are important in practice, and can be derived from the Maxwell-Stefan description of diffusion. The Maxwell-Stefan multicomponent diffusivities are obtained from the binary diffusivities, which are easy to measure. 

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