Mass balances model compounds

The mixture of PAHs present in a particular sample in many cases mirrors the sources that produce them. Several methods can be used to qualitatively identify the probable sources of PAHs. Commonly used methods include the abundance ratios of individual compounds, the fossil fuel pollution index (FFPI), and diagnostic ratios indicative of sources (petrogenic vs. pyrogenic). Quantitative apportionment of sources needs sophisticated statistical approaches such as the chemical mass balance models (Li et al., 2003). 

Organic compounds, natural, fossil or anthropogenic, can be used to provide a chemical mass balance for atmospheric particles and a receptor model was developed that relates source contributions to mass concentrations in airborne fine particles. The approach uses organic compound distributions in both source and ambient samples to determine source contributions to the airborne particulate matter. This method was validated for southern California and is being applied in numerous other airsheds. ... 

Concentration of Model Compounds in the Absence of Humic Substances at 120-150 Bed Volumes/h. Resin studies using XAD-4 quaternary resin in the hydroxide form were performed several times at 150 bed volumes/h at various concentrations of the model compounds. The primary objective of these studies was to make a preliminary evaluation of the separation and concentration capacity of XAD-4 quaternary (OH ) resin for the model compounds. Emphasis was thus placed on the measurement of each compound in the final eluant concentrate. However, whenever convenient, analyses were also made of the aqueous effluent and reservoir to provide for more complete mass balances. 

Table III. Summary of Percent Recovery and Percent Total Mass Balance of All Model Compounds in Bench-Scale Studies...

Table IV. Summary of Mass Balance and Percent Recoveries of All Model Compounds in All Pilot Studies...

Table III. Mass Balance of Model Compounds Recovered from Concentrator System Components...

Tremaine et al. (1994) conducted pilot-scale studies to compare the effect of a suspended-growth reactor and a fixed-film bioreactor with a constructed wetland environment in removing creosote-PAHs from contaminated water recovered from a wood-preserving facility. Mass balanced chemical analysis of 5 PAHs used as model constituents of creosote showed that the wetland yielded between 20 and 84% removal, whereas the fixed-film reactor yielded 90 to 99% PAH removal. Biodegradation accounted for >99% of the losses observed in the fixed-film reactor, but only 1-55% of the compounds removed in the artificial wetland was attributable to biodegradation. Again, physical sorption of PAHs, especially HMW PAHs, was found to be significant. 

The results of irradiating the pora-quinoid structures (compounds 1-4) absorbed onto cellulose sheets are summarized in Figure 2. Examination of the photolysis data indicates that with the notable exception of 2-methoxy-l,4-benzoquinone the remainingpara-quinone model compounds did not cause any further darkening of the handsheets during irradiation. Indeed, several of the quinones exhibit a minor brightening response upon photolysis which could be attributed to a photo-bleaching effect, but the lack of a complete mass balance makes this conclusion tenuous. 

Vectors, such as x, are denoted by bold lower case font. Matrices, such as N, are denoted by bold upper case fonts. The vector x contains the concentration of all the variable species it represents the state vector of the network. Time is denoted by t. All the parameters are compounded in vector p it consists of kinetic parameters and the concentrations of constant molecular species which are considered buffered by processes in the environment. The matrix N is the stoichiometric matrix, which contains the stoichiometric coefficients of all the molecular species for the reactions that are produced and consumed. The rate vector v contains all the rate equations of the processes in the network. The kinetic model is considered to be in steady state if all mass balances equal zero. A process is in thermodynamic equilibrium if its rate equals zero. Therefore if all rates in the network equal zero then the entire network is in thermodynamic equilibrium. Then the state is no longer dependent on kinetic parameters but solely on equilibrium constants. Equilibrium constants are thermodynamic quantities determined by the standard Gibbs free energies of the reactants in the network and do not depend on the kinetic parameters of the catalysts, enzymes, in the network [49]. 

The main variable of design for a CSTR is the hydraulic retention time (HRT), which represents the ratio between volume and flow rate, and it is a measure of the average length of time that a soluble compound remains in the reactor. Capital costs are related to HRT, as this variable directly influences reactor volume [83]. HRT can be calculated by means of a mass balance of the system in that case, kinetic parameters are required. Some authors obtained kinetic models from batch assays operating at the same reaction conditions, and applied them to obtain the HRT in continuous operation [10, 83, 84]. When no kinetic parameters are available, HRT can be estimated from the time required to complete the reaction in a discontinuous process. One must take into account that the reaction rate in a continuous operation is slower than in batch systems, due to the low substrate concentration in the reactor. Therefore, HRT is usually longer than the total time needed in batch operation [76]. 

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