Carbon mass balance model

In this chapter, we develop a mass balance model of the fractionation in reacting systems of the stable isotopes of hydrogen, carbon, oxygen, and sulfur. We then demonstrate application of the model by simulating the isotopic effects of the dolomitization reaction of calcite. 

Figure 13.22 Mass balance model of carbon in the Baltic proper carbon fluxes are expressed as g C m-2 y-1 and reservoirs are in g C m-2. Unbalanced fluxes are indicated by a question mark and the vertical arrow at the bottom of each organism compartment represents respiration (Elmgren, 1984). (Modified from and Sandberg et al., 2000, with permission.)...

Because dissolved N2 is assumed to be inert in seawater (at least under the most common condition, see discussion below), it can serve as a tracer of physical processes (Emerson et al., 1995) Measurements of dissolved N2 in combination with Ar and O2 measurements were successfully used in mass balance models of the upper ocean in order to quantify the net biological O2 production and the associated carbon production (Emerson et al., 1991, 1995, 1997). 

A mass balance model for carbon based on the observations of many workers in this field is shown in Figure 6.1. It is designed to give some indication of the types of profiles that might be expected in a typical sediment column from a mass balance point of view, rather than to... 

Fig. 6.20 Estimated carbon isotopic fractionation during photosynthesis (broken line) and derived atmospheric 02/C02 ratio (solid line) in comparison with mass-balance model of atmospheric 02/C02 ratio (half-tone band) spanning the Carboniferous-Permian glaciation (after Beerling et al. 2002).

On the other hand, many investigations have shown that Saturation Indices are a reasonably good guide to certain phases, such as some carbonate and sulfate minerals. Saturation Indices are also quite useful in reaction path modeling (Chapter 8) and inverse mass balance modeling (Chapter 9) in the sense that they indicate (within the accuracy of the data) which processes are possible (e.g., precipitation of a phase having an SI > 0), and which are impossible (e.g., dissolution of a phase having an SI > 0). 

Note that the carbon isotopes are solely constrained by the DIC and < 13C values. Therefore, the two inverse mass balance models give the same results with respect to calculated travel time. Precipitation of illite, quartz, or kaolinite, the dissolution of gypsum and plagioclase, and Ca-Na exchange are needed to interpret the increases of Na+, SO2-, and SiC>2(aq), and decreases of Ca2+ and K+ in downgradient wells. 

White, A.F., and Chuma, N.J., 1987. Carbon and isotopic mass balance models of Oasis Valley-Fortymile Canyon groundwater basin, southern Nevada. Water Resources Res., v. 23, no. 4, pp. 571-582. 

The general mass balance model for marine carbon... 

So far, considerable information of the gaseous exhaust pipe emission factors and some of particulate matter is available from the 1990s. More recent studies reported emission factors for PM mass, organic carbon (OC), elemental carbon (EC) and some metals, which improved present knowledge about composition and size distribution of particulate motor vehicle emissions, and more important which allowed the creation of emission profiles—a prerequisite for source apportionment studies with statistic methods such as chemical mass balance models. However, since fuel composition, engines and vehicle technologies evolve (Kleeman et al. 2000) data on the combined mass emission rate and chemical composition of primary particle emissions from motor vehicles need to be updated periodically. 

Is there an explanation for this strong deviation In the model (2.1)-(2.3) the fuel feed is considered within the boundary condition of the carbon mass balance (2.1). Technically this corresponds to the feed of dry coal into the reactor through the sidewall. On the contrary in the existing PFBC plants coal is fed into the reactor as a coal water mixture (CWM) with a water... 

The second effort one was to create a benthic ecosystem model and to combine it with the seafloor plume diffusion and resedimentation model. The ecosystem model was created based on a carbon mass balance in the bottom layer. Then a series of preliminary test calculations under the resedimentaion and the direct desfiuction conditions were conducted introducing the JET and DIETS data, respectively. 

Figure 5. (a) Photocatalyzed mineralization of perchloroethylene (PCE) vs. time. PCE (O), product CO2 (X). Solid curves kinetic model for PCE disappearance carbon mass balance for CO2 appearance. [PCEq] = 207 juM. (b) Photocatalyzed benzene mineralization vs. time. Benzene ( ), product CO2 (X). Solid curves kinetic model for benzene disappearance assuming no one, one, and two important intermediates. Taken from [38]. 

Using a "home made" aneroid calorimeter, we have measured rates of production of heat and thence rates of oxidation of Athabasca bitumen under nearly isothermal conditions in the temperature range 155-320°C. Results of these kinetic measurements, supported by chemical analyses, mass balances, and fuel-energy relationships, indicate that there are two principal classes of oxidation reactions in the specified temperature region. At temperatures much lc er than 285°C, the principal reactions of oxygen with Athabasca bitumen lead to deposition of "fuel" or coke. At temperatures much higher than 285°C, the principal oxidation reactions lead to formation of carbon oxides and water. We have fitted an overall mathematical model (related to the factorial design of the experiments) to the kinetic results, and have also developed a "two reaction chemical model". 

The gas channels contain various gas species including reactants (i.e., oxygen and hydrogen), products (i.e., water), and possibly inerts (e.g., nitrogen and carbon dioxide). Almost every model assumes that, if liquid water exists in the gas channels, then it is either as droplets suspended in the gas flow or as a water film. In either case, the liquid water has no affect on the transport of the gases. The only way it may affect the gas species is through evaporation or condensation. The mass balance of each species is obtained from a mass conservation equation, eq 23, where evaporation/condensation are the only reactions considered. 

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