Reactional assemblage

It will be discussed in the following Chapters how the previous calculations can be inverted in order to retrieve from mixing arrays  

The constrained least-square method is developed in Section 5.3 and a numerical example treated in detail. Efficient specific algorithms taking errors into account have been developed by Provost and Allegre (1979). Literature abounds in alternative methods. Wright and Doherty (1970) use linear programming methods that are fast and offer an easy implementation of linear constraints but the structure of the data is not easily perceived and error assessment inefficiently handled. Principal component analysis (Section 4.4) is more efficient when the end-members are unknown. 

As we will see in more detail in Chapter 2, three vectors in a two-dimensional space cannot be independent and there exists an infinity of relationships such that 

More generally, when a reaction exists among the n minerals or end-members of a mixture, there exist n numbers v, (j = 1,. .., n) such that 

The breakdown of a mixture into its end-members is no longer unique and additional assumptions are needed. 

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Figure 1.4 A reactional assemblage enstatite-forsterite-quartz in the 2-dimensional space Si02-MgO. Enstatite can be decomposed as 3/4 forsterite plus 1/4 quartz.

Tracy R. J., Rye D. M., Hewitt D. A., and Schiffries C. M. (1983) Petrologic and stable-isotopic studies of fluid-rock interactions, south-central Connecticut I. The role of infiltration in producing reaction assemblages in impure marbles. Am. J. Set 283A, 589-616. 

THE OPTIMAL REACTION ASSEMBLAGE IN THE STEAM REFORMING OF METHANE TO PRODUCE SYNGAS... 

The steam reforming of methane to produce syngas includes nine basic reactions. The global equilibrium yield (GEY) and the potential maximal equilibrium yield (PMEY) can be calculated by a new method proposed by this paper. The optimal reaction assemblage (ORA) can be constructed by an optimization method. Where hydrogen is the desired product, the ORA is composed of reactions (1) and (2) in the nine-reaction system. The observed peak yield (OPY) of hydrogen equals 2.410 (mole fraction), its PMEY and GEY equal 3.341 (mole fraction). If carbon monoxide is the desired product, the ORA includes only reaction (1) in the nine-reaction system and the OPY, GEY and PMEY of carbon monoxide equal 0.344, 0.2767 and 0.9789 (mole fraction) respectively. Construction of the ORA is the key and fundamental way to improve the yield of a desired product. In this paper, the method of constructing the ORA is developed. 

THE REACTION SYSTEM OF STEAM REFORMING OF METHANE AND ITS OPTIMAL REACTION ASSEMBLAGE... 

The calculated results of the reaction assemblage of steam reforming of methane... 

The number of reactions subordinated to the optimal reaction assemblage M If H2 is the desired product then P4 and R2 are subordinates of the optimal reaction assemblage M, i.e. 

If a co-product, such as H2 + 00, is the desired product then the demanded ratio of co-products determines the construction of the optimal reaction assemblage. Thereby, the correct strategy to decide which reactions must be accelerated and which have to be inhibited will be adopted commercially. 

Let us take reaction (4) for example. Superficially, it is favourable to product H2 and CO, so that it looks as if the reaction is subordinated to the optimal reaction assemblage M. But this view is not correct. Although C forms CO via reaction (4), the C itself comes from CH4 via reaction (3). 

H2 and CD and the value of the GEY of the reaction set involving reaction (4) will reduce accordingly. Thereby only the reactions belonging to the optimal reaction assemblage can be promoted, and other reactions must be inhibited. 

The reaction system of steam reforming of methane to produce syngas consists of nine basic reactions. If H2 is the desired product, the optimal reaction assemblage involves reactions (1) and (2), i.e. 

The value of IMEY gives the information on the maximal limit of yield of a desired product. The construction of an optimal reaction assemblage is the fundamental way to improve the yield of desired products. 

Kp - chemical equilibrium constant in terms of partial pressure M - symbol of optimal reaction assemblage 0PY - observed peak yield P - pressure... 

For example, assuming anhydrite-magnetite-calcite-pyrite-pyrrhotite buffers redox in sub-seafloor reaction zones and a pressure of 500 bars, dissolved H2Saq concentrations of 21 °N EPR fluid indicate a temperature of 370-385°C. However, the estimated temperatures are higher than those of the measurement. This difference could be explained by adiabatic ascension and probably conductive heat loss during ascension of hydrothermal solution from deeper parts where chemical compositions of hydrothermal solutions are buffered by these assemblages. 

Sometimes the calculation predicts that the fluid as initially constrained is supersaturated with respect to one or more minerals, and hence, is in a metastable equilibrium. If the supersaturated minerals are not suppressed, the model proceeds to calculate the equilibrium state, which it needs to find if it is to follow a reaction path. By allowing supersaturated minerals to precipitate, accounting for any minerals that dissolve as others precipitate, the model determines the stable mineral assemblage and corresponding fluid composition. The model output contains the calculated results for the supersaturated system as well as those for the system at equilibrium. 

The extra pieces of information describe the extent of the system - the amounts of fluid and minerals that are present. It is not necessary to know the system s extent to determine its equilibrium state, but in reaction modeling (see Chapter 13) we generally want to track the masses of solution and minerals in the system we also must know these masses to search for the system s stable phase assemblage (as described in Section 4.4). 

Over the course of a reaction model, a mineral may dissolve away completely or become supersaturated and precipitate. In either case, the modeling software must alter the basis to match the new mineral assemblage before continuing the calculation. Finally, the basis sometimes must be changed in response to numerical considerations (e.g., Coudrain-Ribstein and Jamet, 1989). Depending on the... 

Carbonate-rich rock formations can be observed in most Japanese geothermal fields. In the Sumikawa field, Akita, Japan, for example, C02-rich ground waters are thought to have reacted with reservoir rocks according to reaction (1), to form a carbonate and kaolinite alteration assemblage. An isotopic investigation of... 

Given the mineral assemblage quartz (qz)-pyroxene (px)-garnet (ga)-plagioclase (pi) compositions given in Table 5.18, discuss the possible reactions between mineral end-members. 

This loading approach is successful for the relatively unhindered 6-hydroxyl, but proved to be inefficient for more sterically encumbered alcohols. A modification of the abovementioned method has been developed to enable attachments through these more hindered sites.9 This process is accomplished with inexpensive materials, and the linker is compatible with a variety of reaction conditions. Moreover, it allows for facile recycling of the polymer support for further use once the final carbohydrate assemblage is cleaved from the resin. 

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