Mineral mass, calculation

The dump command serves to eliminate the small mineral masses that precipitate when, at the onset of the calculation, the program brings seawater to its theoretical equilibrium state (see Chapter 6). The delxi and dxplot commands serve to set a small reaction step, assuring that the results are rendered in sufficient detail. 

Figure2 Ohnishi et al. (1985) and Chijimatsu et al. (2000)) and reactive-mass transport model (inside the box named Chemical in Figure 2). This is a system of governing equations composed of Equations (l)-(9), which couple heat flow, fluid flow, deformation, mass transport and geochemical reaction in terms of following primary variables temperature T, pressure head y/, displacement u total dissolved concentration of the n master species C< > and total dissolved and precipitated concentration of the n" master species T,. Here we set master species as the linear independent basis for geochemical reactions, and speciation in solution and dissolution/precipitation of minerals are calculated by a series of governing equations for geochemical reaction. Now we adopt equilibrium model for geochemical reaction (Parkhurst et al. (1980)), mainly because of reliability and abundance of thermodynamic data for geochemical reaction.

Changes in fracture transport characteristics that result from the removal or redistribution of mineral mass within a fracture may be constrained by calculating the evolution of permeability with the concurrent loss or redistribution of mineral mass. Mass loss is unambiguously recorded by the effluent flux, but redistribution may only be discerned by imaging. Independent measurements of fluid and mineral flux, concurrent with non-invasive imaging, are used to constrain the processes controlling mass redistribution within the fracture. 

The results of the fractionation model (Fig. 18.9) differ from the equilibrium model in two principal ways. First, the mineral masses can only increase in the fractionation model, since they are protected from resorption into the fluid. Therefore, the lines in Fig. 18.9 do not assume negative slopes. Second, in the equilibrium calculation the phase rule limits the number of minerals present at any point along the reaction path. In the fractionation calculation, on the other hand, no limit to the number of minerals present exists, since the minerals do not necessarily maintain equilibrium with the fluid. Therefore, the fractionation calculation ends with twelve minerals in the system, whereas the equilibrium calculation reaches an invariant point at which only six minerals are present. 

The theoretical chemical formula of a mineral is unique and identifies only one species. Nevertheless, the actual chemical composition is usually variable within a limited range owing to the isomorphic substitutions (i.e., diadochy), or/and low presence of traces of impurities. The relative atomic or molecular mass (based on C = 12.000) of minerals is calculated from the theoretical formula using the last value of atomic masses adopted by the International Union of Pure and Applied Chemistry (lUPAC) in 2001, and the theoretical chemical composition is commonly expressed in percentage by weight (wt.%) of elements and sometimes oxides for oxygenated minerals. 

C03-0102. Calculate the mass percentages of all of the elements in the following semiprecious minerals (a) lapis lazuli, N34 AI3 Si3 O12CI (b) garnet, Mgg AI2 (Si04)3 (c) turquoise,... 

As geochemists, we frequently need to describe the chemical states of natural waters, including how dissolved mass is distributed among aqueous species, and to understand how such waters will react with minerals, gases, and fluids of the Earth s crust and hydrosphere. We can readily undertake such tasks when they involve simple chemical systems, in which the relatively few reactions likely to occur can be anticipated through experience and evaluated by hand calculation. As we encounter more complex problems, we must rely increasingly on quantitative models of solution chemistry and irreversible reaction to find solutions. 

The first and most critical step in developing a geochemical model is conceptualizing the system or process of interest in a useful manner. By system, we simply mean the portion of the universe that we decide is relevant. The composition of a closed system is fixed, but mass can enter and leave an open system. A system has an extent, which the modeler defines when he sets the amounts of fluid and mineral considered in the calculation. A system s extent might be a droplet of rainfall, the groundwater and sediments contained in a unit volume of an aquifer, or the world s oceans. 

Fig. 2.1. Schematic diagram of a reaction model. The heart of the model is the equilibrium system, which contains an aqueous fluid and, optionally, one or more minerals. The system s constituents remain in chemical equilibrium throughout the calculation. Transfer of mass into or out of the system and variation in temperature drive the system to a series of new equilibria over the course of the reaction path. The system s composition may be buffered by equilibrium with an external gas reservoir, such as the atmosphere.

Once the initial equilibrium state of the system is known, the model can trace a reaction path. The reaction path is the course followed by the equilibrium system as it responds to changes in composition and temperature (Fig. 2.1). The measure of reaction progress is the variable , which varies from zero to one from the beginning to end of the path. The simplest way to specify mass transfer in a reaction model (Chapter 13) is to set the mass of a reactant to be added or removed over the course of the path. In other words, the reaction rate is expressed in reactant mass per unit . To model the dissolution of feldspar into a stream water, for example, the modeler would specify a mass of feldspar sufficient to saturate the water. At the point of saturation, the water is in equilibrium with the feldspar and no further reaction will occur. The results of the calculation are the fluid chemistry and masses of precipitated minerals at each point from zero to one, as indexed by . 

Mass transfer can be described in more sophisticated ways. By taking in the previous example to represent time, the rate at which feldspar dissolves and product minerals precipitate can be set using kinetic rate laws, as discussed in Chapter 16. The model calculates the actual rates of mass transfer at each step of the reaction progress from the rate constants, as measured in laboratory experiments, and the fluid s degree of undersaturation or supersaturation. 

A calculation procedure could, in theory, predict at once the distribution of mass within a system and the equilibrium mineral assemblage. Brown and Skinner (1974) undertook such a calculation for petrologic systems. For an -component system, they calculated the shape of the free energy surface for each possible solid solution in a rock. They then raised an n -dimensional hyperplane upward, allowing it to rotate against the free energy surfaces. The hyperplane s resting position identified the stable minerals and their equilibrium compositions. Inevitably, the technique became known as the crane plane method. 

Set a constraint for each basis member that you want to include in the calculation. For instance, the constraint might be the total concentration of sodium in the fluid, the free mass of a mineral, or the fugacity of a gas. You may also set temperature (25 °C, by default) or special program options. 

The program produces in its output dataset a block of results that shows the concentration, activity coefficient, and activity calculated for each aqueous species (Table 6.4), the saturation state of each mineral that can be formed from the basis, the fugacity of each such gas, and the system s bulk composition. The extent of the system is 1 kg of solvent water and the solutes dissolved in it the solution mass is 1.0364 kg. 

Table 6.6. Calculated saturation indices of various minerals in seawater and the mass of each precipitate in the stable phase assemblage...

Here, we set a vanishingly small free mass for each mineral so that only negligible amounts can dissolve during the calculation s second step, when supersaturated minerals precipitate from the fluid. 

First, we read in the dataset of complexation reactions and specify that the initial mass balance calculations should include the sorbed as well as aqueous species. We disable the ferric-ferrous redox couple (since we are not interested in ferrous iron), and specify that the system contains 1 g of sorbing mineral. 

The calculation begins with an initial fluid of specified isotopic composition. The model, by mass balance, assigns the initial compositions of the solvent and each aqueous species. The model then sets the composition of each unsegregated mineral to be in equilibrium with the fluid. The modeler specifies the composition of each segregated mineral as well as that of each reactant to be added to the system. 

Once we have computed the total isotopic compositions, we calculate the compositions of the reference species using the mass balance equations (Eqns. 19.13, 19.20, 19.21, 19.22). We can then use the isotopic compositions of the reference species to calculate the compositions of the other species (Eqns. 19.10, 19.14, 19.15, 19.16) and the unsegregated minerals (Eqns. 19.11,19.17,19.18, 19.19). 

In the next chapter (Chapter 27) we show calculations of this type can be integrated into mass transport models to produce models of weathering in soils and sediments open to groundwater flow. In later chapters, we consider redox kinetics in geochemical systems in which a mineral surface or enzyme acts as a catalyst (Chapter 28), and those in which the reactions are catalyzed by microbial populations (Chapter 33). 

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