Species basis

The set of components used in a geochemical model is the calculation s basis. The basis is the coordinate system chosen to describe composition of the overall system of interest, as well as the individual species and phases that make up the system (e.g., Greenwood, 1975). There is no single basis that describes a given system. Rather, the basis is chosen for convenience from among an infinite number of possibilities (e.g., Morel, 1983). Any useful basis can be selected, and the basis may be changed at any point in a calculation to a more convenient one. We discuss the choice of basis species in the next section. 

The aqueous species included in the basis are known as basis species, while the remaining species in solution comprise the set of secondary species. 

Aj Aqueous species in the basis, the basis species Aj Other aqueous species, the secondary species... 

Here, v represents the reaction coefficients vwj is the number of moles of water in the reaction to form Aj, v,-j is the number of moles of the basis species Ai, and so on for the minerals and gases. 

Similar logic gives the mass balance equations for the species components. The mass of the i th component is distributed among the single basis species A, and the secondary species in the system. By Equation 3.22, there are v, j moles of component i in each mole of secondary species Aj. There is one mole of Na+ component, for example, per mole of the basis species Na+, one per mole of the ion pair NaCl, two per mole of the aqueous complex Na2SC>4, and so on. Mass balance for species component i, then, is expressed... 

To see how the governing equations might be solved, we consider a system that contains an aqueous fluid and several minerals but has no gas buffer. If we know the system s bulk composition in terms of Mw, Mi, and M, we can evaluate Equations 3.32-3.34 to give values for the unknown variables the solvent mass nw, the basis species molalities m, and the mineral mole numbers nt-... 

According to the mass balance Equation 3.28, the expression in parentheses is Mi. Further, the charge Z, on a species component is the same as the charge z, on the corresponding basis species, since components and species share the same stoichiometry. Substituting, the electroneutrality condition becomes,... 

This relation is useful because it effectively removes the requirement that Mj be known for one of the basis species. Instead of setting this value directly, it can be determined by balance from the mole numbers of the other basis species. When charged species appear in the basis, in fact, it is customary for equilibrium models to force charge balance by adjusting Mi for a component chosen either by the modeler or the computer program. 

The phase rule (Eqn. 3.52), then, predicts that our system has N = Ni degrees of freedom. In other words, given a constraint on the concentration or activity of each basis species, we could determine the system s equilibrium state. To constrain the governing equations, however, we need Nc pieces of information, somewhat more than the degrees of freedom predicted by the phase rule. 

In Chapter 3, we developed equations that govern the equilibrium state of an aqueous fluid and coexisting minerals. The principal unknowns in these equations are the mass of water n w, the concentrations m,- of the basis species, and the mole numbers n/c of the minerals. 

When the system chemistry is constrained by the concentration m, (or activity at) of a basis species, Equation 4.4 gives M, directly. 

Equation 4.4, for each basis species at unknown concentration nij. 

A modeler, however, sometimes constrains one or more components in terms of a basis species free concentration m,- (i.e., by specifying pH). Charge balance cannot be assured a priori because the system s bulk composition is not known until the iteration has converged. To force electrical neutrality, the model adjusts the mole number Mi of a charged component such as Cl- after each iteration. This adjustment may be of little practical importance, because laboratories commonly report chloride concentrations computed from charge balance rather than from direct analysis of the element. 

Choosing the location in the basis for the new mineral is a matter of identifying a basis species Ai that is similar in composition to the mineral to be removed and preferably in small concentration. The best species to be displaced from the basis satisfies... 

A flexible method for modeling redox disequilibrium is to divide the reaction database into two parts. The first part contains reactions between the basis species (e.g., Table 6.1) and a number of redox species, which represent the basis species in alternative oxidation states. For example, redox species Fe+++ forms a redox pair with basis species Fe++, and HS- forms a redox pair with SO4. These coupling reactions are balanced in terms of an electron donor or acceptor, such as 02(aq). Table 7.1 shows coupling reactions from the llnl database. 

A coupling reaction commonly links a redox species to a basis species, as in the examples above, but it is also possible to define couples among the redox species themselves. If HCOJ appears in the basis, for example, methane might be linked... 

In a final example of the use of a sliding activity path, we calculate a speciation diagram, plotted versus pH, for hexavalent uranium in the presence of dissolved phosphate at 25 °C. We take a 10 mmolal NaCl solution containing 1 mmolal each ofUO +, the basis species for U(VI), and HPO4... 

To incorporate nonlinear rate laws into the solution procedure for tracing kinetic reaction paths (Section 16.3), we need to find the derivative of the reaction rate with respect to the molalities m,- of the basis species A,. The derivatives are given by,... 

Manes and Manes-Pozzi have suggested a cluster of the type (Vq 2 Me ), which has been taken as the basis species for a statistical treatment aimed at the interpretation of the thermodynamic data on (Ui yPUy)02 x and Pu02 x. This cluster has later been called by Manes, Sdrensen et al. the tetrahedral defect The reason of this name lies in the fact that the local bond is supposed to occur in a coordination tetrahedron of an oxygen ion in the fluorite structure in this tetrahedron, one oxygen vacancy is formed, and the two electrons are shared with the four surrounding cations, giving rise (formally) to 2(Me ) locally bonded with the vacancy. Manes, Sorensen et al. showed that by... 

Conceptual Basis Species Velocities and Concentration Velocities... 

To do these things, we need to use building blocks different from those we would choose to merely describe bulk compositions as illustrated above. We must use not only a different basis, but a different kind of basis. We could use the elements themselves (Al, B, N,. .., etc.), plus the electronic charge, because this would certainly allow us to describe the composition of any species or phase. However, it has proved to be convenient to use as building blocks , or descriptive composition terms, entities which do exist - ordinary charged ions such as IICO and Na+. These are called basis species, component species, or master species, and they make up a new kind of basis, which is the minimum number of chemical formulas needed to describe the composition of all phases and all species, charged and uncharged in the system. If mineral or gas phases are present, their compositions must also be included in the basis, as described below. 

Suppose a system contains 1 mole of NaCl and 1 kg of water. The components as defined in 3.6.1 are NaCl and H2O, but the basis species needed to describe all the ions present are (in most programs other choices are always possible) Na+, Cl-, H+, and H2O. A speciation calculation gives the following results ... 

Note that the composition of all seven actual species can be described by some combination of the four basis species (e.g., NaOH = Na+ + H2O — H+), and that each basis species (other than H+ and H2O) represents the total amount of some element. Thus... 

Most modeling programs have a selection of 30 to 80 or more basis species, plus a collection of minerals and gases, from which the modeler chooses those required to describe the composition of all aqueous species, gases, and minerals in a particular system. If an element, say rubidium (Rb), does not occur as a basis species (as say, Rb+) in the database, the program is of course then unable to calculate the amounts of various rubidium species or minerals, even if we have an analysis for the rubidium content of our system. 

The distinction, then, between a species which actually exists in the real system, say, the sodium ion Na+, and the basis species, Na+, is very important. Just as in the nitrogen example above, component Na+ represents the total amount of sodium in the system, and species Na+ represents the sodium actually present as the univalent sodium ion in the solution. Similarly, in the output from the program, basis species and real species are commonly mixed together in some way, which is quite clear only if we are perfectly aware of the difference. 

It seems reasonable, then, that the elements actually analyzed appear in the Analyzed columns in the program output. What may be confusing is that many of them appear as both Analyzed and Calculated , and that the numbers in these two categories are completely different. For example, Ca2+ is analyzed at 904 mgL-1, but is calculated to be 654.3 mgL-1. It must be understood that in the Analyzed columns, Ca2+ represents the basis species chosen for calcium it is the calcium component, which equals the total calcium content of the solution. In the Calculated columns however, Ca2+ represents one of the calcium species actually present in the solution. 

We now seem to have two types of components. For example, for the system NaCl-H2O, we have either the two traditional components NaCl and H2O, which allow us to describe the bulk composition of all phases in this system, or we have the four basis speciesNa.+, Cl-, H+, and H20, which allow us to describe not only the compositions of the phases but also the concentration of all dissolved species in the system. Traditional components and basis species are simply different choices of components, which have different purposes and different descriptive powers. We need more basis species because they are called upon to provide more information. 

Readers familiar with Morel and Hering (1993) will recognize that what we have termed traditional components are Morel and Hering s recipes , and what we refer to as basis species they call simply components. 

Basis Species If, however, we use basis species as components, we will have more degrees of freedom to deal with. For example, using components NaCl and H2O, we have no control over the Na/Cl ratio, but using basis species Na+, Cl-, H+, and H2O, we do - we can specify Na+ and Cl- independently - an extra degree of freedom. In this case, the Phase Rule is no different, but we change the notation. Phase Rule (3.33) becomes, for a system having a specified T and P,... 

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