Calculates Mass Transfer for Geochemical Reactions in Ground Water

BALANCE is a USGS computer program for calculating mass transfer for geochemical reactions in ground water. BALANCE is designed to help define and quantify chemical reactions between ground water and minerals. Data required to run BALANCE are:
  • the chemical compositions of two water samples, generally assumed to represent points along a flow path, and
  • the chemical compositions of a set of minerals, organic substances, or gases, which we will call phases, selected as the reactants or products in the system.
    Implicit in this treatment is the assumption that only these selected phases participate in the chemical reactions that determine the composition of the final water.

    BALANCE calculates the mass transfer (amounts of phases entering or leaving the aqueous phase) necessary to account for the observed changes in composition between the two solutions. The purpose of BALANCE is to derive balanced reactions of the form:

    Initial Solution + Reactant Phases-> Final Solution + Product Phases

    A "reaction model" is defined by the selected phases and the calculated amount of each phase necessary to satisfy the equation. In general, many reaction models can account for an observed change in water chemistry. BALANCE alone cannot determine if any one, unique set of phases governs the reactions in the ground-water system.

    BALANCE models are not constrained by any thermodynamic criteria and may imply reactions that are thermodynamically impossible. Methods for identifying reaction models that do not satisfy thermodynamic or other criteria are presented in Plummer and others (1982). In the ideal case, all but one reaction model can be eliminated, leaving one unique chemical model consistent with the available data.
    BALANCE is designed specifically for mineral-water interactions, but essentially, BALANCE solves any set of linear equations formulated by the user. The report includes discussions of several processes which can be formulated as linear equations:
  • (1) mass balance on elements,
  • (2) mixing end-member waters,
  • (3) oxidation-reduction reactions, and
  • (4) simple isotope balance.


    In order to use BALANCE, the chemical composition of two waters must be known. Only the total concentrations of each element are required for models in which redox reactions are not considered. BALANCE accepts two kinds of concentration data as input:
  • (1) the total concentration of each element in the initial and final solution or
  • (2) the difference in total concentration for each element between the final and initial solutions (final - initial). If data are unavailable for some element, reasonable assumptions may describe the change in concentration for that element. For example, if the total concentration of iron is not known but can be assumed to be very low, then it may be reasonable to assume that iron is essentially conserved in any reaction and that the difference in iron concentration between the initial and final solution is zero. The problem of missing analytical data is discussed more thoroughly in Plummer and others (1982).


    The phases to be used in the calculations are selected by the user on the basis of the geology, hydrology, or mineralogy of the system. These "plausible" phases generally are mineral solids but may also include gases, ion exchangers, or (in the special case of mixing) other aqueous solutions. For the purposes of this program, a phase represents a set of chemical elements that enter or leave the initial solution in fixed ratios. The objective in selecting phases is to provide a source or sink for each element in the initial and final solutions. The result is a set of linearly-independent equations which can be solved simultaneously to yield values that describe the amount of each phase participating in the reaction.
    In general, the number of phases must equal the number of elements in order to solve the set of equations. Although the calculated mass transfer for one or more phases might be zero, indicating that the phase(s) did not participate in the reaction, the phase(s) must still be included in the input to BALANCE in order to perform the calculations.


    BALANCE also allows for the following type of problem: Two end-member waters mix in unknown proportions and, in addition, phases dissolve and precipitate to produce a final water. In this problem, the two initial solutions are treated exactly like other phases and a1 is the fraction of initial solution 1 and a2 is the fraction of initial solution 2 which combine, along with mineral reactions, to produce the final solution. In addition to the element mass balance equations, an additional equation is automatically included to ensure the sum of the two fractions is equal to 1.

    a1 + a2 = 1

    For a mixing problem, the number of phases (other than solutions) that must be included is equal to the number of elements minus one, P = J - 1.


    When studying systems involving oxidation and reduction, it is necessary to conserve electrons in chemical reactions. Each mole of electrons released in oxidizing certain species must be consumed by reducing other species. We use the electron-counting convention from the program PHREEQE (Parkhurst and others, 1980) to ensure conservation of electrons. (See also Plummer and others, 1982.)
    A redox species is defined as a species of any element which can occur in more than one oxidation state in natural aqueous environments. The rules for determining the operational valence of aqueous species are: The operational value of a phase is defined in the same way as for a dissolved complex.
    Using these definitions, a linear equation ensuring the conservation of electrons can be formulated. The redox state is included in BALANCE input as an "element."


    The results of running the program BALANCE are a set of numbers indicating the moles of each phase which react with the initial solution to produce the final solution (positive for dissolution, negative for precipitation). In the mixing case, the numbers for solution 1 (a1) and solution 2 (a2) are the mixing fractions for the two solutions.
    BALANCE accesses an external data base file containing default data for phase names, standard abbreviations for the constituent elements in the phase, the stoichiometric coefficients for the phase elements and RS, the operational valence of the phase if redox is considered.
    BALANCE includes an internal editor, BALNINPT for creating/modifying the required BALANCE input data files.
    Both source and executable codes are included with the package.

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