User's Guide to PHREEQC
, are defined that must be solved simultaneously to determine equilibrium for a given set of conditions. Most of these functions are derived from mole-balance equations for each element, exchange site, and surface site and from mass-action equations for each pure phase. Each function is reduced to contain a minimum number of variables, usually, one for each element, exchange site, surface site, and pure phase. The program uses a modified Newton-Raphson method to solve the simultaneous nonlinear equations. This method uses the residuals of the functions and an array of partial derivatives of each function with respect the set of master variables. For clarity, the set of variables used in partial differentiation are referred to as "master variables" or "master unknowns". The total derivatives of each function, 
, will be presented without derivation.After all of the functions are presented, the following section presents the solution algorithm for each type of speciation and forward model that can be solved by PHREEQC: initial solution (speciation), initial exchanger, initial surface, and reaction or transport modeling. A table of notation is included in Attachment A. In general, lack of a subscript or the subscript "(aq)" will refer to entities in the aqueous phase, "(e)" refers to exchangers, "(g)" refers to gases, and "(s)" refers to surfaces.