Infiltration of nonequilibrium fluid causes down-
[4]
stream propagation of pronounced shifts in chemistry and mineralogy
that originate at the upstream end of the flow system. These reaction
fronts were the focus of numerous studies in metamorphic environments as
they provide, potentially, the means to determine rates of fluid flow,
fluid composition, and fluid transport mechanisms. The ``tracers'' used to
identify fronts include
changes in modal mineralogy resulting from progress of fluid-driven
net-transfer reactions, changes in elemental concentrations resulting from
fluid-rock exchange reactions, and shifts in stable and radiogenic isotope
ratios resulting from fluid-rock isotope exchange reactions.
Displacements of chemical fronts allow estimates of one-dimensional fluid fluxes with relations of the form [see Blattner and Lassey, 1989]:
where 
is the tracer front displacement,
is a ``carrier porosity'' equivalent to
in terms of interconnected porosity
and equilibrium distribution coefficient k, u is fluid pore
velocity,
and t is time. It is now becoming clear, however, that
critical application of the above equation to field relations is
warranted. The proviso that k refers only to exchangeable
quantities of the species of interest means that 
depends on
the mechanism of mass transfer; processes that operate within system REVs
must be known in detail if continuum mechanics is to yield useful
information. Recognition of such complexities is driving researchers to
examine more closely the factors that govern formation of reaction fronts.
The duration of flow is also of interest if
metamorphic hydrodynamics is to be quantified, yet
deconvolution of 
, u, and t requires additional
independent information. Shapes of reaction fronts (in terms of distance
versus tracer quantity space), controlled by dispersive forces that act to
distend the fronts, are providing such information. Dispersive forces that
have been considered include diffusion in the fluid and solid phases,
hydrodynamic dispersion, and the kinetics of fluid-mineral reaction
[ Bowman and Willett, 1991].
Lasaga and Rye [1993] analyzed the effects of kinetics that can be propagated down stream during fluid-driven metamorphic reactions. They presented simple analytical equations showing that fluid-rock reaction fronts defined by the exhaustion of a reactant mineral propagating in the direction of fluid flow will likely be associated with a zone of marked nonequilibrium between fluid and rock. The width (in the case of one-dimensional flow) of this zone is determined by the ratio of fluid velocity to reaction rate. Following earlier work by Lasaga, the propagating reaction front and associated zone of nonequilibrium is referred to as a ``kinetic isograd.''
A central theme in the work of Lasaga and Rye is the concept of
``steady state'' in reactive rock systems open to fluid flow.
They stated that the persistence of nonequilibrium between fluid and
rock over a fixed geometry is a form of steady state. It can be
argued that the use of the term ``steady state'' in this context is
unfortunate as it obscures the likely pervasiveness of the phenomenon
that they describe. This is because for many workers steady state has
a very precise meaning: time invariance for the quantity of interest.
In their derivations Lasaga and Rye used as their quantity of
interest the concentration of a chemical species in a packet of fluid
that flows through a rock system. Time invariance of solute
concentration c for a flowing fluid packet
implies 
. Nonequilibrium time-invariance,
by this definition, occurs only under certain special circumstances
(for example, in the case of nonlinear reaction kinetics presented by
Lasaga and Rye) and accordingly is unlikely to be the general case in
nature. However, the steady state referred to by Lasaga and Rye is
the local time invariance customary in fluid mechanics and other
disciplines. In this definition of steady state, the quantity of interest
is the concentration in the fluid at a fixed position in the
rock column rather than in a flowing packet of fluid. That is,
(x, y, and z are spatial
coordinates) while 
; concentration c changes by virtue
of motion through the rock column only. The quantity used in the
derivations is not the same as that used to define steady state.
What is more, the relevant equations are derived without imposing
even this less restrictive steady state condition
.
The latter is simply the consequence of invoking steady rates of
fluid flow and reaction. Local concentrations at a fixed point will
always achieve time invariance when supply and withdrawal occur at
constant rates.
It is worth emphasizing then, that the conclusions reached by Lasaga and Rye [1993] do not depend on fortuitous circumstances leading to time invariance but are, in fact, the inevitable consequences of constant rates of fluid flow and reaction! The question is not whether steady state is viable, but rather whether fluid velocities and reaction rates are likely constant (or nearly so) for geologically long time periods.