Computational simulations of metamorphic fluid flow systems on the scale of kilometers concentrated on the interrelationships among fluid flow, heat transfer, and chemical reaction progress.
Workers have traditionally drawn clear distinctions between metamorphic environments in which reactions were driven by infiltration of disequilibrium fluid, referred to here as ``fluid-driven reactions,'' and those in which fluids and rock maintained equilibrium (or nearly so) as reactions proceeded in response to changes in other factors such as temperature or pressure. Phillips [1991] refers to the latter as ``gradient reactions.'' Models by Steefel and Lasaga [1992] showed that such distinctions are somewhat artificial.
Steefel and Lasaga constructed a finite-difference model for two-dimensional flow of surface-derived water into zones of active low-temperature metamorphism on the scale of several kilometers. Results show that hydrodynamic dispersion can result in mixing among particles of fluid having different temperature-composition histories along closely spaced stream lines of flow. The scale of dispersive mixing is commensurate with the scale of significant temperature gradients in the fictive system, implying that the driving forces for reactions are likely to include both fluid-driven and gradient components. Hydrodynamic dispersion can now be added to the list of processes that influence metamorphic reaction paths.
Whereas Steefel and Lasaga [1992] focused on the effects of hydrodynamic properties on the mineralogical history of rocks, Hanson [1992] and Steefel and Lasaga [1994] emphasized the influence of metamorphic reactions on kilometer-scale hydrodynamics using two-dimensional explicit and implicit finite difference calculations, respectively. The studies by Hanson [1992] and Steefel and Lasaga [1994] examined different aspects of the problem. The difference is made evident by summarizing their work in terms of the equation of continuity for fluid flowing through porous rock:
The left-hand term
describes the time rate of change of the fluid mass where 
is
the volumetric porosity, 
is fluid density, and t is time.
The first term on the right describes the change in mass owing
to a net change in fluid flux J
and the second term R represents the fluid source-sink term.
Hanson [1992] considered the influence of prograde dehydration reactions (reactions that release water from mineral structures in response to increases in temperature) on flow of fluid with constant porosity. Further, the Boussinesq approximation was invoked; fluid expansivity was included in force-balance equations but was deemed sufficiently small that it could be safely neglected in mass-balance equations. In terms of the fluid continuity equation, Hanson concerned himself with situations in which the relation
obtains. Here, R is attributed to progress of metamorphic reactions.
Steefel and Lasaga [1994], on the other hand, investigated the effects of mineral precipitation and dissolution on patterns of fluid flow by allowing porosity to change. With respect to the fluid continuity equation, their model describes environments for which the relation
holds. With the Boussinesq approximation the left-hand term reflects changes in porosity only. Dehydration and hydration reactions were excluded in their calculations (i.e., R=0).
Hanson's modeling shows that reactions giving rise to fluid production can
strongly influence the pattern of fluid flow during contact and
regional metamorphism where permeabilities are on the order of
to 
m
or less. Within the
stipulations of the model, fluid produced by prograde reactions is
expelled as convective flow is diverted around the resulting pressure
maximum. Flow is dominantly down temperature gradients when the rate
of fluid production is high (i.e., when dehydration reactions are
proceeding most vigorously). In as little as 
years production
rates adjacent thermal anomalies will decrease to the point where
expulsion gives way to up-temperature fluid ingress as density-driven
convection is established. Peak fluid-production rates are predicted
to occur early in the metamorphic history. Based on these findings,
one concludes that moderate-grade hydrous metamorphic rocks may
experience drastic changes from expulsion of metamorphic fluid down
temperature gradients to up-temperature convective fluid infiltration
at near-peak temperatures. Such changes in flow regimes would be
accompanied by changes in fluid source and, possibly, fluid
composition, and would occur over small time intervals, 
years, relative to the total durations of most metamorphic events.
In their modeling, Steefal and Lasaga [1994] described
chemical reactions between aqueous fluid and rock composed of quartz,
albite, K-feldpsar, muscovite, and kaolinite with linear rate equations
in the system K-Na-Si-Al-Cl-C-H-O. Their results demonstrate that the
principal effect of reaction progress on fracture permeability
derives from precipitation and dissolution of quartz along fracture
walls in the model system. Quartz precipitates in areas of
down-temperature flow and dissolves in zones of up-temperature flow.
With time (
years) flow is focused into regions where fluids
move up temperature gradients and is dispersed where fluids move down
temperature. Local equilibrium between fluid flowing through
fractures and host rock is generally nearly attained at temperatures
above approximately 200
C where permeabilities are on the
order of 
to 
m
and fracture spacing is less
than approximately 100 m. Local disequilibrium prevails in the
vicinity of permeable thermal boundary layers. These results lend
credibility to many petrological studies of metamorphic fluid flow
that assume local equilibrium.
Multidimensional numerical models were also used to study fluid flow through metamorphosing rock on the meter and centimeter scales. Gerdes et al. [1993] constructed a finite element model that links compressible fluid flow, thermal transport, and advective and dispersive material transport to kinetics of oxygen and carbon isotope exchange between fluids and rocks. The model can be used to simulate the formation of isotopic exchange fronts in two-dimensional flow systems.
Detailed simulations of the effects of fluid flow on mineral parageneses
have been carried out independent of hydrodynamic considerations.
Symmes and Ferry [1991] used equilibrium thermodynamics
coupled with mass balance constraints to show that mineral assemblages
representing pelitic rocks of the classic Barrovian metamorphic sequence
can only be reproduced faithfully if aqueous fluid, in quantities
equivalent to time-integrated aqueous fluid fluxes of 
10
m
/m
, are included. Foster [1993] formulated
a combined equilibrium and nonequilibrium thermodynamic numerical
approach that enables simulation of rock textures formed during mineral
growth in the presence of flowing fluid.