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Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport

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Abstract

Equations are developed describing migration of stable isotopes via a fluid phase infiltrating porous media. The formalism of continuum fluid mechanics is used to deal with the problem of microscopic inhomogeneity. Provision is made explicitly for local equilibrium exchange of isotopes between minerals and fluids as well as for kinetic control of isotopic exchange. Changing characteristic parameters of transport systems such as porosity, permeability, and changes in modal proportions of minerals due to precipitation or dissolution are taken into account.

The kinetic continuum theory (KCIT) is used to show how to deduce the dominant mechanism of mass transport in metasomatic rocks. Determination of the transport mechanism requires data on the spatial distribution of the reaction progress of exchange reactions between minerals and fluids involving at least two stable isotope systems such as 13C-12C and 18O-16O, for example. It is concluded that a combination of field and laboratory measurements of two or more stable isotope systems can be used to place constraints not only on the mechanism of transport but also on the magnitude of fluid fluxes, the identity of fluid sources, and the molecular species composition of fluids.

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Abbreviations

C :

number of chemical components

D i,j :

hydrodynamic dispersion tensor [m2/s]

D ji :

diffusion coefficient matrix [m2/s]

D * :

apparent diffusion coefficient, includes sorption, dispersion, porosity and tortuosity [m2/s]

F :

number of degrees of freedom (variance)

f ji :

mass or number of isotope j in fluid species i

g :

acceleration due to gravity [m/s2]

\(\vec J\) :

flow [m3/m2 s]

j :

isotope species

j′ :

chemical element

k :

coefficient defined in Eq. 17

K′ :

permeability of porous media [m2], [darcy]

L ij :

phenomenological diffusion coefficient matrix [mol2/j m s]

m :

number of fluid species

n :

number of isotope exchange vectors

p :

number of phases

P :

pressure [Pa]

P * :

hydrological pressure potential [Pa]

R j :

ratio of concentration of rare to common isotope of element j

r :

number of restrictions imposed on system

s ji :

mass or number of isotope j in one mole of mineral phase i

t :

time [s]

V :

volume [m3]

X i :

number of moles of fluid species i in unit fluid volume

X l :

number of moles of mineral l in unit volume

X jl :

mole fraction of isotope j in one mole mineral l

X * :

mole fraction with respect to the whole system

z :

space coordinate [m]

z′ :

transformed space coordinate

z * :

location of an infiltration front [m]

α jx−y :

fractionation factor between two phases, x, y, for isotope j

β :

porosity

η :

fluid viscosity [Ns/m2]

λ :

fraction of porosity accessible to a specific mass transport mechanism

μ :

chemical potential [j/mole]

υ :

stoichiometric reaction coefficient

ξ :

normalized reaction progress variable

ρ :

mass, specific mass [gr/cm]

τ :

tortuosity

\(\vec \upsilon _f \) :

fluid velocity [m/s]

c:

common isotope

init:

initial

j:

isotope species

r:

rare isotope

tot:

sum of common and rare isotope

dif:

diffusive

disp:

dispersive

eq:

mineral composition in equilibrium with initial infiltration concentration of the fluid

f:

fluid

inf:

infiltrative

r:

rock, without fluid phase

samp:

sample

std:

standard

sys:

system

tot:

fluid and rock

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Author notes

  1. L. P. Baumgartner

    Present address: Earth and Planetary Sciences, The Johns Hopkins University, 21218, Baltimore, MD

Authors and Affiliations

  1. Mineralogisch-petrologisches Institut, University of Basel, Switzerland

    L. P. Baumgartner & D. Rumble III

  2. Geophysical Laboratory, Carnegie Institution of Washington, Washington, DC

    L. P. Baumgartner & D. Rumble III

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  1. L. P. Baumgartner
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  2. D. Rumble III
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Baumgartner, L.P., Rumble, D. Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport. Contr. Mineral. and Petrol. 98, 417–430 (1988). https://doi.org/10.1007/BF00372362

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