Fluid–rock interaction at a carbonatite-gneiss contact, Alnö, Sweden

Abstract

We evaluate balanced metasomatic reactions and model coupled reactive and isotopic transport at a carbonatite-gneiss contact at Alnö, Sweden. We interpret structurally channelled fluid flow along the carbonatite-gneiss contact at ∼640°C. This caused (1) metasomatism of the gneiss, by the reaction: ${\hbox{biotite} + \hbox{quartz} + \hbox{oligoclase} + \hbox{K}_{2} \hbox{O} +\,\hbox{Na}_{2}\hbox{O} \pm \hbox{CaO} \pm \hbox{MgO} \pm \hbox{FeO} = \hbox{albite} + \hbox{K-feldspar} + \hbox{arfvedsonite} + \hbox{aegirene-}\hbox{augite} + \hbox{H}_{2} \hbox{O} + \hbox{SiO}_{2}}$, (2) metasomatism of carbonatite by the reaction: calcite + SiO₂ = wollastonite + CO₂, and (3) isotopic homogenization of the metasomatised region. We suggest that reactive weakening caused the metasomatised region to widen and that the metasomatic reactions are chemically (and possibly mechanically) coupled. Spatial separation of reaction and isotope fronts in the carbonatite conforms to a chromatographic model which assumes local calcite–fluid equilibrium, yields a timescale of 10²–10⁴ years for fluid–rock interaction and confirms that chemical transport towards the carbonatite interior was mainly by diffusion. We conclude that most silicate phases present in the studied carbonatite were acquired by corrosion and assimilation of ijolite, as a reactive by-product of this process and by metasomatism. The carbonatite was thus a relatively pure calcite–H₂O−CO₂–salt melt or fluid.

Appendices

Appendix 1: Table of symbols, recurring in this manuscript

Symbol	Description	Units
C f	Concentration of the tracer in the fluid at z
C s	Concentration of the tracer in the solid at z
Cs,1, Cs,2	Concentrations of the tracer in the solid upstream and downstream of the front
K V	Fluid solid partition coefficient by volume
ρ	Density	gcm−3
T	Time	s
z	Distance	m
zp.b.	Position of the pinned boundary	m
X j (ork)	Modal% of reactant mineral j (or product mineral k)
nj (ork)	Number of moles of reactant mineral j (or product mineral k) per unit volume of rock	mol m−3
N I	Metasomatic addition (positive) or subtraction (negative) of component I per unit volume of rock	mol m−3
[i]j (ork)	Molar proportion of component i in reactant mineral j (or product mineral k)
N	Modal% of rock involved in the reaction
ξ	Reaction progress
ϕ	Porosity
ω	Fluid velocity	m s−1
ω ϕ	Fluid flux rate	m3 m−2 s−1
ωϕ·t	Time-integrated volumetric fluid flux	m3   m−2 (or m)
D f	Diffusivity in the fluid	m2 s−1
τ	Tortuosity
${{\sqrt {{D}_{\rm f} \varphi {\tau} \cdot {\hbox{t}}}}}$	Characteristic length scale of diffusion	m

Appendix 2: Parameterisation of goodness-of-fit

The goodness-of-fit is parameterised by R ² _a . This is the adjusted coefficient of multiple determination, which is given by:

$$\begin{aligned} R^{2} &= 1 - \frac{{{\sum\limits_{i = 1}^n {{\left({y_{i} - y{\left({z_{i};\omega \varphi \cdot t,{\sqrt {D_{{\rm f}} \varphi \tau \cdot t}},z_{{{\rm p.b}}}.} \right)}} \right)}^{2}}}}}{{{\sum\limits_{i = 1}^n {{\left({y_{i} - \bar{y}} \right)}^{2}}}}} \\ R^{2}_{\rm a} &= \frac{{{\left({n - 1} \right)} R^{2} - k}}{{n - 1 - k}} \\ \end{aligned} $$

for equation (4) rewritten as (7), with k = number of regression parameters, n = number of data points and ${{\sum\limits_{i = 1}^n {{\left({y_{i} - \bar{y}} \right)}^{2}}}}$ = total variation of parameter y. R ²_a is the fraction of the variance in y which is explained by the model, y(z _i; ωϕ·t, ${{\sqrt {D_{{\rm f}} \varphi \tau \cdot t}}},$ z _p.b.) and can vary between 0 and 1.