The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous medium

Lichtner, Peter C.

doi:10.1016/0016-7037(88)90063-4

Cited by 338 publications

(250 citation statements)

References 15 publications

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“…If a very low value of C N is used, the position of the reaction front is proportional to √T, a result expected for diffusional rate-control [33], as in so-called parabolic kinetics.…”

Section: Model Resultsmentioning

confidence: 89%

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A spheroidal weathering model coupling porewater chemistry to soil thicknesses during steady-state denudation

Fletcher

Buss

Brantley

2006

Earth and Planetary Science Letters

201

228

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Spheroidal weathering, a common mechanism that initiates the transformation of bedrock to saprolite, creates concentric fractures demarcating relatively unaltered corestones and progressively more altered rindlets. In the spheroidally weathering Rio Blanco quartz diorite (Puerto Rico), diffusion of oxygen into corestones initiates oxidation of ferrous minerals and precipitation of ferric oxides. A positive ∆V of reaction results in the buildup of elastic strain energy in the rock. Formation of each fracture is postulated to occur when the strain energy in a layer equals the fracture surface energy. The rate of spheroidal weathering is thus a function of the concentration of reactants, the reaction rate, the rate of transport, and the mechanical properties of the rock. Substitution of reasonable values for the parameters involved in the model produces results consistent with the observed thickness of rindlets in the Rio Icacos bedrock (≈ 2-3 cm) and a time interval between fractures (≈ 200-300 a) based on an assumption of steady-state denudation at the measured rate of 0.01 cm/a. Averaged over times longer than this interval, the rate of advance of the bedrock-saprolite interface during spheroidal weathering (the weathering advance rate) is constant with time. Assuming that the oxygen concentration at the bedrock-saprolite interface varies with the thickness of soil/saprolite yields predictive equations for how weathering advance rate and steadystate saprolite/soil thickness depend upon atmospheric oxygen levels and upon denudation rate. The denudation and weathering advance rates at steady state are therefore related through a condition on the concentration of porewater oxygen at the base of the saprolite. In our model for spheroidal weathering of the Rio Blanco quartz diorite, fractures occur every ~ 250 years, ferric oxide is fully depleted over a four rindlet set in ~ 1000 years, and saprolitization is completed in ~ 5000 years in the zone 2 containing ~ 20 rindlets. Spheroidal weathering thus allows weathering to keep up with the high rate of denudation by enhancing access of bedrock to reactants by fracturing.Coupling of denudation and weathering advance rates can also occur for the case that weathering occurs without spheroidal fractures, but for the same kinetics and transport parameters, the maximum rate of saprolitization achieved would be far smaller than the rate of denudation for the Rio Blanco system. The spheroidal weathering model provides a quantitative picture of how physical and chemical processes can be coupled explicitly during bedrock alteration to soil to explain weathering advance rates that are constant in time.

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“…If a very low value of C N is used, the position of the reaction front is proportional to √T, a result expected for diffusional rate-control [33], as in so-called parabolic kinetics.…”

Section: Model Resultsmentioning

confidence: 89%

“…In although the weathering interface is moving downward with time. Such a constant but moving reaction front is expected for some weathering systems, and is termed a quasistationary state [33]. For α << Λ as in our system, the product αΤ controls the form of this quasi-stationary reaction front and its position with time.…”

Section: Model Resultsmentioning

confidence: 91%

A spheroidal weathering model coupling porewater chemistry to soil thicknesses during steady-state denudation

Fletcher

Buss

Brantley

2006

Earth and Planetary Science Letters

201

228

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“…Consequently the system fulfills the quasi-stationary approximation [Lichtner, 1988], and mass conservation resumes:…”

Section: Chemical Modelmentioning

confidence: 99%

Numerical modeling of reaction‐induced cavities in a porous rock

Ormond¹,

Ortoleva²

2000

J. Geophys. Res.

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Abstract. The interaction between mineral reaction and mass transport in a rock can lead to reaction front instability and the development of channel-like voids. This phenomenon is studied with a two-dimensional model accounting for the nonlinear feedback between flow, reaction, and matrix porosity-permeability evolution. In our model we calculate the flow field in both the porous medium and the reaction-induced voids, using the Brinkman equation. While a linear analysis cannot determine the length scale of the channels which can develop in a typical geological system, our simulations indicate that the channel size is actually unique and well characterized. While the onset of instability is favored at a preexisting heterogeneity, the channel growth and orientation is governed by the global flow pattern, even in an initially heterogeneous system.

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“…The kinetics of halite dissolution is controlled by two distinct processes: NaCl detachment from the mineral surface according to surface coordination chemistry [84][85][86][87], and the transport of ions into the bulk solution through the interfacial layer quantified by transition state theory [88]. Alkattan et al [89] proposed the ove reaction rate (molT -1 M -1 ): rall…”

Section: Example Application: Kinetic Halite Dissolutionmentioning

confidence: 99%

Effect of mineral reactions on the hydraulic properties of unsaturated soils: Model development and application

Wissmeier

Barry

2009

Advances in Water Resources

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This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. ACCEPTED MANUSCRIPT AbsThe selective radius shift model was used to relate changes in mineral volume due to precipitation/dissolution reactions to changes in hydraulic properties affecting flow in porous media. The model accounts for (i) precipitation/dissolution taking place only in the water-filled part of the pore space and further that (ii) the amount of mineral precipitation/dissolution within a pore depends on the local pore volume. The pore bundle concept was used to connect pore-scale changes to macroscopic soil hydraulic properties. Precipitation/dissolution induces changes in the pore radii of water-filled pores and, consequently, in the effective porosity. In a time step of the numerical model, mineral reactions lead to a discontinuous pore-size distribution because only the water-filled pores are affected. The pore-size distribution is converted back to a soil moisture characteristic function to which a new water retention curve is fitted under physically plausible constraints. The model equations were derived for the commonly used van Genuchten/Mualem hydraulic properties. Together with a mixed-form solution of Richards' equation for aqueous phase flow, the model was implemented into the geochemical modelling framework PHREEQC, thereby making available PHREEQC's comprehensive geochemical reactions. Example applications include kinetic halite dissolution and calcite precipitation as a consequence of cation exchange. These applications showed marked changes in the soil's hydraulic properties due to mineral precipitation/dissolution and the dependency of these changes on water contents. The simulations also revealed the strong influence of the degree of saturation on the development of the saturated hydraulic conductivity through its quadratic dependency on the van Genuchten parameter . Furthermore, it was shown that the unsaturated hydraulic conductivity at fixed reduced water content can even r tract increase du ing precipitation due to changes in the pore-size distribution.

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The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous medium

Cited by 338 publications

References 15 publications

A spheroidal weathering model coupling porewater chemistry to soil thicknesses during steady-state denudation

A spheroidal weathering model coupling porewater chemistry to soil thicknesses during steady-state denudation

Numerical modeling of reaction‐induced cavities in a porous rock

Effect of mineral reactions on the hydraulic properties of unsaturated soils: Model development and application

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