## 1. Introduction

[2] The dissolution and precipitation of minerals during weathering not only changes the chemistry of rocks, but also their physical properties such as porosity, permeability, effective diffusivity, compressive strength, and tensile strength [e.g., *Lumb*, 1983; *Tugrul*, 2004; *Fletcher et al.*, 2006]. The products of bedrock weathering, detrital rock material and dissolved ions, contribute to important environmental processes including landform development, nutrient cycling in soils and rivers, sedimentation that ultimately leads to oil and gas generation, and the regulation of atmospheric CO_{2} over geologic time scales. Despite its importance to many environmental processes, rock weathering and the formation of saprolite, rock that is chemically weathered in situ, are not well understood partly because of the difficulty in understanding complex interactions between physical and chemical processes. Our inability to link chemical and mineralogical changes within a weathering environment to the evolution of physical features such as porosity, effective diffusivity, and permeability hinders our understanding of the important process of saprolite/sediment formation from bedrock weathering.

[3] In weathering systems, the pore network is arguably the most important physical characteristic of a rock because it provides pathways for water flow or infiltration and solute transport. The permeability and diffusivity of porous media are functions of the geometry of the pore network that is described in terms of the total porosity, tortuosity, pore throat size, and pore/mineral interfacial area. Chemical weathering reactions can induce changes in the pore network geometry and can therefore change the rates of fluid transport, and thus potentially the overall rates of mineral weathering [e.g., *Lebedeva et al.*, 2007; *Fletcher et al.*, 2006]. Differences between laboratory and field systems in terms of their mineral surface area and transport properties are two of the potential sources of the observed 2–6 order of magnitude difference between rates determined in these systems [e.g., *Velbel*, 1993; *White and Brantley*, 1995; *Navarre-Sitchler and Brantley*, 2007; *Maher et al.*, 2006; *White*, 2008; *Brantley*, 2008]. Therefore, a fundamental understanding of how the pore network evolves with mineral dissolution and precipitation is necessary for predicting field processes from laboratory dissolution kinetics [*Navarre-Sitchler and Brantley*, 2007].

[4] The coupling of reaction and transport in numerical models [e.g., *Steefel and Lasaga*, 1994; *Lichtner*, 1996] has made it possible to study the impacts of mineral dissolution and precipitation on fluid transport in important environmental systems such as bedrock weathering. Two complementary modeling techniques used to study changes in transport as a result of mineral alteration are pore network models and continuum models [*Steefel et al.*, 2005]. Pore network models are used to model processes at the pore scale, while continuum models are generally used to model processes at larger scales where average properties such as porosity, permeability, and diffusivity are defined. One of the differences between these modeling techniques is that pore network models explicitly consider pore geometry and spatial distribution when calculating mass transport, while continuum models do not except in some average sense. For example, there is no need to define an effective porosity or diffusivity within a grid cell corresponding to a discrete pore in a pore network model; the porosity is equal to one and the diffusivity is equal to that of the solute of interest in water. While pore network models can be used to explicitly investigate porosity changes at the pore-scale, continuum models are better suited for modeling large-scale problems, such as weathering at the soil profile or watershed scale. Single continuum modeling efforts are now being used to interpret weathering in field systems [*Maher et al.*, 2006; *Hausrath et al.*, 2008; *Moore*, 2008; *Sitchler*, 2008]. The results from these modeling efforts indicate a need to understand changes in mineral surface area and fluid transport (parameters that are influenced by porosity) with weathering. Thus, relationships are required to extrapolate processes occurring at the scale of the pore network up to the continuum scale. Scaling of such processes can be achieved through multicontinuum models or functional relationships such as Archie's law.

[5] In continuum models, effective upscaled transport parameters such as effective diffusivity and hydraulic conductivity are used to extrapolate pore-scale processes up to the continuum scale [*Saripalli et al.*, 2001; *Steefel et al.*, 2005]. When determining effective transport parameters in porous rocks at the continuum scale, it is necessary to account for tortuosity (*τ*), defined as the ratio of the path length the solute would flow in water alone, *L*, relative to the tortuous path it follows through the rock, *L*_{e} [*Bear*, 1972]

According to this definition, tortuosity is always <1 (the inverse of equation (1) has also been used). If the tortuosity is known, the effective diffusion coefficient (*D*_{e}, cm^{2} s^{−1}) in porous media can be calculated from equation (2)

where *D*_{o} is the diffusion coefficient in pure water (cm^{2} s^{−1}). Tortuosity, however, changes with changing porosity [*Shen and Chen*, 2007] and pore geometry as weathering progresses. Therefore, in models of diffusion-dominated weathering systems where porosity is allowed to vary with reaction, a functional relationship between porosity and the effective diffusivity is defined. A common way to do so is by using Archie's law [*Archie*, 1942; *Oelkers*, 1996]. Archie's law is used to estimate the effective diffusion coefficient of porous media (*D*_{e}, cm^{2} s^{−1}) according to

where ϕ is the measured total porosity of the porous media and *m* is the cementation exponent determined experimentally by fitting data describing diffusivity and porosity for multiple samples [*Dullien*, 1992]. Values of the cementation exponent vary in geological samples from 1.33 for diffusive gas in soils to 5.4 for diffusive transport of water in clays [*Millington and Quirk*, 1964; *Ullman and Aller*, 1982; *Adler et al.*, 1992; *Oelkers*, 1996]. The porosity in equation (3) may either be measured as total or effective porosity depending on the sample characteristics and measurement methods. Effective porosity is all porosity that is connected and available for fluid transport [*Tarafdar and Roy*, 1998]

Here, ɛ is the connectivity, or fraction of total porosity contained in pathways that are connected across a sample (values range from 0 to 1) and ϕ_{T} is the total porosity of the sample. The distinction between total and effective porosity is important because only changes in total porosity are typically tracked as a result of mineral alteration in continuum reactive transport models. Therefore, total porosity in these models is used to estimate effective diffusion coefficients.

[6] The water saturation method is commonly used to measure porosity in geological samples. However, in systems containing dead-end and isolated pores, not all of the porosity is connected and accounted for when using this method. It has been shown that models better predict diffusion experiments in granite when dead-end pores are accounted for [*Lever et al.*, 1985]. Interpretations of diffusion experiments with Archie's law are not consistent in the use of either total or effective porosity [*Tarafdar and Roy*, 1998]. For example, in the study of *Boving and Grathwohl* [2001] porosity is measured by water saturation methods. Therefore, the porosity measured is likely effective porosity not total porosity, but a distinction is not made between total and effective porosity in the analysis of the diffusion experiments. In this study, *Boving and Grathwohl* [2001] report a cementation exponent of 2.2 for sandstones and carbonates ranging in porosity from 3.7 to >40%. It is unclear whether effective diffusion coefficients scale with total or effective porosity in this study. These authors do suggest that Archie's law describes the relationship between porosity and effective diffusion coefficients better in the high-porosity samples where effects of dead-end and isolated pores are minor compared to the low-porosity samples. Here we examine the difference between using total porosity and effective porosity as the scaling parameter in Archie's law when estimating *D*_{e} across a weathering interface in basalt.

[7] The weathering of basalt is of particular interest because it is one of the fastest weathering silicate rocks. Furthermore, approximately 8.5% of the surface area of silicate rock at Earth's surface is basaltic [*Amiotte-Suchet et al.*, 2003]. Almost thirty five percent of continental CO_{2} consumption by silicate weathering is due to basalt [*Dessert et al.*, 2003; *Navarre-Sitchler and Brantley*, 2007]. Since transport through low-porosity crystalline rocks is typically very slow in the absence of fractures [*Lebedeva et al.*, 2007], the evolution of the pore network and diffusivity during chemical weathering is integral to the weathering process. An understanding of how the pore network and diffusivity evolve can help predict rates of basalt weathering in natural systems. Here, we use pore connectivity as an indicator of changes to the pore network and quantify the relationship between total and effective porosity using synchrotron X-ray microcomputed tomography (*μ*CT) images of the weathered basalt clasts. Computed tomography has proven to be a useful, nondestructive technique for imaging porosity in complex lithologies [*Ketcham and Iturrino*, 2005]. We then relate the porosity to estimated effective diffusion coefficients at different stages of weathering as determined from experimental and numerical tracer diffusion experiments. These techniques allow us to quantify in situ changes in both total and effective porosity resulting strictly from the chemical dissolution of parent minerals during bedrock weathering.