## 1. Introduction

[2] Geologic sequestration of CO_{2} is considered one of the viable approaches for mitigating the climatic impact of greenhouse gas emissions [*White et al.*, 2003; *Pacala and Socolow*, 2004]. However, knowledge of the fate of CO_{2} injected into deep subsurface aquifers, particularly over long time periods (thousands of years), is still inadequate [*Bruant et al.*, 2002]. Similar limitations exist for other subsurface environments where the interpretation and prediction of chemical fate and transport is essential. These include contaminated subsurface systems [e.g., *Bain et al.*, 2001; *Essaid et al.*, 2003; *Steefel et al.*, 2003; *Prommer et al.*, 2006; *Molins et al.*, 2010], chemical weathering [e.g., *Maher et al.*, 2009], and redox stratified biogeochemical systems [e.g., *Wang et al.*, 2003; *Thullner et al.*, 2005; *Li et al.*, 2009]. Geochemical transport modeling has served as a valuable predictive tool in evaluating sequestration scenarios, but there are limitations to the application of continuum reactive transport models to such systems [*Steefel et al.*, 2005]. Traditionally, the consideration of flow and reactive transport in subsurface porous media has focused on treating the media as continuous domains with macroscopic flow and transport parameters such as hydraulic conductivity, porosity, dispersivity, as well as geochemical parameters such as reactive surface area and reaction rates. In these formulations, flow is usually assumed to obey phenomenological laws, e.g., Darcy's law [*Zhang et al.*, 2000]. Similarly, reactive surface area is estimated from adsorption isotherms (Brunauer-Emmett-Teller, or BET) or geometrically based on the average physical grain size, but this approach does not account for the hydrologic accessibility of the reactive phases within the pore structure [*Maher et al.*, 2006; *Peters*, 2009]. The problem is perhaps particularly acute for geochemical processes, since geochemical parameters are often determined for pure mineral suspensions that do not account for the pore structure of the media. It has been long realized that these parameters are scale-dependent and mass transport limitations can introduce large deviations from volume-averaged processes [*Li et al.*, 2006, *L. Li et al.*, 2008]. The pore scale variation of species concentrations is also suspected to contribute to the discrepancy commonly observed between laboratory and field measurements [*Li et al.*, 2006]. A number of theoretical works have established conditions under which it is possible to accurately upscale pore scale reactive transport processes to the continuum scale [*Kechagia et al.*, 2002; *Battiato and Tartakovsky*, 2011]. These studies suggest that transport phenomena dominated at the pore scale by reactive and/or advective processes require the microscopic and macroscopic scales to be considered simultaneously. The growing evidence of the importance of the pore scale is reflected in the increasing interest in modeling reactive transport in the subsurface at the this scale [*Salles et al.*, 1993; *Bekri et al.*, 1995; *Kang et al.*, 2006; *Tartakovsky et al.*, 2007a, 2007b; *Tartakovsky et al.*, 2008a; *X. Li et al.*, 2008; *Flukiger and Bernard*, 2009; *Algive et al.*, 2010].

[3] Pore scale modeling can be used to gain insight into the scale dependence of continuum macroscale parameters by first resolving physicochemical processes that would otherwise not be modeled in an effective medium Darcy approach. Popular approaches to pore scale modeling applied to reactive geochemical systems include pore network models [e.g., *Li et al.*, 2006, *Algive et al.*, 2010], the lattice Boltzmann method [e.g., *Kang et al.*, 2006; *Van Leemput et al.*, 2007; *Kang et al.*, 2010a, 2010b] and particle methods [e.g., *Tartakovsky et al.*, 2007a, 2007b, 2008a]. Pore network models are efficient for large systems, but they need to approximate the pore geometry and the physics of the problem [e.g., *Li et al.*, 2006]. Lattice Boltzmann models are also efficient and scalable for flow and transport problems, but they do not typically incorporate the wide range of geochemical reactions available in many geochemical models [e.g., *Kang et al.*, 2006]. Particle methods such as the smoothed particle hydrodynamics are very robust, but are generally not applied to large systems [*Tartakovsky et al.*, 2007a, 2007b]. Hybrid pore scale-continuum scale models have also been developed to combine the rigorous microscopic description of the pore scale approach and the more modest computational requirements of the continuum scale approach [*Van Leemput et al.*, 2007; *Tartakovsky et al.*, 2008b, *Battiato et al.*, 2011]. Existing reactive transport models based on conventional discretization methods have also been used to simulate pore scale processes when a solution of the flow field was not required, that is for diffusion-reaction problems [*Navarre-Sitchler et al.*, 2009], or when a solution of the flow field was obtained with a lattice Boltzmann method [*Yoon et al.*, 2012]. In conjunction with high-performance computing, well-established numerical methods used in computational fluid dynamics (CFD), such as finite volume and finite difference methods, have also become practical for direct numerical simulation of flow and transport in the complex geometry of heterogeneous pore space [*Trebotich et al.*, 2008]. Direct numerical simulation using these traditional CFD methods presents the additional advantage of ease of implementation using existing extensively validated geochemical models that include the wide range of reactions relevant to subsurface systems.

[4] In this work, we present a model to simulate subsurface flow and reactive transport at the pore scale by direct numerical simulation techniques based on advanced finite volume methods and adaptive mesh refinement, and apply it to the problem of carbonate mineral dissolution in porous media. Specifically, we have combined the high-performance simulation tools and algorithms for incompressible flow and conservative transport in the software framework, Chombo [*Trebotich et al.*, 2008], with the geochemical package, CrunchFlow [*Steefel et al.*, 2003]. The objective is to demonstrate this computational tool for its use in evaluating reaction rates in natural sediments in combination with advanced characterization techniques [e.g., *Peters*, 2009; *Armstrong and Ajo-Franklin*, 2011]. Here, as an example application, we demonstrate the modeling approach to calculate average reaction rates in ideal and complex 2-D and 3-D geometries, using calcite dissolution with no solid-liquid geometry update. Dissolution of discrete calcite grains is described with rate laws determined in laboratory reactors, with rates normalized to physical surface area [*Plummer et al.*, 1978]. Two verification examples are presented, one involving a single cylindrical pore investigated by *L. Li et al.* [2008], and another involving an example in which calcite grains are packed into a capillary tube. In each case, for cross-validation, the pore scale results are compared with the results from continuum scale simulations using the general purpose reactive transport simulator CrunchFlow. In addition, upscaling of the reaction rates is carried out so as to assess the validity of the continuum approximation in more heterogeneous grain packs.