## 1. Introduction

[2] Biomineralization is a natural subsurface process that can dramatically alter the physical properties of porous media. In particular, porosity and permeability changes, attributed to biologically assisted CaCO_{3} precipitation, can have a direct effect on fluid flow and transport properties [*Whiffin et al.*, 2007]. A key factor relevant to permeability alteration is the characteristic pattern of precipitation with respect to the granular matrix, i.e., are precipitates localized in pore throats, pore bodies, or on grain surfaces? Since effective medium models describing permeability [e.g., *Carrier*, 2003] and elastic properties [*Dvorkin et al.*, 1999] are dependent on such patterns, the appropriate choice of a scenario or trajectory between scenarios (i.e., where is precipitation localized and how does localization change temporally) is a key step in building a quantitative understanding of the effects of biomineralization.

[3] We selected *Sporosarcina pasteurii* as our model organism for studying the mineralization process, a prevalent aerobic, rod-shaped, motile, soil microbe with a very active urease enzyme [*Whiffin et al.*, 2007]. Hydrolysis of urea by the urease enzyme generates carbon dioxide and ammonia {CO(NH_{2})_{2} + H_{2}O → 2NH_{3} + CO_{2}}, causing an increase in pH {2NH_{3} + 2H_{2}O ←→ 2NH_{4}+ + 2OH^{−}}. Within this alkaline environment carbonate ions form {CO_{2} + 2OH^{−} ←→ CO_{3}^{2−} + H_{2}O} and precipitation of calcium carbonate is favored {CO_{3}^{2−} + Ca^{2+} ←→ CaCO_{3}(s)}, [*Stocks-Fischer et al.*, 1999].

[4] One of the simplest permeability models is the Kozeny-Carman (KC) model which attempts to describe permeability in terms of porosity starting from first principles [*Carrier*, 2003]. The KC function often fails to represent empirical data, however, this type of relationship is vital for the design and modeling of many engineered processes (e.g., geological carbon storage and hydrocarbon recovery).

[5] A complete derivation of the KC functions (equations (1) and (2)) used herein is presented by [*Costa*, 2006]. Permeability can be calculated using:

where, R is effective radius, *τ* is tortuosity, and θ is porosity. However, R and *τ* are hard to measure/define, thus the concept of hydraulic radius is usually defined and incorporated into equation (1) which gives the following formula:

where, C_{kc} is an empirical constant. Equation (2) is essentially the classical KC function and is the starting point of our analysis. Average effective throat radius measured from CMT imagery is incorporated into equation (1) and fitted to the empirical data.