Darcy-scale modeling of microbially induced carbonate mineral precipitation in sand columns

Authors


Abstract

[1] This investigation focuses on the use of microbially induced calcium carbonate precipitation (MICP) to set up subsurface hydraulic barriers to potentially increase storage security near wellbores of CO2 storage sites. A numerical model is developed, capable of accounting for carbonate precipitation due to ureolytic bacterial activity as well as the flow of two fluid phases in the subsurface. The model is compared to experiments involving saturated flow through sand-packed columns to understand and optimize the processes involved as well as to validate the numerical model. It is then used to predict the effect of dense-phase CO2 and CO2-saturated water on carbonate precipitates in a porous medium.

1. Introduction

[2] Mineral precipitation influenced by microbial activity in the subsurface (particularly through the urea-hydrolysis pathway), commonly referred to a microbially induced calcium carbonate precipitation (MICP), can be exploited for a variety of engineered applications including the immobilization of groundwater contaminants [Ferris et al., 2003; Fujita et al., 2010, 2004, 2008], ground reinforcement or altering properties of porous materials [DeJong, 2006; Harkes et al., 2010; Ivanov and Chu, 2008; van Paassen et al., 2010; Whiffin et al., 2007], and the creation of hydraulic barriers for purposes such as enhanced oil recovery or increasing storage security of CO2 [Cunningham et al., 2009, 2011; Ebigbo et al., 2010; Ferris et al., 1996]. Many organisms are capable of hydrolyzing urea, which can alter the saturation state of the formation water, and in the presence of calcium, may favor the precipitation of calcium carbonate [Ferris et al., 2003; Mobley and Hausinger, 1989; Stumm and Morgan, 1996].

[3] In previous studies, greater calcium carbonate precipitation was observed near injection sites which could potentially lead to restricted transport of nutrients and have adverse effects on well injectivity [Fujita et al., 2008; Whiffin et al., 2007]. Before a biomineralization technology can be considered field relevant, mineral deposition must be demonstrated to be controllable at a relevant scale while maintaining economic feasibility [Harkes et al., 2010]. Controlling mineralization has been investigated by balancing the reaction with transport, for example, altering injection strategies or injection rates, manipulating the reactant concentrations, increasing the number of applications of treatments, or controlling the distribution of active microbes [De Muynck et al., 2010a; Harkes et al., 2010; Whiffin et al., 2007]. Additionally, it has been reported that the types and sizes of crystals formed are affected by the number and form (planktonic or attached) of cells, and that the environmental conditions in surrounding fluids can affect precipitation [Achal et al., 2009b;Cuthbert et al., 2012; Dupraz et al., 2009a, 2009b; Mitchell and Ferris, 2006; Mortensen et al., 2011; Tobler et al., 2011]. Multiscale and extensive cross-disciplinary research on the feasibility of such a technology is key for its successful implementation [DeJong et al., 2010, 2012].

[4] The challenges to creating effective and extensive hydraulic barriers for increasing CO2 storage security are to make efficient use of resources and to promote mineralization in the regions of interest without plugging other regions. Analyzing all combinations of these precipitation-influencing factors in the laboratory would be laborious and time consuming. Several other researchers have utilized models to assist in the understanding or optimization of MICP treatment technologies [Barkouki et al., 2011; Fauriel and Laloui, 2011; van Wijngaarden et al., 2011; Zhang and Klapper, 2010]. The model described in this paper was also developed to quickly analyze parameters and optimize experimental efforts with the aim of improving the understanding of the relevant processes involved. The bench-scale column results and Darcy-scale modeling efforts reported here address the challenge of demonstrating control of mineral deposition (i.e., CaCO3) uniformly along the flow path in a porous medium.

[5] Four separate column experiments were performed in order to: develop an injection strategy to produce homogenous CaCO3 distribution along the length of the column, calibrate the model, and validate the model by comparing it to the physical data.

[6] Finally, while not supported by experimental data, the model also examines some of the potential interactions of dense-phase CO2 with CaCO3. The model simulates two-fluid-phase (water and CO2) experiments, providing a useful tool for the optimization of injection strategies, the design of high-pressure CO2 experiments, and, ultimately, prospective field-scale application.

2. Model Description

[7] The system of interest consists of two fluid phases (water and CO2), three immobile phases (rock/porous medium, calcite precipitates, and biofilm), and suspended/dissolved components (see Figure 1). It shall be noted that other calcium carbonate morphotypes are possible products of the ureolysis-induced calcium carbonate precipitation process described in this work. However, calcite is the most frequently described calcium carbonate morphotype observed and was chosen as the representative morphotype in this model. In addition, biofilm as described here refers to attached microorganisms capable of producing extracellular polymeric substances (EPS) [Cuthbert et al., 2012; Schultz et al., 2011].

Figure 1.

Schematic porescale representation of system of interest.

[8] Here the system is addressed on the so-called Darcy (macro) scale which is obtained if the processes on the pore (micro) scale can be averaged adequately [Bear, 1972; van Duijn and Pop, 2004; van Noorden, 2009a, 2009b, 2010; Golfier et al., 2009]. In this article, the equations and variables of the model are defined on the macroscale. Thus, only volume-averaged information is available within a representative elementary volume.

2.1. Definition of System and Main Assumptions

[9] The components the model accounts for include water (w), carbon dioxide (CO2), suspended biomass (b), attached biomass/biofilm (f), substrate (s), electron acceptor/oxygen (e), calcite (c), urea (u), ammonia/ammonium (a), calcium (Ca2+), chloride (Cl), and sodium (Na+).

[10] Two fluid phases may be present in the pores of the porous medium (water [w] and CO2 [n]), which are the wetting and the nonwetting phases, respectively. Before the injection of CO2, only water is present. Thus, the set of primary variables can change depending on the number of phases present [Class et al., 2002].

[11] The water phase consists of the components water, dissolved CO2, suspended biomass, substrate, oxygen, urea, ammonia/ammonium, calcium, chloride, and sodium. The CO2 phase consists of CO2, water, and oxygen. All other components are assumed not to dissolve/partition into this phase. Calcite and biofilm are immobile.

[12] Even though brines consist of several salts, it is assumed here that their combined effect on density, viscosity, and CO2 solubility can be represented by an equivalent sodium chloride concentration [Michaelides, 1981].

[13] There is no differentiation between molecularly dissolved CO2 and carbonic acid. The sum of both is referred to as H2CO3 [Chou et al., 1989; Flukiger and Bernard, 2009].

[14] In the explanations and diagrams that follow, it is assumed that the host rock (or other porous medium) does not contain significant amounts of carbonate minerals. However, if this is not the case, the amount of calcite initially present in the model can be set to a nonzero value.

2.2. Chemical Reactions

[15] In the presence of the enzyme urease, urea is hydrolyzed to give ammonia and carbonic acid. The bacterial strain Sporosarcina pasteurii is capable of producing large amounts of urease [Ciurli et al., 1996]. The subsequent protonation of ammonia to ammonium causes an increase in pH, shifting the equilibrium of the calcite precipitation/dissolution reaction toward precipitation by increasing the availability of the carbonate ion ( inline image).

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[16] The dissociation reactions are fast compared to ureolysis, precipitation, and dissolution. Hence, these are assumed to occur instantaneously and are accounted for with equilibrium coefficients. Slower reactions are described by using rate expressions.

2.2.1. Rate of Ureolysis

[17] As described by Fidaleo and Lavecchia [2003], the rate of urea hydrolysis is given by,

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where inline image is the molality of urea, inline image is the Monod half-saturation constant, and inline image is an inhibition parameter due to high inline image concentrations. The maximum rate of ureolysis inline image is calculated as follows:

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Dissociation constants for the enzyme-urea complex are denoted by inline image, and k is a rate constant. Note that these rate expressions from Fidaleo and Lavecchia [2003] were determined for jack beans urease. It is assumed here that the same expressions can be used for microbially produced urease. The concentration of intra- and extracellular urease in the porous medium inline image is difficult to determine [Klose and Tabatabai, 1999]. Urease is released when bacterial cells rupture and may sorb to polymers of the biofilm and to the porous medium [Lloyd and Sheaffe, 1973; Brotherton et al., 1976; Ciurli et al., 1996]. For the purposes of this model, it is assumed that most of the urease is associated with the biofilm (either intracellularly or sorbed to biofilm polymers). Hence, the amount of urease is assumed to be related nonlinearly to the amount of attached biomass (i.e., biofilm),

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Suspended biomass is not included since its contribution is considered small compared to that of the biofilm [Li et al., 2000; Resch et al., 2005]. Here inline image is the biofilm density (dry mass per unit volume), inline image is the volume fraction of the porous medium occupied by the biofilm, inline image is a proportionality coefficient, and inline image accounts for the nonlinear dependence of inline image on inline image.

2.2.2. Rate of Calcite Precipitation/Dissolution

[18] The net rate of precipitation or dissolution of calcite is governed by the calcite saturation state inline image which provides a measure of the distance of the system from equilibrium, i.e., inline image,

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The activity coefficients inline image and inline image are calculated using Pitzer equations as described by Wolf et al. [1989], Millero et al. [1984], and Clegg and Whitfield [1995]. To this end, the influence of the interactions of all the ions considered are included in the calculations. However, the concentrations of some of the ions are determined using apparent dissociation coefficients as described in section 2.2.3. Figure 2 shows how the activities of calcium and carbonate ions vary with chloride concentration in NaCl and NaCl2 solutions. inline image is the solubility product of calcite.

Figure 2.

Ca2+ and inline image activities as calculated from Wolf et al. [1989], Millero et al. [1984], and Clegg and Whitfield [1995] using Pitzer equations as a function of Cl concentration in NaCl and NaCl2 solutions.

[19] The rate at which equilibration occurs is assumed to depend on the distance from equilibrium. When inline image, net precipitation occurs, and net dissolution occurs when inline image. There are several empirical approaches for determining these rates. There are also some approaches which obtain the rates from the upscaling of porescale processes [van Noorden, 2009a; van Duijn and Pop, 2004]. Here common empirical rate functions for precipitation and dissolution are chosen [Zhong and Mucci, 1989],

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The empirical parameters inline image and inline image are available in the literature [e.g., Zhong and Mucci, 1989]. The specific interfacial surface between solid (i.e., both porous matrix and calcite) and water phases inline image is estimated from the porosity inline image with an empirical relation [e.g., Clement et al., 1996] as follows:

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The subscript “0” denotes initial values.

[20] Similarly, the dissolution rate is calculated as given by [Chou et al., 1989; Compton et al., 1989],

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Again, inline image, inline image, and inline image are empirical parameters. inline image is the specific interfacial surface between calcite and water phases. Assuming the porous rock matrix originally in place does not dissolve, inline image may differ significantly from inline image as shown in Figures 3 and 4. For small values of inline image (which is the volume fraction of porous medium occupied by calcite), inline image is proportional to inline image, i.e.,

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where inline image represents the specific surface area of the calcite grains (surface area per volume of calcite). However, when significant amounts of calcite are present in the porous medium, i.e., for large inline image, this relationship is not valid. Instead, inline image and inline image become equivalent. Thus, inline image is chosen in such a way that the limiting of the two options, i.e., the smaller of the two is chosen (see also Figures 3 and 4):

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Figure 3.

Solid-water interfacial areas: At low values of inline image, the interfacial surface between calcite and water phases, inline image, and that between solid (i.e., both porous matrix and calcite) and water phases, inline image, differ significantly, inline image.

Figure 4.

Solid-water interfacial areas: At high values of inline image, the interfacial surface between calcite and water phases, inline image, and that between solid (i.e., both porous matrix and calcite) and water phases, inline image, are equivalent, inline image.

2.2.3. Dissociation Coefficients

[21] The dissociation of NH3 and H2CO3 in water are accounted for with apparent (i.e., stoichiometric) dissociation coefficients inline image. Calculating activity coefficients as is done for the computation of inline image would unnecessarily increase the complexity and computational cost of the model. As such, correlations from literature are chosen, with which one can determine the apparent dissociation coefficients as functions of ionic strength I,

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For H2CO3, dissociation coefficients are calculated using correlations given by Millero et al. [2007], and those by Bell et al. [2008] are used for the dissociation of NH3. The dissociation coefficient of water is also required and approximated as a function of ionic strength [Ji, 1994].

2.3. Mass Balance Equations

[22] Mutual dissolution of the water and CO2 phases are accounted for with the mass fractions inline image and inline image which represent the amount of CO2 in the water phase and of water in the CO2 phase, respectively. Equations which balance the mass of each component in the phases inline image can be written as in equation (14),

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Here inline image is density, S is the fluid-phase saturation within the rock pores, v is the Darcy flux (fluid-phase velocity), D is the hydrodynamic dispersion tensor, q represents sources/sinks.

[23] The components which are assumed to exist exclusively as dissolved/suspended components of the water phase can be expressed with concentrations C, and the following mass balance equations hold,

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Oxygen can be present in both water and CO2. Thus, the mass balance equation for oxygen is,

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Additionally, the equations for the immobile phases, attached biomass, and calcite are,

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2.4. Sources and Sinks

[24] The sources and sinks given in equations (14)–(17) accounting for reactions (urea hydrolysis, precipitation, dissolution) and bacterial activity are described in detail in the following [cf. Ebigbo et al., 2010]:

[25] Suspended and attached biomass:

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and

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where inline image and inline image are growth rates for suspended and attached biomass, respectively; inline image and inline image are the corresponding decay rates; and inline image and inline image are the rates of attachment to and detachment from the biofilm, respectively [e.g., Taylor and Jaffé, 1990],

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The growth coefficient inline image is calculated with double-Monod kinetics [e.g., Rockhold et al., 2004],

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Here inline image is the maximum substrate utilization rate, and inline image and inline image are half-saturation coefficients. Decay rates are calculated as first-order relationships with respect to live-cell concentrations,

display math
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where inline image and inline image are decay coefficients. They comprise constant endogenous decay inline image and process-dependent decay inline image ( inline image b, f). For the suspended biomass, inline image is assumed to be primarily dependent on pH. Since Sporosarcina pasteurii is an alkaliphile, only low pH conditions due to high CO2 concentrations in water are taken to be harmful to the bacterial cells. In addition, it is assumed that the biofilm bacteria are protected from the adverse effects of CO2. This assumption is supported by the findings of Mitchell et al. [2008] in which they propose mechanisms which contribute to the protective nature of the biofilm including mass transfer resistance offered by the biofilm structure and immobilization of CO2 molecules due to their interaction with the extracellular polymers of the biofilm. Thus, the following decay relationship is chosen [Kim et al., 2000]:

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where inline image is an empirical constant.

[26] Precipitation of calcite occurs mainly in and on the biofilm [Zhang and Klapper, 2010; Schultz et al., 2011]. This can lead to inactivation of bacterial cells embedded in the biofilm, either by disruption when a calcite nucleus develops within a cell or due to a coating of the cells by the calcite (which effectively leads to inactivation) [De Muynck et al., 2010b; Whiffin et al., 2007; Parks, 2009; Dupraz et al., 2009a]. Thus, inline image is a function of the calcite precipitation rate:

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Equation (26) assumes that the rate of inactivation due to precipitation is inversely proportional to the free space available for precipitation, inline image.

[27] As in the work of Ebigbo et al. [2010], attachment and detachment rates are calculated as follows:

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The attachment [cf. Taylor and Jaffé, 1990] and detachment [cf. Rittmann, 1982; Speitel and DiGiano, 1987] coefficients are given by,

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The parameters inline image, inline image, and inline image are all constants [cf. Taylor and Jaffé, 1990; Ebigbo et al., 2010], p is fluid-phase pressure, and g is the gravity vector. Speitel and DiGiano [1987] fit the value of inline image, whereas Ebigbo et al. [2010] obtained a better fit in their model with inline image. In this model, better results were obtained with an expression similar to the latter approach. However, since it is required that inline image and that the influence of reduced porespace due to precipitation needs to be included,

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was used to calculate inline image.

Substrate:

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where Y is the yield coefficient.

Electron acceptor (oxygen):

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The coefficient F quantifies the amount of oxygen consumed per unit mass of substrate [Murphy and Ginn, 2000].

Urea:

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Ammonia:

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Calcite:

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Calcium:

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CO2:

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Water, sodium, and chloride:

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2.5. Charge Balance

[28] With the charge balance equation, it is possible to calculate pH,

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where zi is the charge of the ion i.

2.6. Numerical Model

[29] Some supplementary equations (Appendix A) are required to complete the description of the model. The mass balance equations form a system of 10 partial (equations (14)–(16)) and two ordinary (equation (17)) differential equations. These are implemented, as outlined by Ebigbo et al. [2010], in MUFTE-UG using a vertex-centered finite-volume scheme and a fully implicit time discretization.

[30] Depending on the conditions at hand, the sources and sinks, which arise from the chemical and biological reactions, can impose a very strong coupling on the set of equations. In addition, constitutive relationships such as the permeability-porosity function augment this coupling and increase the nonlinear character of the system. Hence, an efficient numerical solution is challenging.

[31] Time-step sizes are automatically adapted to the rate of convergence that depends on the rate at which the processes occur. The process which has the highest influence on time-step size in this model is the rate of calcite precipitation. High-saturation states can lead to very fast precipitation events which, of course, reduce the time step size. In the simulations conducted in this study, the time step sizes ranged from several seconds to several hours.

[32] More information on MUFTE-UG is available in the work of Assteerawatt et al. [2005] and Helmig et al. [1998].

3. Experiments: Saturated Flow Through Sand-Packed Columns

[33] Laboratory experiments involving saturated flow through sand-packed columns were carried out to optimize the precipitation process and validate part of the numerical model.

[34] As previously described by Cunningham et al. [2011], vertically positioned columns (61 cm in length, 2.54 cm in diameter) were packed with 40-mesh (0.5 mm effective filtration size) quartz sand (Unimin Corporation, Emmet, ID) under water to minimize air inclusions. Columns were disinfected and rinsed by injecting two pore volumes followed by 30-min stagnation periods of each of the four following solutions:

[35] 1% bleach (Clorox, Oakland, Calif.) v/v and 3.5% Tween 80 (Acros, N. J.) w/v solution;

[36] 10% w/v NaCl (Fisher, Fair Lawn, N. J.) solution;

[37] 1.26% w/v sodium thiosulfate (Fisher, Fair Lawn, N. J.) solution; and

[38] 4.10% w/v ammonium chloride (Fisher, Fair Lawn, N. J.) solution.

[39] Cultures of Sporosarcina pasteurii were grown overnight from a frozen stock culture and washed via centrifugation and resuspension in fresh sterile medium prior to injection into the column in up-flow configuration. A cell-attachment period (no flow) of ∼6 h was followed by 18 h of pumping growth medium to develop biofilm. After biofilm establishment and an overnight delay, two pore volumes of calcium-rich (1.25 M calcium) growth medium were injected to initiate biomineralization. The columns were then allowed to remain static for 24 h (biomineralization stage). For columns 2–4, calcium-rich medium from the first 7.6 cm of the columns was displaced immediately after injection with calcium-free medium to minimize injectivity reduction near the injection point. Between biomineralizing stages, the columns were flushed with two pore volumes of calcium- and urea-free medium to restore a low saturation state. Periodically, throughout the experiments, the biofilm was resuscitated by injecting at least two pore volumes of fresh growth medium without calcium. Flow rates were controlled by a Masterflex (model 7553-70) pump and controller (Cole Parmer, Vernon Hills, Ill.). The filling and flushing strategy for all four columns is described in Table 1. The experiments were terminated when the systems' pressure limits were reached. However, column 4 was terminated when as much calcium had been injected as for columns 2 and 3.

Table 1. Injection Strategy and Physical Parameters for Each Column Experiment
ColumnBiomass Concentration of Inoculuma (cfu mL−1)Ca2+-Rich-Medium PulsesMass of Total Ca2+ Injected (g)Resuscitation EventsAverage Flow Rate (mL s−1)Rinse Influent Region
  • a

    cfu: colony-forming units.

1 inline image35303.4150.167no
2 inline image20130.3100.150yes
3 inline image1183.340.155yes
4 inline image22135.290.155yes

[40] Growth medium was prepared by mixing 3 g of Difco Nutrient Broth (BD, Sparks, Md.), 20 g of urea (Fisher, Fair Lawn, N. J.), 10 g of ammonium chloride (Fisher, Fair Lawn, N. J.), and 185 g of calcium chloride dihydrate (not included in calcium-free growth medium) (Acros, N. J.) and stirring continuously until dissolved in 1 L of nanopure water. As necessary, the pH of the medium was adjusted to between 6.0 and 6.3 (the final pH of calcium-rich medium was 5.4–5.6).

3.1. Monitoring and Sampling Methods

[41] Column effluent was collected and monitored for ammonium and residual calcium concentration after each biomineralization stage. A portion of the effluent sample was filtered using a inline image SFCA Corning syringe filter (Corning Incorporated, N. Y.) and analyzed with a modified Nessler assay for ammonium production. The unfiltered remainder of the effluent sample was used to monitor pH. The details are described in Appendix B.

[42] At the termination of the experiment, each column was destructively sampled by cutting it into eight 7.6 cm sections and digesting triplicate portions of each section's sand contents with 10% trace-metal-grade nitric acid (Fisher, Fair Lawn, N. J.). Calcium analysis was performed on an Agilent 7500 ICP-MS after a 1:5000 or 1:10,000 dilution in 5% trace-metal-grade nitric acid (Fisher, Fair Lawn, N. J.) and compared with certified standards (Agilent Technologies, Environmental Calibration Standard 5183–4688) to estimate the total CaCO3 mineral per mass of sand.

[43] Additionally, images and elemental maps were acquired using the Zeiss Supra 55VP scanning electron microscope located in the Imaging and Chemical Analysis Laboratory at Montana State University. CaCO3 precipitates on sand samples were air-dried and sputter coated with iridium. High-resolution images were taken at 1.0 kV at a working distance of 4.0 mm. Elemental analysis with energy-dispersive X-ray spectroscopy (EDS) was performed at ∼20 kV and a working distance of 15 mm.

3.2. Results and Discussion

3.2.1. Residual-Effluent Analysis

[44] CaCO3 precipitation may inactivate microorganisms or create nutrient-diffusion limitations [De Muynck et al., 2010b; Whiffin et al., 2007; Parks, 2009; Dupraz et al., 2009a], leading to reduced ureolysis and subsequently less biomineralization. It has also been hypothesized that larger carbonate crystals, less likely to redissolve, are produced when greater bacterial concentrations are present during ureolysis [Mitchell and Ferris, 2006]. As such, the biofilm was periodically resuscitated by injecting at least two pore volumes of fresh growth medium without calcium to stimulate the recovery of bacterial populations after precipitation events [Dupraz et al., 2009b]. Both residual-effluent populations and inline image concentrations (an indication of ureolysis) are greater directly after the biofilm resuscitation events, while these parameters were observed to decrease during active biomineralization periods (Figure 5).

Figure 5.

Effluent inline image concentration and pH data from column 4. Gray areas indicate resuscitation periods. Although not presented here, similar results were observed for the other columns. Note that the injected medium contained 3.4 g L−1 of inline image.

[45] Directly after resuscitation events, effluent pH was restored to above 9 and the inline image concentrations rose to above 12 g L−1, while during active biomineralizing periods, the pH averaged 6.9 and inline image concentrations dropped as low as 5.1 g L−1.

3.2.2. Distribution of CaCO3 Deposition

[46] Unlike columns 2–4, column 1 did not employ a calcium-medium-displacement strategy for the injection region. As described previously and observed by other researchers [Whiffin et al., 2007; Achal et al., 2009a; Cunningham et al., 2011; Barkouki et al., 2011], higher CaCO3 concentrations per mass of sand were observed in column 1 in the first section near the injection point. Concerns regarding locally reduced injectivity near the injection point of the column [Whiffin et al., 2007; Fujita et al., 2008; Cunningham et al., 2009] led to a modified injection strategy (used for columns 2–4) which involved rinsing Ca2+-rich medium from the influent area before significant ureolysis, and thus CaCO3 precipitation could occur. Favorable results of homogeneous CaCO3 distribution were achieved for columns 2–4 as shown in Figures 6–8. The average CaCO3 contents from each column study are summarized in Table 2. To obtain inline image, the ICP-MS results were converted assuming inline image = 2710 g L−1 and inline image, in order to make direct comparisons to the model output results.

Figure 6.

Calcite volume per bulk volume inline image. Columns 1 (at t = 58 d) and 2 (at t = 35 d) were used for the calibration of the model as shown in Table 3. Six model parameters were fitted here. The symbols show experimental data with standard deviations, and lines are simulation results. In the simulations, calcite precipitation is lower directly at the inlet as a result of the high ionic strength caused by the injection of inline image which reduces the activity of inline image as shown in Figure 2.

Figure 7.

Calcite volume per bulk volume inline image for column 3 at t = 17 d. Results of predictive modeling of the column 3 experiment using the calibrated set of parameters from columns 1 and 2. Symbols show experimental data, and lines are simulation results. Model predictions are in good agreement with experimental results except toward the outlet of the column. It is worth noting that in the first evaluation of this experiment, the amount of calcite estimated in the last column section was significantly higher (gray symbol). This was attributed to an inclusion of calcite precipitates from the effluent tubing in the calculation of inline image. The amount of calcite in this section was subsequently re-evaluated separately, and the resulting value is shown in black.

Figure 8.

Calcite volume per bulk volume inline image for column 4 at t = 34 d. Results of predictive modeling of column 4 experiment using the calibrated set of parameters from columns 1 and 2. Symbols show experimental data, and lines are simulation results. Model predictions are in good agreement with the experiment.

Table 2. Results of Sand-Packed Column Experimentsa
ColumnSection
12345678
  • a

    Average concentration per column section ±1 SD [mg CaCO3/g sand].

1479 ± 29256 ± 61274 ± 30227 ± 29250 ± 74254 ± 71211 ± 22202 ± 73
2222 ± 30193 ± 13196 ± 10188 ± 80174 ± 60178 ± 10169 ± 15173 ± 24
3150 ± 10136 ± 60130 ± 40154 ± 29132 ± 12133 ± 11134 ± 60201 ± 34
4112 ± 18165 ± 40141 ± 40118 ± 21117 ± 24121 ± 12117 ± 80109 ± 80

4. Model Validation

[47] The numerical model was calibrated using the experimental data for inline image of the first two experiments (i.e., columns 1 and 2) in Table 2. The columns are idealized as 80 cm one-dimensional reactors, purposefully longer than the length of the experimental column (61 cm) to reduce the effect of the boundary conditions at the effluent on the simulations.

[48] The initial conditions were:

[49] 1. inline image at the top of the column (effluent) and a hydrostatic pressure profile in the rest of the column;

[50] 2. inline image (i.e., inline image g L−1);

[51] 3. inline image g L−1;

[52] 4. inline image g L−1;

[53] 5. NH4Cl concentration (from which inline image and inline image can be calculated): 10 g L−1;

[54] 6. inline image is adjusted such that the pH of the solution matches the experimental value, i.e., 6.2. All other components are not present initially.

[55] Flux boundary conditions were used at the inlet for all components. The water-inflow velocity was chosen to match those of the experiments (see Table 1). The fluxes of the dissolved/suspended components depended on the composition of the injected solution. Calcium-free solutions were identical to the solution initially present in the column. Additionally, the flux of NaCl2 during the injection of the calcium-rich solution was chosen such that it corresponded to a NaCl2 concentration of 139.7 g L−1 (which corresponds to 185 g L−1 of inline image), and that of Na+ such that the pH equals 5.4 (no significant dissolution of calcite is expected due to the high calcium concentrations).

[56] Column inoculation was simulated by setting a biomass flux for 15 min at the inlet corresponding to the bacterial concentrations listed in Table 1. It is assumed here that the dry cell weight is inline image [e.g., Norland et al., 1987].

[57] After the biofilm was established ( inline image d), the strategy was generally to inject two pore volumes each of the calcium-free and calcium-rich solutions, a small amount (equivalent to the pore volume of the first 7.6 cm of the porous-medium column) of calcium-free solution (not for column 1) to minimize precipitation at the inlet, and then shutting off the injection (no flow) for ∼24 h. This cycle was repeated for the duration of each experiment. In addition, periodic resuscitation (injection of at least two pore volumes of calcium-free growth medium) was simulated as appropriate. The various injections and rest periods carried out in the different experiments are reproduced by the model. It should be noted that, in the experiments, the columns are not geomechanically confined. Volume changes, which may be caused by calcite precipitation, are not accounted for by the model. At the effluent, all boundary conditions are Dirichlet and set to zero, except the pressure which is atmospheric.

[58] The parameters used for the simulations are shown in Table 3. Six parameters were fitted, including inline image, inline image, inline image, inline image, inline image, and inline image. This was done manually by varying these parameters within plausible ranges of validity (see footnotes in Table 3) to match the calcite distribution along the columns in the experiments.

Table 3. Parameters Used for Simulation of Experimentsa
ParameterValueComment/sourceBrief description
  • a

    Fitting is done using columns 1 and 2. Fitted parameters are highlighted in bold.

  • b

    The relatively large values of inline image ( inline image0.3) at the influent of column 1 suggest that inline image is lower than the range of porosities achieved in these experiments.

  • c

    Literature values for inline image include (in g L−1) 14–91 [Melo, 2005], 2.5 and 3 [Taylor and Jaffé, 1990], 29.3 and 38.4 [Zhang and Bishop, 1994], 34–76 [Tanyolac and Beyenal, 1997].

  • d

    Estimated as inline image (assuming the “effective” radius of a calcite crystal inline image). The results of these simulations were not sensitive to inline image.

  • e

    Literature values for inline image vary with bacterial strain and environmental conditions, e.g., inline image [Hao et al., 1983], inline image [Taylor and Jaffé, 1990].

  • f

    These values are lower but not very different from those of Taylor and Jaffé [1990] where inline image and inline image.

φ00.4MeasuredInitial porosity
φcrit0EstimatedbCritical porosity
  inline imageColumns 1 and 2, measuredInitial permeabilities
K0 inline imageColumn 3, measuredInitial permeabilities
  inline imageColumn 4, measuredInitial permeabilities
ϱc2710 g L−1Calcite density
ϱf10 g L−1FittedcBiofilm density (dry)
Dw inline imageMolecular diffusion
αL0.25 dmEstimated from Frippiat et al. [2008]Long. dispersivity
inline image inline imageEstimated from φ0Specific surface areas
ac2000 dm2 dm−3EstimateddSpecific surface areas
kprec1.5 × 10−12 mol/(dm2 s)Zhong and Mucci [1989]Precip. parameters in equation (5)
np3.27Zhong and Mucci [1989]Precip. parameters in equation (5)
kdiss,1 inline imageChou et al. [1989]Dissolution parameters in equation (7)
kdiss,26.5 × 10−9 mol/(dm2 s)Chou et al. [1989]Dissolution parameters in equation (7)
nd1Flukiger and Bernard [2009]Dissolution parameters in equation (7)
kμ2.89 × 10−5 s−1FittedeSubstrate utilization
 (2.5d−1)  
Ks inline image g L−1Taylor and Jaffé [1990]Half-saturation constants
Ke inline image g L−1Hao et al. [1983]Half-saturation constants
Y0.5Seto and Alexander [1985]yield coefficient
F0.5Mateles [1971]O2 consumption
b03.18 × 10−7 s−1Taylor and Jaffé [1990]Decay coefficient
 (0.0275 d−1)  
KpH inline imageKim and Fogler [2000]Decay parameter in equation (25)
ca,10.0443 s−1FittedfAttachment parameters
 (3831 d−1) Attachment parameters
ca,29.19 × 10−4 s−1FittedfAttachment parameters
 (79.38 d−1)  
cd,12.89 × 10−8 s−1Ebigbo et al. [2010]Detachment parameter
 2.5 × 10−3 d−1  
k0.0417 mol/(g s)Krajewska [2009]Rate of ureolysis
 (2500μ mol/(mg min))  
Ku inline imageKrajewska [2009]Parameters in equation (1) for calculation of ureolysis rate
KEU,1 inline imageFidaleo and Lavecchia [2003]Parameters in equation (1) for calculation of ureolysis rate
KEU,2 inline imageFidaleo and Lavecchia [2003]Parameters in equation (1) for calculation of ureolysis rate
inline image inline imageFidaleo and Lavecchia [2003]Parameters in equation (1) for calculation of ureolysis rate
kub0.11FittedParameters in equation (3)
nub1.5FittedParameters in equation (3)
T25°CConstantTemperature

[59] Figure 6 shows the results of the simulation for the columns used for model calibration. The calibrated model predicted inline image for columns 3 and 4 with little error: the root-mean-square errors were 0.0046 and 0.0032, respectively. However, in column 3 (Figure 7), the results differ slightly from the experimental data toward the effluent. These differences, particularly toward the effluent, could be the result of an artifact in the experiments of calcium carbonate precipitating in the nonporous-medium-containing effluent section and settling onto and possibly into the effluent section. Additionally, increased bacterial (and thus ureolytic) activity could be due to diffusion of oxygen through the silicon tubing in the effluent leading to increased microbial concentrations, and thus precipitation.

[60] In addition to the calcite distribution along the column, the modeling results are compared to the pH of the effluent samples taken during the experiments. The samples were taken after mineralization phases, 7 min after flow was restarted. While the pH data was not used in the model calibration, good correlation between the model and experimental results were achieved (Figure 9).

Figure 9.

Comparison of effluent pH over time resulting from the experimental procedure for all four experiments. Continuous lines are model predictions, while the symbols are the measurements.

[61] However, the experiments generally show a stronger variation of pH than the model. This may indicate an overestimation of the buffering capacity of the carbonate mineral by the model, i.e., an overestimation of the rates of precipitation and dissolution. Data for precipitation and dissolution rates were taken from studies without the interference of microorganisms capable of forming biofilms. It is possible that the presence of the biofilm reduces these rates. This may also be a source of error for the model prediction of the amount of inline image precipitates, particularly toward the effluent of the columns.

[62] The effect of the injection strategy used for columns 2–4 on the saturation state inline image of calcite and hence on calcite precipitation within the column is illustrated in Figure 10. It can be seen that the injection of a small amount of calcium-free medium into the column just before the biomineralization phase leads to a reduction of inline image next to the injection point. The figure also shows that the biomass does not distribute uniformly within the column, but accumulates mostly at the inlet due to the availability of oxygen at the inlet.

Figure 10.

Results of simulation for column 4 showing the calcite saturation state inline image and biofilm volume fraction along the column length (at t = 33 d) during the final biomineralization phase.

5. Sensitivity Study

[63] In order to gain some insight into the importance of the uncertain parameters fitted in section 4, a sensitivity study was conducted. All six parameters ( inline image, inline image, inline image, inline image, inline image, and inline image) were varied within a given range to determine their effects on the error as compared to the experimental measurements. It must be noted, however, that the parameters are varied individually. A detailed investigation of parameter correlations is beyond the scope of this study, although it might give further valuable insight. Nonetheless, the main sources of uncertainty for the model with respect to parameterization can be shown with this study.

[64] For each parameter, a lower and an upper limit were defined. For the substrate utilization rate inline image and the biofilm density inline image, these can be determined from literature (see the footnotes in Table 3). However, for the other parameters, the lower and upper limits are more difficult to determine. As such, they were approximated by the variation of the fitted values given in Table 3 by approximately an order of magnitude in both directions (see Table 4). Intermediate parameter values, defined as either half or double the fitted value, are referred to as low and high values, respectively (Table 4). Intermediate-value simulations were carried out only for the parameters to which the system is most sensitive, as shown in Table 4.

Table 4. Variation of Parameters for Sensitivity Study
 ϱf[g L−1]kμ[1 d−1]ca,1[1 d−1]ca,2[1 d−1]kubnub
Upper limit50440,00080012.5
Lower limit5140080.010.5
High value7662158.760.222
Low value0.0551
Original value102.5383179.380.111.5

[65] The results of the sensitivity study as shown in Figure 11 clearly demonstrate that for this setup, the model is most sensitive to the proportionality factor inline image. A quantification of this parameter experimentally would significantly reduce the model uncertainty.

Figure 11.

The effect of six parameters on the error made by the numerical model as compared to the experimental data on calcite distribution. The histogram shows error (i.e., total sum of the squared errors for both columns) relative to the error with the calibrated parameters.

6. Simulations With Two Fluid Phases

[66] The effect of dense-phase CO2 on the mineral barrier is the focus of current research by the authors. The numerical model is a useful tool with which several processes can be investigated and new experiments can be designed. As an example, in this section, possible effects of free-phase CO2 on carbonate precipitates are investigated with the help of the numerical model.

[67] A simple simulation is shown here in which CO2 is injected into a column in which a given amount of calcite ( inline image) and biofilm ( inline image) are initially present and uniformly distributed. The other initial and boundary conditions are identical to those of the experiments with saturated flow except pressure which is assumed to be 80 bar.

[68] Two injection scenarios were tested. In both cases, the total injection rate and other parameters were the same as in the column 4 experiment (i.e., 0.155 mL s−1), and a constant mass fraction of water in CO2 of inline image g g−1 is assumed (corresponding to the saturation pressure of water in the CO2 phase at 25°C and 80 bar): injection of pure CO2 and injection of 90% (by volume) CO2 (i.e., 0.1395 mL s−1) and 10% water (i.e., 0.0155 mL s−1).

[69] These result in two fluid phases within the column. A simulation time of 3 d is chosen. Two-phase-flow parameters used here include residual water and CO2 saturations inline image and inline image, pore size-distribution index inline image, entry pressure inline image (see A4 for the capillary-pressure-saturation and relative-permeability-saturation relations). The molecular diffusion coefficient for the CO2 phase is approximated with inline image.

[70] As can be seen in Figure 12, the simulations show that:

Figure 12.

Results of simulations (at t = 3 d) showing the effect of pure CO2 and a CO2-water mixture on calcite within the sand column. The black lines show the calcite distribution, while the gray lines show the saturation of CO2.

[71] 1. The injection of pure, dense-phase CO2 leads to limited calcite dissolution within the column because the dissolution of CaCO3 buffers the pH of the medium, minimizing further dissolution.

[72] 2. The injection of both CO2 and water leads to relatively fast dissolution. The injected water flushes out resident water reducing the buffering capacity of the calcite. As such, limited success of this technology may be seen with CO2 injection strategies involving large volumes of simultaneously injected water.

7. Conclusions

[73] 1. Relatively uniform microbially mediated precipitation could be achieved in three of the four experiments involving water-saturated flow through 61 cm, sand-packed columns when near-injection-point calcium-medium displacement strategies were used.

[74] 2. Calcium deposition efficiency may be optimized by balancing biomineralizing periods with bacterial resuscitation events. Long biomineralization periods could lead to inactivation of bacterial cells (due to cell encapsulation), reduced ureolysis, and, ultimately, reduced calcium deposition efficiency.

[75] 3. A numerical model has been developed, capable of describing microbially induced carbonate precipitation and dissolution in porous media in the presence of water and CO2 flow.

[76] 4. Part of the numerical model, i.e., for water-saturated flow through sterilized sand, was validated with experimental data for one-dimensional column experiments. It should be noted that a transfer of the model to field scenarios might not be straightforward while focusing on model scale-up is currently ongoing [A. Phillips, et al. (2012), Potential CO2 leakage reduction through biofilm-induced calcium carbonate precipitation, submitted to Environmental Science and Technology, 2012].

8. Outlook

[77] 1. The model can and will be used to optimize injection strategies to achieve a large radius of influence in larger-scale, three-dimensional experiments.

[78] 2. High-pressure, dense-phase-CO2 experiments will be designed using the model as a predictive tool.

[79] 3. In the future, the two-phase-flow model will be validated with the results of high-pressure laboratory experiments.

[80] 4. The model would also be suitable, with slight modifications, for other applications involving microbially induced CaCO3 precipitation including (but not limited to) strontium coprecipitation as well as soil and dike stabilization.

Appendix A:: Supplementary Equations for Description of Model

A1. Changes in Permeability

[81] The porosity of the porous medium can be calculated from inline image, inline image, and the initial porosity inline image

display math

Given porosity, permeability K is calculated using a Kozeny-Carman-type equation [e.g., Xu et al., 2004],

display math

The critical porosity inline image is the porosity at which the permeability is zero.

A2. Solubilities

[82] The solubility of CO2 in the water phase is calculated from Duan and Sun [2003] as a function of temperature, pressure, and equivalent salinity. When both phases are present, the concentration of H2CO3 is equivalent to the solubility. In the absence of the CO2 phase, the solubility is the maximum possible concentration of H2CO3 in water. For simplicity, inline image is assumed to be constant [Bielinski, 2006].

[83] Henry's law is used for the calculation of the solubility of oxygen in water (R. Sander, Compilation of Henry's Law constants for inorganic and organic species of potential importance in environmental chemistry (version 3), 1999, available at http://www.henrys-law.org).

A3. Velocity (Darcy Equation)

[84] Velocity is calculated as

display math

inline image is the relative permeability (calculated as a function of saturation using Brooks-and-Corey relationships as done by Ebigbo et al. [2010]).

A4. Capillary Pressure

[85] Capillary pressure is the difference between the phase pressures:

display math

It is calculated using the relationship of Brooks and Corey [e.g., Ebigbo et al., 2010].

A5. Dispersion

[86] The hydrodynamic dispersion coefficient is calculated as follows [Bear, 1979]:

display math

where inline image and inline image are the longitudinal and transverse dispersivities, I is the unit tensor, D is the molecular diffusion coefficient, the velocity is calculated as inline image, and inline image is tortuosity calculated as given by Millington and Quirk [1961]:

display math

A6. Fluid Properties

[87] CO2 density is calculated using the equation of state by Span and Wagner [1996], and viscosity from Fenghour et al. [1998]. The effects of small amounts of water and oxygen in this phase are not accounted for in these calculations.

[88] The density and viscosity of the water phase is calculated as a function of salinity as given by Batzle and Wang [1992]. For the calculation of salinity, the NaCl and NaCl2 salts are considered.

Appendix B:: Monitoring of Activity in Sand-Packed Columns

[89] During the experiments, the activity in the column was monitored as follows:

[90] 1. Ammonium concentration was determined with a modified Nessler assay; effluent samples were diluted in deionized water and compared to standards made from inline image. Each sample and standard (250μL) was added in triplicate to a 96-well microplate (Fisher, Fair Lawn N. J.) to which 3 μL of mineral stabilizer and polyvinyl alcohol, and 10 μL of Nessler reagent (potassium tetraiodomercurate(II)) (Hach, Loveland, Colo.) were added. Ammonium concentration was quantified in the resulting solution after 13 min reaction time via spectrophotometry at 425 nm (BioTek, Synergy HT).

[91] 2. The pH of effluent samples was assessed with a Fisher Scientific pH meter (model 50) equipped with a Corning glass electrode, which was calibrated daily with pH 7 and 10 buffers.

Appendix C:: Image and EDX Analysis of Minerals

[92] Figure 13 depicts the surface of sand from a treated column where calcium carbonate crystals were observed in the size range of inline image. Spot EDX analysis of the crystals confirmed the presence of elemental calcium (data not shown). In addition, EDX elemental mapping revealed calcium in regions where obvious crystals had formed and silica in the region of the base materials (see Figure 13). This result leads to additional support that the formed minerals were calcium carbonate.

Figure 13.

Scanning electron micrograph of CaCO3-crystal structure on sand particle along with EDX elemental maps for calcium and silicon (scale bar: 100 μm).

Notation
inline image

Longitudinal and transverse dispersivities [dm]

inline image

Porosity

inline image

Initial porosity

inline image

Volume fraction of calcite inline image

inline image

Critical porosity at which K = 0

inline image

Volume fraction of biofilm inline image

inline image

Activity coefficient

inline image

Biomass growth coefficient [1 s−1] or [1 d−1]

inline image

Dynamic fluid-phase viscosity inline image or [g/(dm s)]

inline image

Pore size-distribution index

inline image

Maximum specific rate of urea hydrolysis inline image

inline image

Calcite saturation state

inline image

Density [kg m−3] or [g L−1]

inline image

Tortuosity

inline image

Specific surface area of calcite grains [dm2L−1]

b

Decay coefficient [L s−1] or [L d−1]

inline image

Endogenous decay coefficient [L s−1] or [L d−1]

inline image

Parameters for the calculation of inline image

inline image

Parameters for the calculation of inline image

g

Gravitation vector [ms −1]

k

Specific rate of urea hydrolysis inline image

inline image

Maximum substrate utilization rate [L s−1] or [L d−1]

inline image

Attachment coefficient [L s−1] or [L d−1]

inline image

Detachment coefficient [L s−1] or [L d−1]

inline image

Parameter for calculation of inline image inline image

inline image

Parameter for calculation of inline image inline image

inline image

Parameter for calculation of inline image inline image

inline image

Relative permeability

inline image

Parameter for the calculation of inline image

m

Molality inline image

inline image

Parameter for calculation of inline image

inline image

Parameter for calculation of inline image

inline image

Parameter for the calculation of inline image

p

Phase pressure [Pa] or [bar]

inline image

Capillary pressure [Pa] or [bar]

inline image

Entry pressure [Pa] or [bar]

q

Source/sink inline image

inline image

Biomass attachment rate [g/(L s)]

inline image

Biomass decay rate [g/(L s)]

inline image

Biomass detachment rate [g/(L s)]

inline image

Net rate of calcite dissolution [mol/(L s)]

inline image

Biomass growth rate [g/(L s)]

inline image

Net rate of calcite precipitation [mol/(L s)]

inline image

Rate of urea hydrolysis [molurea/(L s)]

v

Darcy flux/velocity [dm s−1]

z

Ionic charge

inline image

Specific surface area between water and calcite [dm2 L−1]

inline image

Specific surface area between water and solids (i.e., both porous matrix and calcite) [dm2 L−1]

inline image

Initial value of inline image [dm2 L−1]

C

Concentration [g L−1]

D

Hydrodynamic dispersion [dm2 s−1]

D

Molecular diffusion coefficient [dm2 s−1]

F

Oxygen consumption per unit mass of substrate

K

Permeability inline image

inline image

Apparent dissociation coefficient of H2CO3 inline image

inline image

Apparent dissociation coefficient of inline image

inline image

Apparent dissociation coefficient of inline image inline image

inline image

Dissociation constants for enzyme-urea complex inline image

inline image

Parameter for inhibition due to inline image inline image

inline image

Constant for calculation of pH-dependent decay inline image

inline image, inline image

Monod half-saturation constant [g L−1]

inline image

Ureolysis half-saturation constant inline image

inline image

Calcite solubility product inline image

inline image

Apparent dissociation coefficient of water inline image

M

Molecular mass [g mol−1]

S

Saturation

inline image

Residual saturation

T

Temperature [°C]

X

Mass fraction

Y

Yield coefficient

inline image

Concentration of urease in porous medium [g L−1]

Subscripts
c

Calcite

f

Attached biomass/biofilm

n

Nonwetting phase

w

Wetting phase

Superscripts
a

Ammonia/ammonium

b

Suspended biomass

c

Calcite

Ca2+

Calcium

Cl

Chloride

CO2

Carbon dioxide

e

Electron acceptor/oxygen

f

Biofilm

Na+

Sodium

s

Growth substrate

u

Urea

w

Water

Acknowledgments

[93] This work was carried out within the framework of the International Research Training Group NUPUS funded by the German Research Foundation DFG, the Netherlands Organisation for Scientific Research NWO, and the Norwegian Research Council NRC. Funding for the experimental work was provided by the Zero Emissions Research and Technology (ZERT) program (DOE award DE-FC26-04NT42262), DOE EPSCoR program (DOE award DE-FG02-08ER46527), and the DOE Office of Science, Subsurface Biogeochemical Research Program (SBR), contract DE-FG02-09ER64758. Any opinions, conclusions, findings, or recommendations expressed herein are those of the authors and do not necessarily reflect those of DOE. Also, the authors acknowledge funding for the establishment and operation of the Environmental and Biofilm Mass Spectrometry Facility at Montana State University (MSU) through the Defense University Research Instrumentation Program (DURIP, contract W911NF0510255) and the MSU Thermal Biology Institute from the NASA Exobiology Program (project NAG5-8807). Joshua Stringam is acknowledged for his help in the laboratory and Johannes Hommel for proofreading. The reviewers are also acknowledged for their constructive criticism. The experimental work in this paper was conducted by A. Phillips.

Ancillary