Transp Porous Med (2011) 90:23–39 DOI 10.1007/s11242-011-9804-z
Forward and Inverse Bio-Geochemical Modeling of Microbially Induced Calcite Precipitation in Half-Meter Column Experiments T. H. Barkouki · B. C. Martinez · B. M. Mortensen · T. S. Weathers · J. D. De Jong · T. R. Ginn · N. F. Spycher · R. W. Smith · Y. Fujita
Received: 4 February 2010 / Accepted: 9 July 2011 / Published online: 3 August 2011 © Springer Science+Business Media B.V. 2011
Abstract Microbially induced calcite precipitation (MICP) offers an alternative solution to a wide range of civil engineering problems. Laboratory tests have shown that MICP can immobilize trace metals and radionuclides through co-precipitation with calcium carbonate. MICP has also been shown to improve the undrained shear response of soils and offers potential benefits over current ground improvement techniques that may pose environmental risks and suffer from low “certainty of execution.” Our objective is to identify an effective means of achieving uniform distribution of precipitate in a one-dimensional porous medium. Our approach involves column experiments and numerical modeling of MICP in both forward and inverse senses, using a simplified reaction network, with the bacterial strain Sporoscarcina pasteurii. It was found that the stop-flow injection of a urea- and calcium-rich solution produces a more uniform calcite distribution as compared to a continuous injection method, even when both methods involve flow in opposite direction to that used for bacterial cell emplacement. Inverse modeling was conducted by coupling the reactive transport code TOUGHREACT to UCODE for estimating chemical reaction rate parameters with a good match to the experimental data. It was found, however, that the choice of parameters and data was not sufficient to determine a unique solution, and our findings suggest that additional time and space-varying analytical data of aqueous species would improve the accuracy of numerical modeling of MICP.
T. H. Barkouki · B. C. Martinez · B. M. Mortensen · T. S. Weathers · J. D. De Jong · T. R. Ginn (B) Department of Civil and Environmental Engineering, University of California, Davis, USA e-mail:
[email protected] N. F. Spycher Division of Earth Sciences, Lawrence Berkeley National Laboratory, Berkeley, USA R. W. Smith Department of Biological and Agricultural Engineering, University of Idaho, Idaho Falls, USA Y. Fujita Department of Biological Sciences, Idaho National Laboratory, Idaho Falls, USA
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Keywords Calcite precipitation · Urea hydrolysis · Ureolysis · Strontium remediation · Soil improvement · Inverse · Biogeochemistry · Biogeochemical · Biogrout · Biocementation · Bioremediation · Reactivetransport
1 Introduction Heavy metal and radionuclide contamination threaten groundwater quality at sites worldwide. In situ bioremediation techniques have been shown to be among the most promising strategies for remediating toxic chemicals (e.g., Iwamoto and Nasu 2001). Strontium-90 is a uranium fission byproduct present in the deep subsurface at several U.S. Department of Energy sites. Uranium processing activities at the Idaho National Laboratory have raised concerns about the possibility of 90 Sr contamination in the Eastern Snake River Plain (ESRP) aquifer which provides drinking water to much of southwestern and south-central Idaho (Fujita et al. 2000). This case is not suited for ex situ groundwater treatment methods due to the extent of contamination and the inaccessibility of the subsurface. Another area in which induced calcite precipitation is promising is in the in situ control of the mechanical properties of soils and porous media. Current soil strengthening processes including chemical and cement grouting are energy intensive and introduce synthetic and sometimes toxic materials into the subsurface (e.g., De Jong et al. 2010). Common approaches, such as the injection of acrylamide grouts, have been reported to cause water poisoning in Japan (Karol 2003), thus, reflecting increasing regulation on some common ground improvement techniques. As these techniques come under increased scrutiny from public policies and opinions, there exists increased necessity for alternative construction techniques for stabilizing subsurface materials that do not introduce toxic synthetic materials to the environment. In addition, common techniques suffer from low “certainty of execution,” or the ability to realize the design level of treatment. Microbially induced calcite precipitation (MICP) has been shown to be a promising solution for remediating 90 Sr when groundwater is at or above saturation with respect to calcium carbonate, as it is in the ESRP aquifer (Fujita et al. 2000). Sr+2 can either precipitate as a pure carbonate or co-precipitate with calcite, thus, becoming immobilized in calcite by substituting for Ca+2 , or otherwise becoming entrained, in the mineral structure. MICP also offers alternatives to soil grouting applications including liquefaction prevention, building settlement reduction, dam and levee safety, and tunneling by using prevalent bacteria and natural materials to change the mechanical properties of soil. Precipitated calcite has been shown to increase the shear strength and stiffness of soil while decreasing its permeability and compressibility (De Jong et al. 2006, 2010). Measuring shear wave velocity has been shown to be an effective tool for monitoring calcite precipitation during treatment (De Jong et al. 2010). MICP has also been proposed for applications such as sealing subsurface reservoirs for geologic CO2 sequestration (Dupraz et al. 2009), sealing the contact between sheet piling and bedrock (Suer et al. 2009), and repairing cracked concrete structures (van Tittelboom et al. 2010; Ramakrishnan et al. 1998, 2001; Ramachandran et al. 2001). Concerns about the use of MICP include the impacts of the production of ammonium on groundwater quality (e.g., Ip et al. 2001), costs (e.g., Ivanov and Chu 2008), and life cycle impacts (Suer et al. 2009). Suer et al. (2009) concludes that biogrouting was less expensive than jet grouting with lower overall environmental impact. The process of using Bacillus pasteurii for mediating calcite precipitation by microbial ureolysis to alter the geologic properties of an aquifer, specifically reducing the permeability and porosity, was first developed for enhancing oil recovery from reservoirs and controlling
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the transport of groundwater contaminants (Ferris et al. 1996). Further research investigated the kinetic rates (Ferris et al. 2004), microbial ecology in reactors (Hammes et al. 2003), temperature dependence (Mitchell and Ferris 2005), nucleation, and growth of MICP with and without strontium present (Fujita et al. 2004; Mitchell and Ferris 2006a,b; Fujita et al. 2000, 2004) demonstrated that bacteria native to the ESRP aquifer would hydrolyze urea and induce calcite precipitation, while B. pasteurii were found to uptake 90 Sr in synthetic groundwater mimicking the properties of the ESRP aquifer. MICP has also been demonstrated to increase soil shear strength and load bearing capacity in triaxially loaded sand specimens (De Jong et al. 2006), five-meter sand columns (Whiffin et al. 2007), and a 100-m3 sand box (van Paassen et al. 2008). Results from a field test at the Idaho National Laboratory Vadose Zone Research Park show that MICP can be enhanced by stimulating the growth of already-present native biomass by the addition of molasses (Fujita et al. 2008). Technical challenges in the application of MICP include design of the injectate rates and aqueous chemistry (e.g., calcium, carbonate, urea, pH buffer, and microbial nutrients) in order to control the timing and rate of calcite precipitation to generate the desired spatial distribution. Both applications rely on manipulation of site-specific aqueous chemistry including the supply of organics for ureolytic agents to oxidize during ureolysis. Ureolytic agents may be augmented, or native species may be enlisted, and in all applications wells are used to control hydraulics and inject reactants. Consequently, modeling ultimately requires incorporation of representative, yet practical, multicomponent reaction networks into transport simulators for non-uniform flow with, e.g., radial components. van Paassen et al. (2008) developed a two-dimensional (2D) domain with randomly distributed circular solid surfaces (grains) of distributed sizes. Calcite precipitation rates were calculated as a linear function of the diffusive flux of urea onto the grain surfaces, which was itself calculated by a Michaelis-Menten equation. Dupraz et al. (2009) conducted batch experiments and modeled MICP using a first-order kinetic ureolysis relationship to urea, and saturation-dependent calcite precipitation. Booster et al. (2008) used a one-dimensional (1D) model with a simple constant rate model for ureolysis and calcite precipitation. They suggest that the Fidaleo and Lavecchia (2003) model may provide a good starting point for developing a more accurate rate expression for B. pasteurii ureolysis, but that the true rate expression could be very different. Harkes et al. (2010) suggest controlling ionic strength following injection of microbial agent in order to sequentially reduce detachment along a flow path so as to achieve a more uniform distribution of biotic agent, and thus, reactant, for ureolysis. Here, we address the problem in an alternative way by injecting bacteria in one direction and then the urea in the reverse direction. The objective of this study is to identify effective means of achieving uniform distribution of precipitate in a 1D porous medium. To this end, we report column experiments and simplified numerical modeling of MICP in both forward and inverse senses, with the bacterial strain Sporoscarcina pasteurii. Column experiments included continuous and repeat stop-flows, with mass flux equal in both cases. Aqueous chemistry and calcite distribution were monitored as well as small-strain shear waves that correlate to the stiffness of the column (De Jong et al. 2006). TOUGHREACT (Xu et al. 2006; Xu 2008; Xu et al. 2008) was coupled with the inversion code UCODE (Poeter et al. 2005), Hill and Tiedeman (2007) to determine apparent rate parameters for the kinetically-controlled ureolysis and calcite precipitation rates. The rates are based on simplified and conventional constitutive kinetic expressions, while the effect of available grain surface and role of bacteria as nucleation or growth substrate and other details are not evaluated. The inverse modeling is applied in order to fit observed pH and calcite precipitate data simultaneously to two separate transport
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regimes, and to establish a relationship between observed shear wave velocity and calcite abundance, with good results.
2 Materials and Methods 2.1 Experimental Two 1D flow column experiments were conducted simultaneously to compare a continuous flow treatment technique versus a stop-flow treatment technique. Ottawa 50–70 sand, a silica sand, sub-rounded, with a uniform grain size distribution (D50 = 0.2 mm), was dry pluviated into 50 × 5 cm2 acrylic cylinders (Fig. 1) with soil filters and end caps on both termini to provide treatment solutions to the samples. The columns were fitted at four evenly distributed ports along the length of the sand column with piezoelectric bender element pairs for measuring shear wave velocities, and sampling ports for pore fluid extraction. Shear wave velocities were used to non-destructively monitor cementation during the experiment (De Jong et al. 2006; Mortensen et al. 2010). Velocity was measured by recording the time required for a square wave voltage signal to travel from the tip of a transmitting bender element to the receiving bender element. Bender elements were constructed and operated using guidelines by Lee and Santamarina (2004). A vertical load of 100 kPa was applied to the top cap to provide sufficient overburden pressure for achieving reasonable shear wave velocities. pH was measured at port locations along the length of the column as well as at the effluent and influent end caps using the sampling ports with EMD pH strips in the range of 6.5–10.0 with a ±0.15 precision. Aqueous ammonium concentration were analyzed from effluent and
Fig. 1 Schematic diagram and photograph of column setup
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Table 1 Summary of microbial induced cementation treatment formulations Solution
Constituents
Urea medium (used in treatments below)
Contains per liter of double distilled water 3 g Bacto nutrient broth 20 g Urea 20 g NH4 CI 2.12 g NaHCO3 2 × 106 cells/ml Sporoscarcina pastuerii
Initial biological treatment
400 ml Urea medium
Cementation
400 ml Urea medium
Treatments
11 g/l CaCI2
Table 2 Column properties Flow treatment
Soil
Relative Height density (cm) (%)
I. StopOttawa 5070 96.8 flow II. Contin- Ottawa 5070 91.1 uous treatment
Porosity Average initial shear wave velocity (m/s)
Injection rates Part I. bio- Flow logically direction based (ml/min)
Part II. calcium based (ml/min)
Flow direction
42.9
0.36
96.7
10
Down
10a
Up
42.6
0.37
112.6
10
Down
2
Up
a Intermittent 0.5 h injections with 2.5 h no-flow retention times
port samples taken during treatment, filtered with a 0.2-µm syringe filter, and stored at 4◦ C, using a flow injection method following Mansell et al. (2000). Aqueous calcium concentrations of collected samples were measured using an Agilent 7500i inductively coupled mass spectroscope (IC-PMS) with better than 1 ng resolution on metals. Detailed information on preparation of substrates, as well as the cultivation and measurement of S. pasteurii was done in accordance with the procedures outlined by De Jong et al. (2006). See Table 1 for detailed information on the solution chemistry. The MICP treatment solution was delivered in two steps to two separate columns with an initial bulk porosity of 0.36. Bulk porosity was measured from the total volume and weight of sand in the column after dry pluviation, and did not change until MICP treatments were administered. First, during Part I, (Table 2), 1.3 pore volumes of the urea medium (3 g/l Bacto, 20 g/l Urea, 20 g/l NH4 Cl, 2.12 g/l NaHCO3 ) mixed with the bacterial strain Sporoscarcina pasteurii at 2×106 cells/ml were injected at 10 ml/min via peristaltic pumping from the top of the column, with downward flow. The urea medium/bacteria mixture was allowed to sit for roughly six hours at rest in each column. During Part II, (Table 2) 1.3 pore volumes of the urea medium (3 g/l Bacto, 20 g/l Urea, 20 g/l NH4 Cl, 2.12 g/l NaHCO3 ) without bacteria, but mixed with 100 mM calcium chloride were injected from the bottom of the column, with upward flow. The reversing of flow during injection of the amendments with respect to the flow during microbial augmentation was done on the following hypothesis.
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Optical Density (OD600)
Stopped Flow 0.6
6.E+05
Continous Flow
0.4
4.E+05
0.2
2.E+05
Cell Density (cells/mL)
8.E+05
0.8
0.E+00
0.0 0
10
20
30
40
50
Time (hrs) Fig. 2 Effluent optical density breakthrough curves during the course of MICP treatment for stopped-flow and continuous column experiments
Effluent optical density measurements were used to monitor microbial breakthrough during the course of treatment using a spectrophotometer with wavelength set to 600 nm (Shimadzu™ UV–Vis, UV-160). For the accuracy of optical density measurements (103 cells/ml), the data indicates that all appreciable unattached bacteria are flushed out of the columns during the first injected pore volume, followed by insignificant change for the rest of treatment (Fig. 2). Based on no change in the optical density time histories for both columns after the first pore volume of injected fluid, it is assumed for the model that the attached distribution of microbes does not significantly change over the course of treatment. We assume that bacterial attachment is described by first-order generally irreversible removal from the aqueous phase in accordance with colloid filtration theory, and under these conditions the aqueous and attached concentrations of bacteria should exhibit an exponential distribution along the column (e.g., Ginn et al. 2002). Accordingly a two-parameter exponential form for the attached cell number density as a function of space along the column was adopted for the inverse model. The reverse of this profile is hypothesized to be the best for inducing uniform rates of calcite precipitation because reactant reduction along the flow path will be countered by increased biomass along the flow path. Therefore, to take advantage of this aspect, we reverse the flow of amendments with respect to that of the bacterial augmentation. The amendment injection schedule differed among the two columns while retaining equivalent total injected mass. One column received continuous flow at an injection rate of 2 ml/min. The other column received a stop-flow injection, that is, cycled injections every three hours of 450 ml at 10 ml/min (roughly 45 min of injection) followed by a retention period. The objective of this comparison is to evaluate steady versus pulsed injection schemes, while retaining the same total mass flux of injectants. For the stop-flow case, effluent pH was collected within the first minute while the pump was operating for each pumping cycle. Toward the end of the experiment, sampling frequency was increased during the pumping period to monitor dynamic pH. For the continuous case, pH was collected simultaneously with stop-flow data collection. Post-treatment calcite measurements were taken by extruding the treated sand from the column, dividing the sample into four equal sections, and performing a gravimetric acid wash (by immersing oven dried samples in 2 M hydrochloric acid, allowing carbonates to dissolve, rinsing the sand, and oven drying).
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Table 3 Equilibrium reactions Species
ZH+a 2 Z−a OH− CaOH+ NH3 (aq) CaNH3 +2 Ca(NH3 )2 +2 CaN0+ 3 HC0− 3 H2 C03 (aq) CaHC0+ 3 CaC03 (aq) − NaC03 NaHC03 (aq)
log K (25◦ C) Basis components
−6.121 7.896 13.997 12.697 9.244 9.144 18.788 −0.5 −10.329 −16.681 −11.599 −3.2 −1.27 −10.079
H2 0 H+
Na+
Ca+2
Cl−
C0−2 3
N0− 3
NH+ 4
02 (aq) Urea ZH
0 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 1
0 0 0 1 0 1 1 1 0 0 1 1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 1 1 1 1 1
0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 1 1 2 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 −1 −1 −1 −1 −1 −2 0 1 2 1 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0
a Not originally in minteq.v4 thermodynamic database. Added according to Fidaleo and Lavecchia (2003)
2.2 Modeling The experiments were modeled in TOUGHREACT (Xu et al. 2006; Xu 2008; Xu et al. 2008), a reactive transport model developed at the Lawrence Berkeley National Labs. TOUGHREACT is capable of modeling non-isothermal multiphase 3D fluid flow in heterogeneous and variably saturated porous and fractured media and multi-component transport with equilibrium and kinetic aqueous speciation, mineral precipitation/dissolution, gas dissolution/exsolution, cation exchange, linear sorption/desorption, and radioactive decay. The reader is referred to the appendix and to Barkouki (2010) for explanation of the reactive flow and transport solution method of TOUGHREACT as it is configured for the model presented herein. The minteq.v4.dat thermodynamic database was adopted and reformatted from PHREEQC (Parkhurst and Appelo 1999), while the actual mass action relations called from the database for this model are listed in Table 3. In implementing the ureolytic reaction (Eq. 1) model into TOUGHREACT, the kinetic expression for jack bean (Canavalia ensoformis) derived enzymatic ureolysis by Fidaleo and Lavecchia (2003) was adopted to represent bacterial ureolysis using S. pasteurii, and modeled by Eqs. 2, 3, and 4. ru
−2 (NH2 )2 CO + 2H2 O → 2NH+ 4 + CO3
ru = νmax [ZH]
KP [S] K M + [S] K P + [P]
(1) (2)
log(K 1 ) ZH + H+ = ZH+ 2
(3)
ZH − H+ = Z− log(K 2 )
(4)
The variables ru , νmax , S, P, K M , and K P are the rate of ureolysis (mol l−1 s−1 ), ureolysis rate constant (s−1 ), concentrations of substrate (S, urea) and product inhibitor (P, ammonium), half-saturation for substrate (K M , units of S), inhibition constant for ammonium
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(K P , units of P), respectively. K 1 and K 2 (mol l−1 ) are the conventional speciation constants for the protonation/deprotonation reactions in (3) and (4). Equations 3 and 4 are not meant to represent specific interactions between urease and protons, but are simply a necessary adaptation of the pH driven inhibition term in the original Fidaleo and Lavecchia (2003) model to fit the TOUGHREACT input structure (Barkouki 2010). Values used in the modeling to follow are: K M = 3.21 × 10−3 , K P = 1.22 × 10−2 , K 1 = 7.57 × 10−7 , and K 2 = 1.27 × 10−8 . The calcite precipitation reaction and kinetic rate expression are shown in Eqs. 5 and 6. rc
Ca+2 + Co−2 3 ↔ CaCo3(s)
(5)
(Ca+2 )(CO−2 s ) rc = −kc Ac 1 − K sp
(6)
−1 The variables rc , kc , Ac , and K sp are the rate of precipitation (mol kg−1 H O s ), kinetic rate 2
constant (mol m−2 s−1 ), specific mineral reactive area (m2 kg−1 H2 O ), and solubility product, respectively. Because the initial value of Ac is initially calculated from the input parameter AMIN, a calibration parameter, and appears as a factor with kc , the product kc Ac can be viewed as an effective parameter, and the setting of kc merely sets the initial scale of searchable Ac . The value of kc was set at 1.0 × 10−8 mol/m2 s, a typical value within the range of published data, e.g., (Nilsson and Sternbeck 1999; Ferris et al. 2004). Measured calcite mass and pH data were fitted for both continuous and stop-flow columns by calibrating the precursor mineral reactive surface area (AMIN) and urease (ZH) distributions as fitting parameters in an inverse problem, as follows. Ac is zero when there is no calcite present (the initial conditions used in this simulation), therefore, to initiate precipitation in the absence of calcite, the minimum specific reactive surface area, AMIN, is assigned as the initial surface area. TOUGHTREACT accepts the input value of AMIN in units of cm2 /g mineral, and performs internal conversion to yield minimum Ac in units of m2 /kgH2 O when calculating rc using molecular properties of calcite. Once the simulated reactive surface area, Ac , of calcite exceeds that which is computed by AMIN, the rate is based upon the new value of Ac . In fact, product kc and Ac may depend on the precipitation mechanism (mononuclear, polynuclear, etc), mineral phase (calcite, vaterite, CaCO3 monohydrate, etc.) and the available crystal surface area. These factors are not evaluated in our simplified modeling approach that relies on the classical form (6) for approximation of our rate. Urease was simulated as an immobile species, and the amount of urease in each grid-block was modeled as an exponential function of distance from injection inlet (Eq. 7). ZHt (x) = c1 e−c2 x
(7)
ZHt represents the total moles of the urease basis component, from which the species Z− , ZH+ 2 , and the reactive species ZH are derived according to Eqs. 3 and 4. This form was chosen for its congruence with bio-colloid advection and filtration theory and confirmed with optical density measurements taken from samples collected at all four ports immediately after injecting bacteria (assuming the detached microbe concentration profile reflects the general trends of the attached microbial concentration profiles); the pre-multiplier, c1 , and exponential coefficient, c2 , were treated as fitting parameters. Thus, the inverse problem was constructed such that the fitting parameters for urease were the coefficients of an exponential relationship (one set of parameter values applicable to both columns) which would yield the optimal data fit. Unknown parameters c1 , c2 , and AMIN were estimated in the model-independent parameter calibration program UCODE (Poeter et al. 2005; Hill and Tiedeman 2007), that performs
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a modified Gauss-Newton search to optimize parameter values of a given model (TOUGHREACT in this case) in order to fit observed data. UCODE calculates a suite of sensitivity analysis and statistical quantities on all parameters and observations before, during, and after a model regression run to aid in model analysis. The fitting was done simultaneously for both the continuous and stop-flow columns together, so that the same parameter values are used in both scenarios. This is done in order to determine if parameter values exist that fit our simplified models to both of the two different flow and transport regimes. The forward model was run with a wide range of parameter values to explore the objective function in order to determine the best initial values that would produce a stable inverse run. The initial values c1 = 1 × 10−5 molurease /l and c2 = 0 cm−1 , such that the inverse problem began with a uniform urease concentration of 1 × 10−5 mol/l and with AM I N = 5000 cm2 /g.
3 Results The results from these experimental and numerical analyses indicate that MICP spatial distribution is a result of the combined effects of reaction rate limitation, urease enzyme activity in space, and flow magnitude, direction and transience. The model calibration was performed using effluent pH (breakthrough curve) data and final calcite precipitate (profile) data. The optimal parameter values were c1 = 2.785 × 10−5 molurease /l, c2 = 0.02346 cm−1 , and AMIN = 2920 cm2 /g (Eqs. 6 and 7). Measured calcite profiles plotted with fitted numerical results (Fig. 3) show that stop-flow injections result in a more uniform calcite distribution as opposed to a continuous injection. In the continuous flow case, calcite precipitation is greater near the injection port or source of aqueous calcium. In the stop-flow case, calcite is precipitated more or less uniformly across the length of the column with little precipitation bias toward the injection source. Experimental and fitted numerical results are shown for effluent pH during the course of treatment in Fig. 4. In addition, the calibrated model was used in the forward sense to predict ammonium and calcium concentrations of selected samples, shown in Figs. 5 and 6 (model not fitted to these data). In general, the model predicts reasonable trends and magnitudes in mineral precipitation and transient aqueous concentrations for the data collected despite a poor fit of the minimum and maximum values of pH data used to calibrate the model. The accumulation of calcite at particular locations over time was monitored during the course of treatment utilizing piezoelectric bender elements which measured shear wave velocity changes. The simulated calcite accumulations over time corresponding to the bender element locations are plotted along with experimental shear wave velocities at these locations (Fig. 7). The congruence of curve trends implies the potential for predicting soil strength from simulated calcite abundances.
4 Discussion The current study demonstrates that a stop-flow treatment scheme is more effective for obtaining uniform calcium carbonate content utilizing MICP at a 1D treatment distance of 0.43 m, i.e., intermittent injections at higher flow rate followed by a rest period allows calcium to precipitate more evenly along the length of the column than a continuous flow. Shear wave velocities (Fig. 7), confirmed with calcium carbonate contents at four locations along the columns, support the cementation uniformity seen in Fig. 3b. This result indicates a promising injection strategy for controlling precipitation in order to avoid clogging due to excessive
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Fig. 3 Calcite results from experiment (measured) and fitted numerical simulation. Calibration points are the averages of the simulated profile over a length of the column equal to the sections of the columns that were analyzed gravimetrically to obtain data points. a Continuous flow injection, b stopped-flow injection
Fig. 4 pH results from experiment and fitted numerical simulation. The narrow vertical bands indicate times when pumping was on, the time in between being the retention period for the stop-flow pumping scheme. a Continuous flow injection, b stopped-flow injection
calcium carbonate formation near the injection source, to achieve flow rerouting in a higher dimensional case, and to uniformly and predictably sequester contaminants. The optimal strategy is the stop-flow injection of aqueous reactants in the opposite direction to flow used to emplace microbial agents. Considering the stop-flow treatment technique, a uniform
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Fig. 5 Measured and predicted aqueous ammonium concentration at a single location (port D) over treatment duration. a Continuous flow injection, b stopped-flow injection
Fig. 6 Measured and predicted aqueous calcium concentration at a single location (port B) over treatment duration. a Continuous flow injection, b stopped-flow injection
distribution in calcite precipitation is evidently due to a combination of the gradient in microbial concentration due to the reverse-flow augmentation of microbes prior to cementation, and the pulsing flow regime of calcium and urea as opposed to the continuous flow. Modeling results are consistent with the hypothesis that the reverse-flow injection of microbes results in a log-linear distribution of active urease. The calibrated TOUGHREACT model reflects the phase of the transient effluent pH data, however, does not capture the amplitude in pH values seen in the experiment. Microbial distribution in situ has a significant effect on the spatial distribution of calcium carbonate. A closer look at the data from the stop-flow column experiment indicates a small but noticeable reverse trend with higher calcium carbonate precipitation further from the injection port as opposed to nearer to the injection port (Fig. 3b). This trend that appears only in the stop-flow case is evidently due to the spatial distribution of reactants imposed by the
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Fig. 7 Comparisons of measured shear wave velocity and simulated calcite growth profiles for four locations (see Fig.1) along the length of the column. Time = 0 represents the beginning of the urea- and calcite-rich injection (shear wave measurements were taken before this, that is, at “negative” times); simulation began at time = 0. The −100 shift in the right axis is due to the measured initial shear wave velocity of 100 m/s with no calcium. The shift puts the initial shear wave velocity level with the initial zero calcite condition. a Continuous flow injection, b stopped-flow injection
higher fluxes associated with the stop-flow pumping scheme. One explanation for a reverse trend in cementation is microbial density that is biased toward the top of the columns due to filtration during microbe injection. This hypothesis is congruent with the modeling results that a log-linear shape distribution of urease (higher concentration at the top) yielded the best overall data fit. The optimized model was analyzed in a forward manner by plotting reaction rate, saturation index, and reactive surface area as indicators of system behavior (Figs. 8 and 9). As shown in Eq. 6, the rate of calcite precipitation depends on the current reactive calcite surface area, Ac , and the saturation ratio (the second term of the bracketed factor). The saturation ratio is abbreviated Q/K, and the log of this term is known as the saturation index (SI). The continuous flow column (Fig. 8) was analyzed for the entire experiment at 10h time-increments since changes in these factors occurred gradually throughout the 50 h experiment. The profiles in Fig. 8a show a higher saturation index at upstream locations which results in higher precipitate toward the upstream terminus of the column, as shown in Fig. 8b and c. Figure 8c shows the peak of reactive surface area increasing and approaching the port throughout the experiment. This sharp peak in surface area causes the high reaction rate close to the injection port, and is a sign of immanent clogging in that part of the column. Conversely, the pulsed injection technique of the stop-flow column distributed a sufficient amount of calcium solution downstream to produce a more uniform reaction rate profile. Here, the stop-flow column is analyzed for only a single, three-hour stop-flow period at short increments to capture the cyclic processes that occur both during pumping (Fig. 9a–c, at 5 min increments) and during retention (Fig. 9d–f, at 20 min increments). Figure 9a and b shows a pulse of high saturation and reaction rate moving up the column during injection, and reaching a uniform profile for about fifteen minutes prior to shutting off the pumps. Figure 9d and e shows the profiles decrease faster in the downstream half of the column due to the higher downstream urease concentrations.
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Fig. 8 Calcite precipitation factors in the continuous column presented at 10 h intervals for the entire experiment. Note that for the continuous injection, one pore volume corresponds to 10.71 h, so the first curve shown above (10 h) shows conditions near the completion of the first complete displacement of initial fluid
5 Summary This study reveals promising results for controlling, monitoring, and simulating MICP, and it highlights topics that are in need of further research. It has been shown that a stop-flow treatment scheme more uniformly distributes microbially induced calcite precipitation as opposed to a continuous flow treatment scheme. Non-destructive shear wave velocity measurements, in conjunction with calcite abundance measurements through gravimetric analysis of samples, were used to determine calcium carbonate precipitation during and after treatment. In the stop-flow case, ureolysis and precipitation were reflected through pH measurements that revealed, respectively, rises in pH during dominant ureolytic activity and drops in pH during precipitation and flushing. In this study, simplified and conventional rate expressions were adopted and inverse modeling was used to determine effective parameter values; this approach is designed to provide insight into relative overall rates and consistency of conventional constitutive theories of ureolysis and precipitation rates for interpretation of our column experiments. Our simulations yielded positive results for simulating MICP in this context and in the conditions of our experiments, in that the general behavior of the experiments are captured by quantification of the hypothesized dominant processes. However, the primary controls on rates of both ureolysis and precipitation in the presence of nonuniform advective transport including limitations on mixing in natural media are still incompletely understood, and useful predictive modeling may require increased sophistication of the kinetic expression for ureolysis and for precipitation, and possibly for explicit modeling of microbial attachment and detachment.
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Fig. 9 Stop-flow calcite precipitation factors for one 3-h stop-flow cycle only (from 25.25 to 28.25 h): a, b, c are for the first 40 min of the stop-flow cycle, this is during injection. d, e, f are for the remaining 140 min, which is the retention period. The arrows indicate the progression of time, and the value in parentheses is the time-increment between each profile
Indirect inverse modeling was used to determine ureolysis and calcite precipitation rate parameters. Although a good solution was achieved, it demonstrated non-uniqueness, and this suggests the need for more diverse observation data in future experiments. It has been shown here the important role of the microbial distributions in controlling calcite precipitation rates. Therefore, predictive modeling will require a priori knowledge of the microbial population distributions, and the fate of such populations when subjected to flow. Further exploration of these research questions may expand experimental data to include more comprehensive observations of reactants and products, microbial occurrence, phase-association, and activity, etc., under different flow regimes. Acknowledgments Funding provided by the Office of Science (Biological and Environmental Research), U.S. Department of Energy (#DE-FG02-07ER64404) and the United States National Science Foundation (#0727463 and #0628782) in support of this research is appreciated.
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Appendix: Equations of TOUGHREACT TOUGHREACT solves the multi-component chemical transport equation derived from the classic Advection-Dispersion Equation (ADE): φ
∂C = −∇ · J + q + R ∂t
(A.1)
where φ, C, J, q, and R denote porosity, aqueous phase concentration, total mass flux, external mass sinks/sources, and chemical reaction sinks/sources, respectively. Solute advective flux is given by Darcy velocity u multiplied by aqueous concentration C while dispersive/diffusive fluxes are calculated numerically by a discretized version of Fickian diffusion. Mixed equilibrium-kinetics chemical reactions are solved from a mass balance on a basis of components following Parkhurst et al. (1980) and Reed (1982). Kinetically controlled reactions are developed from a predefined set and the relevant forms for enzyme kinetics and precipitation are described above (Eqs. 2 and 6). Equilibrium reactions are handled as follows. Mass action laws describe aqueous complexation reactions that occur at local equilibrium. One secondary species is identified per each equilibrium reaction, and the concentration of the secondary species is defined in terms of primary species concentrations, according to the mass action equation for that particular equilibrium reaction. For example, for aqueous speciation equilibria with a given number of components Nc in the basis set, secondary species Ci can be described as: Ci =
Nc 1 ν ν Cj i j γ j i j K i γi
(A.2)
j=1
Equilibrium constants K i per reaction i are cataloged in a thermodynamic database (e.g., Table 3). To calculate activity coefficient γ , TOUGHREACT uses a modified Debye-Hückel solution (Morel and Hering 1993). The mass balance equation for components and mass action equations for species comprise the governing equations that are solved to determine the concentrations of all the chemical species.
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