3D characterization of microbially induced carbonate precipitation in rock fracture and the resulted permeability reduction

Accepted Manuscript 3D characterization of microbially induced carbonate precipitation in rock fracture and the resulted permeability reduction

Wu Chuangzhou, Jian Chu, Wu Shifan, Yi Hong PII: DOI: Reference:

S0013-7952(18)30831-7 https://doi.org/10.1016/j.enggeo.2018.12.017 ENGEO 5021

To appear in:

Engineering Geology

Received date: Revised date: Accepted date:

21 May 2018 29 November 2018 21 December 2018

Please cite this article as: Wu Chuangzhou, Jian Chu, Wu Shifan, Yi Hong , 3D characterization of microbially induced carbonate precipitation in rock fracture and the resulted permeability reduction. Engeo (2018), https://doi.org/10.1016/ j.enggeo.2018.12.017

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ACCEPTED MANUSCRIPT

3D Characterization of Microbially Induced Carbonate Precipitation in Rock Fracture and the Resulted Permeability Reduction

Chuangzhou WU1,2 [email protected], Jian CHU1,* [email protected], Shifan WU1

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[email protected], Yi HONG2 [email protected] 1

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Corresponding author

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*

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School of Civil and Environmental Engineering, Nanyang Technological University, Singapore, 639798 2 College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China, 310058

ACCEPTED MANUSCRIPT Abstract A new seepage control method for fractured rock is biogrouting through a microbially induced calcite precipitation (MICP) process. A study on the spatial distribution of biogrout in a rock fracture and its effect on permeability reduction is presented in this

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paper. A series of experiments together with 3D scanning and 3D flow simulation

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were performed on rock fractures with various initial apertures treated by bio- grouting.

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A lognormal distribution of MICP precipitates along the flow direction in a fracture

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was observed. The 3D flow simulation of biogrouted fracture has revealed that the routinely adopted parallel plate model (cubic law) for estimating permeability of

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channel flow is no longer applicable when the fracture aperture is less than the critical value of 0.7 mm based on this study. This is because partially clogging will occur

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when the fracture aperture is less than the critical value, resulting in a transition of the

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flow type from surface flow to channel flow. A semi- empirical equation which can account for the effect of flow type has been proposed for estimating the permeability

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reduction due to bio-grouting for rock fractures. Keywords: Permeability reduction, Fracture sealing, Rock fracture, Biogrouting.

ACCEPTED MANUSCRIPT 1. Introduction 1.1 Biogrout distribution in rock fracture Recently, intensive study on the potential use of biogrouting for rock fractures has been carried out (Arnon et al. 2005; van Paassen et al., 2010; Mitchell et al. 2010;

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DeJong et al., 2013; Mountassir et al. 2014; Salifu et al., 2016; Phillips et al, 2012,

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2015, 2016; Proto et al., 2016; Wu et al., 2018). The primary advantage of biogrouting over the traditional cement grouting for fracture sealing is that the former

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enables fluid transportation over a longer distance and intrusion into smaller cracks

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compared with the use of cement grouting (Mitchell et al., 2010; Cuthbert et al., 2013; Mountassir et al. 2013; Phillips et al, 2012, 2015). Although chemical grout can also

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be used, it is expensive and the lifespan of chemical grouting is limited to 10-20 years (Minto et al., 2016; Mountassir et al., 2014).

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The MICP process can be explained as follows:

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CO(NH2 )2 + 2H2 O → 2NH4 + + CO3 2− Ca2+ + CO3 2− → CaCO3 (s)

(Eq. 1) (Eq. 2)

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Several laboratory and field tests on the feasibility of biogrouting for fracture sealing have been carried out. Laboratory studies of MICP processes in fracture are often limited to small scale (Mitchell et al., 2010; Cuthbert et al., 2013; Mountassir et al. 2014, Phillips et al, 2015). It is not easy to obtain the spatial distribution of MICP precipitates within fracture in a quantitative manner (Phillips et al, 2012, 2016). In the past, relatively less attention has been paid to obtain the spatial distribution of MICP precipitation in a single rock fracture quantitatively in meso-scale, which can be a significant factor governing permeability of fracture and the effectiveness of

ACCEPTED MANUSCRIPT biogrouting.

1.2. Permeability assessment of biogrouted rock fracture Laboratory estimation of the permeability of fractured rock with or without obstacles are often limited to geologic heterogeneity of fractured rock and the

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distribution of the obstacles (Figueiredo et al., 2017; Huang et al., 2017; Park and Oh,

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2018). Therefore, the permeability of natural rough fracture with obstacles is often estimated by analytical or numerical methods. Estimation of the permeability of small

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apertures with obstacles (such as biogrouted fractures) can be considered as an

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analogy of contact areas in natural rock (Kumar et al., 1991 ; Shen et al., 2013 Wu et al., 2017).

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Several analytical models and numerical approaches for measuring the permeability of fractured rocks with the consideration of fracture tortuosity have been proposed

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(Witherspoon et al., 1980; Brown, 1987; Jasinski and Dabrowski, 2018). For fractures without obstacles (i.e. contact areas), the simplest model of flow through a rock

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fracture is the parallel plate model (Witherspoon et al., 1980; Brown, 1987). In this model, an exact solution for the hydraulic conductivity is given using the well-known

1986):

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‘cubic law’ (Witherspoon et al., 1980). One expression is given as (e.g., Brown,

𝑑3

d𝑝

𝑞 = 𝑊 12𝜇 ∙ d𝑥

(Eq. 3)

where 𝑞 is the volume flow rate (𝑚3 /𝑠), 𝑑 is the channel diameter or fracture aperture(𝑚), 𝜇 is the dynamic viscosity of flow (𝑘𝑔/(𝑚 ∙ 𝑠)), 𝑊 is the fracture width in the direction normal to fluid flow, fracture.

d𝑝 d𝑥

is the fluid pressure gradient along the

ACCEPTED MANUSCRIPT For fractures with cylindrical obstacles (i.e. fractures propped with large proppant), numerical methods based on the Brinkman flow model or Maxwell’s effective medium approach (Yeo, 2001; Cardenas et al., 2015; Jasinski and Dabrowski, 2018) were widely used to model the flow condition in fractures. Furthermore, for fractures with irregular obstacles (such as biogrouted fractures) and rough surface (such as

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MICP aggregates coated), the numerical method used for permeability prediction

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(Singh et al. 2015) was based on the Navier-Stokes equation (Jasinski and Dabrowski,

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2018). In the present study, the irregular profile of the MICP precipitates generated within the fracture was obtained experimentally using 3D scanning of the test

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specimens.

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1.3. Motivation for investigation

To study the reduction in permeability for fractured rocks after injection of

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biogrouts, the hydraulic behaviour of a single fracture during biogrouting needs to be understood and quantified. The modelling of the permeability change of a single

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fracture is the basic building block for a realistic model of the flow condition in a fractured rock mass and the subject of this paper. The objectives of this study are to

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experimentally and numerically investigate the effectiveness of biogrouting for rock fractures with different apertures and to model the spatial distribution of the MICP precipitates and the related permeability reduction along a single rock fracture.

2. Experimental Test Setup 2.1. Experimental apparatus and setup A small-scale artificial fracture composed of two granite sheets was used for the

ACCEPTED MANUSCRIPT biogrouting model test and the study of the topography of CaCO 3 precipitation formed in the fractures shown in Fig. 1 (Wu et al., 2018). The surface of granite sheet is flat and macroscopically smooth. Fig. 1 illustrates the experimental setup. Leakage blockage using biogrouting was carried out in three fracture samples with three different apertures. The rock sample used was granite obtained in Singapore. Two

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identical pieces of granite sheets with a dimension of 40 cm × 7 cm × 1 cm were put

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one on top of another to form a horizontal fracture. As shown in Fig. 1(b), rubber

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strips were placed on the lower piece of granite sheet and the gap between two pieces of granite sheets were closed and sealed with epoxy to contain the biogrouts inside.

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Three different sizes of fracture aperture were prepared marked as sample #1, #2 and #3 with apertures equals to around 1.5, 1.1 and 0.7 mm, respectively. Two pieces of

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short PVC tubing were inserted into the gap as inlet and outlet with inner radius equals 5 mm. Table 1 summarizes the dimensions of fractures, the initial equivalent

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the range of 23 to 25o C.

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hydraulic aperture and initial Reynolds number. The experimental temperature was in

2.2. Cultivation of bacteria culture

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The urease producing bacteria (UPB) strain used in this study was Sporosarcina pasteurii (DSM 33), formerly known as Bacillus pasteurii. The optical density (OD600 ) was in a range of 0.6 to 0.7. The urease activity was determined by a conductivity probe with a highest value of 0.1 mS/min, which was equivalent to a urea consumption rate around 11 mM/min (Whiffin et al. 2007).

2.3. Treatment strategy The one-phase injection method (Cheng et al. 2018) was adopted for all the fracture-sealing tests. The biogrout solution was recirculated in the grouting process

ACCEPTED MANUSCRIPT to simulate the seepage condition. The biogrouts solution consisted of equal volume ratio of bacteria culture and cementation solution (i.e. mixed urea and calcium chloride solution). After a thoroughly mixing, 500 mL of biogrout was immediately injected into the fracture sample by using a peristaltic pump. At the same time, the outflow was collected from the outlet and circulated back into the fracture

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continuously. A constant flow rate of 20 ml/min was employed for all three tests. This

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one-phase recirculating injection was repeated twice over two days (48 hrs) with each

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treatment for 24 hrs to ensure a fully consumption of the cementation solution.

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2.4. 3D scanning of MICP precipitates distribution

After the fracture sealing tests, the spatial distribution of MICP precipitates was

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measured using a 3D scanner (DAVID VISION Structured Light 3D Scanner). Data obtained from the 3D scanner (in X Y Z format) were exported to MATLAB to

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produce a grid file. The data were then used to develop a 3D surface model indicating the formation of bio-precipitates and a partial clogging model using the COMSOL

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software for further numerical analysis of permeability reduction (Wu et al., 2018).

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3. Experimental Results 3.1. Visual examination

Bio-precipitates (e.g., calcium carbonate) were observed in the form of white mineral deposited (see Fig. 2) on the surface of rock after biogrouting. Major differences in the bio-precipitate profile were observed in the three model tests under the same injection solution and strategy. For Test #1 with a fracture width of 𝑑𝑖1 = 1.5 mm, only the lower surface was covered with biogrout as shown in Fig. 2a. The precipitates due to MICP had a planar and smooth profile. On the other hand, for

ACCEPTED MANUSCRIPT Test #3 with a fracture width of 𝑑𝑖3 = 0.7 mm, the fracture was partially clogged (see Fig. 2c) and both the upper and lower surfaces were covered with MICP precipitates. For Test #2 with a fracture width of 𝑑𝑖2 = 1.1 mm, , the surface of the lower rock sheet showed a thin layer of MICP precipitates and the surface of the upper rock sheet showed sparsely distributed spots of calcites as shown in Fig. 2b, suggesting a

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mixture effect of settlement of precipitates and partial clogging. Similar results were

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reported by EI Mountassir et al. (2013). These results suggest that the fracture

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aperture is a key factor governing the distribution of precipitates. The testing results further indicate that there appears to be a critical aperture value beyond which the

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flow will change from a surface flow type to a channel flow type. It can has been reported that precipitates formed in fine apertures around 0.1-0.3mm show channel

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profile (EI Mountassiret al. 2014). The critical aperture is mainly dependent on the type of bacteria (e.g., bacterial cell, flocs) and cementing agent, flow rate, and initial

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following sections.

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roughness of the flow channel. The influence of these factors are discussed in the

3.2. Spatial distribution of MICP precipitates

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To assess the permeability reduction associated with bio-clogging, the distribution of MICP precipitates needs to be assumed. It is for this reason that the determination of the spatial distribution of MICP precipitates is of primary importance. Most of the previous studies were performed on relatively short samples or field tests without measuring the amount of MICP precipitates and incapable of deducing the exact sealing locations in the fractures or the amount of permeability reduction. In this study, relatively large samples were used and 3D scanning was adopted to obtain the spatial distribution of MICP precipitates.

ACCEPTED MANUSCRIPT Fig. 3 shows the distribution of MICP precipitates accumulated on the surface of the rock fracture after biogrouting. The differences in the distributions of MICP precipitates in the three tests are evident. The largest mass of MICP precipitates was observed on the lower surface of Sample #3 which was the coarsest, while the least MICP precipitates occurred on the lower surface of Sample #1 which was the finest.

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The experimental results indicate that the sedimentation process controls the transport

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of the MICP aggregates and flocs within the fractures and majority of the precipitates

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are on the lower surface due to gravity.

In terms of the spatial variation in the distribution of the MICP precipitates, a

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similar trend was observed for all three tests or apertures. The average thickness of calcite increased along the transport direction and reached a peak value at 6 ~ 8 cm as

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shown in Fig. 3. The average thickness decreases dramatically at zone 8~15 cm from the inlet. The slope of the curve approaches a constant value at zone 15~38 cm, which

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is referred to as the uniform zone as the distribution of precipitates is restively more

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uniform as compared to the distribution in the filtration zone at which the mass has peak values. The relatively more pronounced non- uniform distribution in the filtration zone is due to the fact that larger MICP aggregates settle quicker than smaller ones

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and cause the formation of a filtration zone close to the inlet point. This filtration effect has inhibited the transport of biogrouts to a farther distance and led to the permeability reduction in this area (filtration zone). After the formation, the filtration zone would expand or densify due to either the calcium carbonate formed on the filtration matrix or the small MICP particles attached to the filtration matrix during the transportation process. The size of the filtration zone in the fracture is controlled by the balance of the hydraulic shear force and the attachment of the MICP aggregates to the filtration matrix (Mountassir et al. 2014).

ACCEPTED MANUSCRIPT 3.3. Effect of fracture aperture on the efficiency of MICP precipitation The effect of the fracture aperture and the initial flow velocity on the efficiency of bio-sealing was investigated. Using the experimental data obtained from this study, Fig. 4a is plotted to show the relationship between the precipitation efficiency 𝑅𝑒

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and the aperture size as well as the relationship between the filling ratio (calcite fraction) 𝑅𝑓 and the aperture size. The precipitation efficiency 𝑅𝑒 can be calculated

[CaC O3 ( s)]T ∙1 mol Ca2+⁄1 mol CaC O3 ( s) [CaCl2 ]T ∙1 mol Ca2+⁄2 mol Cl −

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𝑅𝑒 =

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as follows (Martinez et al., 2014):

(Eq. 4)

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where [CaCO3 (s)]T is equal to the total amount of calcium carbonate measured after

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treatment over the entire fracture and [CaCl2 ]T is the total amount of calcium chloride injected into the fracture during treatment. Precipitation efficiency was less

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than 50% in all cases ranging from 28% to 45%, which was in line with the test result reported by Martinez et al. (2014). Many factors contribute to the precipitation

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efficiency and affect the results of biomediated calcium carbonate precipitation. It can be found from Fig. 4b that the fine aperture shows the lowest value in 𝑅𝑒 which is

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probably due to the higher velocity (shearing force) in the rock fracture in comparison with the medium and coarse aperture given the flow rate is constant (EI Mountassir et al. 2014). Although the fine aperture shows the lowest efficiency, the filling ratio of fracture with fine aperture (𝑑𝑖3 = 0.7𝑚𝑚) is the highest (70%) as compared with the other two apertures: 53 % and 57 % for medium and coarse aperture respectively, given the same injection method and solution. Apart from the fracture aperture, the flow velocity shows dramatically influences on spatial distribution of calcite on the fracture surface s (Van Rijn, 1984; EI

ACCEPTED MANUSCRIPT Mountassir et al., 2014). The effect of flow velocity on the MICP precipitates is complex and dependent on many factors including: bacterial density, type of flocs, size of precipitate aggregates, concentration of the cementation solution, etc. The initial and final flow velocity adopted for the tests conducted in this study are given in Table 1. The relationship between the flow velocity and the efficiency of MICP

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precipitates is shown in Fig. 4b. Based on the test results, it is obvious that the

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efficiency of MICP precipitates decreases with the increase in flow velocity.

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In terms of injection method, more MICP precipitates was found forming when the aperture was 0.1mm or less using the two-phase flow method (EI Mountassir et al.

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2014) compared to that one-phase injection method adopted in presented study due to inlet clogging when the aperture lower than 0.7 mm or less. Thus, the two-phase

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method seems to be more suitable for very fine apertures due to the relative uniform distribution of bacterial and less clogging around the inlet (van PASSEEN, 2009;

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Martinez et al., 2013; EI Mountassir et al. 2014). These observations tend to support

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the hypothesis that there is a combined effect of aperture and flow velocity on the

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precipitation efficiency.

4. Numerical Estimation of Permeability 4.1. Numerical model of biogrouted fracture According to the Reynolds number (1 < 𝑅𝑒 = 7.5 < 100 in present test), the bio-solution flow within fractures belong to the laminar flow regime, which is governed by Navier-Stokes equation: ρ (∇𝑢)u = 𝜇∇2 𝑢 − ∇𝑝

(Eq. 5)

ACCEPTED MANUSCRIPT where 𝑢 is the flow velocity, 𝜇 denotes the fluid shear viscosity and 𝑝 is the local fluid pressure. Numerical analysis was conducted with the assumption that the fracture was filled with a single-phase, incompressible Newtonian fluid, which was characterized by a constant viscosity. 3-D Navier-Stokes model was employed to perform direct

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numerical simulations, in which fluid flow was computed using the exact

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three-dimensional fracture geometry from 3D scanning data. Pressure gradient for

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numerical model was achieved by constant pressure difference of 10 Pa at the upstream and downstream boundaries. The tangential components of the velocity

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vectors were set to zero at these walls. The no-slip boundary conditions were used at the remaining boundaries, that is, the other pair of the sidewalls, the top and bottom

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fracture walls, and at the rims of the obstacles. No obstacles intercepted the boundaries of a regular computational box. The density and fluid dynamic viscosity of

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the solution were assumed as 1000 kg/m3 and 0.0089 kg/(m·s), respectively.

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4.2. Permeability estimation procedure The spatial distributions along the granite fracture after bio- grouting treatment

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were based on the 3D scanning data, and the corresponding flow analysis was conducted piece by 36 pieces with each dimension of 10×10 mm. A representative numerical model is shown in Fig. 5. It was assumed in the numerical analysis that the solution could not flow through MICP precipitates, but only the pores in the granite fracture. The numerical models were solved using software COMSOL to obtain the permeability variation prior to/after biogrouting. A total of 72 simulations were carried out including 36 simulations for fracture #1, 18 for fracture #2, and 18 simulations for fracture #3. The details of the numerical experimental programme are

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5 Simulation Results

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5.1. Spatial distribution of permeability with different initial apertures The permeability reduction of rock fracture versus transportation distance curves

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for different apertures is shown in Fig. 6. It can be seen that the three curves indicate

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the same trend: the rapidly decreasing zone (zone A), the rapidly increasing zone (zone B), and the gradually increasing zone (zone C). Zone A was within the first 6

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cm, Zone B within 6~15 cm from the inlet point, and Zone C from 15~38 cm.

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Although the permeability reduction trend of the three apertures is similar and in line with the distribution of MICP precipitates, major differences can be found in

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terms of the magnitude. For instance, for aperture 1.5mm, the slope of curve in zone C is 0.11, which is slightly slower than that in zone A (0.75) and zone B (0.67).

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However, in the case of aperture 0.7 mm, the slope in zone C is 0.82, which is dramatically slower than that of Zone A (7.5) and Zone B (6.7). In addition, the slope

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in Zone C for aperture 0.7 mm is more than 7 times of that for aperture 1.5 mm, which is due to the filtration zone in aperture 0.7 mm. For aperture 1.1 mm, the slopes of the three zones took the intermediate values. This spatial distribution of permeability reduction with transport distance as shown in Fig. 6 follows a Lorentz relationship as follows: 𝜅⁄𝜅0 = 𝑦0 +

2𝐴

𝑤

𝜋 4(𝐿−𝑥 𝑐) 2 +𝑤2

(Eq. 6)

ACCEPTED MANUSCRIPT where 𝜅 is the permeability of the fracture with MICP precipitates, 𝜅0 is the permeability of the fracture with no MICP aggregates, 𝐿 is the transport distance. The 𝑦0 , 𝐴, w, 𝑥 𝑐 are coefficients of Lorentz function. The fitting lines with the parameters are given in Fig. 6.

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5.2. Relationship between permeability reduction and filling ratio

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In order to quantify the fracture sealing efficiency by biogrout, the relationship

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between permeability reduction and filling ratio (i.e., calcite fraction in fracture) of MICP precipitates is established in Fig. 7 using test data.

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For the surface flow type, the experimental results are compared with the curve

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given by the Cubic Law in Fig 7a. Permeability reduction along both the flow direction (𝜅𝑥 ⁄𝜅0 ) and the normal to the flow direction (𝜅𝑦 ⁄𝜅0 ) have been taken into

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account in Fig. 7a. It can be seen that both 𝜅𝑥 ⁄𝜅0 and 𝜅𝑦 ⁄𝜅0 agree well with the cubic law. The results shown in Fig. 7a suggest that the asperity of the fracture wall

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due to MICP precipitates under the flow condition shows no obvious effect on the 𝜅⁄𝜅0 relationships, as all the data points follow more or less the same ‘cubic law’. In

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other words, the flow direction does not appear to induce significant anisotropy in permeability. Furthermore, the standard deviation of the permeability reduction predicted using the cubic law after biogrouting is only 4.55%, which implies that the cubic law seems still valid for predicting the permeability of biogrouted fracture. For the channel flow type, the permeability reduction as shown in Fig. 7b deviates from the relationship given by the cubic law. The deviation is due to the CaCO 3 formed within fractures and the fluid flow within the fracture is different from that in parallel plate model (Jasinski and Dabrowski, 2018). There is a nonlinear relation

ACCEPTED MANUSCRIPT between permeability reduction and the filling ratio of MICP precipitates as shown in Fig. 7(b) which can be written as: 𝜅 ⁄𝜅 0 = ( 1 − 𝑐 ∙ 𝑓 ) 𝑑

(Eq. 7)

where 𝜅⁄𝜅0 is the permeability reduction in rock fracture, 𝑓 is the calcite fraction

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of the fracture after biogrouting. The c and d are coefficients of power function

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considering the partial clogging effect due to the MICP precipitates. Eq. 7 is an

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empirical function proposed to assess the permeability for the channel flow type. 5.3. Evolution of permeability during the bio-grouting process

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To infer the permeability evolution from a surface flow type to a channel flow

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type during the MICP process, the permeability variation with the aperture was established by combining both sets of data from both the rough surface flow type and

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the channel flow type (see Fig. 8).

The initial permeability for aperture 1.5mm is employed as the initial

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permeability κ0 for channel flow type rather than that of the aperture 0.7mm used in the last section. Two different asperity of fracture wall with the maximum and

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minimum value of 𝑅𝑟𝑚𝑠 (Singh et al. 2015) was adopted for rough surface type in Fig. 8. It can be seen that the κ/κ0 can be predicted by the cubic law with high accuracy from aperture 1.5 mm to around 1.0 mm for rough surface type. When aperture decreases gradually and reaches the critical aperture, the permeability for channel flow type starts to deviate from the cubic law relationship significantly, as shown in Fig.8. The critical aperture can be determined as the value where the permeability versus filling rate relationship starts to deviate from the cubic law. An empirical equation can be established based on the permeability for both

ACCEPTED MANUSCRIPT rough surface flow type and the channel flow type. Given the initial 𝑑𝑖 and the calcite filling ratio acquired from 3D scanning data, the permeability ratio 𝜅⁄𝜅0 can be estimated by following piecewise functions: 𝜅⁄𝜅0 = [𝑑𝑖 (1 − 𝑓)]2 𝜅⁄𝜅0 = 𝑎 ∗ [𝑑𝑖 (1 − 𝑓)]𝑏

𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝐹𝑙𝑜𝑤 𝐶ℎ𝑎𝑛𝑛𝑒𝑙 𝐹𝑙𝑜𝑤

(Eq. 8)

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{

where 𝜅 and 𝜅0 are absolute (i.e. single phase) permeability of fracture after

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biogrouting and before biogrouting respectively, 𝑎 and 𝑏 is the parameters of the

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power function. This function can be applied for predicting the permeability of

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fracture after biogrouting for fracture with various aperture given the amount of CaCO3 . Further study is still required in the future to investigate the threshold that the

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average permeability reduction in the granite fracture.

It should be pointed that this study is confined only to rock fractures with flat

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surface and uniform roughness. Whether the results can be extended to the

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applications for natural rock fracture needs further study. Nevertheless, this study provides at least a reference for natural rack fracture. Knowing the mass of the MICP precipitates formed in the fracture, the permeability reduction can be estimated

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approximately.

6. Conclusions

Both experimental and numerical studies were carried out to obtain the distribution of MICP precipitates and estimate permeability reduction of biogrouted fracture with various initial apertures. The methodology for this study includes: (a) model tests of fracturing sealing via biogrouting conducted on a single rock fracture

ACCEPTED MANUSCRIPT model under a constant flow condition, (b) the spatial distribution of MICP from the high precision 3D digital scanning, and (c) permeability estimation by flow simulation based on spatial distribution of MICP precipitates within the fracture. Based on the model test results, two distinct flow types, the rough surface flow and the channel flow, were identified for rock fractures. For the rough surface flow,

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the fracture surface covered with a MICP precipitate layer exhibits various roughness

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due to the settlement of calcium carbonate on the lower part of the fracture model. For

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the channel flow, the fracture is clogged partially with MICP precipitates and exhibits channel profile. The results also show that there exists a critical aperture and when the

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apertures are lower than the critical aperture, a rough surface flow will change to a

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channel flow during the biogrouting process.

From the flow simulation, it was found that there is a large difference in the

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permeability reduction of these two types: surface flow and channel flow. For a rough surface flow, the parallel plate mode is still valid for permeability prediction of

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biogrouted fracture, as the permeability variation caused by roughness of the surface was negligible base on the numerical results. On other hand, for a channel flow, the

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permeability shows significant deviation from the theoretical value calculated by ‘cubic law’. An empirical equation for permeability estimation was proposed to predict the permeability variation during biogrouting of fracture for both coarse and fine apertures.

ACCEPTED MANUSCRIPT Acknowledgement The financial supports from the Ministry of National Development, Singapore (No. SUL2013-1) and the Ministry of Education (MOE2015-T2-2-142) are greatly acknowledged.

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applications: progress, opportunities and challenges. Geotechnique, 63(4), 287. Figueiredo, B., Tsang, C. F., Rutqvist, J., & Niemi, A. (2017). The effects of nearby fractures on hydraulically induced fracture propagation and permeability changes.

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Engineering Geology, 228, 197-213. Huang, N., Jiang, Y., Liu, R., & Li, B. (2017). Estimation of permeability of 3-D discrete fracture networks: An alternative possibility based on trace map analysis. Engineering Geology, 226, 12-19. Jasinski, L., & Dabrowski, M. (2018). The Effective Transmissivity of a plane‐ walled fracture with circular cylindrical obstacles. Journal of Geophysical Research: Solid Earth, 123(1), 242-263. Martinez, B. C., DeJong, J. T., & Ginn, T. R. (2014). Bio-geochemical reactive transport modeling of microbial induced calcite precipitation to predict the treatment of sand in one-dimensional flow. Computers and Geotechnics, 58, 1-13.

ACCEPTED MANUSCRIPT Min, K. B., Rutqvist, J., & Elsworth, D. (2009). Chemically and mechanically mediated influences on the transport and mechanical characteristics of rock fractures. International Journal of Rock Mechanics and Mining Sciences, 46(1), 80-89. Minto, J. M., MacLachlan, E., El Mountassir, G., & Lunn, R. J. (2016). Rock fracture grouting with microbially induced carbonate precipitation. Water Resources

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Research, 52(11), 8827-8844.

Mitchell, A. C., Dideriksen, K., Spangler, L. H., Cunningham, A. B., & Gerlach, R.

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(2010). Microbially enhanced carbon capture and storage by mineral-trapping and

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solubility-trapping. Environmental Science & Technology, 44(13), 5270-5276. EI Mountassir, G. E., Lunn, R. J., Moir, H., & MacLachlan, E. (2014). Hydrodynamic

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coupling in microbially mediated fracture mineralization: Formation of self‐ organized groundwater flow channels. Water Resources Research, 50(1), 1-16.

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Park, D., & Oh, J. (2018). Permeation grouting for remediation of dam cores. Engineering Geology, 233, 63-75.

microbially- induced

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Phillips, A. J., Cunningham, A. B., et al. (2016). Fracture sealing with calcium

carbonate

precipitation:

A

field

study.

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Environmental science & technology, 50(7), 4111-4117. Phillips, A. J., Lauchnor, E., et al. (2012). Potential CO2 leakage reduction through biofilm- induced calcium carbonate precipitation. Environmental science &

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technology, 47(1), 142-149. Phillips, A. J., Eldring, J. J., et al. (2015). Design of a meso-scale high pressure vessel for the laboratory examination of biogeochemical subsurface processes. Journal of Petroleum Science and Engineering, 126, 55-62. Proto, C. J., DeJong, J. T., & Nelson, D. C. (2016). Biomediated permeability reduction of saturated sands. Journal of Geotechnical and Geoenvironmental Engineering, 142(12), 04016073. Rong, G., Hou, D., Yang, J., Cheng, L., & Zhou, C. (2017). Experimental study of flow characteristics in non-mated rock fractures considering 3D definition of fracture surfaces. Engineering Geology, 220, 152-163.

ACCEPTED MANUSCRIPT Salifu, E., MacLachlan, E., Iyer, K. R., Knapp, C. W., & Tarantino, A. (2016). Application of microbially induced calcite precipitation in erosion mitigation and stabilisation of sandy soil foreshore slopes: A preliminary investigation. Engineering Geology, 201, 96-105. Shen, S. L., Wang, Z. F., Horpibulsuk, S., & Kim, Y. H. (2013). Jet grouting with a

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newly developed technology: the twin-jet method. Engineering Geology, 152(1), 87-95.

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Singh, K. K., Singh, D. N., & Ranjith, P. G. (2015). Laboratory simulation of flow through single fractured granite. Rock Mechanics and Rock Engineering, 48(3),

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987-1000.

van Paassen, L. A., Ghose, R., van der Linden, T. J., van der Star, W. R., & van

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Loosdrecht, M. C. (2010). Quantifying biomediated ground improvement by ureolysis: large-scale biogrout experiment. Journal of Geotechnical and

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Geoenvironmental Engineering, 136(12), 1721-1728. Rijn, L. C. V. (1984). Sediment transport, part II: suspended load transport. Journal of

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Hydraulic Engineering, 110(11), 1613-1641. Whiffin, V. S., van Paassen, L. A., & Harkes, M. P. (2007). Microbial carbonate

417-423.

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precipitation as a soil improvement technique. Geomicrobiology Journal, 24(5),

Wu, C., Chu, J., Wu, S., Guo, W., (2018). Quantifying the Permeability Reduction of

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Biogrouted Rock Fracture. Rock Mechanics and Rock Engineering, 1-8. Wu, Z., Fan, L., Liu, Q., & Ma, G. (2017). Micro-mechanical modeling of the macro- mechanical response and fracture behavior of rock using the numerical manifold method. Engineering Geology, 225, 49-60.

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List of Tables Table 1 Experimental programme Table 2 Details of numerical experimental programme for permeability test List of Figures

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Figure 1 Evolution of flow types of rock fracture during biogrouting.

Figure 2 Experimental test setup: (a) Schematic of rock fracture flow arrangement, (b)

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photogrammetry method by digital camera.

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Plan view of upper and lower granite rock sheets, and (c) MICP distribution using 3D

Figure 3 Photos and 3D morphology of MICP precipitates in: (a) Fracture 1#

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(1.5mm); (b) sample 2# (1.1mm) and (c) sample 3# (0.7mm). Figure 4 Distributions of calcite precipitation in rock fracture 1#~3# based on

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precipitation scanning.

Figure 5 The effect of aperture and velocity on the efficiency of precipitation: (a)

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fracture aperture and (b) flow velocity.

Figure 6 3-D flow model for permeability estimation: (a) Surface flow model and (b)

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Channel flow model

Figure 7 Spitial distribution of relative permeability versus displacement for different flow types: (I) Surface flow, (II) Transit type and (III) Channel flow.

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Figure 8 The relationship of relative permeability with the filing ratio of MICP precipitation, in case of (a) surface flow (b) channel flow, considering the κx and κy. Figure 9 The relationship of relative permeabtility with mean remain aperture d during MICP process.

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Parallel plate fracture

(a)

Peristaltic pump

(b)

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Premixed biogrouts solution

Outlet

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Inlet

(c)

39 cm

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MICP precipitates

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5 cm

MICP precipitates surface scanning system

Fracture aperture: Sample 1#: 1.5mm Sample 2#: 1.1mm Sample 3#: 0.7mm

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Figure 1 Experimental test setup: (a) Schematic of rock fracture flow arrangement, (b) Plan view of upper and lower granite rock sheets, and (c) MICP distribution using 3D

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photogrammetry method by digital camera.

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(a) Fracture 1#: surface flow Upper part

Thick calcite layer

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Lower part

No calcite

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(b) Fracture 2#: transition

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Upper part

Thick calcite layer

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Lower part

Sparsely distributed calcite

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(c) Fracture 3#: channel flow Upper part

Symmetrical distribution of calcite Lower part

Figure 2 Photos and 3D morphology of MICP precipitates in: (a) Fracture 1# (1.5mm); (b) sample 2# (1.1mm) and (c) sample 3# (0.7mm).

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1.2

Lower part of Fracture 1#

Upper part of Fracture 1#

Lower part of Fracture 2#

Upper part of Fracture 2#

Lower part of Fracture 3#

Upper part of Fracture 3#

1

0.8

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0.6

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0.4 0.2

0 0

50

100

150

200

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Average thickness of calcite h (mm)

1.4

250

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350

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450

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Distance L (mm)

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Figure 3 Distributions of calcite precipitation in rock fracture 1#~3# based on

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precipitation scanning.

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1

0.8

Rf and Re

Rf : Vcalcite/Vvoid

Filling ratio decreasing

Re : Vcalcite/VTcalite

0.6 Precipitation efficiency

0.4

0.2

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Corase aperture

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Fine aperture

0 0.7

0.9

1.1

1.3

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0.5

1.5

1.7

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Initial fracutre aperture di (mm)

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(a) Fracture aperture

Static condition

Flow condition From present test reuslts

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0.4

Test results

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0.8

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Efficiency of precipitation

1.0

Flow condition From Mountassir et al. (2014)

0.0

0

20

40

60

80

100

120

140

160

-3

Velocity 10 m/s

(b) Flow velocity Figure 4 The effect of aperture and velocity on the efficiency of precipitation: (a) fracture aperture and (b) flow velocity.

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MICP layer

(a)

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∇𝑝 u m/s

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Remain flow aperture

MICP layer

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(b)

∇𝑝

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u m/s

Remain flow channels

Figure 5 3-D flow model for permeability estimation: (a) Surface flow model and (b)

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Channel flow model

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1

Zone C

Zone B

x (Type I)

0.1

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y (Type I) x (Type II)

y (Type II)

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w  / 0  a   4L  Lc 2  w2

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x (Type III) y (Type III)

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Relative permeability 

Zone A

Model Type I Type II Type III

0

50

100

150

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0.01

200

a 0.35 0.5 0.63

250

Lc 57.8 57 62.5

w 67.9 113.6 131

R-Square A -11.8 0.95 -70.1 0.97 -125 0.96

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Transport distance L (mm)

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Figure 6 Spitial distribution of relative permeability versus displacement for different

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flow types: (I) Surface flow, (II) Transit type and (III) Channel flow.

In line with the cubic law

1

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0.1 κx/κ0 κy/κ0 Cubic Law

0.01 0.2

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0.6

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0

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Relative permeability κ/κ0

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0.8

1

Calcite fraction f

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(a) Surface flow

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κx/κ0 κy/κ0 Cubic Law

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0.1

0.01

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Relative permeability κ/κ0

1

Deviation

κ/κ0= (1-1.2f)4 R² = 0.97

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0.001

0

0.2

0.4

0.6

0.8

1

Calcite fraction f (b) Channel flow

Figure 7 The relationship of relative permeability with the filing ratio of MICP precipitation, in case of (a) surface flow (b) channel flow, considering the κ x and κy .

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Parallal plate model Surface flow 0.1

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Transition

Channel flow 0.01

Surface flow with Rmin

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Relative permeability κ/κ0

1

Surface flow with Rmax

Deviation 0.001 0.2

0.4

0.6

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0

Channel flow

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κ/κ0 = 1.83d5.6 R² = 0.94

Cubic Law

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1.2

1.4

1.6

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Mean remain aperture 𝑑 (mm) Figure 8 The relationship of relative permeabtility with mean remain aperture d

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during MICP process.

ACCEPTED MANUSCRIPT Table 1 Experimental programme

Fracture sample

Hydraulic aperture (mm)

Flow rate (ml/min)

Initial Reynolds Number

Initial mean

Final mean

velocity (m/s)

velocity (m/s) 9.2×10-3

1.5

20

7.5

4.4×10-3

Fracture #2

1.1

20

7.5

6.1×10-3

13.6×10-3

Fracture #3

0.7

20

7.5

9.5×10-3

31.8×10-3

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Fracture #1

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The fluid flow is laminar flow when Reynolds number <10.

ACCEPTED MANUSCRIPT Table 2 Details of numerical experimental programme for permeability test Test Series

Specimen

Specimen

numbers

size (mm)

Fracture #1

36

10×10

Fracture #2

18

20×20

Fracture #3

18

20×20

14

10×10

18

10×10

Specimen type

based on the real scanning data

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Numerical models

Numerical models

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Fracture #1 with maximum roughness

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based on asperity Fracture #1 with minimum

assumption

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roughness

ACCEPTED MANUSCRIPT Highlights 

Spatial distribution of microbially induced calcite precipitation (MICP) within a single rock fracture has been investigated visually and quantitatively in meso-scale



A novel approach was developed to study the spatial distribution of MICP within rock fracture by employing 3D scanning The flow simulation of biogrouted fracture based on the 3D distribution of MICP precipitates

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was conducted to achieve the permeability variation during biogrouting A semi-empirical equation is proposed for estimating the permeability variation due to fracture sealing via bio-grouting.”

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