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Numerical modeling of colloid-assisted BTEX transport in a saturated fractured aquifer

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Abstract

Colloid occurrence is a crucial factor influencing the movement of hydrophobic components like petroleum hydrocarbons in fractured aquifers. In this study, an attempt is made to examine the influence of colloids on the movement of Benzene, Toluene, Ethylbenzene, and Xylene (BTEX) in a saturated fractured rock aquifer. A numerical model is developed to simulate the colloid-BTEX co-transport in a fracture-matrix system (F-M-S). The modeling investigation is performed by adopting the dual-porosity modeling approximation for the fractured aquifer. The study's outcome suggests that the colloid influence is more on the transport of less soluble BTEX components: ethylbenzene and xylene. The colloid presence does not influence the Benzene (component with the highest pure phase solubility) movement in F-M-S. The impact of various colloid parameters such as velocity, inlet concentration, filtration rate at fracture-matrix interface, attachment rate on the fracture surface, on BTEX transport in fracture and matrix, is estimated. Migration of Toluene, Ethylbenzene, and Xylene (TEX) in fracture and matrix is turned out to be sensitive to these parameters. The peak dissolved concentration and the peak location of these components are found to be sensitive to these parameters. The colloid impact on the dissolved concentration levels of TEX is more evident in the later simulation stages.

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Fig. 1
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source zone (Cf0) at fracture inlet (left fracture boundary)

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Abbreviations

b :

Half fracture thickness [L]

\({C}_{\text{cf}}\) :

Suspended colloid concentration in fracture [ML−3]

\({C}_{\text{cm}}\) :

Suspended colloid concentration in the matrix [ML−3]

\({C}_{\text{f}}^{i}\) :

Dissolved BTEX concentration in fracture [ML−3]

\({C}_{\text{m}}^{i}\) :

Dissolved BTEX concentration in matrix [ML−3]

\({D}_{\text{cm},y}\) :

Diffusion coefficient of colloids in matrix [L2T−1]

\({D}_{\text{f}}^{i}\) :

Dispersion coefficient of BTEX in fracture [L2T−1]

\({D}_{\text{m}}^{i}\) :

Diffusion coefficient of BTEX in matrix [L2T−1]

\({\varepsilon }_{\text{f}}\) :

Colloid attachment on Fracture surface [L−1]

\({f}_{\text{C}}\) :

Colloid filtration rate at the interface [−]

\(H\) :

Distance from fracture center line to half matrix width [L]

\(i\) :

Index of BTEX component [−]

\({k}_{\text{f}}^{i}\) :

Kinetic attachment BTEX on fracture wall [T−1]

\({k}_{\text{f,mc}}^{i}\) :

Kinetic attachment of BTEX on mobile colloids in fracture [T−1]

\({k}_{\text{f,ic}}^{i}\) :

Kinetic attachment of BTEX on immobile colloids in fracture [T−1]

\({K}_{\text{f}}^{i}\) :

Distribution coefficient of BTEX on fracture wall [L3M−1]

\({K}_{\text{f,mc}}^{i}\) :

Distribution coefficients of BTEX on mobile colloids in fracture [L3M−1]

\({K}_{\text{f,ic}}^{i}\) :

Distribution coefficients of BTEX on immobile colloids in fracture [L3M−1]

\({k}_{\text{m}}^{i}\) :

Kinetic attachment of BTEX on matrix grains [T−1]

\({k}_{\text{m,mc}}^{i}\) :

Kinetic attachment of BTEX on mobile colloids in matrix [T−1]

\({k}_{\text{m,ic}}^{i}\) :

Kinetic attachment of BTEX on immobile colloids in matrix [T−1]

\({K}_{\text{m}}^{i}\) :

Distribution coefficient of BTEX on matrix grains [L3M−1]

\({K}_{\text{m,mc}}^{i}\) :

Distribution coefficients of BTEX on mobile colloids in matrix [L3M−1]

\({K}_{\text{m,ic}}^{i}\) :

Distribution coefficients of BTEX on immobile colloids in matrix [L3M−1]

\({kd}_{\text{cm}}\) :

Kinetic attachment rate of colloids on matrix grains [T−1]

\({Kd}_{\text{cm}}\) :

Distribution coefficient of mobile colloids in matrix [L3M−1]

\(L\) :

Fracture length [L]

\({MF}^{i}(t)\) :

Mole fraction of the BTEX component at time

\({\rho }_{\text{m}}\) :

Matrix density [ML−3]

\({R}_{\text{r,f}}\) :

Remobilization rate of colloid in fracture [T−1]

\({R}_{\text{r,m}}\) :

Remobilization rate of colloid in the matrix [T−1]

\({S}^{i}\) :

Pure phase solubility of BTEX [ML−3]

\({S}_{\text{cf}}\) :

Colloid concentration attached on fracture surface [ML−3]

\({S}_{\text{cm}}\) :

Sorbed colloid concentration on matrix grains [ML−3]

\({S}_{\text{f}}^{i}\) :

BTEX concentration attached on fracture walls [ML−3]

\({S}_{\text{f,ic}}^{i}\) :

BTEX concentration attached on immobile colloids in fracture [ML−3]

\({S}_{\text{f,mc}}^{i}\) :

BTEX concentration attached on mobile colloids in fracture [ML−3]

\({S}_{\text{m}}^{i}\) :

BTEX concentration attached on matrix grains [ML−3]

\({S}_{\text{m,ic}}^{i}\) :

BTEX concentration attached on immobile colloids in matrix [ML−3]

\({S}_{\text{m,mc}}^{i}\) :

BTEX concentration attached on mobile colloids in matrix [ML−3]

t :

Temporal variable [T]

θ m :

Matrix porosity [−]

v:

Groundwater flow velocity [LT−1]

\({V}_{\text{cf}}\) :

Fracture colloid velocity [LT−1]

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Authors and Affiliations

  1. Department of Civil Engineering, IIT (ISM), Dhanbad, Jharkhand, 826004, India

    Renu Valsala

  2. Reservoir Simulation Laboratory, Petroleum Engineering Program, Department of Ocean Engineering, IIT-Madras, Chennai, 600036, India

    Suresh Kumar Govindarajan

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  1. Renu Valsala
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Valsala, R., Govindarajan, S.K. Numerical modeling of colloid-assisted BTEX transport in a saturated fractured aquifer. Environ Earth Sci 81, 37 (2022). https://doi.org/10.1007/s12665-021-10161-3

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