Groundwater can be stored abundantly in granula-composed aquifers with high permeability. The microstructure of granular materials has important effect on the permeability of aquifers and the contaminant migration and remediation in aquifers is also influenced by the characteristics of porous media. In this study, two different microscale arrangements of sand particles are compared to reveal the effects of microstructure on the contaminant migration and remediation. With the help of fractal theory, the mathematical expressions of permeability and entry pressure are conducted to delineate granular materials with regular triangle arrangement (RTA) and square pitch arrangement (SPA) at microscale. Using a sequential Gaussian simulation (SGS) method, a synthetic heterogeneous site contaminated by perchloroethylene (PCE) is then used to investigate the migration and remediation affected by the two different microscale arrangements. PCE is released from an underground storage tank into the aquifer and the surfactant is used to clean up the subsurface contamination. Results suggest that RTA can not only cause more groundwater contamination, but also make remediation become more difficult. The PCE remediation efficiency of 60.01–99.78 % with a mean of 92.52 and 65.53–99.74 % with a mean of 95.83 % is achieved for 200 individual heterogeneous realizations based on the RTA and SPA, respectively, indicating that the cleanup of PCE in aquifer with SPA is significantly easier. This study leads to a new understanding of the microstructures of porous media and demonstrates how microscale arrangements control contaminant migration in aquifers, which is helpful to design successful remediation scheme for underground storage tank spill.

Groundwater is an essential natural resource for water supply to domestic, agricultural, and industrial activities as well as ecosystem health (Boswinkel, 2000; Valipour, 2012, 2015; Yannopoulos et al., 2015; Valipour and Singh, 2016). Unfortunately, with the rapid development of economic activities such as mining, agriculture, landfills and industrial activities (Bakshevskaia and Pozdniakov, 2016; Cui et al., 2016; H. Liu et al., 2016; An et al., 2016; Shen et al., 2017), more and more contaminants released from human activities are contaminating the precious groundwater resource and subsurface environment (Dawson and Roberts, 1997; Liu, 2005; Hadley and Newell, 2014; Carroll et al., 2015; Essaid et al., 2015; Huang et al., 2015; Y. Liu et al., 2016; Schaefer et al., 2016; Weathers et al., 2016). Among the contaminants detected in groundwater, dense nonaqueous phase liquids (DNAPLs) such as perchloroethylene (PCE) and other polycyclic aromatic hydrocarbons (PAHs), are highly toxic and carcinogenic (Dawson and Roberts, 1997; Hadley and Newell, 2014). When DNAPLs are released into aquifer from underground storage tanks, they will infiltrate through the entire aquifer and form residual ganglia and pools of DNAPLs due to their large densities, high interfacial tension, and low solubility. The residual ganglia and pools of DNAPLs can serve as long-term sources of groundwater contamination which are harmful to the subsurface environment and human beings (Bob et al., 2008; Liang and Lai, 2008; Liang and Hsieh, 2015). Consequently, it is very important to explore DNAPL migration in aquifers and associated remediation of groundwater contamination.

When DNAPLs migrate in aquifers on a macroscopic scale, the transport
properties such as permeability, diffusivity and dispersivity are closely
related to the aquifer's microstructures and can affect DNAPL behavior (Yu
and Li, 2004; Yu, 2005; Yun et al., 2005; Feng and Yu, 2007; Yu et al.,
2009). Therefore, characterizing the effect of microstructures on macroscopic
properties is a key point of research on heterogeneity of porous media
(Mishra et al., 2016). In the classical Kozeny–Carman equation, the
permeability

In this study, we focus on the effect of microarrangement of sand particles on macroscopic DNAPL migration and associated remediation for underground storage tank spills. With the help of fractal theory, the microstructures of two different microscale arrangements of sand particles are explored. Afterwards, the mathematical relationships between porosity, permeability, and entry pressure are derived for regular triangle arrangement (RTA) and square pitch microscale arrangement (SPA). An idealized heterogeneous contaminated site is generated using a sequential Gaussian simulation (SGS) method. An underground storage tank releases PCE into heterogeneous aquifer composed of granular material. After a long-term migration, PCE contamination is alleviated using a surfactant remediation method. A multicomponent, multiphase model simulator, UTCHEM, is then used to simulate the entire process of DNAPL migration and remediation. Effects of arrangements of sand particles on migration and remediation of DNAPLs are comparatively analyzed based on the simulations to reveal how the microstructure of porous media controls the contaminant migration and remediation on a macroscopic scale.

The porous media can be treated as the bundle of tortuous capillary tubes,
and the relationship between the diameter and the length of the capillary
tube is as follows (Yu and Cheng, 2002):

If an infinitesimal element consisting of a bundle of tortuous capillary
tubes from porous media is selected, the total number of capillary tubes in
infinitesimal element can be calculated by the power–law relation:

Afterward, the derivative of Eq. (

Dividing Eq. (

The probability density function satisfies the following relationship:

The differentiation of flow rate of capillary tubes is as follows (Yu and Cheng, 2002):

Two different microscale arrangements of solid particles:

RTA and SPA are shown in Fig. 1. An equilateral triangle and a square are selected from the two microstructures as unit
cells (Fig. 1a and b). The unit cell of the equilateral triangle is composed of three solid particles with the pore among
them, while the unit cell of square is composed of four solid particles. For the unit cell of RTA in Fig. 1a,
corresponding porosity is given by the following:

Three kinds of Sierpinski gasket [30]:

The area of irregular pore among solid particles is given by the following:

Approximate the pore in the equilateral triangle as a circle, then the
maximum diameter of pore can be obtained:

Generally, the tortuosity of flow path in porous media is the ratio of the
length of tortuous flow path to the straight length of flow path along the
flow direction (Taiwo et al., 2016):

For the flow path shown in Fig. 1a,

Consequently, the tortuosity of RTA is yielded:

From Eq. (

The dimensionless total area of RTA (

Afterward,

Substituting Eqs. (

For the unit cell of square shown in Fig. 1b, the porosity is as follows:

Again, the side length of the square is as follows:

Using the following equation, the pore as a circle and obtain corresponding
maximum diameter can be approximated:

For the tortuous flow path in Fig. 1b,

Afterward, the tortuosity of SPA yields the following:

The procedure of deriving

The dimensionless pore area of SPA (

Substituting Eqs. (

The entry pressure of a tortuous capillary tube (

In this study, SGS is used to generate random realization of a heterogeneous porosity field. SGS is a stochastic simulation method combining sequential principles and a Gaussian method. It assumes variable fit to a Gaussian random field. The Gaussian distribution function is constructed at each simulated spatial location based on the characteristics of variation function and afterward randomly selects a value as the variable at the location. In the SGS method, observation data are transformed to Gaussian distributions or normal distributions. Based on current sample data, the conditional probability distribution of points to be simulated is calculated by the SGS method and then simulation is performed based on a semivariogram model. Each simulated value, together with measured data and previous simulation data, becomes the conditional data set for the next step. As simulation proceeds, the conditional data set increases. Previous research suggests 50–400 realizations are required to obtain a statistically stable mean realization (Eggleston et al., 1996; Hu et al., 2007).

The DNAPL migration and remediation are modeled using a multicomponent, multiphase, and multicomposition simulator named UTCHEM (University of Texas Chemical Compositional Simulator) (Delshad et al., 1996). As an extension to Delshad's work, UTCHEM was developed by the University of Texas as a comprehensive and practical tool. In numerous applications, UTCHEM has proved to be particularly useful in simulation of contaminant migrations and has been a popular multiphase-flow, multiconstituent, reactive transport model used widely in groundwater simulations. UTCHEM accounts for chemical, physical and biological reactions; complex non-equilibrium sorption; decay and geochemical reactions; and surfactant-enhanced solubilization and mobilization of DNAPLs. Moreover, heterogeneous properties of porous media are also considered. As a result, UTCHEM has been adapted for a variety of environmental applications such as surfactant-enhanced aquifer remediation (SEAR). In this study, DNAPL migration and remediation for cleaning up DNAPL contamination in idealized heterogeneous sites are simulated by UTCHEM.

The idealized domain of synthetic application is a two-dimensional confined
aquifer (Fig. 3). The length, width and depth of aquifer are 101, 25 and
25

The porosity of aquifer is assumed to be spatially and uniformly distributed
with an average value of 0.220 and SD (standard deviation) of 0.060. In this
study, porosity follows normal distribution and its SD represents the
enhanced geological heterogeneity. A total of 200 realizations of the
porosity field are generated using SGS. One of the 200 realizations of
heterogeneous field is shown in Fig. 4a. Simultaneously, statistical
assessment is undertaken on the individual realization of the porosity field,
and corresponding histograms are shown in Fig. 4b. We find that the frequency
of the individual realization of the porosity field is close to normal
distribution, which conforms to the situation that most characteristics of
natural aquifer can be expressed as a normal distribution (Montgomery et al.,
1987). Based on the heterogeneous porosity field, the fractal dimension of
tortuosity

The average pore diameters of two different microscale arrangements of
particles are derived using corresponding fractal models. In detail, the
average diameter of RTA is calculated by Eq. (

The purpose of this study is to explore the effects of microstructure of
aquifer on DNAPL migration and remediation. A PCE spill event (the leaking of
underground storage tank) occurs on the top of the aquifer and a surfactant
remediation is designed to clean up the contaminated aquifer. The total
duration of 300 days is divided into four stages: (1) 300

Parameters used in the simulation.

Simulated PCE saturation for individual realization of RTA over the
entire migration and remediation periods (0

The simulation results of PCE migration for individual realization of the
porosity field for RTA are shown in Fig. 5a–f. When PCE is released into an
aquifer at the top layer of spill position, PCE almost infiltrates vertically
under the effect of gravity (Fig. 5a). Due to the heterogeneity of the
aquifer, some preferential flow appears and the PCE plume becomes irregular
(Fig. 5b). After 30 days, PCE plume almost touches the bottom of aquifer
(Fig. 5c). When the PCE leakage is stopped, PCE migrates continuously in
aquifer for 70 days (Fig. 5d–f). The released PCE is migrating downward and
entrapped by capillary forces as residual ganglia and globules. The
heterogeneity of the aquifer makes PCE migrate along a preferential pathway.
When the PCE plume touches the zones of low permeability and high entry
pressure, it will bypass these zones and migrate continuously, which leads to
an increasing variability in PCE distribution. After the PCE plume reaches
the bottom of aquifer, PCE begin accumulate and form a contaminant pool at
the bottom. At

Simulated PCE saturation for individual realization of SPA over the
entire migration and remediation periods (0

Figure 6a–f show the simulated PCE saturation for individual realization of porous media for SPA during migration period. Under the effects of gravity and the natural hydraulic gradient, PCE is migrating and the contaminant plume becomes larger and larger. The heterogeneity of the aquifer significantly changes the migration paths and leads to irregular morphology of the PCE plume (Fig. 6a–c). However, due to the different microarrangements of the aquifer, the entry-pressure distribution is also different, which leads to some differences. After the PCE injection, the simulated PCE saturation in Fig. 6d–f indicates that further trapping and spreading of the PCE occurs during this period. Compared with the simulation results of RTA in Fig. 5, the PCE plume slightly seems similar in Fig. 6. Moreover, PCE infiltrates more quickly in porous media of RTA in Fig. 5. After 70 days, the PCE plume has touched the bottom for RTA (Fig. 5e), while the PCE plume based on SPA still keeps a significant distance from the bottom (Fig. 6e).

To clean up the DNAPL, 4 % surfactant solution is injected through two
injection wells at a constant rate of 80

The same surfactant remediation is also conducted for individual realization
of SPA. Compared with the remediation for RTA, the remediation effect is more
apparent for SPA (Fig. 6g–l). As the remediation progresses, more DNAPL is
removed and less DNAPL remains at the bottom of aquifer. At

PCE migration and remediation processes are simulated for 200 realizations of
the porosity field for porous media of RTA and SPA. The variations of
contaminant mass, the ganglia-to-pool (GTP) ratio and moments of PCE plume
vs. time are presented in Fig. 7a–h. During 0–30 days, the PCE in aquifer
increases linearly at a constant rate of 10

Figure 7c shows cumulative PCE removal from the contaminated aquifer vs.
flushing time for RTA and SPA. During the surfactant injection period,
100–150 days, the DNAPL removal is not apparent. However, DNAPL is removed
effectively and quickly during the water-flushing period. Through long-term
remediation, the removal of PCE from the contaminated aquifer reached
179.89–298.98

Figure 7d shows the GTP value as a function of cumulative PCE removal for the
contaminated aquifer. The GTP remains at a relatively low level before
30 % of the DNAPL is removed from the aquifer. When 40 % of the total
300

For the center of the PCE plume on the horizontal axis, associated variations
vs. time are similar for 200 realizations based on RTA and SPA (Fig. 7e).
Significantly, the PCE plume vertical-infiltration rate in aquifer of RTA is
slightly faster than PCE infiltration in the aquifer of SPA for
200 realizations (Fig. 7f). Simultaneously, the second PCE plume moments in
the horizontal direction of RTA are different from the second PCE plume
moments in the horizontal direction of SPA (Fig. 7g). After PCE migration
under natural conditions at

This study takes an important step toward exploring how microscale
arrangements control contaminant migration on a small-aquifer scale. Results
are essential to the macroscopic aquifer composed of porous media without
large heterogeneity, such as sandy aquifers containing rich groundwater
resources. However, there are many problems associated with the upscaling of
aquifers in real-world conditions (Dagan et al., 2013;
Pacheco, 2013; Pacheco et al., 2015). Due to the large heterogeneity of
natural aquifers, research results may be very different and can not be
extrapolated to complex regional aquifer on a large scale. However, the
finding in this study is absolutely applicable for natural aquifers with
similar heterogeneities. If the heterogeneity and anisotropy of natural
aquifers are very different, the effect of the microscale arrangements on the
macroscopic contaminant migration and remediation will be different. Although
real-world conditions are complex, the new findings achieved from this
research are very significant for understanding the effect of microscale
arrangement on contaminant behaviors on an aquifer scale.
The upscaling problem of the results obtained on the simulation scale
(100

The microstructure of aquifers has an important effect on
macroscopic-scale characteristics of contaminant migration and remediation.
In this study, we focus on the DNAPL migration and remediation in
heterogeneous aquifers composed of granular porous media with RTA and SPA.
The microscale models of RTA and SPA are developed to obtain the mathematical
expressions of permeability and entry pressure using fractal methods. A total
of 200 realizations of the porosity field are generated using the SGS method,
and PCE is released from an underground storage tank into a heterogeneous
aquifer. To clean up contamination caused by the underground storage tank
spill, a surfactant remediation technique is used to remove contaminants in
the aquifer. The entire process of DNAPL migration and remediation is
simulated by a multicomponent, multiphase model simulator, UTCHEM. Results
suggest RTA not only cause more groundwater contamination than RTA, but also
the contaminated aquifer of RTA is harder to clean up compared with SPA. The
second PCE plume moments in the horizontal direction are
10.61–40.50

Research data are available from Jianfeng Wu (jfwu@nju.edu.cn), Jichun Wu (jcwu@nju.edu.cn), or Ming Wu (wumingnanjing@gmail.com).

The authors declare that they have no conflict of interest.

This research was financially supported by the National Key Research and Development Plan of China (2016YFC0402800), the National Natural Science Foundation of China (41772254 and 41372235), and the National Natural Science Foundation of China-Xianjiang (project U1503282). The authors are also profoundly grateful to Pacheco Fla and an anonymous reviewer whose precious suggestions and constructive comments helped to improve the paper significantly. Edited by: Sabine Attinger Reviewed by: Fernando Pacheco and one anonymous referee