Introduction

Non-aqueous phase liquids (NAPLs) contamination will change the soil physicochemical characteristics, posing severe threat to human and animals (Ting et al. 1999; Vasudevan and Rajaram 2001). Spillage and leakage accidents during petroleum production and processing, storage and shipping are the main sources of NAPLs contamination (Vasudevan and Rajaram 2001). Due to interaction of capillary and interfacial forces between the subsurface and contaminant, NAPLs can become trapped in the soil pores in the form of non-continuous globules (Duffield et al. 2003), which are difficult to remove. Researchers have done some jobs from different scales to investigate the migration and displacement rule of NAPLs in soils (Cooper et al. 1998; Reddi et al. 1998; Lee et al. 2002; Taylor et al. 2004; Wood et al. 2005; Putzlocher et al. 2006). Researches at Mega- and macro-scale can get general laws of NAPLs migration. Studies at micro-scale would enhance understanding of the micro-mechanisms of NAPLs migration in porous media. Network model experiment is an effective method that can be used to investigate NAPLs migration at micro scale.

Network model research could be dated back to 1950s, when the concept of network model was first put forward by Fatt (1956a, 1956b, 1956c). In petroleum area, network model has been used to research the size distribution of residual oil droplets (Egbogah and Dawe 1980), the immiscible displacement of gas-oil (Campbell and On 1985), trapping of NAPLs in pore and throat (Wardlaw 1982), permeability and dispersivity (Corapcioglu et al. 1997; Corapcioglu and Fedirchuk 1999; Theodoropoulou et al. 2003), the relationship between relative permeability and capillary pressure (Theodoropoulou et al. 2005), and so on. In the recent years, with the increasing concern for NAPLs contamination, network model was used to visualize the removal process of residual NAPLs in soil and aquifer. For example, Jeong et al. (2000) studied the mass transfer processes during NAPL remediation; Jia et al. (1999) investigated the removal mechanisms of trichloroethylene by surfactant foam; Jeong and Corapcioglu (2003) researched the factors influencing the removal of NAPL by surfactant foam flooding; Sharmin et al. (2006) researched the effect of surfactant partitioning on the dissolution kinetics of residual perchloroethylene (PCE) by Triton X-100 solution; Sahloul et al. (2002) investigated the pore-scale removal mechanism and mass transfer rates of residual NAPL. To our knowledge, a little work has been done on the quantitative relationships between the residual/dissolved LNAPLs and percolation time of injected fluid at pore scale.

This paper aims to the following goals: (1) observing the removal processes of residual LNAPLs at pore scale, (2) establishing quantitative relationships between the residual/dissolved LNAPLs and percolation time of injected fluid, which would be useful to the design of remediation projects.

Materials and methods

Chemical materials

The chemical reagents used in this research are analytical grade n-hexadecane (Tianjin Chemical Research Institute, China) and Sudan IV (Tianjin Chemical Research Institute, China). Sudan IV was added to the n-hexadecane to enhance its visibility. De-ionized water was produced by Beijing Jiangchuan water treatment technology Co. Ltd. Other materials include: 10 mL beakers used to contain n-hexadecane, 100 mL Erlenmeyer flasks used to collect waste liquids.

Experimental set-up

Figure 1 shows the experimental setup used in this research. It is composed of SMZ-168 stereomicroscope (Motic China Group Co. Ltd, China); Motic Images Advanced 3.2 image acquisition and processing system (Motic China Group Co. Ltd, China); TJ-3A syringe pump (Lange Constant Flow Pump Co. Ltd, Baoding, China); glass micromodel (Xinyi Instrument Co. Ltd, Yixing, China); silica gel pipes; glass injector (Shanghai Zhenge Medical Injector Co. Ltd, China); computer. The micromodel was put in the view field of the stereomicroscope. Motic Images Advanced 3.2 image acquisition and processing system was installed on the computer. Video camera was installed on the stereomicroscope.

Fig. 1
figure 1

Experiment set-up: 1 syringe pump, 2 network models, 3 outflow collection, 4 ring lamp, 5 stereomicroscope, 6 moticam device, 7 PC, 8 monitor

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Digital pattern of the micromodel pore network, and inlet and outlet channels, were designed using AutoCAD software. A glass plate was selected to be refinished and polished before the pattern was etched on it. The etched glass plate was washed in an ultrasonic cleaner. Another glass plate was put onto the etched one and they were hot bonded together. Dyed de-ionized water was injected to check up the connectivity of the glass model. There were six pores in the micromodel, with coordination number of four. The mean pore and throat radius are 0.244 and 0.091 mm, respectively, which are the statistical pore and throat radius values of media composed of coarse sand with particle size of 0.5–1 mm. The depths of pores and throats are 0.182 mm.

Methods

Connection and debugging

The apparatus were connected according to Fig. 1. Every part should be adjusted to make the apparatus work in harmony. Adjustment includes the following aspects: (1) Stereomicroscope: appropriate microscope stage and size of object lens were chosen according to the object size and observing scope. Halogen bulb or ring lamp should be selected according to demand for light. Ring lamp was used in this research for its excellent performance such as low heat emission, soft and natural light, no color distortion, and efficiency in easing the eyestrain. (2) Computer: data acquisition and analysis system was connected with stereomicroscope through data lines. The data acquisition and analysis software was set up. (3) Syringe pump: proper injector was fixed onto the syringe pump. (4) Micromodel: two silica gel pipes were connected to the micromodel. One at the inlet was used to connect the micromodel and the syringe pump, the other at the outlet was used to discharge the waste liquids into the waste collector.

Parameter optimizing

In order to acquire clear images, parameters of experimental apparatus were optimized. Main operations were as follows: (1) the object distance of stereomicroscope was adjusted and kept unchanged in the whole experimental process; (2) adjusting exposal parameters, setting up image size, collection and store mode through the software; (3) choosing the right injector model and manipulate mode of syringe pump. Manipulate modes include infuse, withdraw, infuse first then withdraw, withdraw first then infuse. Infuse mode was used in the experiment; setting parameters of injected fluid volume, infuse/withdraw time, distribution and interval times; (4) adjusting the position of the network model in the vision field.

Calibration

The stereomicroscope was calibrated with calibration slides (1,500,600 μm). The true size of each pixel stands for should be established according to the image of calibration slides. The injector size (internal diameter/flow rate) was calibrated through the calibration mode. The flow rate was calibrated through comparing the measured and the set fluid flow rate.

Images acquisition and processing

At different experimental stages, images were collected and processed by Motic Images Advanced 3.2 (Fig. 2). The images were processed through the following steps: (1) choosing the image region needed to process; (2) color segmentation and noise removal; (3) choosing target object, calculating its area, percentage, perimeter, roundness, radius of its equivalent area circle, and some other parameters.

Fig. 2
figure 2

Image data processing (a) electing range and color dividing, (b) removing offending points, (c) choosing calculation objects, (d) calculating objects

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Results and discussion

Volume change of residual n-hexadecane

The micromodel was initially saturated with n-hexadecane at a constant volumetric flow rate of 0.167 mL/h, followed by injection of de-ionized water at the same flow rate to establish conditions of trapped n-hexadecane ganglia. The research started at the time when n-hexadecane ganglia were formed (Fig. 3a). Water was continuously injected and the dissolution process of individual ganglia was monitored. Figure 3 is snapshots of the dissolution evolution of single n-hexadecane ganglion. Figure 4 is the projected area change of residual n-hexadecane ganglion during de-ionized water injection. Define pore numbers as 1–6 from left to right on the micromodel. According to Figs. 3 and 4, it is evident that the area of n-hexadecane decreased remarkably at the interval of 0–3,420 s. At the time of 0 s, there was residual n-hexadecane in all the six pores. The drops in pore one and six were smaller than the others. This is because pore one and pore six were directly connected to the inlet and outlet of the micromodel, the fluid pressures in pore one and pore six were bigger than that in other pores. In the process of displacing NAPL with water to form residual NAPL droplet, all the influx flowed through pore one and pore six, so the drops of the pore one and six would be smaller than the others. For the same reason, the displacement and dissolution of NAPL drops in pore one and pore six would be faster than the others. At the time of 840 s, there was no residual n-hexadecane in the fifth and the sixth pore. At the time of 3,420 s, there was no residual n-hexadecane in the first, the fourth and the sixth pore, while there was n-hexadecane again in the fifth pore. The experiment was repeated several times, although there were some differences in the drop size for a given pore in all the experiments, this phenomenon appeared every time. This can be explained as follows: at the initial time, the hexadecane was displaced by water, then, the n-hexadecane in other pores and throats was displaced into this pore again. After 3,420 s, the area of residual n-hexadecane remained nearly invariable. There are two possible conditions. One is that the changes of the residual n-hexadecane were too small to discern, the other is that there was no influx to the pore, the n-hexadecane would also remain constant. The droplet size after a definite time depends on its initial value. The relationship between total residual n-hexadecane volume and time can be described by a logarithmic equation: V = V 0 − 0.0152lnt + 0.0360 (0 < t <9,420, R 2 = 0.9621), where V 0 is the initial volume of residual n-hexadecane. The n-hexadecane volume equals to the product of the projected area and the pore depth.

Fig. 3
figure 3

Snapshots of the dissolution evolution of single n-hexadecane droplet

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Fig. 4
figure 4

Area changing of n-hexadecane during de-ionized water injected

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Residual NAPL droplet dissolution characteristics

To analyze the relationship between the removal of single NAPL droplet and the total NAPLs in the same flow channel, the residual droplet in the third pore was chosen to do analysis. The evolution of the total NAPLs projected areas in the micromodel was compared with that of a single NAPL droplet (Fig. 4). It can be seen that the dissolution rule of single droplet is the same as that of the total NAPLs, indicating that the dissolution of total residual NAPLs can be reflected by single residual droplet in the same flow channel. Analyzing the change of single residual n-hexadecane, it can be found that the n-hexadecane droplet diminished rapidly at first, then removal became slower, finally, the residual n-hexadecane remained nearly invariable. The changing process was closely related to the flow rate of injected fluid in the pores.

Figure 5 is a conceptual model of pore-scale mass transfer from a single trapped NAPL ganglion given by Sahloul et al. (2002). Water flows around the trapped NAPL droplet, mass transfer by convection and diffusion occurs in the space between the pore wall and the NAPL/water interface. As time goes on, organic solute is transported by convection and diffusion away from the NAPL/water interface, the trapped NAPL ganglion becomes smaller and smaller, and the distance between the pore wall and the NAPL/water interface increases, which can be described as follows:

$$ S = R - r $$
(1)
Fig. 5
figure 5

Mass transfer model of NAPL in pores (after Sahloul et al. 2002)

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where S is the distance between the pore wall and the NAPL/water interface, R is the pore radius, r is the radius of NAPL droplet which changes with time

$$ r = \sqrt {A/\pi } $$
(2)

where, A is the projected area of NAPL droplet. In this study, the value of A in pore three can be fitted with t as follows:

$$ A = A_{0} - 0.0 1 1 {\text{ln}}t + 0.0 2 7 1 (R^{ 2} = 0. 7 9 3 2 ) $$
(3)

where A 0 is the initial projected area of NAPL droplet.

Water velocity, u can be simply calculated by the following equation:

$$ u = {\frac{Q}{2S \cdot D}} $$
(4)

where Q is the flow rate of injected fluid, D is the depth of pore channel. Then the flow velocity as a function of time can be written as:

$$ u = {\frac{Q}{{2(R - \sqrt {(A_{0} - 0.011\ln t + 0.0271)/\pi } ) \cdot D}}} $$
(5)

As time goes on, the NAPL ganglia decreases in size, the water flow velocity decreases. When injection flux is constant, the concentration gradient between water and NAPL decreases. Furthermore, the interface area between water and NAPL decreases too. The mass transfer becomes slower and slower. The projected area of residual NAPL droplet decreases rapidly then tends to remain a steady state. This phenomenon is similar to the result of soil column flushing experiment where dissolution of residual NAPL is a rate-limited process and present a tailing effect (Boving and Brusseau 2000; Bradford et al. 2003). It appeared that the macro phenomenon in column flushing can be explained by the microcosmic mass transfer mechanism in the pore-scale network model.

To obtain the changing rule of n-hexadecane dissolution in a single pore, Gaussian model was used to fit the cumulated dissolved n-hexadecane quantity normalized by micromodel volume as a function of time. The Gaussian model is as follows:

$$ y = y_{0} + {\frac{A}{{w \cdot \sqrt {{\frac{\pi }{2}}} }}}e^{{ - {\frac{{2(x - x_{0} )^{2} }}{{w^{2} }}}}} $$
(6)

where y is the cumulated dissolved n-hexadecane quantity normalized by micromodel volume; x is time (s). Model (6) involves four fitting parameters; the meaning of each parameter is as follows: y 0 is baseline offset, A is total area under the curve from the baseline, x 0 is center of the peak, w is 2σ approximately 0.849 the width of the peak at half height.

Figure 6 is the Gaussian model fitting result, the correlation coefficient R 2 = 0.97269, which means that Gaussian model could describe the changing characteristics of cumulated dissolved n-hexadecane quantity normalized by micromodel volume.

Fig. 6
figure 6

Gaussian model fitting of the cumulated dissolved n-hexadecane quantity per unit volume as a function of time

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Conclusions

Based on pore network model, residual LNAPLs droplet removal experiment was done in this paper, and some conclusions can be drawn:

  1. (1)

    Displaced by water, residual n-hexadecane droplet was removed quickly at first, then gradually became slow and finally remained nearly invariable, the droplet size after a definite time depends on its initial value. The changing rule of single residual n-hexadecane droplet is as the same to the total n-hexadecane volume in the same flow channel. The relationship between total residual n-hexadecane volume and time can be described by a logarithmic equation: V = V 0−0.0152lnt + 0.0360 (0 < t <9,420, R 2 = 0.9621).

  2. (2)

    According to percolation theory, the flow rate of injected fluid in pores as a function of time can be obtained through analysis of residual n-hexadecane droplet projected area and the flow characteristics of injected fluid.

  3. (3)

    The dissolution of residual NAPL in column flushing can be explained by the microcosmic mass transfer mechanism in the pore-scale network model.

  4. (4)

    Gaussian model can be used to fit the changing of cumulated dissolved n-hexadecane quantity per unit volume as a function of time (R 2 = 0.97269).