Mobilization of NAPL Ganglia due to Dissolution: Effect on Modeling
Department of Chemical Engineering, Iowa State University, 1037 Sweeney Hall, Ames, IA 50011-2230, Phone: (515)294-1516, FAX: (515)294-2689, email: email@example.com
The contamination of groundwater from Nonaqueous Phase Liquids (NAPLs) poses a serious threat to those who consume it. After a spill or leakage, NAPLs become trapped as small, discrete ganglia which dissolve over time, contaminating water flowing through the region. Models of NAPL dissolution have failed to provide a predictive representation of real spills. One very common simplification made in one-dimensional dissolution models is that ganglia are stationary throughout the dissolution process. This assumption is typically justified by arguing that the pressure gradients across the length of any ganglion are not great enough for its displacement. A recent experiment using Magnetic Resonance Imaging (MRI) to image ganglion structure during a dissolution experiment showed that substantial displacement occurred at pressures well below those normally thought to induce motion. Typically, this displacement was seen early in the dissolution process, and it has been hypothesized that displacement can be attributed to mechanical instabilities which arise as a ganglion loses volume. This work discusses the evidence for dissolution-induced displacement and its implications for modeling efforts.
Keywords: NAPL, ganglia, mobilization, modeling
NAPL-contaminated groundwater in the saturated zone is a three-phase system consisting of a porous medium and two nearly immiscible liquids. Many workers have attempted to construct one-dimensional continuum models of this system but little success has been attained in developing a model which can predict (rather than describe) remediation, even in a simple sand-column experiment. The purpose of this work is to study NAPL ganglia at the pore-scale in order to evaluate the appropriateness of various assumptions that underlie some or all of the continuum models in the literature.
Significant information about NAPL dissolution can be obtained from measurement of the saturation of either of the liquid phases as a function of time and position. This has recently been accomplished via gamma radiation by Imhoff, et al. (1994), X-ray computed tomography by Holmes, et al. (1993), and magnetic resonance imaging (MRI) by Baldwin and Gladden (1996). While the work by Holmes, et al. (1993) did not result in data which could be used to model a 1-D remediation process, both Imhoff, et al. (1994) and Baldwin and Gladden (1996) produced 1-D saturation profiles of NAPL during dissolution that was capable of testing various models against. The comparison of saturation data to various models by these workers, however, only highlighted the inadequacy of all current models.
Imhoff, et al. (1994) correlated the mass-transfer rate that they observed as a Sherwood number, Sh, with interstitial Reynolds number, Rei, porosity, f, NAPL saturation, Sn, distance down from the inlet of pure water (x), and mean particle diameter . The phenomenological model which best fit the data was given by
The relationship to distance was a new finding, and no theoretical arguments were made for its inclusion or for the appearance of the mean particle diameter which was presumably chosen arbitrarily in order to make the equation dimensionless, since this was not varied over the course of the experiment. One possibility which was not apparently considered was the mobilization of individual ganglia. The assumption that the mobilization of ganglia is insignificant in terms of the modeling of NAPL remediation will now be considered, and an experiment which provides an opportunity to evaluate the assumption using MRI data will be proposed.
Experimental studies of ganglion entrapment and remediation have been limited primarily due to the difficulty in non-destructively monitoring such a process. Three methods have been previously utilized: glass micromodels, "destructometric" polymerization, and pore network models.
Chatzis, et al. (1983) used micromodels to study the effect of aspect ratio, coordination number, and network regularity on saturation. Conrad, et al. (1992) used a pseudo-random micromodel to observe drainage and imbibition of a colored NAPL. The experiment allowed the visualization of this process, but provides little data, aside from the residual saturation, which was around 30% and which does not constitute pore-scale information.
Another approach to pore-scale research are the techniques referred to as "destructometric." Here, an NAPL is entrapped in a column filled with sand or other porous media via drainage and imbibition and is then solidified and removed from the column. This has been performed by Chatzis, et al. (1983), Chatzis, et al. (1988), Conrad, et al. (1992), and Powers, et al. (1992). The most comprehensive quantifications of ganglion casts have been performed by Mayer and Miller (1992). These workers polymerized styrene in three types of glass bead packs, having mean particle diameters of 115, 385, and 777 mm. The recovered ganglia (created via drainage/imbibition at Ca = 3 ¥ 10-6) were sieved and weighed to provide a blob length, l, and a representative sample was weighed and counted to determine the average blob volume, Vb. From these two measures a blob shape factor y was determined by
This result is useful in the consideration of an MRI investigation of ganglia.
Both experimental processes described above provide information about the entrapment of ganglia, but they have not or could not observe displacement processes. Payatakes and co-workers formulated a pore network model to investigate the motion of oil ganglia. Payatakes, et al. (1980) describe the development of the model, which is created to simulate water-wet unconsolidated media. The model consisted of volumeless nodes connected by constricted tube cells whose radii were sinusoidal and went through a single minima half the distance between the nodes it connected. Ng and Payatakes (1980) used the model to simulate mobilization of an individual ganglion. Their results indicate that mobilization and breakup of large ganglia (28 51 pores) are possible at Ca < 10-4 and likely when Ca _ 5 ¥ 10-4. For ganglia smaller than five pores, the capillary number at which mobilization or breakup becomes likely ranges from 2 ¥ 10-3 6 ¥ 10-3. Thus, entrapment is most likely for small blobs. It should also be noted that the measured probabilities refer to the likelihood of a single jump. For a blob to travel a macroscopic distance, the probability of mobilization would have to be very high for it not to become trapped after a series of jumps. This problem is compounded by the fact that as a ganglion breaks into smaller components, it becomes more able to be trapped. The workers found that for these reasons, unless the pressure gradient is enough to almost completely mobilize single pore ganglia (Ca _ 10-2), that blob migration over a large distance is unlikely.
Further studies have been made by Dias and Payatakes (1986a; Dias and Payatakes (1986b) and Constantinides and Payatakes (1996), which have included possibilities of ganglion rupture and coalescence, but all results suggest that immiscible displacement of ganglia is not a significant transport process for flow rates that would be encountered in either the field or NAPL dissolution experiments.
Due to the non-invasive imaging capabilities of MRI, it is possible to obtain 3-D images of oil ganglia at various times during a dissolution experiment; however, it is not possible to obtain images in real sand systems due to resolution issues. For a 2563 image, the theoretical limit of resolution is a voxel of length 113 mm, giving a minimum mean particle diameter greater than 1 mm, roughly an order of magnitude larger than those found in real sands. The model system of interest is composed of glass beads of 2 mm and 6 mm in diameter. In order to assure that this model system can be accurately applied to the smaller system, it is necessary to consider the effect of this change upon the dimensionless ratios which govern immiscible displacement (drainage and imbibition) and mass transfer, namely the capillary number, Ca, the Bond number, Bo, the particle Reynolds number, Rep, and the Péclet number, Pé. This analysis will neglect the obvious differences between real sand and glass beads, such as grain shape and uniformity.
In this model system, Bo is approximately 100 times greater than would be the case in a bed of real sand. This, however, can be accounted for by simply including buoyancy effects into a new capillary number as will now be shown. As shown by Mayer and Miller (1992) , a ganglion of length, l (measured in the direction of flow), will only be stable when
where rt is the radius of a pore throat through which a Haines jump may occur and k is the permeability of the porous medium. This suggests that a hypothetical capillary number which takes into account gravity-based forces (buoyancy), Cag, can be written
where g is the gravitational acceleration vector, rn and rw refer to the densities of the NAPL and aqueous phase, and s is the interfacial surface tension between the two liquids. The vector notation in Eq. (4) indicates that the two terms are additive if the bulk flow rate is in the same direction as gravity and that the difference should be taken when they are opposed. This analysis shows that rather than attempting to maintain similar capillary and Bond numbers for the model system (an impossibility), the hypothetical capillary number defined here should be of a similar value to that in the real system.
While the proportionality of the system during drainage and imbibition is most important in this study (since the primary objective is to observe model NAPL ganglia), it is also worth considering the effects of the larger system upon the rate of mass transfer. Since nearly all mass-transfer correlations in the literature suggest that dissolution is proportional to some power of Rep or Pé, it is useful to ensure that these values are close to those found in a real system. For both of these values, velocity and particle size are inversely proportional, so flow rates should be roughly 10 times slower in the model system than in the real system in order to maintain a similar rate of mass-transfer. To achieve this, however, means that Ca would drop by a factor of 10, which would in turn change Cag. Thus, without changing the wettability of the model system with respect to the real system, the model system will not be a perfect representation of the real system. Clearly, in these experiments either Cag or Rep (and Pé) will not scale correctly.
While the applicability of results from this approach need to be considered and the inability to scale precisely acknowledged, this experimental approach is still highly valuable, since it allows, for the first time, observation of ganglia shape, size, and position during the course of a dissolution experiment. Used in conjunction with knowledge obtained from other, more realistic experiments, this information can be useful in the conceptualization of mass-transfer models.
Three-dimensional images were obtained using a Bruker Spectrospin DMX 200 NMR spectrometer with a 4.77 T, 150 mm bore vertical magnet. A glass column with a 4.5 cm inner diameter was submersed in deionized water and filled with an equal mass of 2 mm and 6 mm diameter ballotini until a bed height of approximately 4 cm was reached. After all sphere surfaces had been stirred to remove any attached air bubbles, a second glass disk was seated on a ledge within the column approximately 2 mm above the top of the bed. A Viton o-ring was placed above the disk, which was used to form a seal and hold the disk in place. The column was sealed by a specially designed top which had a ground joint directly above the o-ring and was held in place by external elastic bands. The top had a small glass tube (2 mm i.d.) running through it for the purpose of connecting a tube which could deliver liquid above the glass disk. The entire assembly procedure was performed under water to prevent air bubbles from being trapped within the column.
Once the bed was sealed, it was placed inside the coil and the NMR, and the tubing system was connected as shown in Figure 1. A three-dimensional image was then obtained of the bed. Images of array size 2563 were obtained using the three-dimensional spin echo pulse sequence. The echo time was 6.3 ms and the repetition times were 1.2 s. The magnetic field gradients were set so that the field of view was 56.32 mm, which created voxels lengths of 220 mm. The experiment commenced by pumping water into the displacement jar (labelled (2) in Figure 1) via the syringe pump (1), which in turn forced carbon tetrachloride through the Viton tubing and into the base of the experimental column (d) at a rate of 5 mL/min (Ca = 1.164 ¥ 10-6, M = 0.97, Cag = 1.488 ¥ 10-6). The drainage process was monitored via 1-D profiles along the length of the column until the NAPL front approached the upper glass disk. The syringe pump was then reversed and imbibition occurred at the same rate as the drainage. This process was continued until no carbon tetrachloride entered the displacement jar. At this point, a valve leading to the displacement jar was switched so that the bottom of the column lead to the waste water tank (e). A peristaltic pump (b) was then used to fill the feed column (c) from the pure water reservoir (a) at a constant rate of 2.8 ml/min (Rep = 0.117, Ca = 6.52 ¥ 10-7, M = 1.03), which produced a hydrostatic head (between the levels of the feed column and the waste water tank). When equilibrium was reached, the flow through the experimental column was the same as the flow rate of the peristaltic pump.
The interfaces of the feed column and waste water tank were kept above the system in order to maintain positive pressure throughout, thus preventing air from coalescing within the system. After approximately five pore volumes had been flushed through the column, the pump was stopped, a valve connecting the experimental column to the waste tank was shut, and a three-dimensional image was acquired. Once the image was obtained, the pump was started and the valve opened, thus commencing the dissolution process. After 71 hours, flow was again halted and another image was acquired. This process was repeated after another 24 hours of dissolution. The time required for a single image acquisition was very long. Several times during the experiments, the acquisition failed due to faults in the imaging system, which led to fewer data sets than would have otherwise been obtained and to a lack of uniformity in the time between obtained images.
After the images were obtained and transformed into the spatial domain, the images were transferred to a Sun Sparc20. Statistics were determined from the middle 2.2 cm of the bed in the cylindrical direction in order to minimize any end effects caused either by NAPL not initially reaching the top of the column or by NAPL resting as sessile drops on the lower porous disk. The analysis performed on the resulting images followed the approach given in Baldwin, et al. (1996).
From the display of the images shown in Figure 2, changes in the bed structure are readily apparent. Between the first two images, particularly in the region highlighted in Figure 3, ganglia appear and disappear without leaving any remaining smaller ganglia. While ganglion disappearance may be attributed to either dissolution or displacement, other stationary ganglia appear to lose only a small amount of their size over the course of the experiment, suggesting that the disappearance of a large ganglion is almost certainly due to displacement. Furthermore, the appearance of ganglia can only attributed to displacement.
One quantitative measure of topological changes is the coordination of the NAPL ganglia. The distribution of coordination numbers for all three times is shown in Figure 4. Here, the number of ganglia which have a coordination number of unity (i.e. singlets) is roughly an order of magnitude greater than the number of doublets. Initially, there are a considerable number of multiplets, with coordination numbers exceeding 10. Following 71 hours of dissolution, the remaining ganglia were 84.1% singlets, 8.8% doublets, and 7.1% multiplets; while at 95 hours there were 77% singlets, 12.9% doublets, and 10% multiplets. Here, the general make-up of the NAPL remained the same; the drop in the percentage of singlets suggests that between the second and third images, small singlets were being dissolved completely (or flushed out of the analysed region) at more rapid rate than doublets or multiplets were being reduced to lower complexity ganglia. It is also worth noting that by the second image, no multiplet greater than a coordination of 3 existed.
Another approach to understanding the changes in the shape of ganglia over the time-course of the experiment is to investigate relationships between surface area and NAPL volume. In this experiment, the bed exhibited a power-law relationship between logV1/3 and logA, where V is the volume of a pore segment and A is the area of contact between the solid phase and the segment. As shown in Figure 5, the fractal dimension (slope) determined for the pore space within the bed was 2.30 ± 0.01 for all surface area and 2.70 ± 0.02 excluding throat areas, which suggests that the pores exhibit a fractal nature.(1)
When this approach was applied to NAPL segments, smaller fractal dimensions were obtained. For t = 0, the fractal dimension (where the area measured was the area of contact between the ganglia segment and either water or ballotini) was 2.12 ± 0.02 (shown in Figure 6); for t = 71 hrs it was 2.22 ± 0.03; and for t = 95 hrs it was 2.26 ± 0.03.
In order to consider these results and their implications, it is important to first compare them to previous work in order to validate the approach and then to discuss new findings for which no appropriate comparisons exist.
Although there exist no data in the literature to which the coordination number distribution for the images after dissolution may be compared, several workers have reported data which may be compared to the initial data obtained. Chatzis, et al. (1983) measured ganglion sizes using micromodels and styrene polymerization. The results obtained from the micromodels are not similar to those reported here. In particular, in none of the micromodels were more than 31% of the ganglia singlets, compared to 64.2% measured here. The results from ganglion casts, however, agree much more favourably. They found that "the vast majority" of ganglia were singlet or doublet for ganglia trapped in Berea sandstone. Cited within this work were the results of Robinson and Haring (1962), which found that for ganglia trapped within a bead pack 65% were singlets, 20% were doublets, and 15% were multiplets, which agrees well with the initial distribution of 64.2% singlets, 8.4% doublets, and 27.4% multiplets. Since no further information about the porous medium or experimental conditions was noted in Chatzis, et al. (1983), analysis of the larger proportion of multiplets to doublets found here is not possible.
It is clear that between t = 0 and t = 71 hrs, considerable displacement occurred, while between images t = 71 hrs and t = 95 hrs, displacement was less noticeable. Mobilization played a very important role in the change of saturation along the length of the bed. From the pore network modelling of Ng and Payatakes (1980) and later Dias and Payatakes (1986b), mobilization of NAPL ganglia was found to begin around Ca = 10-4 for very large ganglia and at 2 ¥ 10-3 for ganglia held in five pore bodies. These values are considerably greater than the gravity-inclusive capillary number during this experiment (Cag = 2.792 ¥ 10-6). The difference in these values is likely because the previous work did not consider effects of ganglion shrinkage upon their stability.
None of the models presented in Imhoff, et al. (1994) or Baldwin and Gladden (1996) attempt to model the displacement of NAPLs, which has been observed here to occur concurrently with dissolution. As previously mentioned, the phenomenological dissolution model proposed by Imhoff, et al. (1994) included a correlation between the spatial position and rate of mass transfer. They found that the rate of saturation removal was faster near the front of the column than near the far end of the column. The spatially dependent mass-transfer term is inexplicable in terms of dissolution; however, if displacement was occurring simultaneously, then a spatial correlation would be expected for two reasons. First, the arrival of new ganglia from upstream due to displacement will mask the amount of dissolution that has occurred at the downstream position where it becomes lodged. This will appear as rapid dissolution upstream and slow dissolution downstream, as was observed. Second, the displacement process can be expected to slowly reduce a multiplet shape into one or more (via rupture) singlets, which can be expected to be much more as it proceeds along the column, which would also lead to the appearance of dissolution slowing spatially along the length of the column.
Not only does mobilization add an additional transport mechanism to models of dissolution, it also will affect the rate of mass transfer between the liquid phases. by changing the topology of ganglia, the amount of interfacial surface area can be seen to be changing in a way that cannot be characterized by the shrinking of a dimple, Euclidean shape. Powers, et al. (1991) considered the effect of initial ganglion shape by comparing the different surface areas to volume relationships for various geometries. The results above suggest that ganglion segments abide by power-law relationships which become more and more fractal, suggesting that models based on shrinking Euclidean geometries, such as that of Geller and Hunt (1993) may be improved through incorporation of a saturation-dependent fractal dimension. Initial results in Baldwin (1996) suggest that this is indeed useful.
Further evidence to suggest that displacement phenomena are significant during the dissolution of NAPL is the strength of the velocity dependence measured in the above works. All of the models considered in Baldwin and Gladden (1996) suggest that the proper exponential factor for velocity exceeds 0.6. This is considerably higher than empirical work performed in benzoic acid spheres which has been measured to be 0.33 (Wilson and Geankoplis, 1966). If dissolution-induced displacement occurs, it is clear that it can occur at any capillary number, and it is likely that displacement will increase as some power of Ca. This would explain the increase in the velocity dependence obtained for NAPL dissolution.
From the observations and statistics calculated for a bed of dissolving NAPL ganglia, it is clear that all of the models in the literature are based in part upon invalid assumptions. First, mobilization is a significant mechanism for local saturation changes, particularly early on in the remediation process. Displacement was shown to occur well below the value of the gravity inclusive capillary number where mobilization commences in studies of non-dissolving ganglia. These results indicate that ganglion mobilization is an important phenomena which has been widely disregarded. Second, mobilization changed the topology of the ganglia. Large, highly branched ganglia ruptured or were reduced via dissolution to lower coordinated bodies. Third, it was shown that the process of ganglia breakdown from multiplets into singlets can be measured as change in the fractal dimension of the collection of ganglia segments comprising the saturation. Given the proposed relationship between coordination changes and surface area, the fractal analysis does not provide new information about the system, but rather it provides a simple means for describing how changes in coordination affect surface area.
The author wishes to thank Dr. L. F. Gladden and Dr. P. Alexander at the
University of Cambridge for their contributions to the work on which this paper is based.
In part, this material is based upon work supported under a National Science Foundation
a = interfacial surface area per unit volume[L2/L3]
Bo = Bond number (g(rn - rw)rt2/scosq)
Ca = capillary number (mv/scosq)
Cag = hypothetical capillary number, including buoyancy forces (see Eq. (4))
Dn,w = diffusivity of NAPL in aqueous phase [L2/T]
= mean particle diameter [L]
f = porosity
g = gravitational acceleration vector [L/L2]
k = permeability [L2]
kl = mass-transfer coefficient [L/T]
l = ganglion length in the direction of bulk flow [L]
m = fluid viscosity [M/L T]
Pé = Péclet number (v/fSnDn,w)
Rei = interstitial Reynolds number (rv/mfSn)
Rep = particle (superficial) Reynolds number (rv/m)
rt = radius of pore neck [L]
rn = density of NAPL [M/L3]
rw = density of water [M/L3]
Sh = Sherwood number (kla/Dn,w)
Sn = saturation of NAPL
s = interfacial surface tension [M/T2]
t = time [T]
q = contact angle [Rad]
Vb = volume of a NAPL blob [L/T]
v = Darcy velocity (superficial) [L/T]
y = blob shape factor
Baldwin, C.A. and L.F. Gladden, 1996. NMR Imaging of Nonaqueous-Phase Liquid Dissolution in a Porous Medium, AIChE J., 42, pp. 1341-1349.
Baldwin, C.A., 1996. Nuclear Magnetic Resonance Studies of Multiphase Systems: Application to Remediation Processes. Ph.D. Dissertation, University of Cambridge, pp. 204.
Baldwin, C.A., A.J. Sederman, M.D. Mantle, P. Alexander, and L.F. Gladden, 1996. Determining and Characterizing the Structure of a Pore-Space from 3-D Volume Images, J. Colloid Interface Sci., 181, pp. 79-92.
Chatzis, I., M.S. Kuntamukkula, and N.R. Morrow, 1988. Effect of Capillary Number on the Microstructure of Residual Oil in Strongly Water-Wet Sandstones, SPE Reservoir Eng., 3, pp. 902-912.
Chatzis, I., N.R. Morrow, and H.T. Lim, 1983. Magnitude and Detailed Structure of Residual Oil Saturation, Soc. Pet. Eng. J., 23, pp. 311-326.
Conrad, S.H., J.L. Wilson, W.R. Mason, and W.J. Peplinski, 1992. Visualization of Residual Organic Liquid Trapped in Aquifers, Water Resour. Res., 28, pp. 467-478.
Constantinides, G.N. and A.C. Payatakes, 1996. Network Simulation of Steady-State Two-Phase Flow in Consolidated Porous Media, AIChE J., 42, pp. 369-382.
Dias, M.M. and A.C. Payatakes, 1986a. Network Models of Two-Phase Flow in Porous Media. Part 1. Immiscible Microdisplacement of Non-Wetting Fluids, J. Fluid Mech., 164, pp. 305-336.
Dias, M.M. and A.C. Payatakes, 1986b. Network Models of Two-Phase Flow in Porous Media. Part 2. Motion of Oil Ganglia, J. Fluid Mech., 164, pp. 337-358.
Geller, J.T. and J.R. Hunt, 1993. Mass-Transfer from Nonaqueous-Phase Organic Liquids in Water-Saturated Porous-Media, Water Resour. Res., 29, pp. 833-845.
Holmes, J.L., R.L. Peyton, and T.H. Illangasekare, 1993. Spatial Distribution of Nonaqueous-Phase Liquid in Sand Using X-Ray Computed Tomography, In: Proceedings of the 8th Conference on Hazardous Waste Research, Kansas State University, Manhattan, KS, vol. , pp. 35-40.
Imhoff, P.T., P.R. Jaffe, and G.F. Pinder, 1994. An Experimental Study of Complete Dissolution of a Nonaqueous-Phase Liquid in Saturated Porous Media, Water Resour. Res., 30, pp. 307-320.
Mayer, A.S. and C.T. Miller, 1992. The Influence of Porous Medium Characteristics and Measurement Scale on Pore-Scale Distributions of Residual Nonaqueous-Phase Liquids, J. Contam. Hydrol., 11, pp. 189-213.
Ng, K.M. and A.C. Payatakes, 1980. Stochastic Simulation of the Motion, Breakup and Stranding of Oil Ganglia in Water-Wet Granular Porous Media During Immiscible Displacement, AIChE J., 26, pp. 419-430.
Payatakes, A.C., K.M. Ng, and R.W. Flumerfelt, 1980. Oil Ganglion Dynamics During Immiscible Displacement: Model Formulation, AIChE J., 26, pp. 430-442.
Powers, S.E., C.O. Loureiro, L.M. Abriola, and W.J. Weber, 1991. Theoretical Study of the Significance of Nonequilibrium Dissolution of Nonaqueous-Phase Liquid in Subsurface Systems, Water Resour. Res., 27, pp. 463-477.
Powers, S.E., L.M. Abriola, and W.J. Weber, 1992. An Experimental Investigation of Nonaqueous Phase Liquid Dissolution in Saturated Subsurface Systems - Steady-State Mass-Transfer Rates, Water Resour. Res., 28, pp. 2691-2705.
Robinson, R.L. and R.E. Haring, 1962. Experimental Study of Residual Oil Configuration in Unconsolidated Sand, Jersey Prod. Research Co. Report, Prod. Div.
Wilson, E.J. and C.J. Geankoplis, 1966. Liquid Mass-Transfer at Very Low Reynolds Numbers in Packed Beds, Ind. Eng. Chem. Fundam., 5, pp. 9.
Figure 1. Diagram of an experimental system. Initially, water was drained from the experimental column (d) by forcing NAPL in from the bottom. This was done using a syringe pump (1), which forced water into the top of the water/NAPL jar (s) and NAPL out of a bottom tube. After drainage, imbibition was commenced by reversing the syringe pump. Once the NAPL was in place, a valve was switched so that water exiting (d) flowed into the effluent tank (e). A peristalic pump (b) was then started, which drew water from the fresh water supply (a) into the feed column (c). The level in the feed column increased until the flow rate through the column was equal to the flow rate of the peristalic pump. As the experiment progressed, the fluid height in (c) and (e) gradually increased, maintaining a constant head (and thus flow rate).
Figure 2. Images of ganglia in the middle of the column. These images show how the field of ganglia in the centre 1 cm of the bed changed during the course of the experiment. By comparing several individual ganglia, it is possible to observe both dissoltion (within the red circles) and displacement (within the green circle and blue square).
Figure 3. Orthogonal views of a small region within the bed. In the first column, ganglia are shown for a 1.65 cm cube of the bed from the transverse perspective, which the second column show the same images from a longitudinal perspective. Between 0 and 71 hours, displacement has occurred both into and out of the cube, while between 71 and 95 hours, dissolution of the ganglia can be seen.
Figure 4. Changes in coordination with remediation. The initially large number of multiplets (coordination 3 and higher) is reduced considerably at 71 hours. Little change occurs between 71 and 95 hours. This suggests that during mobilisation and dissolution, ganglia are becoming less branched.
Figure 5. Determination of fractal dimension of the entire bed. A power-law relationship again provides a good description of the bed. The resulting slope, 2.30 + 0.01, agrees with the measurements presented in Chapter 5, even though size of each pixel is one-eighth the volume. This is independent confirmation of the results presented there.
Figure 6. Fractal dimension plot for ganglia segments prior to dissolution. The slope, 2.12, is considerably less then the bed as a whole. Nonetheless, the power-law relationship is clearly present.
. The errors reported for the fractal dimensions are based upon the 95% confidence levels determined from linear regression through the data points.