- Email: [email protected]
Weathering of NAPL at an industrial site
779
Weathering of NAPL at an industrial site G.A.M. van Meurs ~, J.P. Pruiksma ~, and E.E. van der Hock ~* ~GeoDelft, P.O. Box 69, NL-2600 AB DELFT, The Netherlands
Spills of non-aqueous phase liquids (NAPL) are present at most urban areas. Once the NAPL enters the subsurface, a complex pattern of transport processes starts. Among them is retention by the porous medium. Therefore, a certain amount of the NAPL is entrapped as a residual phase within the soil system. Whenever residual NAPL is entrapped within the porous medium, interphase mass transfer takes place between the NAPL and the other phases present in the system. For a saturated system, the rate of interphase mass transfer is a function of the aqueous phase velocity, the fluid saturations for the aqueous and non-aqueous phase, and characteristics of the porous medium. The interphase mass transfer can be described by several dimensionless numbers. Within the description, use is made of the constituents measured within the NAPL phase. The description is incorporated within the well known numerical model of RT3D. With the numerical model the risks related with the impact of an actual spill at an industrial site is investigated based upon fate and behaviour of the constituents in the subsoil. 1. I N T R O D U C T I O N
Spills of non-aqueous phase liquids (NAPL) are present at most urban areas. They may result from dry cleaning facilities or from petrochemical activities. Once the NAPL enters the subsurface, a complex pattern of transport processes starts. Among them is retention by the porous medium and flow by gravity. Whenever the NAPL is lighter than water (LNAPL), the full capillary zone just above the groundwater table prevents vertical infiltration of the LNAPL [1]. However, due to variation in time of the groundwater table, the NAPL disperses over a larger vertical distance and a certain amount of the NAPL is entrapped as a residual phase within the soil system. Whenever the NAPL is heavier than water (DNAPL), vertical flow by gravity is present until a layer with low permeability is reached. During the flow, a track of residual NAPL remains due to capillary forces. Whenever residual NAPL, whether it is lighter or heavier than water, is entrapped within the porous medium, interphase mass transfer takes place between the NAPL and the other phases present in the system: aqueous, vapour or solid. For a saturated system the description of the stagnant film model is applied at the interface between a droplet of *Delft Cluster and SKB supplied the research grant for this study
780 the NAPL phase and the surrounding aqueous phase (groundwater) [2]. (1) With, S~ the solute mass contributions from the NAPL phase to the groundwater for compohenri(rag/i/day);
kl the kinetic rate coefficient (1/day); C~ the concentration in the groundwater for component i (film) at the NAPL interface and groundwater which is in thermodynamic equilibrium with the NAPL (rag/l); C~ the concentration in the flow of groundwater for component i (rag/l). Based on dimensional analyses, [3] proposed an expression for the kinetic rate coefficient kl between the residual NAPL and the water phase. The expression is based upon the Sherwood number: S h - kld~
(2)
With: Sh Sherwood number (dimensionless) dp particle diameter (m) D,~ molecular diffusion (m2/day) In the literature, several empirical relations can be found for the Sherwood number [3-5]. The general expression is" S h -- flO R ~ I O~2 SC/~3
(3)
With: Re Reynolds number (-) Sc Schmidt's number (-) 0 content of NAPL phase (m3/m 3) fl empirical constant (-) The Reynolds number is defined as: =
(4)
With. V~ mean pore velocity of the water phase (m/day) p~ density of the water phase (kg/m 3) #~ dynamic viscosity of the water phase (kg/m/day) The Schmidt number is defined as: Sc - p~#w Z)~
(5)
The relation between the concentration in the water phase at the water-NAPL interface and the concentration in the NAPL phase can be given as: G< -
kp . c ?
(6)
781 With. k~ partition coefficient for component i (-) C~ the concentration in the NAPL phase for component i (rag/l) This expression can be rewritten due to Raoult's law. -
(7)
With: Xi molar fraction of component i in the NAPL phase (-) S~ solubility of component i in the water phase (rag/l) For most situations, the NAPL is a mixture in which several chemical constituents are dissolved. These constituents differ in physical and chemical behaviour. Transfer of mass between the NAPL phase and the water phase takes place due to the difference in concentration of a specific constituent. Initially, the rate of transfer is higher for the constituents which are more soluble in the groundwater. Furthermore, the rate of transfer is enhanced when the average concentration in the groundwater is lowered due to the flow of the groundwater. The description of the mass transfer is incorporated within the well known numerical model of RT3D [6]. This model is an extension of I~IT3D [8]. With the numerical model the risks related with an actual spill at an industrial site is investigated With the numerical model the risks related with an actual spill at an industrial site is investigated. 2. A P P L I C A T I O N
AT A S I T E
The general information about the generic properties is derived from the conditions at the site (Table 1).
Table 1 Generic properties of the water phase Parameter Pa density of aqueous phase Va kinematic viscosity of aqueous phase #a dynamic viscosity of aqueous phase Da effective molecular diffusion in water Pb bulk density of the subsoil
value 1,000. 1.79 10 .6 1.79 10 .3 1.1 10 .9 1,600
dimension [kg/m 3] [m2/s] [kg/m.s] [m2/s] [kg/m 3]
Several specific properties about the relevant conditions at the site can be mentioned. Among them are" 9 Some physical properties and conditions; 9 Source characteristics; 9 Dimensionless Reynolds, Schmidt and Sherwood numbers; 9 Transfer from the NAPL phase to the aqueous phase;
782 9 Properties of the NAPL phase; 9 Adsorption; 9 Biodegradation. 2.1. S o m e physical properties and c o n d i t i o n s Table 2 contains the so-called specific parameters based upon the conditions at the site. A groundwater model of the location is created with ModFlow [7]. In the groundwater model of the site, the pore water velocity ranges from about 0.18 m/day to about 0.36 m/day. Therefore, a value of 0.33 m/day (3.82 10 -6 m/s) is given in Table 2. The properties for mechanical dispersion are based upon the problem length L. Together with the effective molecular diffusion they form the basis for the hydraulic dispersion (Table
2). Table 2 Properties and conditions at the site Parameter L problem length H thickness of the layer n effective porosity Va pore water velocity of aqueous phase dp mean particle diameter D~a molecular diffusion in aqueous phase c~L Longitudinal dispersion length c~ur Horizontal transversal dispersion length c~vr Vertical transversal dispersion length
value 50 4 0.3 3.82 10 -6 2.50 10 -4 1.10 10 -9 5 0.5 0.05
dimension [m] [m] [m3/m 3] [m/s] Ira] [m2/s] [m] [m] Ira]
2.2. Source characteristics Furthermore, density of the NAPL and conditions in the source area consisting of residual NAPL, are used (Table 3). Values for the residual volumetric content of the NAPL phase depend on the permeability" the higher the permeability, the lower the residual volumetric content. For 'low permeability', residual fraction amounts to about 30 to 50 1/m 3 which means 0~ amounts of 0.03 to 0.05 m3/m 3 [1]. For 'high permeability', residual fraction amounts to about 3 to 5 1/m 3 which means On amounts of 0.003 to 0.005 m3/m 3 [1]. Based upon the volumetric content of the NAPL and of the aqueous phase, the degree of saturation is calculated. 2.3. D i m e n s i o n l e s s n u m b e r s Now, several dimensionless numbers are calculated: the Reynolds number, the Schmidt number and the Sherwood number (Table 4). For a specific situation, the Schmidt number and the Reynolds numbers are constant. Their actual value can be determined by substitution of the relevant parameters. In the literature, several expressions can be found for the Sherwood number. Based upon the Sherwood number, the coefficients can be found
783 Table 3 Source characteristics Parameter Sa degree saturation aqueous phase S~ degree saturation NAPL Oa volumetric content of aqueous phase 0~ volumetric content of NAPL
value 0.90 0.10 0.27
dimension [-] [-] [ma/m a]
0.03
[ma/m 3]
governing the transfer of dissolved constituents from the NAPL phase to the water phase. Substitution of the site-specific properties at the site and substituting the initial value for the volumetric content of the NAPL phase, leads to the values of Table 4. Table 4 Dimensionless numbers relevant at the site Parameter value Re Reynolds number 5.33E-04[-] Sc Schmidt number 1.63E+03[-] Sh Sherwood number value 1. 2. 3. 4. 5.
Miller et al. Parker et al. Miller et al. Parker et al. Imhoff et al.
[3]; [5]; [3]; [5]; [4].
2.07E-01[-] 5.30E-01[-] 5.13E-03[-] 1.68E-02[-] 7.29E-03[-]
kl Kinetic rate coefficient 1. [3]; 2. [5]; 3. [3]; 4. [5]; 5. [4].
value 315 [1/day] 807 [l/day] 7.81 [l/day] 25.5[1/day] 11.1 [1/day]
2.4. T r a n s f e r from t h e N A P L p h a s e to t h e a q u e o u s p h a s e Based upon the Sherwood number, the kinetic rate coefficient can be determined (Table 4). The value ranges from about 10 to 800 1/day. It is expected that more research results about the kinetic rate coefficient will become available in the near future. For the time being, the first expression of Miller et al. [3] (1) is taken. For an actual situation, this expression is not a constant but a function of volumetric content of the NAPL phase (0~). Due to leaching this value diminishes in time. 2.5. P r o p e r t i e s of t h e N A P L p h a s e At the site, a product called LCCCO is leaked to the subsoil. Analyses of a sample showed that LCCCO consists of several constituents. The constituents are grouped into six blocks based upon their characteristic "Equivalent Carbon" (EC) number (Table 5). This characteristic is based upon the methodology of the Total Petroleum Hydrocarbon Criteria Working Group (TPHWG). For each block, its mass, its molar weight, the number of moles, the mole fraction and the volumetric concentrations are determined. Based upon solubility and molar fraction, the partition coefficient for each block is calculated (Table 6). Notice the following aspects within Table 6. The solubility of the
784 Table 5 Several properties of the Blocks that are present within LCCCO mass molar weight moles molar fraction NAPL phase Block [mg/g] [g/mole] 1/g NAPL 1 Aliphatics 72 226 0.3186 0.0638 2 EC < 11 24 107 0.2243 0.0449 3 EC11-EC13 124 162 0.7654 0.1532 4 EC13-EC15 372 190 1.9579 0.3918 5 EC15-EC18 311 225 1.3822 0.2766 6 EC18-EC23 98 281 0.3488 0.0698
concentration NAPL phase [mg/1] 57,600 19,200 99,200 297,600 248,800 78,400
Aromatics diminish going from Block 2 to Block 6. The solubility of the Aliphatics (Block 1) is the lowest. The equilibrium concentrations in the aqueous phase are comparable for Block 2, Block 3 and Block 3. This means that these Blocks leach out easiest followed by Block 5 and Block 6. For Block 1 it is the hardest to leach out. Initially, the content of the NAPL phase consists particularly of Block 4 and Block 5. The contribution of Block 2 is only slight.
Table 6 Partition coefficient of each Block solubility molar fraction
Block 1 Aliphatics 2 EC < 11 3 ECll-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
[rag/l] 0.000032 50.7 15.1 5.8 1.7 0.2
[1/g NAPL] 0.0638 0.0449 0.1532 0.3918 0.2766 0.0698
concentration water phase
concentration NAPL phase
partition coefficient
[rag/l] 2.04 10 .6 2.28 2.31 2.27 4.70 10 -1 1.40 10 .2
[mg/1] 57,600 19,200 99,200 297,600 248,800 78,400
[-] 3.54 1.19 2.33 7.64 1.89 1.78
10 -11 10 -4 10 .5 10 -6 10 .6 10 .7
2.6. Adsorption The mechanism of adsorption is described as a linear process. This means that the concentration dissolved in the aqueous phase is proportional to the concentration adsorbed at the solid phase. The proportionality factor is called the coefficient of distribution [9].
k . - c; Ca With, kd distribution coefficient [1/kg] C~ concentration adsorbed at the solid phase [mg/kg]
(8)
785 Ca~ concentration dissolved in the aqueous phase [mg/1] The distribution coefficient can be written as:
(9)
= f o c . koc
With, ka distribution coefficient between the aqueous phase and the solid phase [kg/1] foe mass fraction of organic carbon [-] ko~ partition coefficient of the solute in a granular medium of organic carbon [1/kg] So for adsorption the fraction of organic carbon (fo~) is relevant. At the site the mass fraction of organic matter (fo,~) is estimated as 0.03. The fraction organic carbon now can be calculated as: (10)
foc - fo~ / 1.7 - 0.03/1.7 ~ 0.018
Values for koc are derived from handbooks. The value for kd is used in the numerical model to calculate the retardation factor 1R which yields [9]"
R = 1 + p~ kd
1--rt
(11)
n
with, R retardation factor [-] p~ specific density of the solid material [kg/1] ke distribution coefficient between aqueous phase and solid phase [kg/1] n porosity of the porous medium [m3/m 3] Table 7 Adsorption and degradation for each Block of constituents
fo, Block 1 Aliphatics 2 EC
[l/kg) 8.90 102 1.78 102 2.00 102 5.01 103 8.91 103 2.24 10 4
[-] 0.03 0.03 0.03 0.03 0.03 0.03
kd [-] 0.018 0.018 0.018 0.018 0.018 0.018
[l/kg] 15.7 3.14 3.52 88.5 157. 395.
[l/day] 5.70E-01 3.00E-01 3.52E-02 9.60E-03 2.62E-03 1.95E-04
2.7. Biodegradation For the aqueous phase degradation is also taken into account due to biological activity. For the rate of degradation distinction is made between aerobic and anaerobic conditions. In practice, other conditions also affect the rate of degradation. However, for the site such detailed information is not available. Furthermore. the main objective for the current research is to implement the rate of depletion of constituents dissolved in the NAPL phase and transferred to the aqueous phase. Therefore as indication of the effect of biodegradation, values for anaerobic degradation were taken into account (Table 7). This information is used to estimate the rate of degradation kra for the six blocks. However, in practice the actual rate can be an order lower [10].
786 3. N U M E R I C A L
RESULTS
Several calculations are carried out as an example based upon data from the site. All the calculations started with a groundwater flow model. Each flow model is created with the computer code ModFlow [7]. The dimensions of the example are 510 m by 110 m by 4 in. In the horizontal plane (Figure 1), the number of grid cells is 69 (x-direction) by 29 (y-direction). In vertical direction only one layer is distinguished, which means that the calculation is two-dimensional. Due to a difference in groundwater head and the hydraulic conductivity, a horizontal flow of groundwater is created. The pore water velocity agrees with the value at the site (Table 2). In the example a source of NAPL is represented (Figure 1). The dimensions of the source area are 2 by 2 m. It is assumed that the presence of the source does not affect the flow of groundwater. So the groundwater flow is purely horizontal. Within the source area residual NAPL is present with a degree of saturation of 10 %. Based upon the dimensions of the source area and the degree of saturation of the NAPL, 0.480 m a NAPL is present in the source area. Together with the density of 800 kg/m a, the mass of NAPL amounts 384 kg.
Figure 1. Planar view of the situation
3.1. T w o b l o c k s of c o n s t i t u e n t s To gain information about the competition of blocks of constituents, the following calculation is carried out. Initially, only Block 2 (Aromatics E C < l l ) and Block 6 (Aromatics EC18-EC23) are present in the NAPL phase. The initial concentration equals 400 g/1 (400.000 rag/l) for both of them. Due to this initial concentration in the NAPL phase~ the molar fraction differs from the values given in Table 5 and Table 6. Looking to the effect of dissolution from the NAPL phase to the water phase (groundwater)~ the concentration of Block 2 in the NAPL phase diminishes, while at the same time the concentration of Block 6 increases (Figure 2)" enrichment. This enrichment is due to the difference in solubility: the solubility of Block 2 is about 150 times higher than the one of Block 6. The sum of both concentrations equals the density of the NAPL phase. Looking to the effect of dissolution into the water phase, initially the concentration in the aqueous phase equals the equilibrium concentration governed by Raoult~s law: compare the initial concentration of Figure 3 with the values of Table 10. At first instance, competition in dissolution takes place between Block 2 and Block 6. As soon as Block 2 is depleted in the NAPL phase, competition vanishes. Now the concentration in the NAPL
787
Table 8 Several properties of the different Blocks (only two Blocks are present in the NAPL phase)
Block 1 Aliphatics 2 EC < 11 3 EC11-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
mass NAPL phase ling/g] 0 500 0 0 0 500
molar weight [g/mole] 226 107 162 190 225 281
moles
molar fraction
0 4.673 0 0 0 1.779
1/g NAPL 0 0.724 0 0 0 0.276
concentration NAPL phase [mg/1] 0 400,000 0 0 0 400,000
Table 9 Partition coefficient for each Block (only two Blocks are present in the NAPL phase) solubility molar fraction concentration concentration partition water phase NAPL phase coefficient Block 1 Aliphatics 2 EC < 11 3 EC11-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
[rag/l] 0.000032 50.7 15.1 5.8 1.7 0.2
[1/g NAPL] 0 0.724 0 0 0 0.276
(Ca)
(On)
(Ca/On)
[rag/l] 0. 36.7 0. 0. 0. 0.0552
[rag/l] 0 400,000 0 0 0 400,000
[-] 3.54 1.19 2.33 7.64 1.89 1.78
10 -11
10 -4 10 -5 10 -6 10 -6 10 -7
788
Figure 2: Concentration of Block 2 and Block 6 in the NAPL phase in time.
Figure 3" Concentration of Block 2 and Block 6 in the water phase in the source area.
phase is enhanced and reaches the density of the NAPL (Figure 2) and the concentration of Block 6 in the water phase approaches its solubility of 0.20 rag/1 (Figure 3). It takes about 1.5 year for Block 2 to deplete. Due to the difference in solubility, it will take more then 225 year before Block 6 will be depleted. 3.2. Six B l o c k s of c o n s t i t u e n t s Subsequently, the calculation is repeated with all the six Blocks of constituents. The initial concentration of each block in the NAPL phase is based upon the content of the oil. The values for the solubility and the partition coefficients can be found in Table 6. Looking to the effect of dissolution from the NAPL phase to the water phase (groundwater), the concentration of Block 2 in the NAPL phase diminishes at first (Figure 5), followed by the concentration of Block 3 and Block 4 respectively. Within a time period of fifteen years, these three Blocks are leached out of the NAPL phase. Block 5 is leached out within thirty years. However, after thirty years Block 1 (Aliphatics) and Block 6 (Aromatics EC18-EC23) still are present within the NAPL phase. The concentration of the Aliphatics (Block 1) gradually increases in time during this time period of thirty years. Looking to the previous results with only two Blocks, it takes now about 8 years instead of 1.5 years for Block 2 to be depleted in the NAPL phase due to the competition with the other Blocks. The sum of the concentration of each Block in the NAPL phase is equal to the density of the NAPL. Therefore, this summation can be used as a check for the mass balance of the NAPL. For this situation, the total concentration needs to remain 800 kg/m 3 (Figure
4). Looking to the effect of dissolution into the water phase, competition now is taking place between the Blocks during the complete period of thirty years. Initially, the (equilibrium) concentrations of Block 2, Block 3 and Block 4 in the water phase are comparable (Figure 5). However, Block 2 is depleted at first, followed by Block 3 and then Block 4 due to their
789
Figure 4" Concentration development in the NAPL phase of the six Blocks.
Figure 5" Concentration of each Block in the water phase in the source area.
respective concentration in the NAPL phase. After thirty years, Block 5 and Block 6 still are present in the groundwater. However, the concentration of Block 1, the Aliphatics, does not reach 0.1 #g/l: even when all the Aromatics are leached out. This is a result of its low solubility of 0,032 #g/1.
3.3. Six Blocks of constituents" adsorption and degradation Subsequently, a calculation is carried out in which adsorption and degradation in the subsoil is taken into account. For each Block different values are incorporated (Table 7). The development of the concentration calculated for each block in the NAPL phase can be found in Figure 6. As expected, the initial concentration of Block 4 and Block 5 are comparable. Also the order in leaching is comparable. At first, Block 2 leaches out, then followed by Block 3, Block 4 and Block 5. After thirty years still Block 6 and Block 1 (Aliphatics) are present in the NAPL phase. Compared with the previous calculation in which neither adsorption nor degradation were taken into account, depletion of Block 2, Block 4 and Block 5 takes place earlier. After thirty years the contribution of Block 1 (Aliphatics) is slightly higher than the contribution of Block 6. So degradation in the subsoil stimulates also the process of leaching. The development of the concentration calculated in the aqueous phase in the source area can be found in Figure 7. Again the order in leaching is comparable. At first, Block 2 leaches out, followed by Block 3 and Block 4. After thirty years, only Block 1 (Aliphatics/, Block 5 and Block 6 are present within the aqueous phase. However, the concentration of Block 1 and Block 5 are below 1 #g/1. So only the concentration of Block 6 might be harmful for the environment. Compared with the previous calculation in which no adsorption nor degradation in the subsoil are present, the depletion of Block 2, Block 3 and Block 4 takes place faster and the concentration in the water phase after thirty years is lower for Block 5 and for Block 6. Looking to the development and extension of the plume of Block 6 dissolved in the groundwater, the following remarks can be made. The plume has reached stationary conditions. After thirty year, the highest concentration found in the centre of the plume
790
Figure 6: Concentration of each Block in the NAPL phase.
Figure 7: Concentration in the water phase for each Block (logarithmic scale) in the source area.
starts declining. The extension of the plume based upon the concentration level of one microgram per litre is about 250 m. 4. C O N C L U S I O N S
Taking the mass transfer between the NAPL phase and the aqueous phase into account, gives the ability to judge the fate and behaviour of this type of contamination in the subsoil. Therefore, the results of the calculations, together with measurements in the field, can be assessed from an environmental point of view. It can be concluded that the extended numerical code of RT3D gives the opportunity to determine the depletion of residual NAPL in the subsoil. This behaviour can be compared with formal regulations about the risk of migration. Taking into account the properties of the current situation at the particular site, it can be concluded that for relatively small oil spills of about 500 litres, natural processes will deplete the NAPL within a time period of thirty years. Whenever, the amount of spilled product is larger, much more time is needed before depletion of the oil results in concentrations in the water phase which are below national standards. REFERENCES
1.
2. 3.
F. Schwille, Migration of Organic Fluids Immiscible with Water in the Unsaturated Zone, In Pollution in Porous Media: The Unsaturated Zone Between Soil Surface and Groundwater, Ecological Studies, Volume 47, Springer Verlag, Berlin (1984) 27-48. T.K. Sherwood, R.L. Pigford, C.R. Wilke, Mass Transfer, McGraw Hill, New York (1975) C.T. Miller, M.M. Poirier-McNeill and A.S. Mayer, Dissolution of trapped non-aqueous phase liquids: Mass transfer characteristics, Water Resources Research, Vol. 26, No. 11 (1990) 2783-2796.
791 4. P.T. Imhoff, A. Frizzell, C.T. Miller, Evaluation of thermal effects on the dissolution of a NAPL in porous media, Environmental Science Technology, Vol. 31 (1997) 16151622. 5. J.C. Parker, A.K. Katyal and J.J. Kaluarachichi, Modeling multiphasc organic chemical transport in soils and groundwater, U.S. EPA, Ada, Oklahoma (1990). 6. T.P Clement, A Modular Computer Code for Simulating Reactive Multi-species Transport in 3-Dimensional Groundwater Systems, U.S. DoE, DE-AC06-76RLO 1830, PNNL, Richmond, Washington (1997). 7. M.G. McDonald and A.W. Harbaugh, A Modular Three-Dimensional Finite Difference Ground-Water Flow model, U.S.G.S. Techniques of Water Res. Inv., Book 6 (1988) 586. 8. C. Zheng, MT3D: A Modular Three-Dimensional Transport Model for Simulation of Advection, Dispersion and Chemical Reaction in Groundwater Systems, US EPA, Oklahoma (1990). 9. C. Zheng and G.D. Bennett, Applied Contaminant Transport Modeling: Theory and Practice, Van Nostrand Reinold, New York (1995) 440. 10. T.H. Wiedemeier, H.S. Rifai, C.J. Newell and J.T. Wilson, Natural Attenuation of Fuels and Chlorinated Solvents in the Subsurface, John Wiley &~ Sons, New York (1999) 617.
Weathering of NAPL at an industrial site G.A.M. van Meurs ~, J.P. Pruiksma ~, and E.E. van der Hock ~* ~GeoDelft, P.O. Box 69, NL-2600 AB DELFT, The Netherlands
Spills of non-aqueous phase liquids (NAPL) are present at most urban areas. Once the NAPL enters the subsurface, a complex pattern of transport processes starts. Among them is retention by the porous medium. Therefore, a certain amount of the NAPL is entrapped as a residual phase within the soil system. Whenever residual NAPL is entrapped within the porous medium, interphase mass transfer takes place between the NAPL and the other phases present in the system. For a saturated system, the rate of interphase mass transfer is a function of the aqueous phase velocity, the fluid saturations for the aqueous and non-aqueous phase, and characteristics of the porous medium. The interphase mass transfer can be described by several dimensionless numbers. Within the description, use is made of the constituents measured within the NAPL phase. The description is incorporated within the well known numerical model of RT3D. With the numerical model the risks related with the impact of an actual spill at an industrial site is investigated based upon fate and behaviour of the constituents in the subsoil. 1. I N T R O D U C T I O N
Spills of non-aqueous phase liquids (NAPL) are present at most urban areas. They may result from dry cleaning facilities or from petrochemical activities. Once the NAPL enters the subsurface, a complex pattern of transport processes starts. Among them is retention by the porous medium and flow by gravity. Whenever the NAPL is lighter than water (LNAPL), the full capillary zone just above the groundwater table prevents vertical infiltration of the LNAPL [1]. However, due to variation in time of the groundwater table, the NAPL disperses over a larger vertical distance and a certain amount of the NAPL is entrapped as a residual phase within the soil system. Whenever the NAPL is heavier than water (DNAPL), vertical flow by gravity is present until a layer with low permeability is reached. During the flow, a track of residual NAPL remains due to capillary forces. Whenever residual NAPL, whether it is lighter or heavier than water, is entrapped within the porous medium, interphase mass transfer takes place between the NAPL and the other phases present in the system: aqueous, vapour or solid. For a saturated system the description of the stagnant film model is applied at the interface between a droplet of *Delft Cluster and SKB supplied the research grant for this study
780 the NAPL phase and the surrounding aqueous phase (groundwater) [2]. (1) With, S~ the solute mass contributions from the NAPL phase to the groundwater for compohenri(rag/i/day);
kl the kinetic rate coefficient (1/day); C~ the concentration in the groundwater for component i (film) at the NAPL interface and groundwater which is in thermodynamic equilibrium with the NAPL (rag/l); C~ the concentration in the flow of groundwater for component i (rag/l). Based on dimensional analyses, [3] proposed an expression for the kinetic rate coefficient kl between the residual NAPL and the water phase. The expression is based upon the Sherwood number: S h - kld~
(2)
With: Sh Sherwood number (dimensionless) dp particle diameter (m) D,~ molecular diffusion (m2/day) In the literature, several empirical relations can be found for the Sherwood number [3-5]. The general expression is" S h -- flO R ~ I O~2 SC/~3
(3)
With: Re Reynolds number (-) Sc Schmidt's number (-) 0 content of NAPL phase (m3/m 3) fl empirical constant (-) The Reynolds number is defined as: =
(4)
With. V~ mean pore velocity of the water phase (m/day) p~ density of the water phase (kg/m 3) #~ dynamic viscosity of the water phase (kg/m/day) The Schmidt number is defined as: Sc - p~#w Z)~
(5)
The relation between the concentration in the water phase at the water-NAPL interface and the concentration in the NAPL phase can be given as: G< -
kp . c ?
(6)
781 With. k~ partition coefficient for component i (-) C~ the concentration in the NAPL phase for component i (rag/l) This expression can be rewritten due to Raoult's law. -
(7)
With: Xi molar fraction of component i in the NAPL phase (-) S~ solubility of component i in the water phase (rag/l) For most situations, the NAPL is a mixture in which several chemical constituents are dissolved. These constituents differ in physical and chemical behaviour. Transfer of mass between the NAPL phase and the water phase takes place due to the difference in concentration of a specific constituent. Initially, the rate of transfer is higher for the constituents which are more soluble in the groundwater. Furthermore, the rate of transfer is enhanced when the average concentration in the groundwater is lowered due to the flow of the groundwater. The description of the mass transfer is incorporated within the well known numerical model of RT3D [6]. This model is an extension of I~IT3D [8]. With the numerical model the risks related with an actual spill at an industrial site is investigated With the numerical model the risks related with an actual spill at an industrial site is investigated. 2. A P P L I C A T I O N
AT A S I T E
The general information about the generic properties is derived from the conditions at the site (Table 1).
Table 1 Generic properties of the water phase Parameter Pa density of aqueous phase Va kinematic viscosity of aqueous phase #a dynamic viscosity of aqueous phase Da effective molecular diffusion in water Pb bulk density of the subsoil
value 1,000. 1.79 10 .6 1.79 10 .3 1.1 10 .9 1,600
dimension [kg/m 3] [m2/s] [kg/m.s] [m2/s] [kg/m 3]
Several specific properties about the relevant conditions at the site can be mentioned. Among them are" 9 Some physical properties and conditions; 9 Source characteristics; 9 Dimensionless Reynolds, Schmidt and Sherwood numbers; 9 Transfer from the NAPL phase to the aqueous phase;
782 9 Properties of the NAPL phase; 9 Adsorption; 9 Biodegradation. 2.1. S o m e physical properties and c o n d i t i o n s Table 2 contains the so-called specific parameters based upon the conditions at the site. A groundwater model of the location is created with ModFlow [7]. In the groundwater model of the site, the pore water velocity ranges from about 0.18 m/day to about 0.36 m/day. Therefore, a value of 0.33 m/day (3.82 10 -6 m/s) is given in Table 2. The properties for mechanical dispersion are based upon the problem length L. Together with the effective molecular diffusion they form the basis for the hydraulic dispersion (Table
2). Table 2 Properties and conditions at the site Parameter L problem length H thickness of the layer n effective porosity Va pore water velocity of aqueous phase dp mean particle diameter D~a molecular diffusion in aqueous phase c~L Longitudinal dispersion length c~ur Horizontal transversal dispersion length c~vr Vertical transversal dispersion length
value 50 4 0.3 3.82 10 -6 2.50 10 -4 1.10 10 -9 5 0.5 0.05
dimension [m] [m] [m3/m 3] [m/s] Ira] [m2/s] [m] [m] Ira]
2.2. Source characteristics Furthermore, density of the NAPL and conditions in the source area consisting of residual NAPL, are used (Table 3). Values for the residual volumetric content of the NAPL phase depend on the permeability" the higher the permeability, the lower the residual volumetric content. For 'low permeability', residual fraction amounts to about 30 to 50 1/m 3 which means 0~ amounts of 0.03 to 0.05 m3/m 3 [1]. For 'high permeability', residual fraction amounts to about 3 to 5 1/m 3 which means On amounts of 0.003 to 0.005 m3/m 3 [1]. Based upon the volumetric content of the NAPL and of the aqueous phase, the degree of saturation is calculated. 2.3. D i m e n s i o n l e s s n u m b e r s Now, several dimensionless numbers are calculated: the Reynolds number, the Schmidt number and the Sherwood number (Table 4). For a specific situation, the Schmidt number and the Reynolds numbers are constant. Their actual value can be determined by substitution of the relevant parameters. In the literature, several expressions can be found for the Sherwood number. Based upon the Sherwood number, the coefficients can be found
783 Table 3 Source characteristics Parameter Sa degree saturation aqueous phase S~ degree saturation NAPL Oa volumetric content of aqueous phase 0~ volumetric content of NAPL
value 0.90 0.10 0.27
dimension [-] [-] [ma/m a]
0.03
[ma/m 3]
governing the transfer of dissolved constituents from the NAPL phase to the water phase. Substitution of the site-specific properties at the site and substituting the initial value for the volumetric content of the NAPL phase, leads to the values of Table 4. Table 4 Dimensionless numbers relevant at the site Parameter value Re Reynolds number 5.33E-04[-] Sc Schmidt number 1.63E+03[-] Sh Sherwood number value 1. 2. 3. 4. 5.
Miller et al. Parker et al. Miller et al. Parker et al. Imhoff et al.
[3]; [5]; [3]; [5]; [4].
2.07E-01[-] 5.30E-01[-] 5.13E-03[-] 1.68E-02[-] 7.29E-03[-]
kl Kinetic rate coefficient 1. [3]; 2. [5]; 3. [3]; 4. [5]; 5. [4].
value 315 [1/day] 807 [l/day] 7.81 [l/day] 25.5[1/day] 11.1 [1/day]
2.4. T r a n s f e r from t h e N A P L p h a s e to t h e a q u e o u s p h a s e Based upon the Sherwood number, the kinetic rate coefficient can be determined (Table 4). The value ranges from about 10 to 800 1/day. It is expected that more research results about the kinetic rate coefficient will become available in the near future. For the time being, the first expression of Miller et al. [3] (1) is taken. For an actual situation, this expression is not a constant but a function of volumetric content of the NAPL phase (0~). Due to leaching this value diminishes in time. 2.5. P r o p e r t i e s of t h e N A P L p h a s e At the site, a product called LCCCO is leaked to the subsoil. Analyses of a sample showed that LCCCO consists of several constituents. The constituents are grouped into six blocks based upon their characteristic "Equivalent Carbon" (EC) number (Table 5). This characteristic is based upon the methodology of the Total Petroleum Hydrocarbon Criteria Working Group (TPHWG). For each block, its mass, its molar weight, the number of moles, the mole fraction and the volumetric concentrations are determined. Based upon solubility and molar fraction, the partition coefficient for each block is calculated (Table 6). Notice the following aspects within Table 6. The solubility of the
784 Table 5 Several properties of the Blocks that are present within LCCCO mass molar weight moles molar fraction NAPL phase Block [mg/g] [g/mole] 1/g NAPL 1 Aliphatics 72 226 0.3186 0.0638 2 EC < 11 24 107 0.2243 0.0449 3 EC11-EC13 124 162 0.7654 0.1532 4 EC13-EC15 372 190 1.9579 0.3918 5 EC15-EC18 311 225 1.3822 0.2766 6 EC18-EC23 98 281 0.3488 0.0698
concentration NAPL phase [mg/1] 57,600 19,200 99,200 297,600 248,800 78,400
Aromatics diminish going from Block 2 to Block 6. The solubility of the Aliphatics (Block 1) is the lowest. The equilibrium concentrations in the aqueous phase are comparable for Block 2, Block 3 and Block 3. This means that these Blocks leach out easiest followed by Block 5 and Block 6. For Block 1 it is the hardest to leach out. Initially, the content of the NAPL phase consists particularly of Block 4 and Block 5. The contribution of Block 2 is only slight.
Table 6 Partition coefficient of each Block solubility molar fraction
Block 1 Aliphatics 2 EC < 11 3 ECll-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
[rag/l] 0.000032 50.7 15.1 5.8 1.7 0.2
[1/g NAPL] 0.0638 0.0449 0.1532 0.3918 0.2766 0.0698
concentration water phase
concentration NAPL phase
partition coefficient
[rag/l] 2.04 10 .6 2.28 2.31 2.27 4.70 10 -1 1.40 10 .2
[mg/1] 57,600 19,200 99,200 297,600 248,800 78,400
[-] 3.54 1.19 2.33 7.64 1.89 1.78
10 -11 10 -4 10 .5 10 -6 10 .6 10 .7
2.6. Adsorption The mechanism of adsorption is described as a linear process. This means that the concentration dissolved in the aqueous phase is proportional to the concentration adsorbed at the solid phase. The proportionality factor is called the coefficient of distribution [9].
k . - c; Ca With, kd distribution coefficient [1/kg] C~ concentration adsorbed at the solid phase [mg/kg]
(8)
785 Ca~ concentration dissolved in the aqueous phase [mg/1] The distribution coefficient can be written as:
(9)
= f o c . koc
With, ka distribution coefficient between the aqueous phase and the solid phase [kg/1] foe mass fraction of organic carbon [-] ko~ partition coefficient of the solute in a granular medium of organic carbon [1/kg] So for adsorption the fraction of organic carbon (fo~) is relevant. At the site the mass fraction of organic matter (fo,~) is estimated as 0.03. The fraction organic carbon now can be calculated as: (10)
foc - fo~ / 1.7 - 0.03/1.7 ~ 0.018
Values for koc are derived from handbooks. The value for kd is used in the numerical model to calculate the retardation factor 1R which yields [9]"
R = 1 + p~ kd
1--rt
(11)
n
with, R retardation factor [-] p~ specific density of the solid material [kg/1] ke distribution coefficient between aqueous phase and solid phase [kg/1] n porosity of the porous medium [m3/m 3] Table 7 Adsorption and degradation for each Block of constituents
fo, Block 1 Aliphatics 2 EC
[l/kg) 8.90 102 1.78 102 2.00 102 5.01 103 8.91 103 2.24 10 4
[-] 0.03 0.03 0.03 0.03 0.03 0.03
kd [-] 0.018 0.018 0.018 0.018 0.018 0.018
[l/kg] 15.7 3.14 3.52 88.5 157. 395.
[l/day] 5.70E-01 3.00E-01 3.52E-02 9.60E-03 2.62E-03 1.95E-04
2.7. Biodegradation For the aqueous phase degradation is also taken into account due to biological activity. For the rate of degradation distinction is made between aerobic and anaerobic conditions. In practice, other conditions also affect the rate of degradation. However, for the site such detailed information is not available. Furthermore. the main objective for the current research is to implement the rate of depletion of constituents dissolved in the NAPL phase and transferred to the aqueous phase. Therefore as indication of the effect of biodegradation, values for anaerobic degradation were taken into account (Table 7). This information is used to estimate the rate of degradation kra for the six blocks. However, in practice the actual rate can be an order lower [10].
786 3. N U M E R I C A L
RESULTS
Several calculations are carried out as an example based upon data from the site. All the calculations started with a groundwater flow model. Each flow model is created with the computer code ModFlow [7]. The dimensions of the example are 510 m by 110 m by 4 in. In the horizontal plane (Figure 1), the number of grid cells is 69 (x-direction) by 29 (y-direction). In vertical direction only one layer is distinguished, which means that the calculation is two-dimensional. Due to a difference in groundwater head and the hydraulic conductivity, a horizontal flow of groundwater is created. The pore water velocity agrees with the value at the site (Table 2). In the example a source of NAPL is represented (Figure 1). The dimensions of the source area are 2 by 2 m. It is assumed that the presence of the source does not affect the flow of groundwater. So the groundwater flow is purely horizontal. Within the source area residual NAPL is present with a degree of saturation of 10 %. Based upon the dimensions of the source area and the degree of saturation of the NAPL, 0.480 m a NAPL is present in the source area. Together with the density of 800 kg/m a, the mass of NAPL amounts 384 kg.
Figure 1. Planar view of the situation
3.1. T w o b l o c k s of c o n s t i t u e n t s To gain information about the competition of blocks of constituents, the following calculation is carried out. Initially, only Block 2 (Aromatics E C < l l ) and Block 6 (Aromatics EC18-EC23) are present in the NAPL phase. The initial concentration equals 400 g/1 (400.000 rag/l) for both of them. Due to this initial concentration in the NAPL phase~ the molar fraction differs from the values given in Table 5 and Table 6. Looking to the effect of dissolution from the NAPL phase to the water phase (groundwater)~ the concentration of Block 2 in the NAPL phase diminishes, while at the same time the concentration of Block 6 increases (Figure 2)" enrichment. This enrichment is due to the difference in solubility: the solubility of Block 2 is about 150 times higher than the one of Block 6. The sum of both concentrations equals the density of the NAPL phase. Looking to the effect of dissolution into the water phase, initially the concentration in the aqueous phase equals the equilibrium concentration governed by Raoult~s law: compare the initial concentration of Figure 3 with the values of Table 10. At first instance, competition in dissolution takes place between Block 2 and Block 6. As soon as Block 2 is depleted in the NAPL phase, competition vanishes. Now the concentration in the NAPL
787
Table 8 Several properties of the different Blocks (only two Blocks are present in the NAPL phase)
Block 1 Aliphatics 2 EC < 11 3 EC11-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
mass NAPL phase ling/g] 0 500 0 0 0 500
molar weight [g/mole] 226 107 162 190 225 281
moles
molar fraction
0 4.673 0 0 0 1.779
1/g NAPL 0 0.724 0 0 0 0.276
concentration NAPL phase [mg/1] 0 400,000 0 0 0 400,000
Table 9 Partition coefficient for each Block (only two Blocks are present in the NAPL phase) solubility molar fraction concentration concentration partition water phase NAPL phase coefficient Block 1 Aliphatics 2 EC < 11 3 EC11-EC13 4 EC13-EC15 5 EC15-EC18 6 EC18-EC23
[rag/l] 0.000032 50.7 15.1 5.8 1.7 0.2
[1/g NAPL] 0 0.724 0 0 0 0.276
(Ca)
(On)
(Ca/On)
[rag/l] 0. 36.7 0. 0. 0. 0.0552
[rag/l] 0 400,000 0 0 0 400,000
[-] 3.54 1.19 2.33 7.64 1.89 1.78
10 -11
10 -4 10 -5 10 -6 10 -6 10 -7
788
Figure 2: Concentration of Block 2 and Block 6 in the NAPL phase in time.
Figure 3" Concentration of Block 2 and Block 6 in the water phase in the source area.
phase is enhanced and reaches the density of the NAPL (Figure 2) and the concentration of Block 6 in the water phase approaches its solubility of 0.20 rag/1 (Figure 3). It takes about 1.5 year for Block 2 to deplete. Due to the difference in solubility, it will take more then 225 year before Block 6 will be depleted. 3.2. Six B l o c k s of c o n s t i t u e n t s Subsequently, the calculation is repeated with all the six Blocks of constituents. The initial concentration of each block in the NAPL phase is based upon the content of the oil. The values for the solubility and the partition coefficients can be found in Table 6. Looking to the effect of dissolution from the NAPL phase to the water phase (groundwater), the concentration of Block 2 in the NAPL phase diminishes at first (Figure 5), followed by the concentration of Block 3 and Block 4 respectively. Within a time period of fifteen years, these three Blocks are leached out of the NAPL phase. Block 5 is leached out within thirty years. However, after thirty years Block 1 (Aliphatics) and Block 6 (Aromatics EC18-EC23) still are present within the NAPL phase. The concentration of the Aliphatics (Block 1) gradually increases in time during this time period of thirty years. Looking to the previous results with only two Blocks, it takes now about 8 years instead of 1.5 years for Block 2 to be depleted in the NAPL phase due to the competition with the other Blocks. The sum of the concentration of each Block in the NAPL phase is equal to the density of the NAPL. Therefore, this summation can be used as a check for the mass balance of the NAPL. For this situation, the total concentration needs to remain 800 kg/m 3 (Figure
4). Looking to the effect of dissolution into the water phase, competition now is taking place between the Blocks during the complete period of thirty years. Initially, the (equilibrium) concentrations of Block 2, Block 3 and Block 4 in the water phase are comparable (Figure 5). However, Block 2 is depleted at first, followed by Block 3 and then Block 4 due to their
789
Figure 4" Concentration development in the NAPL phase of the six Blocks.
Figure 5" Concentration of each Block in the water phase in the source area.
respective concentration in the NAPL phase. After thirty years, Block 5 and Block 6 still are present in the groundwater. However, the concentration of Block 1, the Aliphatics, does not reach 0.1 #g/l: even when all the Aromatics are leached out. This is a result of its low solubility of 0,032 #g/1.
3.3. Six Blocks of constituents" adsorption and degradation Subsequently, a calculation is carried out in which adsorption and degradation in the subsoil is taken into account. For each Block different values are incorporated (Table 7). The development of the concentration calculated for each block in the NAPL phase can be found in Figure 6. As expected, the initial concentration of Block 4 and Block 5 are comparable. Also the order in leaching is comparable. At first, Block 2 leaches out, then followed by Block 3, Block 4 and Block 5. After thirty years still Block 6 and Block 1 (Aliphatics) are present in the NAPL phase. Compared with the previous calculation in which neither adsorption nor degradation were taken into account, depletion of Block 2, Block 4 and Block 5 takes place earlier. After thirty years the contribution of Block 1 (Aliphatics) is slightly higher than the contribution of Block 6. So degradation in the subsoil stimulates also the process of leaching. The development of the concentration calculated in the aqueous phase in the source area can be found in Figure 7. Again the order in leaching is comparable. At first, Block 2 leaches out, followed by Block 3 and Block 4. After thirty years, only Block 1 (Aliphatics/, Block 5 and Block 6 are present within the aqueous phase. However, the concentration of Block 1 and Block 5 are below 1 #g/1. So only the concentration of Block 6 might be harmful for the environment. Compared with the previous calculation in which no adsorption nor degradation in the subsoil are present, the depletion of Block 2, Block 3 and Block 4 takes place faster and the concentration in the water phase after thirty years is lower for Block 5 and for Block 6. Looking to the development and extension of the plume of Block 6 dissolved in the groundwater, the following remarks can be made. The plume has reached stationary conditions. After thirty year, the highest concentration found in the centre of the plume
790
Figure 6: Concentration of each Block in the NAPL phase.
Figure 7: Concentration in the water phase for each Block (logarithmic scale) in the source area.
starts declining. The extension of the plume based upon the concentration level of one microgram per litre is about 250 m. 4. C O N C L U S I O N S
Taking the mass transfer between the NAPL phase and the aqueous phase into account, gives the ability to judge the fate and behaviour of this type of contamination in the subsoil. Therefore, the results of the calculations, together with measurements in the field, can be assessed from an environmental point of view. It can be concluded that the extended numerical code of RT3D gives the opportunity to determine the depletion of residual NAPL in the subsoil. This behaviour can be compared with formal regulations about the risk of migration. Taking into account the properties of the current situation at the particular site, it can be concluded that for relatively small oil spills of about 500 litres, natural processes will deplete the NAPL within a time period of thirty years. Whenever, the amount of spilled product is larger, much more time is needed before depletion of the oil results in concentrations in the water phase which are below national standards. REFERENCES
1.
2. 3.
F. Schwille, Migration of Organic Fluids Immiscible with Water in the Unsaturated Zone, In Pollution in Porous Media: The Unsaturated Zone Between Soil Surface and Groundwater, Ecological Studies, Volume 47, Springer Verlag, Berlin (1984) 27-48. T.K. Sherwood, R.L. Pigford, C.R. Wilke, Mass Transfer, McGraw Hill, New York (1975) C.T. Miller, M.M. Poirier-McNeill and A.S. Mayer, Dissolution of trapped non-aqueous phase liquids: Mass transfer characteristics, Water Resources Research, Vol. 26, No. 11 (1990) 2783-2796.
791 4. P.T. Imhoff, A. Frizzell, C.T. Miller, Evaluation of thermal effects on the dissolution of a NAPL in porous media, Environmental Science Technology, Vol. 31 (1997) 16151622. 5. J.C. Parker, A.K. Katyal and J.J. Kaluarachichi, Modeling multiphasc organic chemical transport in soils and groundwater, U.S. EPA, Ada, Oklahoma (1990). 6. T.P Clement, A Modular Computer Code for Simulating Reactive Multi-species Transport in 3-Dimensional Groundwater Systems, U.S. DoE, DE-AC06-76RLO 1830, PNNL, Richmond, Washington (1997). 7. M.G. McDonald and A.W. Harbaugh, A Modular Three-Dimensional Finite Difference Ground-Water Flow model, U.S.G.S. Techniques of Water Res. Inv., Book 6 (1988) 586. 8. C. Zheng, MT3D: A Modular Three-Dimensional Transport Model for Simulation of Advection, Dispersion and Chemical Reaction in Groundwater Systems, US EPA, Oklahoma (1990). 9. C. Zheng and G.D. Bennett, Applied Contaminant Transport Modeling: Theory and Practice, Van Nostrand Reinold, New York (1995) 440. 10. T.H. Wiedemeier, H.S. Rifai, C.J. Newell and J.T. Wilson, Natural Attenuation of Fuels and Chlorinated Solvents in the Subsurface, John Wiley &~ Sons, New York (1999) 617.