Environ. Sci. Technol. 2004, 38, 4627-4634
Modeling Crude Oil Droplet-Sediment Aggregation in Nearshore Waters M I C H A E L C . S T E R L I N G , J R . , * ,† JAMES S. BONNER,‡ CHERYL A. PAGE,‡ CHRISTOPHER B. FULLER,‡ ANDREW N. S. ERNEST,§ AND ROBIN L. AUTENRIETH† Environmental and Water Resources Division, Civil Engineering Department, Texas A&M University, College Station, Texas 77843-3136, Conrad Blucher Institute for Surveying and Science, Texas A&M UniversitysCorpus Christi, 6300 Ocean Drive, Corpus Christi, Texas 78412, and Environmental Engineering Department, Texas A&M UniversitysKingsville, Kingsville, Texas 78363
This paper describes a modeling approach that simulates changes in particle size distribution and density due to aggregation by extending the Smoluchowski aggregation kinetic model to particles of different density. Batch flocculation studies were conducted for clay, colloidal silica, crude oil, clay-crude oil, and silica-crude oil systems. A parameter estimation algorithm was used to estimate homogeneous collision efficiencies (RHOMO) for single-particletype systems and heterogeneous collision efficiencies (RHET) for two-particle-type systems. Homogeneous collision efficiency values (RHOMO) were greater for clay (0.7) and for crude oil (0.3) than for silica (0.01). Thus, clay and crude oil were classified as cohesive particles while silica was classified as noncohesive. Heterogeneous collision efficiencies were similar for oil-clay (0.4) and oil-silica (0.3) systems. Thus, crude oil increases the aggregation of noncohesive particles. Data from the calibrated aggregation model were used to estimate apparent first-order flocculation rates (K′) for oil, clay, and silica and apparent second-order flocculation rates (K′′) for oil and clay in oilclay systems and for oil and silica in oil-silica systems. For oil or clay systems, aggregation Damko¨ hler numbers ranged from 0.1 to 1.0, suggesting that droplet coalescence and clay aggregation can occur on the same time scales as oil resurfacing and clay settling, respectively. For mixed oil-clay systems, the relative time scales of clay settling and clay-oil aggregation were also within an order of magnitude. Thus, oil-clay aggregation should be considered when modeling crude oil transport in nearshore waters.
Introduction Crude oil is released in coastal waters through offshore exploration and production activities, petroleum pipeline * Corresponding author present address: U.S. Army Corps of EngineerssERDC, EP-E, 3909 Halls Ferry Rd., Vicksburg, MS 39180-6133; telephone: (601)634-2726; fax: (601)634-4844; e-mail:
[email protected]. † Texas A&M University. ‡ Texas A&M UniversitysCorpus Christi. § Texas A&M UniversitysKingsville. 10.1021/es035467z CCC: $27.50 Published on Web 07/24/2004
2004 American Chemical Society
and tanker transport, and natural seeps (1, 2). This crude oil is physically or chemically dispersed, primarily in the form of micron-sized droplets. In nearshore waters, oil droplets may aggregate with suspended sediment. Vetical transport of the oil is then altered due to changes in oil-sediment aggregate size and density. Oil-sediment aggregation effects on released oil transport and fate have been highlighted in a number of crude oil releases (3-7). In transport models, the effects of crude oil and sediment interactions have been ignored in most oil spill trajectory models or described using chemical partitioning in spilled oil fate models. For modeling purposes, ignoring crude oilsediment interactions may be appropriate in open ocean waters where suspended sediment concentrations are low and where high horizontal dispersion rates can quickly reduce released oil concentrations. However, in nearshore waters, suspended sediment concentrations are much greater than those in open ocean waters. In addition, the dilution rates may not be adequate due to low horizontal dispersion or large volumes of released oil. Conversely, while chemical partitioning models have been used for describing the fate of crude oil chemical constituents, this approach is inconsistent for describing crude oil droplet interactions with suspended sediment. Applying a particle aggregation model provides a more conceptually accurate approach to crude oil-sediment interactions in nearshore waters. A number of recent investigations have focused on various factors in the formation of crude oil droplet-sediment aggregates (8-13). However, an aggregation and transport model incorporating both changes in aggregate sizes and densities has not been employed. Ernest et al. (14) presented an aggregation and settling model in which multiple-sized sediment particles are described using a discretized particle size distribution. The work presented herein extends this model by incorporating a discretized density distribution to account for multiple particle densities. For a system of suspended sediment and crude oil, differences in aggregate density not only impact its vertical transport rate but also its direction of vertical transport and fate (i.e., resurfacing or deposition). Lee (8) notes that while some studies have linked oil-particle interaction with the physical transport of oil from the sea surface to the ocean bottom, other studies have attributed the added buoyancy contributed by the oil in the oil-clay aggregate to longer suspension periods in the water column. The objectives of this investigation were the following: (i) to calculate aggregation rates of oil droplets, clay aggregates, and silica particles; (ii) to calculate aggregation rates of oil droplets with clay and with silica; (iii) to compare the time scales of oil coalescence and resurfacing, of clay aggregation and settling, and of silica aggregation and settling; and (iv) to compare the time scales of oil-clay and oil-silica aggregation and vertical settling. To apply the aggregation model, an expression relating homogeneous (RHOMO) and heterogeneous (RHET) collision efficiency values to the observed collision efficiency (Robs) (15) was developed using a probabilistic approach. Values of RHOMO were determined experimentally for crude oil droplets, clay aggregates, and silica particles at different mean shear rates (Gm). Values of RHET were determined experimentally for crude oil-clay and crude oil-silica particle systems at Gm values and oilsediment ratios. Data from the calibrated aggregation model was used to estimate apparent first-order flocculation rates (K′) and apparent second-order removal rates (K′′) for free oil in oil-clay and oil-silica systems. VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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Methods Modeling Background. Since coagulation affects the distribution of particle settling rates, one must consider coagulation and settling simultaneously to describe sedimentation kinetics. For a settling column, the dynamic equation for the particle size distribution is described by the following (14, 16, 17):
dnk,q ∂2nk,q ∂nk,q ) Dz 2 - wk,q + θk,q dt ∂z ∂z
(1)
where nk,q is the particle size distribution, given as the number concentration of particles (number cm-3) as a function of particle volume k (cm3) and effective density q (g cm-3); z is the vertical distance from the top of the water column (cm); Dz is the vertical dispersion coefficient (cm2 s-1); wk,q is the settling velocity (cm s-1) of particle volume k and effective density q; and θk,q is the interaction term (number cm-3 s-1) due to coagulation. In a system of primary particles or aggregates with two different densities (Fp1 and Fp2), particles or aggregates of densities o and p (Fo and Fp) can be calculated using the following:
Fo ) (1 - eo)(x1,oFp1 + x2,oFp2) + eoFH2O
(2a)
Fo ) (1 - ep)(x1,pFp1 + x2,pFp2) + epFH2O
(2b)
where eo is the porosity of particle of density o, ep is the porosity of particle of density p, FH2O is the water density, x1,o is the volume fraction of Fp1 in particle of density o (vp1/vo), x1,o is the volume fraction of Fp1 in particle of density o (vp2/ vo), x1,o is the volume fraction of Fp1 in particle of density p (vp1/vp), and x1,p is the volume fraction of Fp1 in particle of density p (vp2/vp). The effective particle density (q) (floc density) can be calculated using the following:
Fq(o,p) ) xoFo + xpFp
(3)
where xo and xp are the volume fractions of particle types o () vo/vq) and p () vp/vq), respectively. In this analysis, aggregate density is assumed constant with size (i.e., no increase in floc porosity due to increased aggregate size). The settling velocity is assumed to follow Stokes law; therefore
wk,q )
Cc(Fq - FH2O)dk2g 18µ
(4)
where Cc is the Cunningham slip factor () 1 in water), µ is the fluid viscosity (g cm-1 s-1), dk is the effective spherical diameter (cm), and g is the gravitational constant (981.0 cm2 s-1). The interaction term (θk,q) represents the particle contact mechanisms of Brownian motion, fluid shear, and differential sedimentation. It is represented by the following relationship:
θk,q )
1
∑
2 Mi,o+Mj,p)Mk,q
Robs(o,p)β(i,j,o,p)ni,onj,p cdensity csize
nk,q
∑ ∑R
obs(o,p)β(i,k,o,q)ni,o
(5)
o)1 i)1
where i, j, and k denote volume categories; o, p, and q denote effective density categories; cdensity and csize are the maximum number of density and volume categories; ni,o, nj,p, and nk,q are the number concentration of particle volumes i, j, and k and of effective particle densities o, p, and q; Robs is the observed collision efficiency function (i.e., number of effective 4628
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collisions/number of total collisions), which depends on the interparticle surface forces; and β is the collision frequency function, which depends on the mode of interparticle contact. Equation 5 is a system of discrete, nonlinear differential equations. The first term on the right-hand side of eq 5 sums the rate of formation of particles of k-volume and q-density classes from all collisions of particles smaller than the k-volume particles. The summation is over all volume classes i and j and all density classes o and p such that the mass of the sum of the i-volume, o-density particle and of the j-volume, p-density particle equals the mass of the k-volume, q-density particle:
Mk,q ) Mi,o + Mj,p
(6)
In the particle conjunction represented by eq 6, mass is conserved. The second set of summation terms reflects the loss of k-volume and q-density aggregates as they combine with all other aggregate sizes to form larger aggregates. The collision frequency function in eq 5 is given by the sum of the individual collision frequencies (14, 16, 17):
β ) βBr,ij + βsh,ij + βds,ijop βBr,ij )
(
)
2kT 1 1 + (d + dj) 3µ di dj i
βsh,ij )
Gm (d + dj)3 6 i
|
|
π βds,ijop ) (di + dj)2 (wi,o - wj,p) 4
(7)
where βBr,ij is the collision efficiency due to Brownian motion, βsh,ij is the collision efficiency due to fluid shear, and βds,ijop is the collision efficiency due to differential sedimentation. The observed collision efficiency (Robs) is defined operationally as the ratio of the actual number of “successful” aggregations to the number predicted in conditions without electrostatic repulsion or hydrodynamic impedance (15). This parameter describes the effects of the electrostatic energy barrier in reducing successful collisions. In previous studies of single-particle-type systems (14, 16, 17), collision efficiency values for a given particle type were assumed constant with size. In systems of two particle types, aggregates are composed of both particle types. Between composite aggregates, observed collision efficiency is defined by the sum of probabilities of successful surface interactions, i.e.,
Robs(o,p) ) RHOMO,1(sf1,o)(sf1,p) - RHOMO,2(sf2,o)(sf2,p) RHET,1-2(sf1,osf2,p - sf1,psf2,o) (8) where sf1,o, sf2,o, sf1,p, and sf2,p are surface fractions of constituent particles 1 and 2 in aggregate with density o and constituent particles 1 and 2 in aggregate with density p, respectively. The coefficients RHOMO,1, RHOMO,2, and RHET are probabilities of successful aggregation through contacts of floc constituent types 1-1, 2-2, and 1-2, respectively. Equation 8 can also be viewed as a weighted average of aggregation probabilities based on the fraction of constituent particles in each pair of aggregating flocs. Assuming that the surface fraction of particle constituents is proportional to their volume fraction, eq 8 can be written as the following:
Robs(o,p) ) RHOMO,1(x1,o)(x1,p) - RHOMO,2(x2,o)(x2,p) RHET,1-2(x1,ox2,p - x1,px2,o) (9) where x1,o, x2,o, x1,p, and x2,p are volume fractions of constituent particles 1 and 2 in aggregate with density o and constituent particles 1 and 2 in aggregate with density p, respectively.
TABLE 1. Single-Particle-Type Studies: Experimental Design for Estimating Homogeneous Collision Efficiency in Synthetic Seawater experiment name
mean shear rate (Gm, s-1)
particle type
particle loading (mg/L)
particle loading (µL/L)
K′ (s-1)
r2
rHOMO
MSSRR
G05_Oil12 G20_Oil12 G35_Oil12 G50_Oil12 G05_Cl08 G20_Cl08 G35_Cl08 G50_Cl08 G05_Si08 G20_Si08 G35_Si08 G50_Si08
5.0 20.0 35.0 50.0 5.0 20.0 35.0 50.0 5.0 20.0 35.0 50.0
crude oil crude oil crude oil crude oil clay clay clay clay silica silica silica silica
12.5 12.5 12.5 12.5 8.3 8.3 8.3 8.3 8.3 8.3 8.3 8.3
14.0 14.0 14.0 14.0 4.9 4.9 4.9 4.9 3.5 3.5 3.5 3.5
1.25E-04 5.17E-04 9.63E-04 1.25E-03 1.82E-04 8.25E-04 1.21E-03 1.60E-03 8.33E-06 2.83E-05 6.50E-05 9.33E-05
0.96 0.92 0.93 0.93 0.95 0.95 0.99 0.97 0.93 0.95 0.97 0.91
0.25 0.22 0.28 0.24 0.77 0.78 0.77 0.76 0.01 0.01 0.01 0.01
0.14 0.09 0.16 0.13 0.17 0.13 0.14 0.08 0.22 0.18 0.07 0.20
The volume fractions of constituent particle 1 and particle 2 in an aggregate with density o is calculated by the following:
Fo - F2 F1 - F2
(10a)
x2,o ) 1 - x1,o
(10b)
x1,o )
In this description of aggregation, the following assumptions have been made: (i) only binary collisions of particles are considered; (ii) particle breakup is neglected; (iii) particles before and after each aggregation are spherical; (iv) particles approach one another on rectilinear paths, the path of one particle not being affected by the presence of another; (v) collision functions for Brownian motion, fluid shear, and differential settling are additive; (vi) flocs of a given density class do not vary with aggregate size, and (viii) RHOMO and RHET are constant with particle size. Apparent Aggregation Rates. A characteristic of a flocculation experiment is the reduction in the number of particles over time. To estimate first-order aggregation rate constants (K′) in a shear reactor, the initial rate of change in total particle concentration (C(t)) with time (t) due to shear aggregation is given by
dC(t) ) -K′C(t) dt
(11)
The solution of the differential eq 11 is given by eq 12:
ln
( )
C ) -K′t C(0)
(12)
where C(0) is the initial number concentration. K′ is determined for these data sets through linear regression of the left-hand side of eq 12 versus time. Values for the total particle number C(t) are related to the moment of the size distribution: Cvolume
Cq )
∑n
k,q
(13)
k)1
For single-particle-type systems, nk,q values are taken directly from particle size measurements. For a single-particle-type batch system, total particle volume Vq remains constant. A second-order rate expression is used to estimate the loss of “free” oil droplets to aggregation with sediment flocs in a two-particle type mixed batch system:
roil loss )
dVoil ) -K′′Voil(V - Voil) dt
(14)
If Voil ) [A] and V - Voil ) [B], then the solution of the differential eq 14 is given by eq 15:
(
)( )
[A]o[B] 1 ln ) -K′′t [B]o - [A]o [A][B]o
(15)
Initial volume concentrations in eq 15 are indicated by the subscript o. Second-order rate constants (K′′) are determined through linear regression of the left-hand side of eq 15 versus time. Summary of Experimental Methods. To estimate homogeneous and heterogeneous collision efficiency values, a series of batch mixing experiments were conducted. More detailed descriptions of reagents, experimental apparatus have been presented previously (17). In the experiments, a 40-L batch-mixing tank was used to measure changes in particle size distribution (PSD) under different experimental conditions. In the experiments, PSD was measured in situ using a light scattering particle size analyzer (LISST100, Sequoia Instruments, Bellevue, WA), and ex situ using an electronic particle counter (Sampling Stand II and Multisizer, Coulter Electronics Limited, Hialeah, FL). Using this tank and artificial seawater (Instant Ocean, Aquarium Systems, Mentor, OH), a series of experiments was performed to measure changes in PSD of bentonite clay, colloidal silica, chemically dispersed crude oil, clay-crude oil, and silica-crude oil systems. For at least 12 h before each experiment, the clay, silica, or oil was soaked in aliquots of synthetic seawater to limit surface charge evolution during the experiment. An initial set of experiments (Table 1) was conducted to determine the effects of particle type (crude oil, clay, or silica) and mean shear rate (Gm) on homogeneous collision efficiency (RHOMO) and apparent first-order collision rate (K′). A second set of experiments (Table 2) was conducted to determine the effects of sediment type (silica, clay) and Gm on heterogeneous collision efficiency (RHET) and apparent second-order collision rates (K′′) of silica or clay and crude oil in a sedimentcrude oil system. The third set of experiments (Table 2) was conducted to determine effects of sediment-crude oil concentration ratios on heterogeneous collision efficiency (RHET) and K′′. Parameter Estimation Procedure. In this research, 24 data sets were used for estimating values of Robs in eq 5. Values of the remaining parameters remained constant (Table 3). The raw Coulter Counter data, which has 256 size categories, was compressed to 32 size-discretized categories to reduce computational effort (14). The Newton Rhapson method implemented in the nonlinear parameter estimation algorithm PARMEST (18) was used in this simulation to find the optimum value of Robs. The optimum value was defined as that which coincided with the minimum squared VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Mixed Oil-Sediment Systems: Experimental Design for Estimating Heterogeneous Collision Efficiency in Synthetic Seawater experiment name
mean shear rate (Gm, s-1)
sediment type
G05_Cl08_ Oil12 G20_Cl08_ Oil12 G35_Cl08_ Oil12 G50_Cl08_ Oil12 G05_Si08_ Oil12 G20_Si08_ Oil12 G35_Si08_ Oil12 G50_Si08_ Oil12
5.0 20.0 35.0 50.0 5.0 20.0 35.0 50.0
clay clay clay clay silica silica silica silica
G20_Cl08_Oil06 G20_Cl08_Oil01.3 G20_Si08_Oil06 G20_Si08_Oil01.3
20.0 20.0 20.0 20.0
clay clay silica silica
sediment:oil volume ratio
K′′ (mL µm-3 s-1)
r2
rHET
MSSRR
Effects of Mean Shear Rate 8.3 12.5 8.3 12.5 8.3 12.5 8.3 12.5 8.3 12.5 8.3 12.5 8.3 12.5 8.3 12.5
1:3 1:3 1:3 1:3 1:4 1:4 1:4 1:4
6.59E-11 2.47E-10 5.52E-10 1.01E-09 8.53E-11 3.50E-10 6.14E-10 1.08E-09
0.96 0.91 0.94 0.94 0.94 0.96 0.94 0.95
0.61 0.55 0.63 0.58 0.38 0.41 0.38 0.39
0.13 0.17 0.23 0.22 0.13 0.13 0.21 0.10
Effects of Sediment:Oil Ratio 8.3 6.2 8.3 1.3 8.3 6.2 8.3 1.3
2:3 6:1 1:2 5:1
2.39E-10 2.53E-10 3.37E-10 3.46E-10
0.96 0.96 0.98 0.94
0.62 0.64 0.44 0.46
0.14 0.18 0.15 0.16
sediment loading (mg/L)
TABLE 3. Fixed Parameters for Estimating robs Values in Particle Aggregation Model parameters
values
absolute temperature (T) density of water (Fw) dynamic viscosity (µ) density of weathered crude oil density (wet) of silica density (wet) of clay
293 K 1.0 g cm-3 1.04 × 10-2 g cm-1 s-1 0.9 g cm-3 3.0 g cm-3 2.4 g cm-3
sum of the relative residuals (MSSRR) (18). The MSSRR is defined as
MSSRR )
1
N
∑
N i)1
( ) yˆi - yi yi
2
(16)
where N is the total number of observations, yˆi and yi are the predicted and the observed number concentrations (no. of particles cm-3) of each size and density class at each time of the ith observation, respectively. In the single-particletype experiments, RHOMO values were equivalent to those of Robs. In the mixed oil-sediment experiments, RΗΕΤ values were derived using eq 9 with RΗΟΜΟ,1 and R ΗΟΜΟ,2 values taken from the results of single-particle-type experiments. All computer simulations for the parameter estimations were compiled with Lahey Fortran 95 and performed on an Dell personal computer equipped with an Intel Pentium 4 CPU 2.0GHz.
Results and Discussion Single-Particle-Type Aggregation. Using inverse parameter estimation and the flocculation model (eq 5), RHOMO values for silica, clay, and crude oil were estimated (Table 1). For a given particle type, RHOMO values remained relatively constant within the mean shear rates tested, supporting the assumption that RHOMO is primarily a function of particle surface chemistry. Additionally, for oil, silica, and clay, RHOMO values were significantly different from each other. The average RHOMO value for silica (0.01) was an order of magnitude lower than that of clay (RHOMO ) 0.7) or oil (RHOMO ) 0.3) aggregation, as predicted by the first-order flocculation rates. These results were consistent with the characterization of silica as a nonflocculating sediment and of clay as a cohesive sediment (19, 20). Because of the influences of water chemistry and ionic strength (15), these collision efficiency values are strictly applicable in seawater solutions only. However, the estimated RHOMO values for clay and oil were similar to those obtained by others for coagulation in seawater solutions (21-23). 4630
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oil loading (mg/L)
Surface chemistry is the primary cause of different RHOMO values for clay, oil, and silica particles. Clay particles have a weak negative charge and are attracted to the polarized water molecules, which attract more clay particles (24). This attraction results in a strong cohesion between clay particles (24) and a relatively high RHOMO value. Oil droplets are cohesive in aqueous systems because of hydrophobic attraction (25). Theoretical and experimental studies indicate that the reorientation, or restructuring, of water around nonpolar surfaces is entropically very unfavorable, since it disrupts the existing water structure and imposes a new and more ordered structure on the surrounding water molecules (25). Under the chemical conditions of this study, negatively charged silica particles tend to repel each other (19). Thus, silica particles have a low RHOMO value. Table 1 lists K′ values for experiments with different mean shear rates Gm and single-particle systems (oil droplets, clay, or colloidal silica). In general, increased shear rates resulted in more rapid flocculation (larger absolute value of K′). Significant differences in K′ values likely resulted from differences in particle collision efficiencies (RHOMO). At higher shear rates, collision frequency increased, thus increasing the opportunity for a “successful” collision to occur. However, a lower K′ magnitude suggests a lower collision efficiency (RHOMO) for flocculation. Assuming equal collision frequencies at a given Gm, the RHOMO value for silica is significantly less than those for crude oil droplets or clay. The flocculation parameters (RHOMO and K′) determined from these experiments are useful themselves in estimating rates of resurfacing of entrained crude oil or resedimenting of suspended sediment in coastal areas. Additionally, RHOMO values for clay, silica, or oil systems were used as constants in the multi-particle aggregation model. Sediment-Oil Aggregation. As with single-particle-type systems, the K′′ values (Table 2) for these two particle-type experimental groups increase linearly with increasing mean shear rate. However, the estimated RHET values (Table 2) for oil-clay aggregates and oil-silica aggregates are approximately constant for a given sediment-oil system. This was somewhat surprising because of the radically different aggregation efficiencies of silica (RHOMO ) 0.01) and clay (RHOMO ) 0.7) systems. Because the RHOMO value of crude oil systems (RHOMO ) 0.3) is equal to that of oil-clay aggregates and oil-silica aggregates, it appears that the oil portion of mixed aggregates increase their overall aggregation. Table 2 also lists the effects of relative oil-sediment concentration on RHET values. Relative sediment-oil volumes (Table 2) ranged from 1:4 to 6:1. The relative consistency in the estimated RHET values suggests the probabilistic formulation of Robs is consistent with the experimental data for a
range of sediment-oil ratios. The formulation of Robs (eq 9) relates the relative volumes of oil and silica or clay in an aggregate, RHOMO values of oil and silica or clay, and RHET values for oil-silica or oil-clay interactions. Because the volume fraction of oil-silica or oil-clay are fixed for each size and density class in the aggregation model and RHOMO values are estimated from single-particle-type experiments, only RHET values can vary when estimating values of Robs. Thus, changing values of RHET with changing oil-sediment ratios would suggest that the formulation was inconsistent with the parameters estimated using measured distributions. This would be especially evident in oil-silica systems, where the RHOMO values of oil and silica differ by an order of magnitude. Consequently, the underlying assumption of eq 9, the ratio of aggregate constituents on the surface is equal to the ratio of the constituent volumes in the aggregate, seems valid. The validity of this assumption suggests that the surface character of sediment-oil aggregates was not disproportionately impacted by the oil or sediment constituents. This result may be due partially to the relative sizes of the sediment and oil droplets (26). In this study, the mean diameters of oil droplets and clay aggregates were approximately equal in the single-particle studies. The silica particles were larger than the oil droplets. For the formation of solid-stabilized emulsions, researchers have recommended that the solid particles are less than 1/10 the volume of the liquid droplets (26). The order in which the crude oil and sediment were mixed (26) may also be important in not creating stable dispersions. In surf washing, sediment is added to a crude oil dispersion (8). In this study, the oil was added to a sediment dispersion to simulate the effects of a crude oil spill in a coastal system. Further studies can be conducted to test the effects of the order of constituent addition on observed collision efficiencies. Sediment-Oil Aggregation Model: Time Series Data. Figure 1a,b illustrates a representative time series of particle size distributions in a mixed clay-oil system in terms of number concentrations (Figure 1a) and volume concentrations (Figure 1b). In Figure 1a, the number of small aggregates decreases with time while the total number of larger aggregates increases. However, because the formed aggregates are larger and distributed over a broader size range, the increase is not as obvious in Figure 1a. The formation of larger aggregates is observable in the time series of particle volume distributions (Figure 1b). The area under each of the size distribution curves corresponds to the total particle volume in the reactor. As the area corresponding to the smaller particles decreases with time, the area corresponding to the larger particles increases. In both cases, clear correspondence between predicted and observed concentration data is highlighted. Figure 2a-c shows the formation of oil-clay aggregates as calculated using experimentally measured R values and eq 5. The density range has been discretized into four equally spaced bins with midpoints of 0.9, 1.4, 1.9, and 2.4 g cm-3, corresponding to aggregate clay volume fractions of 0.0-0.25, 0.26-0.50, 0.51-0.75, and 0.76-1.00, respectively. The total particle volume (Vq) in a given density class q is calculated as the following: cvolume
Vq )
∑n
k,qvk
(17)
k)1
where vk is the median particle volume in size class k. The total particle volume of a given density at a given time was calculated by integrating eq 5 for each size and volume class and using the resulting nk,q values in eq 17. Figure 2a-c illustrates the effects of initial oil-clay ratios on the formation of oil-clay aggregates with dif-
FIGURE 1. Time series of particle number and particle volume concentrations in a batch reactor (G20_Cl08_Oil12). Solid lines represent model-predicted particle distributions; open symbols represent experimentally measured particle distributions. ferent densities. In all cases, the volume fractions of particles with densities 0.9 and 2.4 decrease over time as clay and oil aggregate to form flocs with intermediate densities 1.4 and 1.9. The volume fractions with intermediate densities increased at approximately equal rates. For cases G20_Cl08_Oil12 and G20_Cl08_Oil06, the combined volume fraction of intermediate densities is greater than the combined volume fraction of the initial particle densities at 30 min. For the case G20_Cl08_Oil01.3, the combined volume fraction of intermediate densities remains smaller than the combined volume fraction of the initial particle densities at 30 min. This was due in part to the larger mean volume of oil droplets, which resulted in oil-clay aggregates with a higher oil fraction. Figure 3a-c shows the formation of oil-silica aggregates as calculated using experimentally measured R values and eq 5. The density range has been discretized into four equally spaced bins with midpoints of 0.9, 1.6, 2.3, and 3.0 g cm-3, corresponding to aggregate silica volume fractions of 0.0-0.25, 0.26-0.50, 0.51-0.75, and 0.76-1.00, respectively. In all cases, the volume fractions of particles with densities 0.9 and 3.0 decrease over time as silica and oil aggregate to form flocs with intermediate densities 1.6 and 2.3. As with the oil-clay systems, the volume fractions with intermediate densities increased at approximately equal rates. For cases G20_Si08_Oil1.3, G20_Si08_Oil06, and G20_Si08_Oil012, the combined volume fraction of intermediate densities is greater than the combined volume fraction of the initial particle densities at 30 min. In experiment G20_Si08_Oil01.3, the oil fraction has nearly been removed. Comparison of Aggregation and Settling Time Scales. To estimate the relative influences of settling velocity and particle aggregation, the time scales of each process was VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Formation of clay oil aggregates of different densities at different initial oil-clay ratios in a batch reactor: (a) G20_Cl08_Oil12, (b) G20_Cl08_Oil06, and (c) G20_Cl08_Oil01.3. compared. First, using eq 13, eq 1 is written in terms of total number concentration C with density q:
∂2 C q ∂Cq dCq ) Dz 2 - wk,q + K′Cq dt ∂z ∂z
(18)
The nonlinear aggregation kinetic expression has been replaced with a first-order rate expression (eq 11). Equation 18 is nondimensionalized by letting ψq ) Cq/Cq(0), ζ ) z/Z, and τ ) twk,q/Z:
dψq Dz ∂2ψq ∂ψq K′ψqZ ) + dτ wavg,qZ ∂ζ2 ∂ζ wavg,q
(19)
where Z is a characteristic depth, and wavg,q is the volumeaveraged particle settling velocity as defined in the following:
wavg,q )
1 Vq
cvolume
∑w
k,qvk
(20)
k)1
For this case, Z is specified as 2 m, the mixed layer depth of a coastal estuary. Experimentally, this situation can be approximated using a 2 m settling column. The quantity (K′Z/wavg,q) appearing in eq 19 is called the Damko¨hler number for convection (Da) and physically represents the ratio
Da )
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settling time scale(τset) aggregation time scale(τagg)
)
aggregation rate ) settling rate Z K′ (21) wavg,q
( )
ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 38, NO. 17, 2004
Similarly, the relative influences of settling velocity and oilsediment aggregation in “free” oil removal were estimated by comparing the time scales of each process. While the time scale of settling is calculated as in eq 21, the aggregation time scale for free oil removal (τagg) was calculated using
τagg )
1 K′′[B]o
(22)
where K′′ and [B]o are as defined in eqs 14 and 15, respectively. If Da , 1, then particle settling rates are much faster than the aggregation rates and particle aggregation can be ignored with negligible error. Da numbers for single particle type systems (Figure 4a) and for oil-sediment systems (Figure 4b) have been calculated for a range of Gm values. For both single- and mixed-particle-type systems, Da numbers increased with increasing Gm values. This increase corresponded with increased aggregation rates. Da numbers for oil, clay, and oil-clay systems ranged from 0.1 to 1.0, suggesting that aggregation and settling occur on the same time scale under the prescribed conditions. Conversely, Da numbers for silica systems ranged from 0.0001 to 0.001 and for oil-silica systems ranged from 0.01 to 0.1. These results suggest that silica aggregation and oil-silica aggregation both occur more slowly than aggregate settling. As oil-clay and oil-silica aggregation rates are comparable, differences in aggregation Da numbers result from differences in aggregate settling velocity. In this study, clay particles (vmd ) 20 µm, F )2.4 g cm-3) have a smaller volume mean diameter (vmd) and are less dense than silica particles (vmd ) 50 µm, F ) 3.0 g cm-3). Because of the higher settling velocity of silica particles
FIGURE 3. Formation of silica oil aggregates of different densities at different initial oil-silica ratios in a batch system: G20_Si08_Oil12, (b) G20_Si08_Oil06, and (c) G20_Si08_Oil01.3. relative to clay, the removal of oil by silica is less efficient than that by clay. The settling velocity used in the model is assumed to follow Stokes law. Significant deviations from Stokes law settling velocities have been reported due to real world complexities such as particle shape and hindered settling. The degree of sphericity of aggregates in this paper has been presented in a previous work (17). Most of the aggregate types were approximately spherical at the shear rates studied (17) and small enough to satisfy the Stokes law requirement that the particle Reynolds number (Rep) is less than 1. However, at lower shear rates, clay aggregates become increasingly nonspherical, their settling rates generally described using a modified Stokes settling (27). Additionally, larger aggregates may form under longer aggregation periods. As their Rep is greater than 1, a two-equation settling model would be required (28). Hindered settling results from particle concentration or charge effects. One type of hindered settling occurs when the concentration of settling particles is high enough to affect the viscosity of the aggregate-water dispersion. In this study, hindered settling effects can be ignored throughout most of the water column as the initial particle concentrations by volume are less than 0.002% in all experiments. However, as the particle concentration near the bottom boundary increases over time, hindered settling expressions may be required to estimate aggregate settling near that boundary. Hindered settling can be modeled by multiplying the Stokes settling velocity (eq 4) by a correction factor [2ψp] (29), where is the volume fraction occupied by water and ψp )101.82(-1).
A second type of hindered settling is a product of the negative charge of the aggregate. Aggregate sedimentation results in the concentration of negatively charged aggregates near the bottom of the water column. The magnitude of the ionic concentration polarization determines the reduction in settling rate, as the osmotic pressure resulting from aggregate surface charge counters the aggregate sedimentation. As with the particle concentration effect, hindered settling due to charge accumulation is limited to a boundary effect in this study. Comparing time scales of settling and aggregation can provide insights into the relative influence of each process in sediment and pollutant transport. However, this simplified process is limited to systems in which the vertical dispersion term of the advection-dispersion-reaction equation is smaller than the advection and reaction terms. This condition can occur in estuaries when aggregate concentrations are vertically well mixed (dC/dz ) 0) or follow a near linear gradient (dC/dz ) constant). In either case, the dispersion term (Dz[d2C/dz2]) is approximately zero. As with experimental column settling studies, this analysis assumes that horizontal dispersion terms (Dx[d2C/dx2]) or (Dy[d2C/dy2]) are negligible relative to other transport and reaction terms. While this assumption may not be applicable in open ocean systems, this type of analysis may be reasonable for enclosed coastal bays or estuarine systems, for large oil releases, or for other aquatic systems with significant oil reentrainment or sediment resuspension. Overall, the presented aggregation model can be used to study a number of problems related to sediment and oil VOL. 38, NO. 17, 2004 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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(5) (6) (7) (8) (9) (10) (11) (12) (13)
(14) (15) (16)
(17) (18)
FIGURE 4. Effect of shear on aggregation Damko1 hler (Da) number for oil in two particle type systems in a 2 m settling column. aggregation and transport. Natural oil-clay flocculation after a crude oil release has been termed surf washing and is of interest in the spill responder community. Additionally, the transport and fate of physically or chemically dispersed crude oil droplets in coastal environments can be more accurately modeled by including potential interactions with suspended sediments. Accurately describing each of the above scenarios is important in understanding ecological risks presented by natural crude oil seeps or by response countermeasures to an oil spill.
Acknowledgments We thank our funding agencies: the Texas General Land Office (Robin Jamail) and Texas Water Research Institute for supporting this project.
Literature Cited (1) National Research Council (NRC). Oil in the Sea III: Inputs, Fates, and Effects; National Academy Press: Washington, DC, 2003. (2) Anderson, C. M.; LaBelle, R. P. Update of comparative occurrence rates for offshore oil spills. Spill Sci. Technol. Bull. 2000, 6 (5/6), 303-321. (3) Page, C.; Bonner, J. S.; Sumner, P. L.; McDonald, T. J.; Autenrieth, R. L.; Fuller, C. B. Behavior of a chemically-dispersed oil and a whole oil on a near-shore environment. Water Res. 2000, 34 (9), 2507-2516. (4) Bragg, J. R.; Yang, S. H. Clay-oil flocculation and its role in natural cleansing in Prince William Sound following the Exxon Valdez 4634
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Received for review December 29, 2003. Revised manuscript received June 7, 2004. Accepted June 9, 2004. ES035467Z
