Environ. Sci. Technol. 1982, 16, 757-763
(11) Lentini, M.; Pereyra, V. SIAM J. Numer. Anal. 1977, 14, 91. (12) Faisst, W. K. Report 13, Environmental Quality Laboratory, California Institute of Technology: Pasadena, CA, 1976. (13) Neame, K. D.; Richards, T. G. “Elementary Kinetics of Membrane Carrier Transport”; Blackwell Scientific: London, 1971. (14) Smith, K. Limnol. Oceanogr. 1974,19, 939-944. (15) Hargrave, B. T. J. Fish. Res. Board Can. 1973, 30, 1317-1326. (16) Childress, J. J. Comp. Biochem. Physiol. A 1975, 50A, 781-799. (17) Muellenhoff, W. P. Ph.D. Thesis, Oregon State University, Corvallis, OR, 1977. (18) Sarmiento, J. L.; Feely, H. W.; Moore, W. S.; Bainbridge, A. E.; Broecker, W. S. Earth Planet. Sci. Lett. 1976, 32, 357-370. (19) Chen, K. V.; Jan, T. K.; Rohatgi, N. J. Water Pollut. Cont. Fed. 1974,46, 2663-2675. (20) Morel, F. M. M.; Westall, J. C.; O’Melia, C. R.; Morgan, J. J. Environ. Sci. Technol. 1975, 9, 756-761. (21) Rohatgi, N.; Chen, K. Y. J. Water Pollut. Cont. Fed. 1975, 47, 2298-2316. (22) Bruland, K. W.; Bertine, K.; Koide, M.; Goldberg, E. D. Environ. Sci. Technol. 1974,8,425-432. (23) Bertine, K. K.; Goldberg, E. D. Environ. Sci. Technol. 1977, 11, 297-299. (24) Fiadeiro, M.; Strickland, J. D. H. J. Mar. Res. 1968, 26, 187-201. (25) Goering, J. J.; Cline, J. D. Limnol. Oceanogr. 1970, 15, 306-309. (26) Berner, R. A. In “The Sea”; Goldberg, E. D. Ed.; Wiley: New York, 1974; Vol. V, Chapter 13.
(27) Sholkovitz, E. Geochim. Cosmochim. Acta 1973, 37, 2043-2073. (28) Cline, J. D.; Richard, F. A. Enuiron. Sci. Technol. 1969,3, 838-843. (29) Holm-Hansen, 0.Mem. Inst. Ital. Idrobiol. 1972,29 Suppl., 37-51. (30) Holm-Hansen, 0.; Strickland, J. D. H.; Williams, P. M. Limnol. Oceanogr. 1966,11, 548-561. (31) Boyle, E. A.; Sclater, F.; Edmond, J. M. Nature (London) 1976,263,42-44. (32) Morgan, J. J.;Sibley, T. H. Proc. Civil Eng. Oceans III 1975, 2, 1332-1352. (33) Boyle, E. A.; Sclater, F.; Edmond, J. M. Earth Planet. Sci. Lett. 1977, 37, 38-54. (34) Sclater, F. R.; Boyle, E.; Edmond, J. M. Earth Planet. Sci. Lett. 1976, 31, 119-128. (35) Bruland, K. W.; Knauer, G. A.; Martin, J. H. Nature (London) 1978,271, 741-743. (36) Hulsemann, J.; Emery, K. 0. J. Geol. 1961, 69, 279-290. (37) California State, The Resources Agency, State Water Resources Control Board, Resolution No. 78-12, 1978.
Received for review October 9,1981. Revised manuscript received July 13,1982. Accepted July 19, 1982. This paper reports on part of the ongoing research by Caltech’sEnvironmental Quality Laboratory on alternative practices for disposal of digested sewage sludge in the ocean. Support has been provided by the Ford Foundation (Grant No. 740-0469), the Rockefeller Foundation (Grant No. CA NES 7706), and a consortium of the County Sanitation Districts of Los Angeles County, the City of Los Angeles, and the County Sanitation Districts of Orange County since August 1977.
Initial Sedimentation of Waste Particulates Discharged from Ocean Outfalls Robert C. Y. Koh
Environmental Quality Laboratory, California Institute of Technology, Pasadena, California 9 1 125
A model is developed to evaluate the initial deposition of particles due to discharge of sewage sludge in the ocean. The three-dimensional sedimentation modeling shows that the sludge particles would be widely dispersed. The bottom initial fallout distribution is expected to be much elongated along the bottom contours due to nonisotropy of the ocean current. This is useful in assessing the environmental consequences of alternative strategies for ocean sludge disposal in southern California where offshore deep basins (depths to 900 m) are within short distances from shore (on order of 10-20 km). Introduction Disposal of human wastes, whether on land, in the ocean, or in the atmosphere, always involves an impact on the environment. Availability of deep water relatively close to shore has stimulated ocean discharge of sewage effluent and sludge in southern California. These discharge systems have adequately met the classical design criteria of maintaining aquatic oxygen concentrations and satisfying bathing water standards but have had documented effects on marine benthic ecosystems. While the significance of these ecological changes is not understood, federal policy is to stress land disposal and eliminate ocean disposal of sludge-generally a much costlier alternative which also 0013-938X/82/0916-0757$01.25/0
shifts direct environmental impact from the ocean to the land and the atmosphere. The treatment of the sewage produced by the 10 million people in the Los Angeles and Orange Counties area is predicted to produce (at full secondary treatment as presently mandated by law) 1145 dry tons of sludge per day. The Sanitation Districts of Los Angeles and Orange Counties and the City of Los Angeles organized an investigation known as LA/OMA (Los Angeles/Orange County Metropolitan Area Regional Wastewater Solids Management Program) to determine the optimal alternatives for sludge handling and disposal. Even though ocean discharge is not permitted, the Districts as well as the City felt it wise to include ocean discharge as an alternative to be studied. This paper describes one aspect of the study related to the ocean-discharge alternative. In particular it discusses the physical aspects of the fate of the particulates in sludge if it is discharged into the relatively deep ocean basins off southern California such as the Santa Monica-San Pedro Basin. For definiteness, it will be assumed that a pipeline is terminated at approximately 400 m depth, although the analysis is simiilar for other depths as well as other modes of discharge. The 400 m depth appears more favorable than deeper depths according to the biological modeling results given in Jackson and co-workers (1, 2).
0 1982 American Chemical Society
Envlron. Sci. Technol., Vol. 16, No. 11, 1982 757
When sludge first exists from a pipeline (whether or not equipped with a diffuser), it will undergo a phase of motion that is influenced by its momentum and buoyancy as well as the ambient current and density stratification. This phase typically lasts only a matter of minutes and results in a certain initial dilution and equilibrium height of rise. During this phase, the ambient conditions can be considered steady (since the time scale of changes in ambient conditions is on the order of hours), and the particulates can be assumed to be part of the discharged fluid (since fall velocities are very small). The phenomenon of flocculation may take effect during this time. However, no method is available to estimate its importance. Following this initial phase, the diluted mixture is advected and dispersed by the currents and turbulence in the ocean while the particulates slowly fall down (or float up, as the case may be). We shall not be concerned with the details of how the dispersion occurs on any given day but rather will attempt to estimate the longer term fallout pattern of the particulates when the effects are integrated over a long time (such as months and years). I t is clear that in order to do this, we must have the following information: (i) the fall velocities of the particulates; (ii) The ocean currents and density stratification near the site; (iii) the flow rate and other characteristics of the discharge. Unfortunately, we have little information on either the fall velocities or the currents. It is thus impossible to make reliable estimates. The best that can be achieved would be a parametric estimation of orders of magnitude. However, the method is demonstrated and shows how more input data would be used.
Formulation Consider a single particle of sludge with fall velocity w situated at position xo, yo, zo at time = 0 in an infinite quiescent ocean. We seek the probability density p(x, y,z,t;xO,yO,zO) such that p dxdydz is the probability of finding that particle in the interval x to x + dx, y to y + dy, z to z dz at time t. We assume stationarity and postulate that p is Gaussian of the form
+
1
(x
- xo)'
1
(20
- 2bt+ wt) exp
4mr,ay(m,t)1/2
(Y - YO)' --
{
--( x - x 0 l 2
[ZO - zb
}
- Wtl2
4EZt
2a:
-
2aX2
(3)
which relates to the probability that a particle with fall velocity w which was originally at xo,yo,zoat time t = 0 will get to the bottom at position x,y in time t. If, in addition, we know the distribution of heights g(zo) and fall velocities f(w), then the initial fallout distribution on the bottom is
where zo = H is at the water surface. Distribution of Initial Height g ( z o ) . To obtain an estimate of the distribution of initial height g(zo), we appeal to the body of literature on buoyant jets and plumes in a stratified fluid. We assume that the discharge is buoyancy dominated and use the results of Wright (3) to estimate the equilibrium rise height z,: (5) where lb
= g&O(@P)O/P)/u3
1, = u/[k/P)ldP/dzl11/2
Here u = current speed, p = receiving water density, (Ap), = difference in density between receiving water and effluent, Qo = discharge rate, and g = gravitational afceleration. From Wright, C12can be approximated by 1.8for all his data regardless of whether the experiment was buoyancy dominated near or far field. In addition, if there were no ambient current, we use the result based on buoyant plume theory (see, e.g., Fischer et al. ( 4 ) )
(Y - YOY \
where a, and yy are functions o f t only, a, = (2~,t)l/~, cz = vertical diffusion coefficient, and it has implicitly been assumed that x , y , z are along principal axes of the stochastic velocity field. In the present case, there is an ocean bottom given by z = zb(x,y). We now make the intuitive assumption that the relative rate of particle fallout on z = zb(x,y) is given by
Thus assumption is admittedly simplistic and is used only as a rough approximation. Physically it means that the probability p is unaffected by the bottom (i.e., the bottom is transparent to the particles) and that the fallout is given by the net downward vertical transport implied by p evaluated at z = zb Substitution of eq 1into eq 2 yields 758
E=
Environ. Sci. Technol., Vol. 16, No. 11, 1982
where CY is a numerical factor to account for the difference between equilibrium height and maximum height of rise. For application to the present problem, we use the following typical data (same as in Faisst (5), pp 119-120): Qo = 5 mgd
(Ap), = 24.5 X
g/cm3
and take CY = 0.8 for definiteness (mgd = million gallons/day). Equations 5 and 6 then reduce to z, = 46Q01/3(1/u)1/3 z, = 145Q01/4 (7) The value of zo that applies should be the smaller of the two. The value of Qo in eq 5 and 6 is subject to some control through design. For example, if ten (noninterfering) plumes result from a diffuser, the Qowould only be 0.5 mgd for each. By use of eq 5 and 6 and the current data measured in Santa Monica-San Pedro Basin, the distributions shown
-
INJECTION DEPTH OISTRIBUTIW
01 0.01
" " " 0.1 0.5 I 2
"
5
"
IO
~
+zo 30
rio
"
"
"
"
sa fin 70 eo+ 90 9s
" 98 99
" 39.9
1
95.99
%
