EPA-600/2-81-195
                                              September 1981
     REMOVING WATER-SOLUBLE HAZARDOUS MATERIAL SPILLS

                FROM WATERWAYS WITH CARBON


                             by

                   George  R.  Schneider
                  Rockwell International
        Environmental  Monitoring & Services Center
              Newbury Park, California 91320
                 Contract No. 68-03-2648
                     Project  Officer

                     John E.  Brugger
         Oil  &  Hazardous Materials Spills Branch
        Solid & Hazardous Waste Research Division
Municipal Environmental Research Laboratory - Cincinnati
                     Edison, N.J. 08837
        MUNICIPAL ENVIRONMENTAL RESEARCH LABORATORY
             OFFICE OF RESEARCH AND DEVELOPMENT
           U.S.  ENVIRONMENTAL PROTECTION AGENCY
                  CINCINNATI, OHIO 45268

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                                 DISCLAIMER


     This report has been reviewed by the Municipal Environmental Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommendation for use.
                                       11

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                                  FOREWORD
     The U.S. Environmental  Protection Agency was created because of increas-
ing public and government concern about the dangers of pollution to the health
and welfare of the American  people.  Noxious air, foul water, and spoiled land
are tragic testimonies to the deterioration of our natural  environment.  The
complexity of that environment and the interplay of its components require a
concentrated and integrated  attack on the problem.

     Research and development is that necessary first step in problem solu-
tion; it involves defining the problem, measuring its impact, and searching
for solutions.  The Municipal Environmental Research Laboratory develops new
and improved technology and  systems to prevent, treat, and manage wastewater
and solid and hazardous waste pollutant discharges from municipal and commun-
ity sources, to preserve and treat public drinking water supplies, and to min-
imize the adverse economic,  social, health, and aesthetic effects of pollution.
This publication is one of the products of that research and provides a most
vital communications link between the researcher and the user community.

     This report presents an analysis of the use of in-situ activated carbon
and other adsorbants for the removal  of spilled, water-soluble hazardous sub-
stances from waterways.  The report will  be of interest to all those involved
in hazardous materials spill control  and countermeasures.
                                      Francis T.  Mayo, Director
                                      Municipal  Environmental  Research
                                      Laboratory

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                                  ABSTRACT
     A model for the removal of water-soluble organic materials from water by
carbon-filled, buoyant packets and panels is described.  Based on this model,
equations are derived for the removal of dissolved organic compounds from
waterways by buoyant packets that are either (a) cycled through a water col-
umn, or (b) suspended in the waterway by natural turbulence, and by panels
mechanically suspended in waterways.  Computed results are given for phenol
spills.  The effects of turbulence on the suspension of buoyant packets and of
turbulent mixing and longitudinal dispersion of spills in waterways on the
removal of water-soluble hazardous materials are considered.

     Buoyant packets are found to be ineffective for removing spills from
waterways.  The rapid dilution of spills also renders panels ineffective un-
less the spill is massive and the response is rapid.

     This report was submitted in partial fulfillment of Contract No.
68-03-2648 by Rockwell International, Environmental  Monitoring & Services Cen-
ter, under the sponsorship of the U.S. Environmental Protection Agency.  This
report covers the period June 1978 to January 1979,  and work was completed as
of 15 January 1979.
                                      IV

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                                 CONTENTS
Foreword	iii
Abstract	   iv
Figures	   vi
Tables	vii
Abbreviations and Symbols  	 viii
Acknowledgment 	   xi
Summary	    1

     1.  Introduction  	    4
     2.  Conclusions 	    5
     3.  Recommendations 	    7
     4.  Analysis	    8
               Adsorption Model Basics 	    8
               Analysis of Pollutant Removal by Buoyant Packets  ....   11
                    Buoyant Packet Cycling  	   11
                    Buoyant Packets Suspended in Turbulent Rivers  ...   15
                    River Turbulence and Packet Suspension 	   21
               Carbon-Filled Panels Hanging in Rivers  	   25
               Turbulent Diffusion and Dispersion in Waterways 	   30
               Hazardous Material Spill Statistics 	   36
     5.  Discussion	   40
               Effectiveness of Buoyant Packets  	   41
               Carbon-Filled Panels  	   42

References	   45
Appendices

     A.  Properties of Activated Carbon and Packets	   47
     B.  Application of Ion-Exchange Resins to Hazardous Spills in Water.   49
     C.  Free Dispersed Carbon Particles 	   52

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                                  FIGURES

Number                                     ~                             Page
                                                              o    c
  1     Fluid pumping required to remove 80% phenol from 3785 m  (10
          gal) with buoyant carbon packets (10.2 cm x 10.2 cm xL). ..  16

  2    Model, buoyant packets suspended in turbulent river	17

  3    Computed removal  of phenol by suspended buoyant packets of
          activated carbon (10.2 cm x 10.2 cm x L), C  = 100 ppm  ...  19

  4    Removal of phenol by suspended buoyant packets of activated
          carbon (10.2 cm x 10.2 cm x 1.27 cm), C  = 250 ppm,
          d  = 0.12 cm	°	20

  5    Distribution of buoyant suspended particles in waterways ....  24

  6    Watercourse with carbon-filled panels	26

  7    Percent removal of spills from waterways by carbon-filled panels  29

  8    Longitudinal dispersion of water-soluble spills in the Chicago
          Sanitary and Ship Canal	35

  9    Transverse concentration profiles - water-soluble spill at
          center of Chicago Sanitary and Ship Canal 	  37
                                     VI

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                                  TABLES
Number                                    '                              Page
  1     Summary of Calculated Mass-Transfer Information
          for Buoyant Packets	12
  2     Summary: Calculated Values for Buoyant Packet Cycling   	   14
  3     Removal of Pollutant by Suspended Packets
          (10.2 cm x 10.2 cm x L)	18
  4     Values of the Parameter Z Determined  for Various  Waterways  ...   25
  5     Summary of Mass Transfer Calculation  for
          Hanging Carbon-Filled Panels  	   28
  6     Summary of River Field Data	32
  7     Hazardous Spill Statistics 	   38
  8     Profile of Phenol  Spills 	   38

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                          ABBREVIATIONS AND SYMBOLS
A      --  total cross-sectional area of panels normal to the flow direction
 c         in the watercourse

A      --  cross-sectional area of a packet  (10.2 cm x 10.2 cm [4 in x 4 in]
 p         for this study)

At     --  cross-sectional area of panels in a section of length x

a      --  total exterior particle surface area for mass transfer per unit
           volume of packed space;  defined  for spheres in Eq. 6.

a      —  cross-sectional area of panels in length dx
 X

b      —  a reference point in Eq. 30, b =  0.05D

C      --  concentration in the bulk fluid

Cu     —  concentration at reference point  b

Ci     --  concentration at exterior of adsorbent particle

C.     --  concentration of solute in fluid  entering a panel  or packet

C      --  initial concentration

C  ,    --  concentration of solute in fluid  exiting a panel  or packet

D      --  depth of a waterway

D-,     --  hydraulic mean depth of a waterway
  i
D      --  dispersion coefficient in x direction, longitudinal dispersion
 x         (cm^/sec or m^/sec)

«;?     --  molecular diffusion coefficient  (cm /sec)

d      --  diameter

d      --  diameter of particles in packets or panels

E      --  rate of energy dissipation per unit mass (ergs/gm-sec)

F-     --  friction factor in Eq. 3 (see Ref. 8)
 J
F      --  a factor used to modify d  in Reynolds number calculation (see Ref. 8)

                                     viii

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f     --  friction factor for objects moving through fluid



g     --  acceleration due to gravity



h     --  half width of boundaries used in solution of Eq. 45



k     --  Karman's constant (=0.4 for open channel flow)



k     —  mass transfer coefficient (cm/sec)
 \*


K     --  mass transfer rate constant defined by Eq. 50



L     ~  thickness of carbon-filled packet or panel



a     —  distance from the deepest part of a channel to the furthest bank



mn    "  mass of packet (p) or mass of water displaced (w)
 P >v»


M     —  amount of material discharged in a spill



N     —  number of packets



n     —  number of cycles; used as a summation index in Eq. 49



AP    --  pressure difference



Q     —  volumetric discharge rate relative to carbon panels



q     —  concentration of adsorbed maerial on solid phase (moles/mass)



R     —  hydraulic radius



Re    --  Reynolds number (d vp/u), dimensionless



Re1    --  Reynolds number for packed bed (dJJp/pe), dimensionless
                                           P °


S     --  slope of the channel floor (the slope of the energy grade line)



Sc    --  Schmidt number (v/»<0), dimensionless



t     --  time


^                                                                   Y
t     --  elapsed time following the arrival of fluid particle (t - —)



U     --  superficial  flow velocity, the average linear velocity through a

          bed computed on the basis of the empty cross-sectional area


                                  1 /2
u*    —  shear velocity, = (T /p)    (also see Eq. 32)



V     --  volume



V     --  volume of a packet




                                     ix

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v, v  —  velocity, cross-sectional area mean
v     --  slip velocity, the velocity difference between an object and the
          fluid in which it is suspended
vt    --  terminal velocity
W     --  width of a watercourse
x     —  distance, as defined where used -
y, y1 --  distance, as defined where used
Z     --  defined as (vt/ku*B), Eq. 30
z     --  distance, as defined where used
Greek Letters
3     --  proportionality constant (e^/fig)
ed    —  eddy diffusion coefficient of liquid
e     —  eddy diffusion coefficient of solids suspended in turbulent flow
e     --  eddy diffusion in y and z direction, respectively
n     --  relative number of packets suspended in a watercourse between two
          arbitrary depths (see Eq. 31)
e     —  packed bed void fraction or void space
u     --  viscosity
v     ~  kinematic viscosity (y/p)
5     --  defined by Eq. 14
P     --  density of fluid
p ,Pb --  density of packet, bulk density of adsorbent (carbon)
T ,T ,--  shear stress at point o (wall) and at point y1, respectively
4>     --  phenol
$     —  fraction of flotation material in a packet (1  - \i> = fraction of
          carbon)

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                              ACKNOWLEDGMENT
     This work was sponsored by the U.S. Environmental Protection Agency's
Municipal Environmental Research Laboratory at Edison, New Jersey.  The
author wishes to thank John E. Brugger, Oil & Hazardous Materials Spills
Branch in Edison, for his guidance and support.
                                     XI

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                                  SUMMARY


     An analysis was made of the feasibility of using activated carbon adsor-
bent in packets and panels to clean up water-soluble hazardous material
spills in surface waters.

     A model for the containers is given in which movement of fluid through
the packets is created by buoyancy forces and turbulence and through panels by
causing them to lag the flow velocity of the waterway.  Mass transfer to the
carbon particles from the low-velocity fluid passing through the containers
was assumed to be controlled by the fluid-side resistance.

     Equations were derived to describe the removal of dissolved pollutants
from water by buoyant packets that were either (a) cycled through a water col-
umn, or (b) suspended in the waterway by natural  turbulence.  Cycling con-
sisted of injecting packets of adsorbent at the bottom of a water column,
allowing them to float to the surface where they would be retrieved, and re-
injecting them at the bottom of the water column.  The reduction of pollutant
concentration in volume V from C0 to C by N packets of fresh adsorbent in n
cycles is given by
     Calculations based on the above equation using phenol as a model  pol-
lutant and a carbon-phenol ratio of 10 indicate that the packet cycling ap-
proach is inefficient.  The calculations considered packets with a 10.2-cm by
10.2-cm (4-in by 4-in) cross-section, thicknesses of 1.27 cm (0.5 in)  and
0.64 cm (0.25 in), and carbon particle sizes of 0.12 cm and 0.06 cm.  Pumping
requirements for packet injection at the bottom of the water column were found
to exceed by 5 to 11 times (at a minimum) the volume of fluid that would be
pumped if a packed column of carbon were used for fluid cleanup.  Calculations
performed for representative waterways reveal water-soluble spills are rapidly
diluted by turbulent mixing and longitudinal dispersion.  Dilution increases
the volume of fluid, V, to be treated and as shown by the equation, will in-
crease the number of packet-cycles needed to effect a fixed fractional reduc-
tion in pollutant concentration.  Reasonable estimates of the cycling  time and
the large number of cycles required indicate that the process is inherently
slow and usually incapable of lowering the pollutant concentration in  a water-
way as rapidly as can longitudinal dispersion.

Consideration of pollutant removal by fresh buoyant packets suspended  in tur-
bulent waterways for a time t yields


                                     1

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                     r      uANt  F
                 In ±-= - -^—   1 - exp
                     0             I


Plots of computed values of In C/CQ versus t are given for various packet
buoyancies using phenol as a model pollutant and a carbon-phenol ratio of 10.
Comparisons are made with experimental data from the literature.

     A study of the literature on sediment-suspension and turbulence in water-
ways indicates that natural turbulence in most waterways is insufficient to
suspend the buoyant packets with any degree of uniformity throughout the
depth of the waterway.   Even packets with the lowest buoyancy force for which
calculations were made will concentrate near the water surface.  Information
on the suspension of objects of the size of the packets contemplated in this
study is unavailable; the scale of the waterway turbulence could impose an
upper limit on the size of an object that can be suspended.  No estimate can
be made at present of the increase in suspension time likely to occur as a
result of buffeting of the rising packets by turbulence.

     An equation was also obtained for adsorption of dissolved pollutants from
water by adsorbent-filled panels hanging in waterways.   For a waterway dis-
charge rate of Q relative to the panels and a total panel  area normal  to the
flow, A , the equation  is

                            A_TJ_  f
                                   1  - exp
A plot is given of computed values of percent phenol removed versus the rela-
tive discharge rate with spill size appearing as a parameter.  As seen from
the equation^ the fraction of pollutant removed decreases as the relative dis-
charge rate Q is increased.  For a discharge rate of 25 nr/sec (3000 ft3/sec),
about 5% (at most) of a 1814-kg (4000-lb) spill of phenol can be removed by
carbon panels with a carbon-phenol ratio of 10.  For large nonimpoundable
waterways, i.e., discharge rates in excess of 850 m3/sec (30,000 ft3/sec),
about 5% (at most) of an 18,140-kg (40,000-lb) spill can be removed by
181,400 kg (400,000 Ibs) of carbon panels even with a fast response to a
spill.

     The computed performance of packets and panels given in this study are
probably higher than can be attained in practice.  The reasons for this are:

     a.  The assumption that packets and panels are always turned broadside
         to the flow

     b.  The neglect of flow resistance offered by the fabric that would be
         used to encase the adsorbent

     c.  The assumption of negligible resistance to mass transfer in the
         solid-phase and the assumption of equilibrium concentration at the
         external fluid-solid interface

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     d.  The assumption that fluid leaving a packet or panel is well mixed
         with the surrounding fluid in the waterway before entering another
         packet or panel

     e.  The assumption that adsorbent particles in the packets and panels
         will remain distributed in a uniform bed thickness over the entire
         cross-section

     The rapid dilution of water-soluble .spills by turbulent mixing and lon-
gitudinal dispersion will make the removal* of even a few percent of the dis-
solved pollutant by carbon-filled panels unlikely in large, nonimpoundable
waterways, unless the spill is massive.

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                                  SECTION  1

                                INTRODUCTION
      A growing,  modern  industrial  society  requires  and  produces many  chemi-
 cals  that  can  threaten  public  health  and safety  if  discharged  into waterways
 in  sufficient  quantities.   In  the  course of production,  transportation,  stor-
 age,  and utilization  of these  materials, some  accidental  spillage  is  certain
 to  occur,  and  some  fraction of this spillage will enter  watercourses.  Recent
 barge accidents  on  the  Ohio and Mississippi  Rivers  have  highlighted these
 threats and the  need  for an operational system to remove spilled, water-
 soluble organic  hazardous  materials from large,  nonimpoundable waterways.

      Activated carbon in one form  or  another (packaged or loose, floating or
 sinking in water,  powdered, granular, and  fibrous)  has  been  proposed  for ad-
 sorbing spilled, water-soluble hazardous organics from watercourses.   Limited
 laboratory experiments  and small field tests have been  conducted with  carbon
 to  determine its spill  cleanup potential (Refs.  1,  2, 3, 4,  and 5).   The re-
 sults of these studies   have been  mixed, but as  expected, activated carbon
 was shown  to remove dissolved  organic substances from water.   These studies
 do  not make clear,  however, whether the use of carbon-filled packets  and pan-
 els or loose carbon to  clean up spills in  large, nonimpoundable watercourses
•is  technically or  economically feasible.

      Before further developmental  work in  this area was  funded, a brief feasi-
 bility study was conducted of  the  various  in-situ approaches to the removal of
 water-soluble, hazardous organics  from nonimpoundable watercourses by  means of
 carbon adsorption.  The study  was  to  concentrate on the  adsorption process and
 to  ignore  related  steps such as the harvesting or retrieval of the carbon-
 filled packets and  carbon  regeneration.  Accordingly, it was the objective of
 this  study to  determine the rate of removal  of dissolved pollutant and the
 percent of dissolved  pollutant likely to be removed by using activated carbon
 under the  best possible conditions.   Based on  these determinations, a  recom-
 mendation  was  to be made on the matter of  future funding of work in this area.

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                                 SECTION 2

                                CONCLUSIONS


     1.  Buoyant packets of 0.64-cm (0.25-in) thickness injected into quies-
cent water will require pumping in excess of 5 to 11 times more fluid than
necessary when using a packed column of carbon.  For 1.27-cm (0.5-in) -thick
packets, 7 to 14 times more fluid will be pumped than required for a packed
column.

     2.  Buoyant packets are ineffective for removing spills of dissolved haz-
ardous materials from waterways.  The reasons for this are:

         a.  The rapid dilution of spills in navigable waterways increases
             the number of cycles required to effect a fixed percentage of
             reduction in pollutant concentration.

         b.  Reasonable estimates of the cycling time and the large number
             of cycles required indicate the process is inherently slow.

         c.  Large volumes of fluid-packet mixtures must be pumped.

     3.  Natural turbulence in representative waterways does not appear to be
sufficient to suspend buoyant packets with any uniformity throughout the depth
of the waterway.  No estimate can be made at present of the increase in sus-
pension time likely to occur as a result of buffeting of the rising packets
by turbulence.

     4.  Carbon-filled panels hanging in waterways appear to hold more prom-
ise for the removal of dissolved hazardous materials than do buoyant packets.

     5.  The percent of dissolved material that can be removed by panels de-
creases with an increase in discharge rate of the waterway and increases with
the amount of carbon used.

     6.  Fpr large, nonimpoundable waterways, i.e., discharge rates greater
than 850 m^/sec (30,000 ft^/sec), carbon-filled panels become ineffective.
The reasons for this are:

         a.  Rapid dilution of water-soluble spills as large as 18,140 kg
             (40,000 Ibs) to the point where treatment by any means would be
             difficult

         b.  Under the best circumstances, with a rapid response less than 5%
             of an 18,140-kg (40,000-lb) spill of phenol  will  be recovered by

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         181,400 kg (400,000 Ibs) of carbon panels.

     7.  Turbulent diffusion and longitudinal  dispersion in waterways will
rapidly dilute water-soluble spills to the point where treatment by any means
will be extremely difficult.  Spills of 1814 kg (4000 Ibs) or less in water-
ways of discharge greater than about 35.4 m3/sec (1250 ft^/sec)  will  probably
dilute to less than 4 ppm within 8 hours, spills of 18,140 kg (40,000 Ibs)  or
less in waterways of discharge greater than about 990 m^/sec (35,000 ft^/sec)
will probably dilute to less than 4 ppm within 8 hours.

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                                 SECTION 3

                              RECOMMENDATIONS
     Panels and buoyant packets filled with activated carbon or other adsorb-
ent should not be considered for the removal of water-soluble spilled mate-
rials from nonimpoundable waterways unless the spill is massive with respect
to the volumetric flowrate of the waterway and the adsorbent can be applied
very soon after the spill.

     Proposed approaches involving the application of in-situ adsorbents for
the removal of water-soluble hazardous material spills from waterways should
be examined in light of the results of this feasibility study.  Regardless of
the quality of an adsorbent or its specificity for the spilled compound, the
problems to be addressed are:  (a) the rate of mass transfer to the adsorbent,
(b) the very rapid longitudinal dispersion of dissolved substances in water-
ways, and (c) the removal of the spent adsorbent from the waterway.

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                                 SECTION 4

                                 ANALYSIS
ADSORPTION MODEL BASICS

     Packets or panels of carbon granules will  be considered  to  behave  as
fixed-bed adsorbers with a very small  thickness;  the carbon will  adsorb dis-
solved organic material only from fluid that is inside  the packet (either
stagnant or flowing through).   Packets of carbon  merely immersed  in  fluid,
with no flow of fluid through  them,  will  adsorb organic material  only from
the stagnant liquid in the void space  of the packet.  To work most effici-
ently, fluid must flow through the packet.   Fluid will  flow through  porous
packets in response to a pressure difference, AP, across the  packets.   This
AP will occur as a result of differences in velocity between  the  packet and
the surrounding fluid and will be proportional  to pv^/2 (the  proportionality
factor is called a drag coefficient or  a friction  factor).

     In a watercourse, differences in  velocity  between  packets and the  fluid
will occur quite naturally as  the packet is "dragged" along by the flow.  By
causing packets to lag the flow either by anchoring  them in place or somehow
increasing their drag, one can obtain  various flowrates through them.   A ve-
locity difference between the packet and the surrounding liquid can also be
obtained by employing packets  with a density different  from that  of  water.
The buoyancy force will induce the packets  to rise or fall through a water
column and accelerate to some  velocity (terminal  velocity) where  the fric-
tional drag force on the packet equals the  buoyancy  force.

     The properties of carbon used in  the computations  made  for  this study
are given in Appendix A.

     A force balance can be written for an object rising through  a column of
liquid


                        mPdT=(Vmw) g-f£^V                       (1)

where nip is the mass of a packet and n^ the mass of  water displaced  by  the
packet, Ap is the cross-sectional area of the packet normal  to the flow di-
rection, and g is the acceleration due to gravity (the  definitions of the sym-
bols are given in the list of abbreviations and symbols).  At steady state,
when theterminal velocity is attained, dv/dt = 0. Making this substitution
in  Eq. 1 and letting mp-m  =  (p -p)V,  the terminal velocity,  vt,  is  found to
be                             P

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     The friction factor s f, is related to the shape of the object moving
through the fluid, or V/Ap, and to the Re.  In many engineering texts, Eq. 2
is written with V/Ap given for a sphere and the f vs Re correlation given as
a function of a shape factor, or, sphericity to compensate for the assumed
ratio V/Ap of 4d/3.  For details on this approach, the reader is referred to
Brown and Assoc. (Ref.  6).

     A general review of settling velocities of particles (the same as par-
ticle rising velocities only the buoyancy has a different sign) that also
discusses friction factors (.or drag coefficients) for various shapes is given
by Graf (Ref. 7).  For this feasibility study it was assumed that the thin,
rectangular-shaped packets would pass through the water with the large rec-
tangular face oriented normal to the flow direction.  According to Brown (Ref.
6), particles will tend to move in a manner that offers greatest resistance.
In agreement with this general statement are the experiments reported by
Graf (.Ref. 7) which indicated that at Re numbers outside the Stokes range,
elongated bodies will orient themselves broadside to the relative motion.

     Flow velocities through the porous packets can be computed by using stan
dard calculational procedures for single-phase flow through packed beds.  The
needed equations and dimensionless plots are available in many texts (e.g.,
Ref. 8).  An equation relating the pressure drop across a packed bed to flow
velocity through the bed can be written as

                               / 2 g d  AP \ 1/2
                                   J        '

where TTa is the superficial velocity (the linear velocity of the fluid through
the bed computed on the basis of the total or empty cross-sectional  area), F-
and f are friction factors related to the bed po_rosity, the carbon granule
sphericity, and the Re number written as dp F^e Uap/y; the term FRS is a fac-
tor used to modify dp and is also a function of bed porosity and packing
material sphericity.  The trial and error solution for Ua using Eq.  3 and a
plot of Reynolds number vs f for randomly packed particles (Ref. 8)  converges
rapidly.

     The overall resistance to mass-transfer from the bulk liquid to the solid
includes the resistive contribution of (a) the layer of solution around the
particles, (b) diffusion of solute through pores within the particles, and
(c) physical  adsorption at active sites on the solid.

     The mass-transfer coefficients from the bulk liquid to the exterior sur-
face area of the carbon particles (step [a] above) were computed using general
correlations obtained at low Re numbers (Ref. 9).  For Re1 from 0.08 to 125
(where Re' = dpUap/y6 and e is the bed void fraction), the mass-transfer cor-
relation used was

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                      k      0.58             -0.66
                      ^ (Sc)     = 2.40 (Re1)      .                    (4)

                      Ua
The Schmidt number, Sc, is defined as \>l<&.   The diffusion coefficient, o^,
for the organic compound being adsorbed from the water phase can usually be
computed with fair accuracy using available methods (Refs. 10 and 11).

     for steady-state mass-transfer from the water phase to the carbon, and
piston flow through the packed bed (or packet),

                           -U dC = k a (C-C.) dx,                        (5)
                             a      C      1

where a is the total  exterior particle surface area for mass transfer per
unit volume of packed space.  For spheres,

                              a = £ (i-e) (I-*),                        (6)
                                   P
where e is the bed void fraction and ^ is the fraction of flotation material
in the packet.

     Values of kc obtained from Eq. 4 are applicable to the layer of solution
surrounding the particle.  Evaluation of C-j, the concentration of solute at
the exterior particle-liquid interface, may involve the addition of equations
describing the rate of diffusion through the pores interlacing the solid and
the rate of physical  adsorption.  Ultimately, Cj would be related to the con-
centration of solute at active adsorption sites on the carbon solid.

     The assumption will be made that the resistance offered by the pore dif-
fusion, and physical adsorption steps is very small relative to the resistance
to mass transfer from the bulk liquid to the exterior surface of the carbon.
Therefore, C-j can be closely approximated as the concentration of the solute
in equilibrium with the solid, i.e., the solute concentration given by an ex-
perimentally determined adsorption equilibrium isotherm.  The adsorption
equilibrium isotherm could be used to relate C- to the bulk fluid concentra-
tion, C, via a material balance if the initial moles of solute and the mass of
carbon were known.  Since the carbon packets considered in this study are
fairly thin, and the packets moving through  the liquid may have fluid passing
through them in either direction depending on which of the two broad sides are
facing the flow, C-j will be assumed to be constant for all carbon granules and
hence independent of distance, x, through the packet.   C-j will vary with time
as the concentration of organic material on  the carbon increases.  At any par-
ticular time, the change in concentration across a packet is given by inte-
grating Eq. 5 from 0 to L and C.  to C  t to yield
                     out "  in

                        Cin
(7)
     For fresh activated carbon, C- is negligible for many organics and Eq.  7
can be written as

                                     10

-------
                             C  4.         /   k aL \
                              out. = exp  (--£-).                     (8)
                              Cin          \    Ua  /

Equations 7 or 8 indicate the change in solute concentration occurring in
fluid passing through the packed bed.  The fraction of pollutant removed
from water passing through a fresh carbon packet is
                                                                         (9)
ANALYSIS OF POLLUTANT REMOVAL BY BUOYANT PACKETS

Buoyant Packet Cycling

     It has been suggested that watercourses or lakes polluted by spills of
water-soluble hazardous organic compounds could be cleaned up faster or more
efficiently if packets of activated carbon adsorbent were used.   These pack-
ets would be fabricated in sizes small enough to be mixed with water and in-
jected at the bottom of a polluted volume of water by a solids-handling pump,
and buoyant enough to rise through the polluted water at some known terminal
velocity.  The movement of the packet upward through the water would enhance
mass transfer of the pollutant to the carbon, as described earlier.  Upon ar-
rival at the water surface, the packets would be automatically gathered and
pumped down to the bottom of the water column again to start another cycle.

     For this study, a packet size of 10.2 cm by 10.2 cm (4 in by 4 in) with
a thickness of either 1.27 cm (0.5 in) or of 0.64 cm (0.25 in) was chosen.
Packet buoyancy was assumed to be provided by adding foamed plastic particles
with a specific gravity of 0.2 to the carbon granules used to fill the pack-
ets.  The foamed plastic would have a size equal to the carbon granules used.
Calculations were performed for carbon granules with a diameter of 0.12 cm
and 0.06 cm (14 and 28 mesh).

     For the purpose of this feasibility study, the buoyant-packet-cycling
approach was assumed to be used to clean up 3785 m^ (10° gal) of water con-
taminated  with  100 ppm of phenol.  A carbon-to-phenol  ratio of 10 was
assumed.

     Using the equations and procedures outlined in the previous pages, values
of pD, AP, gm carbon/packet, Ua, and kc were calculated for terminal  rise
velocities of 3.8, 7.62, 15.2, and 22.9 cm/sec (0.125,  0.25, 0.50, and 0.75
ft/sec) for carbon spheres with dp = 0.12 cm and 0.06 cm, a packet thickness,
L, of 1.27 cm (0.5 in) and 0.64 cm (0.25 in), and a packet void fraction, e,
of 0.39.  The relevant calculated results are given in  Table 1.   At v-t = 30.5
cm/sec (1.0 ft/sec), the required buoyancy dictates that the packets  have a
density of 0.29 gm/cc; this density cannot be attained using flotation par-
ticles with a density of 0.20 gm/cc.  A packet composed entirely of flotation
particles with p = 0.2 and e = 0.39 would have a density of 0.512 gm/cc.


                                     11

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      A_packet rising through the water column of depth D at velocity vt will
 treat UaApD/vt units of water.  The fraction of phenol removed from the water
 passing through a packet is given by Eq. 9.  Thus, the amount of phenol re-
 moved from the water by N packets of fresh carbon after one pass through a
 depth D at v. is given by the equation
                  VAC =
1  - exp
(10)
 Equations 9 and 10 were used to compute the values given in columns 4 and 5
 of Table 2.  A depth, D, of 3.05 m (10 ft) was chosen for this exercise.

      As the packets float on the water surface prior to gathering and return-
 ing them to the river bottom, the carbon will adsorb phenol from the fluid
 remaining in the void space of the packets.  To account for this adsorption,
 it has been assumed that for each cycle, in addition to the pollutant ad-
 sorbed while rising through the water, the carbon in a packet will remove
 enough phenol to attain equilibrium with a volume of phenol-water mixture
 sufficient to occupy the packet void space, that is, (C-Cj)NVp9.  Thus, the
 total amount of phenol removed per cycle is given by adding this quantity to
 Eq. 10.  The result of this addition for fresh carbon (C. = 0) is given in
 column 6 of Table 2.

      The total  number of cycles, n, required by fresh carbon packets to re-
 move a given fraction of the phenol (or any pollutant) can be found from
 Eq. 11.
exp
                                                       + V_9
(11)
The total time required to reduce the phenol concentration from CQ to C is
primarily a function of the packet retrieval time, the solids-handling pump
capacity, and the number of cycles, n.  According to Eq. 11, if N should be
increased, the number of packet-cycles will be unaffected.  This is true for
fresh carbon packets only (the restrictions under which Eq. 11  was derived).
Thus, to complete the desired cleanup job, the same number of packets would
have to be retrieved and pumped to the bottom of the water column.  The volume
of fluid-solids handled by the recycling pump, using a 15% maximum solids load-
ing as typical, is NnV /0.15.

     Assuming a sufficiently high carbon-phenol ratio, Eq. 11 was used to de-
termine Nn for 90% removal of phenol for 3785 m3 (10^ gal) of water.   The esti-
mated volume to be pumped is given in column 10 of Table 2.  The computed val-
ues, ranging from 3.71 x 1Q4 to 10.5 x 1Q4 m3 (9.8 x 106 to 27.7 x 1Q6 gal),
though undoubtedly an underestimate, greatly exceed the amount of pumping re-
quired if a packed carbon bed were used to remove the phenol.  If the purified
water exiting the carbon bed was continually dumped back and mixed with the
contaminated water, the pump would be required to handle about 8710 m3 (2.3 x
106 gal) to reduce 3785 m3 (106 gal) of water from 100 ppm to 10 ppm.  If,
however, the purified water was not returned to the reservoir,  only 3407 m3
                                      13

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(0.9 x 10  gal) would have to be pumped.

     Numerical solutions of the mass transfer equations for a carbon-phenol
ratio of 10 (using values of Cj determined from an adsorption isotherm for
phenol and Nuchar C-190 given in Figure A-l in Appendix A) obtained for 80%
removal of phenol from a mixture with an initial concentration of 100 ppm phe-
nol, are given in columns 8 and 9 of Table 2.  The adsorption isotherm and the
carbon-phenol  ratio of 10 will not permit more than about 84.7% of phenol to
be removed without regeneration of the carbon.  The results of these calcula-
tions are also plotted in Figure 1 as pumping volume required versus the ter-
minal rise velocity of the packets.

     A reduction in carbon particle size results_in greater resistance to flow
through the packet and, hence, a lower value of Ua.  The lower value of Ua and
the greater area per unit volume, a, afforded by the smaller particles increas-
es the percentage of phenol removed from the fluid passing through the packet.
The net effect of using the smaller particle size, as shown in Figure 1, is to
slightly raise and shift the minimum of the curve toward higher terminal rise
velocities.  A decrease in the packet thickness from 1.27 to 0.64 cm (0.5 to
0.25 in) increases the number of packets (since the carbon-phenol ratio is as-
sumed to be fixed at 10), offers less resistance to flow through the packet,
and causes the water pumping minimum to shift toward smaller terminal rise
velocities.  Thinner packets appear to require fewer total packet passes, Nn,
through the water column to adsorb the same amount of phenol.

     The calculations do not include a flow resistance for the fabric casing
or container for the carbon and flotation granules comprising the packets.
Smaller particle sizes will require a tighter fabric weave to contain the par-
ticles while decreasing the packet thickness will enhance the importance of
the contribution of the fabric to the overall resistance to flow through the
packet.  For a fixed amount of carbon, halving the packet thickness will more
than double the number of packets, since the resistance to packet movement up-
ward through the water changes very little and maintaining the buoyancy force
constant requires that the percentage of flotation in thinner packets be in-
creased.  The greater number of packets means larger packaging costs.  No con-
sideration has been given here to the problem of how to construct or fabricate
a packet, so as to keep the carbon-flotation granular mixture uniformly dis-
tributed throughout the thin packets rather than lumping all together on one
side or corner of the packet to give a sack!ike appearance.

Buoyant Packets Suspended in Turbulent Rivers

     If buoyant packets, considered for nonflowing water bodies in the previ-
ous pages, were injected into a turbulent river, the random buffeting of the
packets by the eddies will increase the immersion time.  It has been suggested
that a sufficiently high level of river turbulence would result in the packets
remaining suspended in the water indefinitely.  An analysis will  be made and
equations derived to describe the rate of adsorption of dissolved materials by
buoyant packets of activated carbon suspended in a watercourse.  This will  be
followed by a discussion of river turbulence and the suspension of solids.

     To remain suspended in a river, a packet must encounter a net downward


                                      15

-------
Q
LLJ
Q.
2

Q.
Ill
2
3

O
12


11


10


 9


 8


 7


 6


 5


 4


 3


 2


 1
                                                    CARBON/PHENOL = 10
                                                O L = 1.27cm, d  = 0.12cm
                                                               P
                                                A L = 0.64 cm, d  = 0.12 cm

                                                Q L = 1.27 cm, d  = 0.06 cm
                              10          15          20

                              TERMINAL VELOCITY, cm/sec
                                                             25
30
             Figure 1.
              from 3785 m
                   Fluid  pumping  required  to  remove  80%  Phenol
                   m3  (10°  gal) with  buoyant  carbon  packets
                       0.10.2  cm x 10.2  cm  x L)
 force of sufficient strength to counter the steady,  buoyant force.   It is as-
 sumed that suspension occurs when the average slip velocity (the velocity of
 the fluid relative to the packet) is equal  to the terminal  rise velocity of
 the packet.  As in the previous section, it is assumed that the packet will be
 oriented broadside to the flow.  Fluid entering each packet is assumed to be
 well  mixed and hence representative of the  river in  the surrounding vicinity.
 Fluid exiting a packet is assumed to mix very rapidly with  the surrounding
 fluid.   Figure 2 shows a simple schematic to illustrate the adsorption model.
 The change in concentration of solute in the well-stirred river is  equated to
 the rate at which the solute is removed by  the packets.  The fluid  feed rate
 to the  packets is UaApN and the fraction of solute removed  from the fluid by
 fresh,  activated carbon packets is given by Eq. 9.  The differential  equation
 for this case is
                                       16

-------
                                     UaApNC
               RIVER
           WELL STIRRED
                                                                  PACKETS
                                      'out
                                      uaApNCout
            = UaApNC(1-CoutyC)
       Figure 2.   Model,  buoyant packets  suspended  in  turbulent river.
                  - vf • VPNC
                 1  - exp
(12)
        or, separating variables and integrating,
                     c  .
                  In
        or,  simplifying,
                                       -  exp
                                                        (13)
In 7?-= - a-
                                                                         (14)
The V in the denominator of Eq.  13  refers  to  the volume of water to be treated,
and t is the time the packets  remain  in  suspension.

     Calculations of £, were made for  various  terminal  rise velocities and the
packet and granule sizes investigated for  quiescent water.  All of the quanti-
ties required to determine E, were calculated  for packets  in still water and
appear in Tables 1 and 2.   Values of  5 (hrs~')  for the conditions cited above
are tabulated in Table 3.

     Equation 12 was solved numerically  to obtain values  of C/C0 as a function
of t.  When C/C0 is about 0.6  (for  a  carbon-phenol ratio  of 10 and for the
phenol adsorption isotherm used, Figure  A-l),  the concentration of phenol at
the exterior surface of the particle  becomes  large enough to necessitate the
use of numerical methods.   The results of  the numerical solutions for the rate
of removal of phenol by packets  suspended  in  a  turbulent  river are plotted in
Figure 3.
                                      17

-------
TABLE 3.  REMOVAL OF POLLUTANT BY SUSPENDED PACKETS (10.2 cm x-10.2 cm x L)
dp
(cm)
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.06
0.06
0.06
0.06
(cm)
1.27
1.27
1.27
1.27
0.64
0.64
0.64
1.27
1.27
1.27
1.27
vt
(cm/sec)
3.81
7.62
15.2
22.9
3.81
7.62
15.2
3.81
7.62
15.2
22.9
r
-, out
" C-
in
0.8781
0.5406
0.1979
0.0377
0.5406
0.2436
0.0544
1
0.9984
0.8408
0.2686
N
92 ,,700
98,200
131,200
411,800
187,100
204,500
371,100
92,700
98,000
131,200
411,800
Ua
(cm/sec)
0.0115
0.0466
0.201
0.498
0.0172
0.0705
0.329
0.00262
0.01117
0.0481
0.1244
5
(hrs)'1
0.0919
0.2428
0.5124
0.7589
0.1708
0.3448
0.6521
0.0239
0.1073
0.521
1.351
Time (hrs)
to remove
80% 4
21.9
8.10
3.92
2.67
11.76
5.83
3.08
84.27
18.74
3.86
1.49
     Since Eqs. 12 and 13 are quite similar to the equations derived for pack-
ets rising up through a quiescent pool (except for the term Vp6 for the adsorp-
tion of phenol from stagnant fluid in the void space of the packet), the plot
of C/C0 against t reveals about the same information as given in Figure 1 re-
garding immersion times necessary to remove a fixed fraction of the phenol.
The results show that at high terminal rise velocities the packets with the
smaller carbon particles will remove phenol fastest, while at 3.81 cm/sec
(0.125 ft/sec), the lowest terminal rise velocity for which calculations were
made, the thin packet is faster.

     The results shown in Figure 3 are independent of the spill size, or amount
of water to be treated, as long as the water initially contained 100 ppm of
phenol and the ratio of carbon to phenol is 10.  If, for example, the initial
concentration of phenol was 250 ppm, Eq. 13 indicates that the carbon packet
concentration, N/V, would be 2.5 times greater than it would be for a 100-ppm
phenol-water mixture to maintain a carbcn-to-phenoi ratio of 10.  The informa-
tion given in Figure 3 can be easily converted zo 250-ppm phenol-water mixtures
by merely dividing the time axis by 2.5.  This has been done for the 1.27-cm
(0.5-in) -thick packet with a 0.12-cm particle size in Figure 4 in order to
compare these calculated results with experimental data reported by Calspan
(Ref. 1).  The carbon-filled bags used in laboratory channel tests conducted
by Calspan (Ref. 1) were not suspended in the stream by turbulence, but were
attached to floats and permitted to drift with the lab channel current.  A
comparison between the curves calculated for the carbon-flotation packet model
and the lab channel tests indicates a combination of turbulence level and slip
velocity between the stream flow and the carbon-filled bags in the Calspan

                                     18

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channel tests equivalent to a slip velocity between 3. 81 and 7. 62 cm/sec (0.125
and 0.25 ft/sec) for the model. The difference in the shape of the curves is
probably due to the difference in the phenol -carbon adsorption isotherm used
and perhaps to some extent to the assumption that the pore diffusion term in
the overall mass-transfer equation can be neglected for the small values of
Ua encountered. Channel test results in which loose Aqua Nuchar carbon was ap-
plied to the phenol-water mixture (Ref.l) are also given in Figure 4.

River Turbulence and Packet Suspension

     There is a moderately extensive literature on sediment transport in
open-channel flow and the steady-state distribution of suspended matter in
turbulent watercourses.  None of the literature found, however, is concerned
with objects the size of the buoyant carbon packets considered here or with
objects that will float rather than sink (though the latter point is merely
a matter of the sign on the velocity term).  In the derivation of equations
to describe the distribution of suspended solids in a turbulent flow, it is
usually assumed that the effect of turbulence on the solids can be expressed
by a diffusion-dispersion equation(the diffusional theories).  Some deriva-
tions given in the literature are briefly outlined and discussed.

     For incompressible fluids the continuity equation for mass transfer can
be written as
                             + v-vC -^VC = 0.                          (15)

Equation 15 can be modified for a turbulent flow field by expressing the in-
stantaneous values C and v in terms of the mean values C and v averaged over
short time intervals at a given position, and C' and v1, the fluctuating com-
ponent, as given by

                                 C = C"+ C1                              (16)

                                 v = 7 + v1.                             (17)

Substituting Eqs. 16 and 17 into Eq. 15, and averaging each term over a short
time interval , we obtain


                         + 7-vC" + v(CV~) -i2rv2C" = 0.                    (18)
The quantity C'v' can be written as
                      £d^7=-C'vi =edvC'                            (19)


where £d is the eddy diffusivity.   Substituting Eq.  19 into Eq.  15  yields

                     || + 7-7C" - v(edvC") -&v2C = 0.                      (20)

                                     21

-------
Since e^ is usually much larger than the molecular diffusivity,^, the last
term on the left of Eq. 20 can be neglected.

     To calculate the steady-state_ vertical distribution of suspended mate-
rial in a turbulent stream, le;t aC/3t f_ 0 and assume C varies only in the
vertical direction, y, i.e., aC/ax = sC/3z = 0.  The resultant equation is

                           w 3(T   a   /    3C" V    n
                           V 3y -  37l£d  ay j -  °«                        (21)

If C, v, and e
-------
where k is Karman's constant (for open channel flow, k = 0.4), and u* is the
shear velocity.  The shear stress at y' in a turbulent flow is given by the
equation

                                          dv                              /07N
                             V = ' p£d dy^ '                           (27)

Combining Eqs. 25, 26, 27, and 23, it is found that


                           es = Sku* (D-y'O £- .                         (28)


Substituting Eq. 28 for es in Eq. 22 and separating variables, we obtain


                         dC" _    /  vt \ _D_  dy'                         (29)
                         y "  Vku*i3/ y1  (D-y1) '

The result of integrating Eq. 29 from b to y'  is
                                    \ y1
where Z =
     A plot of Eq. 30 illustrating the vertical solids concentration distri-
bution for various values of Z is given in Figure 5.  It is quite obvious
from Figure 5 that more uniform distributions of solids with depth require
low values of Z.  In addition, Eq. 30 unfortunately yields the solids distri-
bution relative to some reference point, b, below the surface; it does not
yield absolute solids concentrations unless the concentration is known at
some reference point.

     To ascertain the relative suspended particles load rate, or, for the
problem of interest here, the relative number of packets_ suspended at various
depths in the watercourse, it is necessary to multiply C by the water velocity
as a function of vertical position and integrate over the vertical region of
interest, that is,

                                    y-, _
                               n = /   Cudy .                             (31)
The fraction of packets at any depth would then be~CTTvy/n.

     The relative distribution of solids in rivers as predicted by Eq. 30 re-
quires that Z be known.  Of the terms comprising Z, v^ can be assigned depend
ing on the packet density, k = 0.4, e can be taken to be equal to 1 (though
for large objects like packets this may be incorrect) and u* is given by the
relation
                               u* = (90,8)     ,                          (32)

                                     23

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-------
where S is the slope of the channel bed and D-j  is the hydraulic mean depth
of the river.  Values of Z for v^ = 3.81  cm/sec (0.125 ft/sec) and g = 1  are
given in Table 4 for a number of rivers and waterways.

     It would appear that even for low values of v-^, Z will  be large enough
to dictate that the vast majority of the packets will be in  the upper 10% to
20% of the river depth.  There is no information on the suspension of objects
of the size of the packets; the scale of .the river or channel  turbulence
could impose upper limits on the size of an object that can  be suspended.  In
addition,  there is evidence that the presence of suspended  matter tends  to
dampen turbulence and smooth out the flow, hence reducing u*,  increasing  I,
and causing the packet distribution shift upward to the river surface.

CARBON-FILLED PANELS HANGING IN RIVERS

     Water-soluble pollutant spills can be removed from watercourses by pan-
els packed with activated carbon hanging in the water flow in  some homogeneous

   TABLE 4.  VALUES OF THE PARAMETER Z DETERMINED FOR VARIOUS  WATERWAYS*
                                                         Z = -£-

                      Waterway                     (v.  = 3.81 cm/sec)


     Chicago Sanitary & Ship Canal  (Calumet Sag)           5.01

     Missouri River (near Omaha, Nebraska)                 1.24

     Clinch River (near Clinchport, Virginia)              2.07

     Copper Creek (near Gate City,  Virginia)              0.92

     Power River (Sneedville, Tennessee)                  1.8.3

     Coachella Canal  (Holtville, California)              2.22

     Bayou Anacoco                                        1.42

     Nooksack River                                       0.36

     John Day River                                       0.53

     Sabine River                                         1.16

     Green-Duwamish (Seattle, Washington)                  1.94


* 3 assumed to be 1.0.
                                     25

-------
pattern downstream of the spill and turned broadside to the flow.  The impact
of the flowing water on the panels will provide the AP for flow through the
porous panels and over the activated carbon granules.

     Figure 6 illustrates the model for the use of carbon-filled panels in
rivers.  A material balance on a section dx of the watercourse festooned with
panels yields
                             S9X
    b at
3t
                                                                         (33)
where 6 is the fraction of the river not occupied by carbon panels.   For the
carbon-phenol ratios used in this study, e > 0.999 and will be assumed to be
unity.  The term pb(3q/3t) describes the rate of accumulation of solute on
the carbon and can be equated to the rate of mass transfer to the carbon-
filled panels, that is,
- Ua ax
                                           *  Cout> '
                             (34)
where ax is the panel area available for flowthrough in the segment dx div-
ided by the volume of the segment.

     Using the transofrmation t = t - x/vs and substituting Eq.  34 into Eq.
33, one obtains
                       - v,. !§= U  a„ (C - C
             'out7'
                                                                         (35)
     The equations can be considered to describe a very loosely packed  bed  of
adsorbers consisting of carbon-filled panels.   Within each panel  the  concen-
tration of adsorbed material  on the carbon will  be assumed to  be uniform



V
S

WATER + SPILLED
HAZARDOUS
MATERIAL



f*


|i|
1 . 1
1

1 ' '
jl|


-, ^ OC rlu
6X








                                 ZONE CONTAINING
                                 CARBON-FILLED
                                 PACKETS


             Figure  6.   Watercourse  with  carbon-filled panels,
                                    26

-------
throughout the panel.  Because the panels would be located at various dis-
tances downstream of a spill, the amount of pollutant adsorbed in a panel
will depend on the location of the panel along the watercourse.  As in a
packed bed, the concentration of pollutant will be assumed to be constant
over any cross-section normal to the flow.

     Assuming fresh carbon (i.e., C  is negligible), Eq. 35 can be written as
                    3C   -      I          /  kCSL'
                -"sf =uaaxc t1 -exP    --=-
                                                a


      Separating variables and integrating, Eq. 36 becomes


                                           /  kcaLM
                                  1 - exp   - -^—)  ,                    (37)
where At is the total panel cross-sectional area in a volume of the water-
course of length x.  Equation 37 can be more conveniently written as

where Q is the volumetric discharge rate relative to the carbon panels and A
is the total cross-sectional area of the panels in the watercourse.

     With the simple treatment of the problem of relating q to C, it would
not have been necessary to go through a more involved analysis starting with
Eq. 33.  If someone wished to deal with a situation requiring a more involved
solid-liquid adsorption relationship for either carbon or ion-exchange res-
ins, Eq. 33 and a suitably described relationship between q and C should aid
in the analysis (Ref. 15).

     Large-cross-section, thin panels hanging in a watercourse were  assumed
to have a drag coefficient equal to that obtained for flat plates, that is,
f = 2 for 3000 < Re < 3.5 x 1Q5 and AP = fpv?2/2 (e.g., Ref.  7).  This led to
higher AP values for the panels than for rising packets at the same  slip
velocities.  In addition, the panels contain only carbon; flotation  is not
required.

     Table 5 contains relevant calculated values for panels of thickness 0.64
and 1.27 cm (0.25 and 0.5 in), filled with 0.12-cm or 0.06-cm-diameter gran-
ules.  Some of the calculated results are plotted in Figure 7 as percent phe-
nol removed per pass over the carbon panels vs Q; the spill size in  kilograms
of phenol appears as a parameter and the carbon-to-phenol ratio is 10.  The
solid curves in Figure 7 are for a slip velocity of 30.5 cm/sec (1 ft/sec).
For spills of 453.6 kg (1000 Ibs) of phenol, dashed curves are given for slip

                                     27

-------
                 TABLE  5.   SUMMARY OF MASS TRANSFER CALCULATION
                         FOR HANGING CARBON-FILLED PANELS
dp
(cm)
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.12
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
0.06
L
(cm)
1.27
1.27
1.27
1.27
1.27
1.27
1.27
1.27
1.27
U27
0.64
0.64
0.64
0.64
0.64
0.64
0.64
0.64
0.64
1.27
1.27
1.27
1.27
1.27
1.27
1.27
1.27
1.27
1.27
VS
(cm/ sec)
3.81
7.62
15.2
22.9
27.4
30.5
45.7
61.0
76.2
91.4
3.81
7.52
15.2
22.9
30.5
45.7
61.0
76.2
91.4
3.81
7.62
15.2
22.9
27.4
30.5
45.7
61.0
76.2
91.4
iP
(Pascals)
1.451
5.798
23.20
52.19
75.17
92.97
208.8
371.1
579.8
835.0
1.451
5.798
23.20
52.19
92.97
208.8
371.1
579.8
835.0
1.451
5.798
23.20
52.19
75.17
92.97
208.8
371.1
579.8
835.0
Ua
(cm/sec)
0.0149
0.0609
0.249
0.537
0.751
0.885
1.75
2.59
3.52
4.53
0.0302
0.1231
0.503
0.990
1.54
2.79
4.20
5.58
6.96
0.00381
0.01476
0.0603
0.1373
0.1989
0.2463
0.5609
0.975
1.47
2.00
kc x iO3
(cm/ sec)
1.003
1.619
2.612
3.393
3.803
4.02
5.07
5.79
6.43
7.01
1.275
2.056
3.319
4.418
4.855
5.942
6.829
7.521
8.108
0.997
1.580
2.549
3.372
3.825
4.113
5.44
6.57
7.55
8.38
1 Cou.\ «,'
1 ' " C
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    1ON3Hd lN30U3d
                                                                      29

-------
velocities of 61.0 and 91.4 cm/sec (2 and 3 ft/sec).  It should be noted that
increasing vs from 30.5 to 61 cm/sec (1 to 2 ft/sec) (which also doubles Q)
for a 453.6-kg (1000-lb) spill, for example, will result in a smaller percent
phenol removed.  For 1.27-cm (0.5-in) -thick panels filled with 0.12-cm carbon
granules, the percent removal is maximized at a v$ of about 15.2 cm/sec (0.5
ft/sec).  If the river velocity was 61.0 cm/sec (2 ft/sec), for example, and
if the panels could be allowed to drift down the river at 45.7 cm/sec (1.5 ft/
sec), the calculations indicate the panels would remove more phenol.  However,
the polluted stretch of water would take four times longer to move past the
panels and during this additional time longitudinal dispersion will further
dilute the pollutant.  The calculations ignore this complicating factor.

     Calculations based on Eq. 38 appearing in Table 5 and Figure 7 are good
for the first portions of the spill-polluted water to pass through the panel -
festooned region of the river.  As more of the contaminated water passes
through the panel region, Eq. 36 would have to be numerically integrated, tak-
ing into account a variation of adsorbed material on the panel, with the axial
distance of the panel from the head of the panel region.  This is especially
true for the large spills and low values of Q.  It is believed that the per-
cent removal results appearing in Figure 7 are higher than can be attained in
practice.

     Experiments performed by Calspan (Ref. 1) with a 21.3-m (70-ft) -long
0.0929 m^ (1 ft^) cross-section recirculation channel containing 1000 liters
of water with 250 ppm phenol  in which carbon-filled bags, attached to floats,
were permitted to drift with the channel current, can be compared with the
predictions of Eq. 34.  Since the carbon bags drifted with the channel cur-
rent, the actual value of Q,  the volumetric discharge relative to the bags,
j_s unknown.  If the slip velocity is assumed to be 3.81  cm/sec (0.125 ft/sec),
Q is 1.787 liters/sec (0.0631 ft-Ysec).  Using values from Table 5 for vs =
3.81 cm/sec (0.125 ft/sec), dp = 0.12 cm, L = 0.64 cm (0.25 in), and a carbon-
phenol ratio of 10, Eq. 34 predicts that 7.73% of phenol would be removed per
pass of the fluid.  One pass requires 560 sec (= 21.3 m/0.0381 m/sec) and 6.43
passes will be made in 1 hour.  Hence, Eq. 34 predicts that 100 (1 - 0.0773)6-43,
or 59.6% of the phenol will remain after 1 hour.  This is less than the values
obtained by Calspan (Figure 4) for channel currents of 30.5 cm/sec (1 ft/sec)
and 15.2 cm/sec (0.5 ft/sec).

TURBULENT DIFFUSION AND DISPERSION IN WATERWAYS

     Turbulence and longitudinal dispersion in waterways will  serve to dilute
spilled water-soluble materials.  The dilution can reduce the toxicity of haz-
ardous water-solubTe spills to levels that can be tolerated by aquatic life or
in drinking water.  Dilution, however, also makes it more difficult to remove
hazardous water-soluble substances.  This section will  examine the effect of
transverse, or lateral eddy diffusion and longitudinal  dispersions on the
spread and dilution of a water-soluble spill.  The effect of the dilution of
the spill on the use of adsorbents will be examined.  The .treatment given here
to the subject of spills cannot be exhaustive.  Spill parameters such as the
amount of material spilled, the rate and duration of the spill, the size and
hydrological properties of the watercourse (velocity, depth, width, slope,
discharge and dispersion coefficient) and the spill location (e.g., center of


                                      30

-------
the river or at the bank) will all affect to some extent the time required for
the dilution of the pollutant.

     The time-averaged continuity equation for mass transfer in a turbulent
field is given by Eq. 20.



                        ff + 7-VC - (ed +£) V2C = 0.                       (20)

The eddy diffusivity, s.^, is a property of the flow field and, unlike,^, is
independent of the molecular properties of fluid.  An expression for the eddy
diffusivity in the vertical direction, £„, can be obtained for open channel
flow from an earlier analysis by substituting Eq. 23 in Eq. 28, i.e.,

                             £y = ku*y (1 - £).                           (39)

The lateral eddy diffusion coefficient, e,, for an open channel flow has been
determined experimentally by Elder (Ref. 15) who reported the value

                                 £z = 0.23Du* .                           (40)


     The eddy diffusion coefficients, though quite large in comparison to
molecular diffusion coefficients, do not describe the primary dilution action
in watercourses, which is longitudinal dispersion.  Longitudinal dispersion
involves the spreading out of a water-soluble substance (in this case a pol-
lutant spill) along the length of a watercourse due to variations in flow
velocity across the channel.  An initial analysis of turbulent axial disper-
sion in pipes by Taylor (Ref. 16) in which it was shown that the process could
be described by a one-dimensional form of Eq. 20 (a Fickian diffusion equation).,
where C" and u" in Eq. 41 are cross-sectional mean values, and Dx is the longi-
tudinal  dispersion coefficient, led to the application of this approach to the
study of dispersion in watercourses (Refs. 15 and 17).  Methods outlined by
Fischer (Ref. 17) permit the evalution of Dx for use in Eq. 41 from field
data.

     Observed values of Dx for a number of rivers and locations are given in
Table 5 (Refs.  18, 19, and 20).  The measurements tabulated were obtained us-
ing fluorescent dye or radio-isotope tracer techniques.  Simplified equations
for the calculation of Dx from various river flow parameters are available.
Because of the complexity of the river flow processes, these expressions can
often be in great error.  They are used to estimate Dx when field measurements
are unavailable.  McQuivey and Keefer (Ref. 18) suggest the equation


                                Dx = 0.058 £. ,                           (42)


                                      31

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-------
where S is the slope of the channel bed and W is the channel width, while
Fischer (Ref. 19) proposed the formula
                               n  =
                                  "
                                    0.011
                                      D1 u*
                                            (43)
A more recent (1978) analysis of dispersion in natural streams by Liu (Refs.
20 and 21) has resulted in the equation
n    n c
D  = 0.5
 x
                                       u* Q
                                        * ^-
(44)
where R is the hydraulic radius.

     Making the substitution x-i = x - ut in Eq. 41 reduces it to
                                                                          (45)
Solutions to Eq. 45 for various boundary conditions are given by Crank (Ref.
23).  For dispersion of an amount of substance M deposited at t = 0 in the
plane x-, = 0, Crank gives

                                            /   x2 \
                         C = 	M-^exp I. -_!_).                   (46)
                             2UDt)1/2
                 4Dxt
It should be remembered that C in Eqs. 45 and 46 is the mean concentration
taken over a cross-sectional area of the watercourse at x] and that M should
be in units of mass  (or moles) £er unit cross-sectional area.  Equation 46 can
be used to determine curves of C vs x] for various times for "instantaneous"
spills.  For more flexibility in specifying the rate of spill, solutions can
be obtained for a solute of concentration C0 initially confined in the region
-h < x < h as shown below
C = 0
I
Co
1
T
1
— 2h— »
I
i
£•= o
                                                          t  =  0
                                       +  x.
                                      33

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The solution given by Crank (Ref. 23) is


                                 h-xl  ,
                                              h+x,
                                         erf
                                                                          (47)
Knowing the mean river velocity, the spill rate, and the volumetric flowrate
of the river, one could calculate CQ and h.

     Equation 47 was used to determine mean concentration vs distance profiles
for phenol spills of 18,144 kg (40,000 Ibs) or 16.96 m3 (599.09 ft3] and of
1814 kg (4000 Ibs) or 1.696 m3 (59.9 ft3) at a spill rate of 3.54 m3/min (125
ft3/min) into the Chicago Sanitary & Ship Canal (CSSC).  Using data given in
Table 6 for v, Q, the half width h for the 18,144-kg (40,000-lb) spill is 39.0
meters and C~Q is 549.5 ppm by volume; for 1814 kg (4000 Ibs), h = 3.90 meters
and C0 is 549.5 ppm by volume.  Using these values and Dx for the CSSC, Eq. 47
was used to compute C vs x-| profiles plotted in Figure 8 for t = 1, 2, 4, and
8 hours.  According to Fischer (Ref. 17), the duration of an initial period in
which the longitudinal dispersion is not properly described by the one-
dimensional mass diffusion equation, Eq. 41, is greater than 6 times the
Lagrangian time scale.  The time is given by the equation
                                t' > 1.8
                                         Ru*'
                                                                          (48)
     Using Eq. 48 and data on the CSSC, t' is determined to be greater than
2.48 hours.  Thus, the curves appearing in Figure 8 are probably valid repre-
sentations of the concentration-distance profile.

     The CSSC was chosen for the dispersion calculation because it was un-
doubtedly used for shipping and had the smallest dispersion coefficient in
Table 6.  It is believed that the concentration profiles in Figure 8 provide
conservative values of the spill dilution that would occur in rivers of com-
parable flowrate.

     Calculations have been made of the concentration-lateral distance pro-
files as a function of time resulting from lateral  eddy diffusion processes.
Longitudinal spreading of the pollutant was ignored. The solution to the one-
dimensional diffusion equation written for the z direction was obtained from
Crank (Ref. 23) for the diffusion of a substance initially confined in the
region -h < x < h, into a field of width W (i.e., at z + W/2, 3C / 3z = 0),
i.e.,
1
2
                    n = -o
                           erf
                                      - z
                                            erf
                                                h * nw
(49)
A uniform flow, v, can be imposed on the solution, Eq. 49, by merely associ-
ating the profile calculated for time t with a distance vt downstream from
the spill point.
                                     34

-------
     The spill may be viewed as a slot source of area 2hD, through which pol-
lutant enters the watercourse at velocity v as shown below:
For a spill rate of 3.54 m /min {125 ft /min) of phenol into the CSSC, 2h was
computed to be 2.69 cm.  The calculated transverse profiles are given in Fig-
ure 9.
                                                     2
     A lateral eddy diffusion coefficient of 276.6 cm /sec was calculated
using Eq. 40 and data from Table 6.  The concentration profiles computed from
Eq. 49 and given in Figure 9 show how quickly eddy diffusion will  spread a
spilled water-soluble substance across the watercourse.  In only 3 hours the
concentration at the bank of the river is 97.4% of the concentration at the
center.  Profiles given in Figure 9 were for a spill at the center of the
watercourse.  Concentration profiles can be computed for spills at any point
from the center of the channel to the bank by using the method of reflection
and superposition (Refs. 22 and 23). Indeed, Eq. 49 is merely a special case
for a centrally located source.  Had the spill occurred at the bank rather
than at the center of the channel (the worst case with regard to time), com-
putations reveal that in 10 hours the concentration at the opposite bank of
the river would be 93.6% of that on the bank where the spill occurred.  Equa-
tion 49 can be utilized to compute the bank spill profiles by doubling the
value of h and W and solving for one-half of the profile (the curves in Fig-
ure 9 represent profiles for 1.77 m3/min (62.5 ft3/min) spills at the bank of
a 24.4-m-wide river as well as 3.54 m3/min (125 ft3/min) spills at the center
of a 48.8-m-wide river.

     The lateral location of the spill is usually of minor importance unless
the width of the river is quite large; the time required for turbulent eddy
diffusion to spread a water-soluble chemical across the river is probably
less than would be required to notify emergency response teams and marshal
resources for attempts at cleaning up the spill.

HAZARDOUS MATERIAL SPILL STATISTICS

     A recent compilation and analysis of hazardous material spills based on
approximately 1500 reported incidents from January 1971 to June 1973 (Ref. 24)
                                     36

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          1200
                                               6Z = 276.6 cnrWsec
                                8   10   12   14   16

                                 DISTANCE, METERS
18  20   22   24
            Figure 9.  Transverse concentration profiles - water-soluble
                 spill at center of Chicago Sanitary and Ship Canal.

and information and studies published by others (Ref. 25) have provided some
useful statistics.  Information on the weight percent of hazardous materials
shipped by various means, the percentage spilled during transport and from
stationary sources, and the percent reaching surface water are given in Table
7.  Unfortunately, there is no information on the size distribution of the
receiving waters exposed to these spills.

     With regard to phenol, the hazardous material  of interest to this study,
data on the reported spill  size and number of occurrences are given in Table
8 (Refs. 24 and 25).  About 293,000 liters of phenol were spilled in 19 re-
ported incidents; in six other reported cases the amount of phenol was not
given.  The three largest phenol spills (Table 8) were all the result of train
derailments and appear to be in a class by themselves.  Together, they account
for 85.3% of the total volume of phenol spilled in  the 2.5-year time interval.
Twelve of the remaining 16 incidents listed with a  spill volume in Table 8
involve less than 453.6 kg (1000 Ibs) each and the  other four range from about
4040 to 20,320 kg (8900 to 44,800 Ibs) of phenol.  These data are in keeping
with the general conclusions of the spill study (Ref. 24) that spills resulting
                                     37

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        TABLE 7.   HAZARDOUS SPILL STATISTICS (Refs.  24 and 25)
"/ lil-l- °l
la Wt h
of all Shipment
Shipments Spilled
Rail 13.3
Barge 32.1
Truck 54.6
Stationary
Source
Total 100%
TABLE
Average Spil
(liters)
Unknown
0 - 50
50 - 385
385-3,800
8,000
11,000
19,000
80,000
83,000
87,000
0.0536
o.om
0.0095
--
8. PROFILE OF
1 Size
(kilograms)
—
0 - 53.5
53.5 - 411
411 - 4,055
8,528
11,750
20,280
85,300
88,450
93,000
%
Total Spillage
Transp. % Total Reaching
Spillage Spillage Water
45 - 26 15
22 12 68
33 19 42
43 59
100% 100%
PHENOL SPILLS (Refs. 24 and 25)
Percent of Total Spill
Volume Represented*
--
0.10
0.37
1.30
2.73
3.75
6.48
27.29
28.31
29.68
%
Total Spill
Entering
Water
4
8
8
25
45%

Number of
Events
6
8
3
2
1
1
1
1
1
1
* Total  spillage reported = 293,000 liters from 1971-1973.
                                  38

-------
from tank ruptures and punctures have by far the greatest probability of high
hazard potential.  The fourth largest spill  in Table 8, a 20,320-kg (44,800-
Ib) spill from a railroad tank car puncture, if added to the train derailment
total, would bring the tank failure total  to 91.8% of the total  spillage.

     Dividing the phenol spills into rail, truck, barge, and stationary source
categories and multiplying each by a probability obtained for all  hazardous
materials (Table 7), one would surmise that about 20,240 liters, or 21,600 kg
(47,600 Ibs) of phenol entered surface waters in the average year from 1971
to 1973.  If, as stated in Ref. 25, 15% of spill volume from rail  accidents
enter surface waters, a rail  tank car failure would send an average of about
12,700 to 14,600 kg (28,000 to 32,200 Ibs) of phenol into rivers or lakes.
Of course, averages and probabilities are  given, not certainties.   It could
well  be that one accident would result in  45,400 to 90,700 kg (100,000 to
200,000 Ibs) entering a watercourse, while several other tank car spills would
not reach a waterway.  It seems very unlikely, however, that the entire con-
tents of a tank car spill would enter a waterway unless the derailment or
other rail accident took place on a bridge.

     Curiously, none of the phenol spills  listed were the result of a barge
accident, although 32.1 weight percent of  all hazardous material shipments  are
reportedly transported by barge.
                                     39

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                                   SECTION 5

                                   DISCUSSION


     A model for the use of containers of carbon adsorbent to remove water-
soluble pollutants spilled into waters has been presented and analyzed.  Fig-
ures and tables have served to summarize the computed performance of the model
systems.  For simplicity, the computed performance was given without considera-
tion for the coupling of turbulent mixing and dispersion in waterways.  This
coupling is further complicated by (a) the dependence of the spill dilution
rate on the relationship between the size of the spill and the volumetric flow-
rate of the affected waterways, and (b) the reaction time of an emergency re-
sponse team.  To correspond to the real world, consideration must also be given
to spill statistical data.  What size spills of a given hazardous material will
occur with what frequency or probability, into what size waterways?  These areas
have all been addressed more or less separately in the previous analysis section.

     With regard to the interaction between dilution by turbulent mixing and dis-
persion, and the adsorption process, these processes could have been described
in a single equation of the form
                                      <3X


where KCN/V is the rate of change of concentration with respect to time due to
adsorption.  The term K can be defined by reference to Eqs. 11 and 12, depend-
ing on the buoyant packet model being applied.  The coupling of the longitudinal
dispersion equation and the adsorption equation for panels is somewhat more com-
plicated because the adsorbing panels are in a fixed location in the flowing
stream and not uniformly distributed throughout the diffusing volume as is as-
sumed in Eq. 50.

     Spill statistics for phenol gathered from 1971 to 1973 (Refs. 24 and 25)
indicate that it is unlikely that a single spill  will result in more than
18,140 kg (40,000 Ibs) of phenol entering a waterway.  In the examples to be
used, 1814- to 18,140-kg (4000- to 40, 000-1 b) phenol spills will be the maximum
considered.  Since no barge incidents appear in the statistics, the maximum num-
ber may be somewhat optimistic.

     The waterway used in the examples as a typical navigable waterway for com-
merce is the Chicago Sanitary and Ship Canal (CSSC).  While its flowrate of
107.1 m3/sec (3780 ft3/sec) may be average, the measured dispersion coefficient,
D , was the lowest value found; this is probably because it is a straight,
 A

                                       40

-------
relatively smooth, man-made canal.  For a comparable natural watercourse, Dx
would be 10 times that of the CSSC.  The amount of dilution occurring in the
CSSC is probably representative of a natural watercourse with a flowrate of
about one-third that of the CSSC, or about 35.4 m3/sec (1250 ft3/sec).

     A large, non-impoundable waterway, one in which the polluted stretch of
the waterway could not be confined behind a holding dam or diverted to some
holding area for treatment by other than in-situ methods, will be taken arbi-
trarily here to be a waterway with a flowrate exceeding 850 m3/sec (30,000 ft3/
sec).

EFFECTIVENESS OF BUOYANT PACKETS

     The equations derived for the adsorption rate of pollutant from waterways
by in-situ application of buoyant carbon-filled packets (Eqs. 11 and 13) con-
tain the total volume of fluid to be treated, V, in the denominator.   As a
result, an increase in V with time resulting from turbulent mixing and disper-
sion in waterways will increase either the number of cycles or the suspension
time required to remove a specified fraction of the pollutant, unless the num-
ber of carbon packets is also increased with time so as to maintain N/V
constant.

     As indicated elsewhere in this study, it does not appear possible to main-
tain buoyant packets in suspension with any degree of uniformity by the turbu-
lence of a waterway.  The distribution given in Figure 5 requires that the
packet concentration be measured at some point between y1 = 0.05D and y1 = D;
it does not yield information on the packet population that merely floats on
the surface.  It is believed that very few packets will be below the water
surface.  However, the turbulence of a watercourse and the swirling action in-
duced by the pumped fluid and packets injected near the channel  bottom might
cause the actual suspension time of the packets to be longer than D/v^.   Per-
haps Eq. 10 could be rewritten with D/vt multiplied by some correction factor
to be determined experimentally.

     Responding to an. 18H-kg (4000-1 b) phenol spill into the CSSC with 18,140
kg (40,000 Ibs) of activated granular carbon and 8645 kg (19,060 Ibs) of flota-
tion material in 897,000 buoyant packets within 1  to 8 hours would mean remov-
ing phenol from a mixture in which the maximum concentration would be between
about 4 ppm and 14.5 ppm (10.5 ppm cross-sectional area mean) by volume (from
Figures 8 and 9) dissolved in roughly 3 x 105 to 6.8 x 1Q5 m3 (80 x 106 to 180
x 106 gal) of water (ignoring the portions of the canal where the calculated
phenol concentration is less than 0.5 ppm) spanning a distance of 800 to 1800
meters along the channel.  For a response 1 hour after the spill, calculations
(Eq. 11) indicate that a 10% reduction in phenol concentration would require
155 cycles of the packets; after 8 hours, 368 cycles would be needed to effect
a 10% reduction in concentration.  Using a factor of 15% solids  by volume that
can be handled by the pumps, this would mean that 6.07 x 10^ m3  (16.05 x 10^
gal) to 1.44 x 105 m3 (38.1 x 10° gal) of water and packets must be pumped
(391.8 m3/cycle [103,500 gal/cycle]).  If it were possible to reduce the packet
cycle time to 10 minutes, the time required for 155 cycles (starting cleanup
operations 1 hour after the spill) would be 25.8 hours, while 368 cycles
(starting 8 hours after the spill) would take 61.3 hours.  The solids-handling


                                      41

-------
                                    3
pumps would have to circulate 39.4 m /min (10,400 gal/min). Of course, during
the cleanup process the phenol will continue to spread longitudinally along
the channel.

     If it were possible to keep the buoyant packets suspended in the CSSC by
turbulence (which appears to be highly unlikely), a response to the 1814-kg
(4000-lb) spill in 1 to 8 hours would produce a situation in which from 25 to
60 hours would be required to remove 10% of the spilled phenol, even if the
dispersion process were to cease.

     For an 18,140-kg (40,000-lb) spill of phenol into the CSSC, a response
within 4 hours with 181,400 kg (400,000 Ibs) of carbon and 86,450 kg (190,600
Ibs) of flotation material contained in 8,973,620 packets would have to deal
with about 6.32 x 105 m3 (167 x 106 gal) of water containing an average of
about 27 ppm phenol (by volume).  Using Eq. 11, we find that 32.35 cycles of
the packet population are needed.  This would require the pumping of 1.27 x
105 m3 (33.5  x 106 gal)  of water and packets.  The time needed for one cycle
will depend either on how rapidly 8.974 x 106 packets can be retrieved and pre-
pared for reinjection by pumping, or on the available pumping capacity.

     An optimistic cycle time of 10 minutes would result in a total  time of 5.4
hours to remove 10% of the spill and a pumping rate of 394 m3/min (104,000 gal/
min).  During the 5.4 hours, even without cleanup, dispersion processes would
reduce the average concentration of phenol to about 19 to 20 ppm and increase
V by 30% to 40% (as stated previously, the interaction of dispersion and ad-
sorption could be more accurately described by solutions to Eq. 50).  The ef-
fect of on-going dispersion would be to increase the number of cycles required
to remove 10% of the pollutant.

     It should be noted that Eq. 11 relates the natural log of the concentra-
tion change to Nn.  Attempts to remove pollutant faster by increasing N will
only decrease n in direct proportion.  There will be fewer cycles but more
packets to retrieve and pump in each cycle; the volume of material pumped into
the channel (NnV/0.15) will not change.

CARBON-FILLED PANELS

     Unlike the equations derived for the buoyant packets, the volume of water
to be treated does not appear in Eq. 38, the equation derived for the adsorp-
tion by panels hanging in a waterway.  The fraction of pollutant removed is
directly proportional to the panel area facing the flow and inversely propor-
tional  to the volumetric discharge rate relative to the panels.

     Carbon panels fixed in a watercourse of the size of the CSSC will  remove
about 4% of an 1814-kg (4000-lb) phenol spill as the polluted fluid passes by
the pane-Is according to the model used to compute Figure 7.  Since the percent
of spill adsorbed is directly proportional to the total panel area,  facing the
flow, if the  carbon-to-phenol ratio was 100, that is, if 181,400 kg (400,000
Ibs) of carbon were used to clean up a 1814-kg (4000-lb) spill, then theoretic-
ally as much  as 33% of the phenol could be removed.  The computation was made
assuming vs = 22.86 cm/sec (0.75 ft/sec) and using data in Table 5 with Eq. 38.
                                     42

-------
     It has been assumed in this work that equilibrium is rapidly established
at the activated carbon surface, i.e., the concentration at the fluid-exterior
particle interface is that value dictated by the adsorption isotherm.  When
working with fluids containing 100 ppm of dissolved pollutant, the neglect of
small deviations from equilibrium at the fluid-particle interface (say 1 or 2
ppm) will cause errors of a few percent in the computations.  However, when
the fluid contains an average of less than 5 ppm of pollutants, as it does
after 8 hours of dispersion of a 1814-kg (4000-lb) spill into the CSSC, the
neglect of similar deviations from equilibrium can result in substantial er-
rors in the computations.

     In the event of a massive spill such as 18,140 kg (40,000 Ibs)  of phenol
into the CSSC, the computations indicate that the use of 181,400 kg  (400,000
Ibs) of carbon in 1.27-cm (0.5-in) -thick panels could remove as much as 33%
of the phenol.  The relative size of the spill with regard to the volumetric
flowrate of the channel and the dispersion coefficient, results in an average
concentration of about 20 ppm over 2000 m of the canal and about 12  ppm after
24 hours.  An 18,140-kg (40,000-lb) spill into a larger, non-impoundable river
such as the Missouri  River (Table 6) would be rapidly diluted, i.e., after 1
hour the maximum concentration (cross-sectional area average) calculated using
Eq. 47 would be about 3.44 ppm.  Using Eq. 48, the estimated time required
after the spill for the Fickian equation (Eq. 45) to become strictly applicable
is estimated to be 18.6 hours.  After that length of time, the maximum area
average concentration of phenol in the channel was calculated to be  0.707 ppm.
According to Eq. 38,  about 4.7% of the phenol could be recovered.  The low
phenol  concentrations found in the river after a few hours would indicate that
4.7% is highly optimistic.  The calculated percent removal will be in error on
the high side if the concentration of phenol at the fluid-carbon external sur-
face deviates from the equilibrium value obtained from an adsorption isotherm.
If the concentration  at the external interface of fresh carbon was 1 ppm, for
example, and the bulk concentration was 2 ppm, the percent recovery  would be
reduced by a factor of 2.

     During the course of this study a number of assumptions and idealizations
have been made.  Whenever possible, they have been made so as to present an
optimum situation for the carbon packets and panels, i.e., the results given
here are believed to  be more favorable than can be realized in practice.  The
reasons for this are:

     a.  The assumption that packets and panels are always turned broadside
         to the flow

     b.  The neglect  of flow resistance offered by the fabric that would be
         used to encase the adsorbent

     c.  The assumption of negligible resistance to mass transfer in the solid-
         phase and the assumption of equilibrium concentration at the external
         fluid-solid  interface

     d.  The assumption that fluid leaving a packet or panel  is well mixed
         with the surrounding fluid in the waterway before entering  another
         packet or panel


                                      43

-------
e.  The assumption that adsorbent particles in the packets and panels
    will remain distributed in a uniform, bed thickness over the entire
    flow cross-section
                                 44

-------
                                REFERENCES
 1.   Pilie, R.J., R.E. Baier, R.C.  Ziegler,- R.P.  Leonard,  J.G.  Michalovic,
     S.L. Pek and D.H. Bock, "Methods to Treat,  Control  and Monitor Spilled
     Hazardous Materials," EPA-670/2-75-042,  June 1975.

 2.   Dawson, G.W., J.A. McNeese,  J.A. Coates, "Slurry Application  of Buoyant
     Mass Transfer Media," Contract 68-03-2204,  1977.

 3.   Mercer, B.W., A.J. Shuckrow  and 6.W.  Dawson, "Treatment of Hazardous
     Spills with Floating Mass Transfer Media,"  EPA-670/2-73-078,  September
     1973.

 4.   Dawson, G.W., B.W. Mercer, and R.G. Parkhurst,  "In  Situ Treatment  of Haz-
     ardous Material  Spills in Flowing Streams,"  EPA-600/2-77-164,  October
     1977.

 5.   Dawson, G.W., and J.A. McNeese, "Advanced System for  the Application of
     Buoyant Media to Spill Contaminated Waters," p.  325,  Proceedings of 1978
     National Conference on Control of Hazardous  Materials,  April  11-13, 1978.

 6.   Brown, G.B. and  Associates,  Chapter 7,  "Unit Operations,"  John Wiley &
     Sons,  New York,  1956.

 7.   Graf,  W.H., "Hydraulics of Sediment Transport,"  Chapter 4,  McGraw-Hill,
     New York, 1971.

 8.   Brown, E.G. and  Associates,  Chapter 16,  "Unit Operations,"  John Wiley
     & Sons, New York, 1956.

 9.   Williamson, J.E., K.E. Bazaire, and C.J. Geankoplis,  "Liquid  Phase Mass
     Transfer at Low  Reynolds Numbers," Ind.  Eng. Chem.  Fundam., 2_, 126 (1963).

10.   Wilke, C.R., and P. Chang, "Correlation  of  Diffusion  Coefficients  in
     Dilute Solutions," A.I. Ch.  E. J., 1,  264 (1955).

11.   Sherwood, T.K.,  R.L. Pigford,  and C.R.  Wilke, "Mass Transfer," Chapter 2,
     McGraw-Hill, Inc., New York  (1975).

12.   Hinze, J.O., "Turbulence," Chapter 5,  pp. 352-370,  McGraw-Hill,  Inc.,
     New York (1959).

13.   Graf,  W.H., Loc. Cit., Chapter 6.

14.   Sherwood, T.K.,  R.L. Pigford,  and C.R.  Wilke, Loc.  Cit., Chapter 10.


                                      45

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15.  Elder, J.W., "The Dispersion of Marked Fluid in Turbulent Shear Flow,"
     J. of Fluid Mech., 5_, 544 (1959).

16.  Taylor, G.I., "The Dispersion of Matter in Turbulent Flow Through a Pipe,"
     Proc. Royal Soc. of London, 223, 446 (1954).

17.  Fischer, H.B., "The Mechanics of Dispersion in Natural  Streams," J.
     Hydraulics Div., ASCE, 9_3, HY6, 187 (1967).

18.  McQuivey, R.S., and T.N. Keefer, "Simple Method for Predicting Dispersion
     in Streams," J. Envir. Engrg. Div., ASCE,  1QO, EE4, 997 (1974).

19.  Fischer, H., discussion of "Simple Method for Predicting Dispersion in
     Streams," by McQuivey, R.S. and Keefer, T.N., J.  Envir. Engrg. Div.,  ASCE,
     101, EE3, 453 (1975).

20.  Liu, H., "Predicting Dispersion Coefficient of Streams," J.  Envir.  Engrg.
     Div., ASCE, 103, EE1, 59 (1977).

21.  Liu, H., closure of discussion of "Predicting Dispersion Coefficient  of
     Streams," J. Envir. Engrg. Div., ASCE,  104, EE4,  825 (1978).

22.  Crank, J., "The Mathematics of Diffusion," Oxford Univ. Press, London
     (1956).

23.  Carslaw, H.S. and J.C. Jaeger, "Conduction of Heat in Solids," Oxford
     Clarendon Press, Oxford, England (1959).

24.  Buckley, J.L., and S.A. Wiener, "Hazardous Material Spills:   A Documenta-
     tion and Analysis of Historical Data,"  EPA-600/2-78-066, April 1978.

25.  Dawson, G.W., and M.W. Stradley, "A Methodology for Quantifying the Envi-
     ronmental Risks from Spills of Hazardous Maeerials," Water -  1975,  AIChE
     Symposium Series No. 151, Vol. 71, 349  (1975).
                                     46

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                                 APPENDIX A

                 PROPERTIES OF ACTIVATED CARBON AND PACKETS


     The calculations performed for this study used the following values of
physical properties for carbon:

         Real density                            2.14 gm/cc

         Bulk density                            0.456 gm/cc

         Particle density                        0.747 gm/cc

         Wet particle density                    1.35 gm/cc

         Volume fraction of pores                0.651

         Void fraction in beds                   0.39

     Figure A-l is the phenol-carbon (Nuchar C-190) isotherm used in this
study (Ref. 2).

     The flotation particles required to buoy packets of carbon were assumed
to have a density of 0.20 gm/cc and the same d  as the carbon

     The packet density p  is given as


          p  = 0.61 [0.2i|» + 1.35 (l-i|))] + 0.39.                          (A-l)


     The mass of carbon, m , in a packet of volume V is


          m  = 0.61-0.747 (1-tlOV,, .                                      (A-2)
                                     47

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        T	T
                          o
                          o
                          o
                                                                                                      o
                                                                                                      o
                                                                                                                    o
                                                                                                                   .a
                                                                                                                    CO
                                                                                                                    
                                          Qi
                                       1- —
                                       o
                                       4- O
                                          CTl
                                                                                                          O
                                                                                                          t/1
                                        d) O

                                       4J  i-
                                        O  "3
                                        10 .C
                                       •i-  O
                                           3
                                                                                                                    Q.
                                                                                                                    S_
                                                                                                                    O
                                                                                                                    (/I
                                                                                                                   •a
                                                                                                                   
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                                 APPENDIX  B

       APPLICATION OF ION-EXCHANGE RESINS TO HAZARDOUS SPILLS IN WATER
     The mass transfer model used in this study of the application of thin
packets and panels filled with activated carbon to the removal of dissolved
hazardous materials from water can be easily extended to ion-exchange resins.
Most of the procedures and equations outlined for activated carbon can be ap-
plied to the analysis of packets and panels filled with ion-exchange particles.
The one exception may be the inclusion of a solid-phase mass transfer term for
ion-exchange particles.  In the activated carbon packet study, the mass trans-
fer resistance due to processes occurring inside the particle (diffusion
through the pores and along the solid surface inside the particle, and the
physical adsorption at active sites) were assumed to be negligible in compari-
son with the fluid-side resistance.  For ion-exchange resins this assumption
may not be valid.  Inclusion of an added resistive step, regardless of how
small, must reduce the overall mass transfer rate.  The adsorption rates com-
puted for carbon in this report are, in this respect, optimistic.

     For ion-exchange particles, the computation and addition of a term for
solid-phase resistance can be accomplished.  The reader is referred to the
detailed explanation, discussion, and examples given in Sherwood, Pigford, and
Wilke (Ref. 14) which will be followed here.

     The procedure of Thomas as given in Ref. 14, in which the rate of adsorp-
tion is described in a form similar to a "kinetic driving force" suggested by
the stoichiometry of 'a monovalent ion-exchange reaction, i.e.,

           Na+  +  RH + H+ +  RNa

           c ,  qm-c   CQ-C  , q .

At  equilibrium,

           K =  [H+] [RNa]
               [Na+]  [RH]  '

The rate expression  for the packet  then becomes
                                      49

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Since the mass adsorbed must pass through the fluid film surrounding the par-
ticle and through the resistance inside the particles, Eq. B-l can be equated
to expressions as
                                           ^^1'    (B"2)

where                 K c

          <1 = qm CQ H- (K-1) C. '                                      (B'3)

For the special condition C = C0/2, Eq. B-2 can be reduced to a form that can
be solved simultaneously with Eq. B-3 to find C-j , given K, C0, and
qm ks/pbC0kc (Ref. 14).  The result can be used to find either kQ/kc or
k0/(ks/qm/pbC0).
     The resulting relationship for k  is obtained (Ref. 14)

where the B factor is given in Figure 10.15 of Sherwood, Pigford, and Wilke
(Ref. 14).

     The value of ks, the mass transfer coefficient for solid phase, can be
obtained using the equation
                                                                       (B-5)

          ks = dp  (1-e)

recommended by Vermuelin,  Klein, and Hiester (Ref. B-l). ^ is the diffusion
coefficient inside the particle  (e.g., Ref. B-2).


      Inside a  packet  of  adsorbent


          >b & •  - "a f •                                            (B-6)

Using Eq. B-4 to find a  value for  k0 and combining Eq. B-6 with Eq. B-l, an
equation  is obtained that  can be solved numerically for the concentration
change across a packet or  panel, (C - Cout).  The amount of pollutant removed
from a volume, V, of water by N  buoyant packets rising through a depth D at
v. can be determined and the total amount for a cycle is
                                   + V  (C-CI)N-                       (B-7)
                                     50

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For suspended packets Eq. 14 would be modified to yield


                                                                       (B-8)
and Eq. 36 for panels festooned in a homogeneous pattern in a watercourse,
will become


          - *s If • Vx 
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                               APPENDIX  C

                      FREE DISPERSED CARBON PARTICLES


     The action of loose, or free carbon particles in a polluted well-stirred
volume can be described by the expression


         - V^-= k(jTdp2N(C-C1),                                       (C-l)


where H is the number of carbon particles of diameter  dp suspended in volume
V.  Letting NTrdp2/v = a, where a is the external area of  the particles per
unit volume,

         -f -kc. (C-C,).                                           (C-2)

Separating variables and integrating, we find


                                                                       (C-3)
For small  values of t (when carbon is fresh)


          lrb£- = - k at.                                               (C-4)
            Lo      c

     From experiments conducted by Calspan (Ref. 1) for loose carbon granules
in a stirred beaker containing 250 ppm phenol, the slope d In C/dt at small  t
was measured to be 0.74 hr~^.  Assuming dp = 0.12 cm and using a carbon-phenol
ratio of 10 with p = 0.747, a is found to be 0.167 cm~l.  For this value of a,
kc = 1.23 x TO'3 cm/sec.

     Experiments with fibrous carbon under similar conditions (Ref.  1) yields
d In C/dt = 2.81.  Whether kc is higher for fibrous carbon depends on the
value of a for this material.  Using p : 1 given for the fibrous carbon (Ref.
1), it can be shown that a = 0.01/dj for a carbon-phenol ratio of 10, where
dj is the diameter (cm) of the carbon fiber.  The value of kc for fibrous car-
bon is then 0.0781 dj cm/sec.  If di = 0.0158 cm (for the fibrous carbon used
in Calspan's experiment), the mass transfer coefficients for granular and
fibrous would be identical.  Since the slip velocity of fluid flowing past the
carbon fibers is bound to be greater than v  for small  particles being stirred
in a beaker, it is expected that the liquid side mass transfer coefficient for
the fiber is higher than for the particles.


                                     52

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     Estimates of the mass transfer coefficients for suspended single par-
ticles can be obtained by using the procedure recommended by Harriott (Ref.
C-l) in which the slip velocity is taken to be the terminal velocity of the
particle falling or rising through quiescent fluid under the influence of
gravity.
tion, i.e.
          This velocity is then used to obtain k  via a Frb'ssl ing-type equa-
              = 2 + 0.6 Re1/2 Sc1/3
                                                                        (C-5)
     Using Harriott's approach, the values of k  given in Table C-l were de-
termined for carbon particles.

             TABLE C-l.  CALCULATED MASS TRANSFER COEFFICIENTS
                    FOR FREE DISPERSED CARBON PARTICLES
Harriot's Approach
dp
(cm)
0.12
0.06
0.01
a*
(cm'1)
0.0669
0.134
0.803
kc x 103
(cm/sec)
4.25
4.31
4.05
kca*
(hr'1)
1.02
2.08
11.7
Brian & Hales! Correlation
kc x 1C)3
(cm/sec)
1.06
1.29
3.18
"'I
(hr ')
0.256
0.621
9.19
     *Assuming 100 ppm contaminant and 10/1 ratio of carbon to contaminant.
     Very similar values of kc will be obtained by using the Ranz and Marshall
correlation (Ref. C-2) for mass transfer to spheres in a fluid stream if Re is
calculated using the terminal velocity of the carbon particle as the slip
velocity.  This correlation is also plotted in Figure 6.9 of Sherwood, et al .
(Ref. C-3).

     It may also be possible to determine kc for particles in rivers by relat-
ing kc to the rate of energy dissipation per unit mass (E) for rivers, that
is, applying the theory of local isotropic turbulence of Kolmogarov.  One would
then utilize a correlation such as that developed by Brian, Hales, and Sher-
wood (Ref. C-4), given as Figure 6.11  in Sherwood, Pigford, and Wilke (Ref.
C-3).  The rate of energy dissipation per unit mass for a river flowing at a
constant velocity v down a slope S is.
                                   E = vgS,
                                                                        (C-6)
where g is the acceleration due to gravity.  One would assume here that the
turbulence is sufficient to keep the particles suspended in the fluid.

     For the Chicago Sanitary & Ship Canal, v = 27.1  cm/sec and S = 5.9 x 10"6,
thus E = 0.1567 ergs/gm-sec.  Using the Brian and Hales correlation (Ref. C-4),

                                     53

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the values given in Table C-l for various particle sizes were calculated.  The
correlation of Levin (Ref. C-5),
               k H             I A 4/3 F1/3> \°'62
                 U             I U     LI        /> o/~
               -4=2-= 2 + 0.471-&	/      Sc°'36 ,               (C-7)
                »A>             \     V      /

yields quite similar values of k .

     Comparing values of kca for dispersed particles given in Table C-l with
5 given for packets in Table 3 of this feasibility study, it is seen that for
dp values of 0.12 and 0.06 cm, the values of kca and £ are fairly close.

     It appears that free dispersed particles of 0.06 and 0.12 cm diameter
will have overall coefficients that are in the same ballpark as the packets
attain at the higher buoyancy forces.  The main advantage of powdered carbon
(0.01 cm) is apparently the increase in the value of a, the external particle
area per unit volume of fluid.  The Harriott approach yields a value of k
which is very nearly independent of d .

     The value of 1.23 x 10~  cm/sec determined from Calspan's experiment with
loose particles of 8 x 30 mesh is fairly close to the values of kc obtained in
this study from literature correlations of fluid-side mass transfer.

                                 REFERENCES

C-l. Harriott, P., AIChE J, 8_, 93 (1962).

C-2. Ranz, W.E., and W.R. Marshall, Jr., Chem. Eng. Progr., 48, 141, 173
     (1952).

C-3. Sherwood, T.K., R.L. Pigford,  and C.R. Wilke, "Mass Transfer," McGraw-
     Hill, Inc., New York (1975).

C-4. Brian, P.L.T., H.B. Hales, and T.K. Sherwood, AIChE J, 1_5_, 727 (1969).

C-5. Levins, D.M., Ph.D. Thesis, U. of Sydney (1969), cited in Boon-Long,  S.,
     C. Laguerie and J.P. Couderc,  Chem. Engrg. Sci., 33_, 813 (1978).
                                     54

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                                   TECHNICAL REPORT DATA
                            /Please read fauructions on the reverse be/ore completing)
 1. REPORT NO.
                              2.
                                                            3. RECIPIENT'S ACCESSIOf*NO.
4. TITLE AND SUBTITLE
  Removing Water-Soluble Hazardous  Materials Spills
  From Waterways With Carbon
                                                            5. REPORT DATE
                                                             September 1981
                                                            6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
  George R.  Schneider
                                                            8. PERFORMING ORGANIZATION REPORT NO
                                                                                         -H
9. PERFORMING ORGANIZATION NAME AND ADDRESS
  Rockwell  International
  Environmental  Monitoring & Services  Center
  2421  W.  Hill crest Dr.
  Newbury  Park,  California 91320
                                                            10. PROGRAM ELEMENT NO.
                                                            11. CONTRACT/GRANT NO.
                                                             EPA 68-03-2648
12. SPONSORING AGENCY NAME AND ADDRESS
 Municipal  Environmental Research  Laboratory -  Cin.
 Office  of Research and Development
 U.S.  Environmental Protection Agency
 Cincinnati,  Ohio 45268
                                                       OH
13. TYPE OF REPORT AND PERIOD COVEREL
  Final,  June 78-Jan 79
                                                            14. SPONSORING AGENCY CODE
                                                             EPA/600/14
15. SUPPLEMENTARY NOTES
 John  E.  Brugger, Project Officer
 201-321-6634
16. ABSTRACT
                                                    materials
                                                     Based on
                                                              from
                                                              this
       water
       model
by carbon-
 equations
A model for the  removal  of water-soluble organic
filled, buoyant  packets  and panels is described.   Based on tnis moaei, equations
are derived for  the  removal of dissolved organic  compounds from waterways by buoy-
ant packets that are either (a) cycled through a  water column, or (b) suspended
in the waterway  by natural  turbulence, and by panels  mechanically suspended in
waterways.  Computed results are given for phenol  spills.   The effects of turbu-
lence on the  suspension  of buoyant packets and of turbulent mixing and longitudinal
dispersion of spills in  waterways on the removal  of water-soluble hazardous mate-
rials, are considered.
 Buoyant  packets are found to be  ineffective for removing spills from waterways.
 The  rapid dilution of spills also  renders  panels ineffective unless the  spill  i
 massive  and the response is rapid.
                                                                                  is
                                KEY WORDS AND DOCUMENT ANALYSIS
                  DESCRIPTORS
                                              b.IDENTIFIERS/OPEN ENDED TERMS
                                                                         c.  COSATI Field/Group
 Hazardous  Material  Spills
 Water  Pollution
 Adsorbents
 Activated  Carbon Treatment
 Decontamination
 Chemical Removal (Water Treatment)
 Pollution  Abatement
                                               Nuchar C-190, Phenol,
                                               Hazardous Material Spill
                                               Cleanup, Hazardous Chemi-
                                               cal  Spills, Longitudinal
                                               Dispersion of Spilled
                                               Materials
               13/02
               07/01
18. DISTRIBUTION STATEMENT
  Release  to  public
                                              19. SECURITY CLASS (This Report)
                                              Unclassified
              21. NO. OF PAGES

                   67
                                              20. SECURITY CLASS (This page)
                                               Unclassified
                                                                         22. PRICE
EPA Form 2220-1 (9-73)

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