United States
                  Environmental Protection
Risk Reduction
Engineering Laboratory
Cincinnati, OH 45268
Mathematical Models

   When  the  membrane  filter  (MF)
method  is  used  to  detect  coliform
bacteria,  the  limit  of  detection is one
organism  per 100  mL for an  individual
grab  sample. The results from one
sample do not, however, provide  much
information about the density of coliform
bacteria in the body of water  that was
sampled. If several samples are collected
from a relatively large amount of  water
containing only  a few coliform bacteria,
the limit of detection is approximate and
depends  on  the  number of  samples
examined and the probability of  capturing
coliform bacteria in any sample. For any
body  of water, there is  a probability  of
capturing one or more coliform bacteria
in  any 100  mL sample,  which can be
represented  at  P{ + /100  mL}.  The
probability of capturing conforms with  n
samples can be calculated from
   P{detection}  = 1-[1-P{ + /100 mL}]".
This formula  is  independent of the
frequency  distribution of the  coliform
counts and can  be generalized for other
sample volumes  by substituting P{ + /V
mL} as the probability  of a positive result
in  a sample  of V  mL. The manner  in
which P{ + /V mL} changes with  a change
in  V can be calculated if the frequency
distribution is known. This  information
can  then  be used  to  calculate the
difference in the probability of  detecting
coliform bacteria by compositing a large
number of small volume  samples  or by
using  a single large  sample having  the
same total volume.
   The frequency distributions  used for
the mathematical  models were the
Poisson as a representation of a random
dispersion and the lognormal as a  repre-
sentative of aggregated  dispersion.
These frequency distributions have been
used to describe coliform data on large
numbers  of samples from water distribu-
tion systems.

Closed Form Model
   If coliform bacteria were ever random-
ly  dispersed in the entire body  of water
(i.e., the colony counts in unit volumes of
water  fitting a Poisson distribution),  the
probability of obtaining  a count of  x
coliform bacteria in a volume,  V,  would
be given by
   P{x} = e-m(nv
for  estimating the  sampled  distribution.
For instance, a lognormal distribution with
GM  = 0.00000112 and GSD -  100 has
an  arithmetic mean density  lower  than
another lognormal  distribution with  GM
= 0.00112 and GSD  = 20;  however,  it
can  produce  samples with densities of
one or  more  coliforms  per  sample
precisely  because,  with  its  greater
variance, it is more likely to produce
samples  with  a very high density. As an
example, for the GM - GSD pairs cited
above, the arithmetic mean and variance
and  the probability of  a positive sample
are shown in Table  1.
   GSD  values  reported  for  water
distribution systems ranged  from  about
10  to 100.  When the  GSD  is  low,
composite sampling gives little advantage
for finding coliform bacteria. For example,
a system with a GM of 0.1 and a GSD of
10  has an arithmetic  mean  density of
1.42/100  ml, and  composite sampling
will  provide  little advantage when
compared with grab sampling since the
probability of a positive 100 mL sample is
0.16.  The more challenging case is the
system that  has the  same  arithmetic
mean  but  much higher variability. A
system with a GM of 0.000025 and a
GSD of 100 also has an arithmetic mean
density of about  1  per 100 mL, but very
few 100 mL aliquots (about 1  in 100) will
have  any coliforms at all.  In this case,
composite sampling would  be  the
method of choice.
Summary on Mathematical
   It was  shown by both  closed form
models and computer simulations that
composite  sampling from  a  lognormal
distribution is  superior  to grab sampling,
if the variance of the  coliform count is
large. The larger the variance, the greater
the advantage of composite sampling for
capturing coliform bacteria. When, how-
ever,  the value  of  the   variance
approaches the mean density, composite
sampling does  not provide  any  great
advantage for  detecting coliform bacteria.
The  agreement of  the simulated results
with  the  predictions of the closed form
model provides some  assurance of  the
reliability of the conclusions.

Laboratory Study
   The laboratory study included con-
trolled experiments  for testing  hypoth-
eses  about  the  effectiveness  of
composite  sampling  for  capturing
bacteria entering  or in a water distribution
system. Evidence  of  the  efficacy  and
 fficiency of composite sampling as com-
pared with grab sampling was developed
by  means  of  these experiments. The
laboratory results turned  out to  be the
primary verification of the results from the
mathematical models, since few coliform
bacteria  were  found in either grab  or
composite  samples during the  field

   The criteria  that governed selection of
a sampler were that  it should (1) be easy
to clean, (2) be  constructed so that the
parts coming  in  contact with the water
could  be sterilized or sanitized, (3)
require only standard fittings and fixtures
to install, and (4)  be  portable and easy to
set up. The intent was to select a stock or
modified commercial sampler;  however,
none of  the suppliers  queried had  or
knew  of such a stock sampler. The
Sigma  Model 6301* (American Sigma PO
Box 300, Middleport, NY  14105-0300)
was selected largely  because of its ability
to  index through a series of sample
containers,   which  would  provide
sequential composite samples. Additional
samplers  were  also  constructed
consisting  of  variable  rate peristaltic
pumps  and  polypropylene  sample
containers (Nalgene 2319 series).
   To  produce large variances  of the
coliform densities, a  syringe pump  driven
by a very accurate timer was selected to
deliver  the  inoculum.  The composite
samples  were  collected by means of  a
peristaltic  pump operated at a rate
selected to provide the  sample size
desired.  Tubing  and pump heads were
selected  to provide  residence  times  in
the experimental  system consistent with
residence times expected or experienced
in field  applications.
   The laboratory composite sampling
systems were modified from time to time
as  experimental requirements  made
additional controls necessary. Composite
samples were collected with variable rate
peristaltic  pumps  set to  collect the
desired  volume.  Volumes  collected for
the composite  samples ranged between
0.1  and 4.0  L/hr.
  All composite  samples were  analyzed
in  their entirety.  Intermittent inoculation
was used to simulate the occurrence of
coliform  bacteria  in  a  real  distribution
system; i.e., relatively high densities were
injected over relatively  short periods  of
time and relatively small portions  of the
flow contained  most  of the bacteria. Both
 "Mention  of trade  names or commercial
 products does not constitute endorsement or
 recommendation for use.
Escherichia  coli (ATCC 8739) and
Enterobacter  cloacae  (ATCC  13047)
were used in the laboratory experiments,
and  there were no  differences in the
results obtained using  the two different
organisms.  The inoculum  density was
changed by using different dilutions of
the  initial  culture; using   different
inoculation  rates;  varying  the  flow rate;
and, to a much lesser extent, varying the
periodicity of inoculation.

   The  laboratory  experiments  were
designed to show that (1) the recovery of
coliform bacteria by  composite samples
from flows  of  water  with known disper-
sions, in which very little  of the water
under test  contained all the  coliforms,
were not significantly different from the
predicted frequency  of  occurrence, (2)
the threshold  for coliform  detection was
generally in the range predicted, and (3)
the  mean  coliform densities  of  the
samples  were  not significantly  different
from those calculated from  the inoculum
density. The control of the  dispersions of
bacteria in the  flow of water to mimic the
occurrence  of  coliform bacteria  in actual
water systems  was  a central  theme of
these experiments.
   An agreement  was obtained  between
the theoretical frequency of occurrence of
various densities and the actual densities
obtained for all overnight  (18  to 24 hr)
composite sampling runs.  These results
indicated that the composite sample den-
sities were substantially in agreement
with  the  densities that  were  introduced
into  the experimental  system by  the
syringe  pump.  The probability of captur-
ing a coliform was directly related to the
highest  density in  the flow  of  water
sampled. The 95% probability of captur-
ing a single coliform in the  composite
was  the 95%  probability  of  a single
coliform occurring in  the sample portion
given the sampled stream density.
   The  data  showed  that composite
sampling provided  equal  or  superior
performance for times of both high and
low  probability  of  capturing  coliform
bacteria  and  hence, for  both levels
coliform  occurrence. All  experiments
accepted for further analysis  were from
systems  tested for  and  found free  of
coliform  contamination.  Bacterial
densities in composite samples  were
consistent  with stream densities
calculated from inoculum  densities and
from  the  volume  of  flow  for all
experiments. Experiments  designed  to
test  the effect of  variability on  the
frequency of  positive  sample  results
followed predictions of  the closed form

Table 1.


Effect of Variability of Conform Counts on Arithmetic Parameters
2.46 X TO7
3.305 x TO'2
5.03 x 10-8
3.305 x 108
Probability of
Any Positive Result
1 x 10'9
Result > 1
1 x 10'9
and simulation models; i.e., that, for any
given  mean density, higher variability will
provide  a greater frequency of  positive
portions.  Further,  the  frequency  of
positive  portions was  directly related to
the maximum stream  density  for  any
given  size of aliquot. Finally, experiments
directly  comparing composite and grab
sampling from the same  stream conclu-
sively demonstrated  the  superiority of
composite  sampling for  capturing
coliform bacteria.

Field Studies
   Field  sampling results  were  obtained
from waters from two different distribution
systems, West Chester  and Downing-
town.  Both  of these  systems are in
Chester  County, Pennsylvania,  about 30
miles west of Philadelphia. Neither have a
record of violations of the  microbiological
maximum contaminant  level. The objec-
tives of the field sampling  were to test the
use of the composite sampler in realistic
situations, to  attempt  to  obtain further
verification  of  the  mathematical model
and to compare grab samples  with the
composite samples.

   The composite  sampling  setups  for
the field  studies were identical  to those
used in the laboratory. The West Chester
sites  were both  at  system  pressure,
approximately 160 to 180  psi at  the plant
and 140 to 160  psi  at  the tank. The
Downingtown  sampler was not used on a
pressurized line but drew  from the top of
the filters and  from  the  filter  effluent.
Composite  and grab samples were col-
lected over  18- to 24-hr periods  and
protected from  sunlight during  transport
in insulated  containers  with   artificial
coolant packs. All microbiological proce-
dures were  completed within  6 hr of
   Each sample,  composite and grab,
was tested for total coliform bacteria and
heterotrophic  plate count. Large aliquots
could  be filtered by the MF procedure for
all the finished  water samples  and both
300 and 500  mL portions were  routinely
filtered  with  no evident  reduction in
filtrate flow due to occlusion or matting of
filter  surfaces.  In  addition  to  the
microbiological  analyses,  each sample
source was tested each day for  free and
total chlorine, temperature,  and  pH. The
turbidity of all except West Chester tank
samples  was  also  determined  each
sampling day.

West Chester Results
   The East  Branch  of the Brandywine
Creek was the source of raw water during
the period of sampling. The  raw water
had very  high  densities  of  coliform
bacteria from  agricultural land runoff and
wastewater discharges. Treatment  con-
sisted  of  prechlorination,  flocculation,
settling, rapid sand filtration, and  post
chlorination.  Composite samples  were
concurrently  taken  of the  treated water
(the high pressure side of one of the high
service  pumps) and  the  flow  to the
storage tank. Overall,  36 sets  of 2
composite samples and   5  individual
composite samples  (77 total  composite
samples) were obtained from this system
from June  to November 1987. In  addition,
grab samples of the raw, finished, and
distribution system  water were collected.
The distribution  system samples  were
obtained from both private residences
and fire hydrants.
   Only  one  of  the  composite samples,
which  was obtained from  the tank  site,
had coliform  bacteria.  Four  500-mL
portions were positive, three with  one
organism  each  and one with two.  This
gave a sample density of 0.00098 per mL
for the  approximately 2-gal composite,
thereby demonstrating the  ability of
composite sampling  to detect  coliform
bacteria at low  densities.  Three of 104
grab samples of the finished water and 2
of  96  grab samples from  private
residences had coliform bacteria.  More
coliform bacteria were detected in  the
grab samples  than  in  the composite
samples. Overall coliform  densities  were
much lower than 1.0 per 100  mL, ai
these results were probably just happe

Dowingtown Results
   Two water sources, Copeland Run ai
Beaver Creek, supplied about 30% ai
70%  of the water treated, respective!
There were approximately  8 miles
mains, most 6  or 8 in., and 2,100 servii
connections. The system had three stc
age sites,  a 4-MG open storage reserve
at the plant and two 2-MG  steel grout
storage  tanks  on elevations  north  ar
south of the Borough proper.
   A history of poor turbidity removal w;
one  reason for selecting  this plant  f
sampling.  There was no  provision  f
continuous sludge removal. Filter influe
turbidities  were sometimes very high, ar
it was hoped that some  coliform  positi>
composite samples would result from th
sampling series despite the 2 mg/L fr«
chlorine residuals maintained through  tt
   The composite samples of  the influe
were analyzed in full. These data showe
that composite sampling can provide da
at least  equivalent to even the  stricte
grab sampling regimen. In these expei
ments, grab samples were  taken  alte
nately from the  top of the filters (har
dipped) and the effluent sampling port
a  rate of  between 8 and  20 per hr f
each sampling location.  Composite sar
piers were operated at a rate  around 3(
mL/hr, which  provided a  1.5 gal 24-I
composite sample.
   The results of the  field sampling  d
not achieve the objectives of  this part
the project. The occurrence  of coliforn
in the plant effluent in these systems w<
not high  enough  to  provide the da
needed. Unfortunately, the samples wi
coliform  bacteria  present came  moi
often  from the grab  samples than fro
the composite sampler. This does  n
prove that the theoretical model or  tt
laboratory results are  incorrect, only th
the  systems  selected  for the  fie
sampling  did not provide  the conditior

needed  for  the composite  sampler
performance to be demonstrated.

1. If  coliform  bacteria  were  ever
   randomly dispersed in a body of water
   (i.e., the variance of the count per unit
   volume is  equal  to the mean  density
   per unit volume), the  probability of
   capturing coliform bacteria  would be
   proportional to  the  total volume of
   water collected and would not depend
   on the total number of samples or how
   the samples were collected.  A random
   dispersion of bacteria in a body of
   water  can be achieved  by  complete
   mixing of the water; this, of  course, is
   very  unlikely to  occur in  a  water
   distribution system.
2. For water supply  systems in  which the
   coliform  bacteria are not randomly dis-
   tributed  but  show  an aggregated
   arrangement (i.e., one  in which the
   variance of the counts per unit  volume
   is  greater than  the  mean  density),
   composite sampling is more effective
   than  grab  sampling  in capturing
   coliform  bacteria in  any volume of
   water tested. This conclusion is based
   on a closed form  mathematical model,
   computer simulation of sampling from
   a lognormal distribution, and  a  lab-
   oratory study of composite sampling.
3. The results of  sampling  municipal
   water systems during this project did
   not demonstrate  the  superiority of
   composite sampling  for collection of
   coliforms under field conditions.
4. The commercially available composite
   samplers could  not  be  adapted  for
   truly continuous, aseptic sampling of a
   stream treated  water  under  pressure.
   The best that could be achieved was
   very frequent intermittent collection of
   very small volumes of water.
5. For intermittent composite sampling of
   a stream of water from a  treatment
   plant,  the  probability  of  capturing
   coliform  bacteria  in any given sample
   volume is a function of the volume of
   sample tested, the size of the  stream
   of  water sampled, and the frequency
   of collecting the component aliquots.

   The full  report  was  submitted in
fulfillment of Cooperative Agreement No.
CR 813337 by Drexel  University  under
the sponsorship of the  U.S.  Environ-
mental Protection Agency.

  Wesley 0. Pipes and Harvey A. Minnigh are with Drexel University, Philadelphia,
        PA 19104.
   Donald J. fteasoner is the EPA Project Officer (see below).
  The complete report, entitled "Composite Sampling for  Detection of Coliform
        Bacteria in Water Supply," (Order  No. PB 90 192-7581 AS; Cost: $17.00,
        subject to change) will be available only from:
           National Technical Information Service
           5285 Port Royal Road
           Springfield, VA22161
           Telephone: 703-487-4650
  The EPA Project Officer can be contacted at:
           Risk Reduction Engineering Laboratory
           U.S. Environmental Protection Agency
           Cincinnati, OH 45268
United States
Environmental Protection
Center for Environmental Research
Cincinnati OH 45268
        •~?A\ =E*