Geoscience Reference
In-Depth Information
Technique: Calculating discharge consents
In England and Wales the setting of discharge
consents for point source pollution control is
carried out by the Environment Agency. A dis-
charge consent gives a company the right to
dispose of a certain amount of liquid waste into a
river system so long as the pollution levels within
the discharge are below certain levels. To calculate
what those critical levels are a series of computer
programs are used. These computer programs are
in the public domain and can be obtained from the
Environment Agency. They use very simple
principles that are described here.
The main part of the discharge consent calcula-
tion concentrates on a simple mass balance
equation (7.3):
n
water quality parameter
Figure 7.8
A log-normal distribution (broken line)
compared to a normal distribution (solid line).
value of
C
D
is calculated many times (often set to
1,000) so that a distribution for
C
D
can be drawn.
The consent to discharge figure is taken from
the distribution of
C
D
, usually looking at the
90 or 95-percentile values, i.e. the target will be
achieved 90 or 95 per cent of the time.
+
+
QC QC
QQ
UU EE
BE
=
(7.3)
C
D
where
Q
refers to the amount of flow (m
3
/s)
and
C
the concentration of pollutant. For the
subscripts:
D
is for downstream;
U
is for upstream
(i.e. the background); and
E
is for the effluent.
With this mass balance equation the down-
stream concentration can be calculated with
varying flows and levels of effluent concentrations.
This variation in flow and concentration is achieved
through a computer program running a Monte
Carlo simulation.
In this case the Monte Carlo simulation involves
a random series of values for
Q
U
,
Q
E
,
C
U
and
C
E
drawn from an assumed distribution for each
variable. It is assumed that the distributions
are log-normal in shape (see Figure 7.8) and there-
fore using the data in Table 7.7 the actual
distribution for each variable is simulated. Once
the distribution for each variable is known then a
random variable is chosen from that distribution.
In the case of a log-normal distribution this means
that it is most likely to be close to the mean value
but more likely to be above than below the mean
(see Figure 7.8). In a Monte Carlo simulation the
Table 7.7
Parameters required to run a Monte
Carlo simulation to assess a discharge consent
Variable
Required data
River flow (
Q
U
)
Mean daily flow and
Q
95
Upstream river
Mean value and standard
quality (
C
U
)
deviation
Effluent flow (
Q
E
)
Mean value and standard
deviation
Effluent quality (
C
E
)
Mean and standard
deviation
The values that are required for calculating
a consent to discharge (see Table 7.7) are derived
from normal hydrological data. River flow data
can be derived from a flow duration curve
(see Chapter 6). The water quality information
requires at least three to four years of regular
measurements. The values to describe
Q
E
and
C
E
will either be known or are to be varied in
the simulation in order to derive a consent to
discharge value.
