Modeling and Assessment of the Produced Water Discharges from Offshore Petroleum Platforms

Abstract

There has been a growing interest in assessing the risks to the marine environment from produced water discharges. This study describes the development of a numerical approach, POM-RW, based on an integration of the Princeton Ocean Model (POM) and a Random Walk (RW) simulation of pollutant transport. Specifi cally, the POM is employed to simulate local ocean currents. It provides three-dimensional hydrodynamic input to a Random Walk model focused on the dispersion of toxic components within the produced water stream on a regional spatial scale. Model development and fi eld validation of the predicted current fi eld and pollutant concentrations were conducted in conjunction with a water quality and ecological monitoring program for an offshore facility located on the Grand Banks of Canada. Results indicate that the POM-RW approach is useful to address environmental risks associated with the produced water discharges.

Full text

* Corresponding author: zhichen@bcee.concordia.ca
303
Modeling and Assessment of the Produced Water Discharges from
Offshore Petroleum Platforms
Zhi Chen,1* Lin Zhao,1 Kenneth Lee,2 and Charles Hannath2
1 Department of Building, Civil and Environmental Engineering, Concordia University, Montreal, Quebec, Canada
H3G 1M8
2 Bedford Institute of Oceanography, Fisheries and Oceans Canada, Dartmouth, Nova Scotia, Canada B2Y 4A2
There has been a growing interest in assessing the risks to the marine environment from produced water discharges. This
study describes the development of a numerical approach, POM-RW, based on an integration of the Princeton Ocean Model
(POM) and a Random Walk (RW) simulation of pollutant transport. Speci cally, the POM is employed to simulate local
ocean currents. It provides three-dimensional hydrodynamic input to a Random Walk model focused on the dispersion of
toxic components within the produced water stream on a regional spatial scale. Model development and  eld validation of
the predicted current  eld and pollutant concentrations were conducted in conjunction with a water quality and ecological
monitoring program for an offshore facility located on the Grand Banks of Canada. Results indicate that the POM-RW
approach is useful to address environmental risks associated with the produced water discharges.
Key words: POM, Random Walk model, simulation, produced water, heavy metal
Introduction
Produced water is the largest ef uent discharge
associated with offshore oil and gas production. The
total volume of produced water ef uent is expected
to increase with future anticipated development of
offshore oil and gas reserves worldwide (Gordon et al.
2000). The environmental impact potentially caused by
produced water is related to the fate and transport of its
individual components including organic and inorganic
compounds (e.g., petroleum hydrocarbons, heavy metals,
nutrients, natural radionuclides) associated with the
formation water and treating chemicals (Hodgins 1993).
Although produced water discharges are associated with
rapid dilution and low-to-trace levels of pollutants, the
potential for cumulative toxic effects under regional
ocean currents warrants a need to assess the long-term
risks to the marine ecosystems (Lee et al. 2005).
There is increasing environmental concern over
the ocean discharge of contaminants, such as metals
and hydrocarbons, in produced water because of their
potential for bioaccumulation and toxicity, particularly
by those dissolved in the water phase (Neff 2002; Neff
et al. 2006). It is noted that hydrocarbons and heavy
metals show different fate and transport mechanisms due
to their differences in physicohemical properties. Low-
concentrations of hydrocarbons in a large discharge of
produced water can be rapidly diluted by tidal currents
and decay over time due to aerobic degradation. Thus,
the effects of hydrocarbons associated with produced
water discharges are primarily linked to localized areas
and unlikely to cause large-scale environmental impacts
(National Research Council 1985). In contrast, a large
number of heavy metals are stable, environmentally
persistent, and highly toxic. Furthermore, they can be
accumulated by marine life in concentrations several
thousand times higher than those in the surrounding
seawater (Foster 1976; Bryan and Langston 1982). For
example, lead (Pb) is a highly toxic metal with persistent
adverse effects in the marine ecosystem, and the toxic
effects on shell sh can occur even in the presence of a
very low concentration of Pb (Dojlido and Best 1993).
Previous models have been developed to predict the
dispersion and transport of produced water discharges
in the coastal environment, especially for sites around
the North Sea and the Gulf of Mexico (Ray and
Engelhardt 1992; Reed and Johnsen 1996). For example,
McFarlane (2005) applied chemometrics to describe the
contamination of produced water by soluble organic
compounds based on a partial least-squares statistical model.
Rye et al. (1996) proposed a dispersion-dilution model
to study the transport and dilution of produced water
and the resulting uptake and biomagni cation in marine
biota. Smith et al. (2004) conducted a  eld veri cation of
the Offshore Operators Committee Mud and Produced
Water Discharge Model. In recent years, the Random
Walk method has been used as a means to model the
dispersion of pollutants in the aquatic system. Gillibrand
et al. (1995) simulated the dispersion of produced water
in the northern North Sea (the East Shetland area) using a
Random Walk model. Riddle et al. (2001) also developed
a Random Walk model to compute the concentration
distribution of dispersed oil in the North Sea resulting
from produced water discharges. The above-reviewed
studies provide a basis for new model development for
managing offshore produced water discharges.
The hydrodynamic nature of the marine environment,
namely the changing current  eld, is known to govern
the transport and dispersion of discharged produced
Water Qual. Res. J. Canada, 2007 · Volume 42, No. 4, 303-310

304
Chen et al.
water constituents linked with potential environmental
impacts. Unfortunately, to date, there has been a lack
of consideration given to current data inputs in fate
and transport models. To address this issue, we propose
a new modeling approach, POM-RW, that integrates
a hydrodynamic ocean current model (POM) with a
dispersion model (Random Walk [RW] model) to simulate
the fate and transport of contaminants associated with
produced water discharges. The POM (Princeton Ocean
Model) three-dimensional (3D) hydrodynamic model
was employed to provide the current  eld data within
a produced water discharge area of Atlantic Canada to
support the application of the Random Walk model to
simulate the dispersion of produced water discharges
in three dimensions. A  eld validation study for the
integrated current simulation and dispersion model was
conducted as part of an environment effects monitoring
program for a representative offshore platform facility
(i.e., Hibernia), which is located on the Grand Banks of
Newfoundland along the east coast of Canada.
Development of a POM-RW Modeling Approach
Integration of Ocean Current Model and Pollutant
Dispersion Model
The ocean current is the most important factor determining
the direction and rate at which produced water disperses.
In the present study, POM, as a sigma-coordinate, free-
surface coastal ocean model, is implemented to simulate
the velocity  eld of the coastal area under study.
A new pollutant dispersion modeling approach that
integrates the pollutant dispersion model (Random Walk
model) with the 3D ocean current modeling components
from POM has been developed. It is hereafter called the
POM-RW approach. The framework of the developed
POM-RW approach is presented in Figure 1. As shown
in the  gure, the POM-RW method includes three major
components: data collection and input processing,  ow
 eld simulation, and 3D pollutant dispersion modeling.
Ocean Circulation Model – POM
POM is a three-dimensional, sigma coordinate, free-
surface estuarine and coastal ocean circulation model.
Its apparently unique feature is the imbedded turbulent
closure submodel, which yields realistic, Ekman surface
and bottom layers (Blumberg and Mellor 1987). The
model represents ocean physics as realistically as possible
and addresses large-scale and long-term phenomena,
depending on the basin size and grid resolution.
The main governing equations used in POM are as
follows (Blumberg and Mellor 1987; Mellor 2004):
The continuity equation:
DU DV 
Z

K
x y Vt
+++= 0 (1)
Fig. 1. The integrated POM-RW approach based on POM
and the Random Walk model.
The momentum equations:
UD U 2D UVD U
Z
- fVD + gD
KgD
2
t x y V x U0
++++
[

U
' V' D
U
'
x D xV'
]
-dV’ =
[
Km U
]
VD V +Fx
(2)
VD UVD V 2D V
Z
+ fUD + gD
t x y V
++
+
KgD
2
y U0
+
[

U
' V' D
U
'
y D xV'
]
-dV’ =
[
Km V
]
VD V +Fy
(3)
The turbulence closure equations:
q2D Uq 2D Vq2D 
Zq
2
t x y V
++
+
[
Kq q2
D V
]
=
V
2KM
D
+U
V
[
(
]
)
2
+V
V
()
2
+2g
U
0
KH

U
V -2Dq3
B1l
~+ Fq
(4)
q2lD Uq 2lD Vq2lD 
Zq
2
l
t x y V
++
+
[
Kq q2l
D V
]
=
V
+ E1lU
V
[
(
]
)
2
+V
V
()
2
+E3g
U
0
KH

U
V
~
{
KM
D
}
-Dq3
B1
W + Fl
~
(5)
where:
U, V are the horizontal velocities (m·s-1);
ω is the velocity component normal to sigma
surfaces (m·s-1);
η is the surface elevation (m);
D ≡ H + η is the total elevation of the surface
water (m);
x, y are the horizontal Cartesian coordinates (m);
σ is the sigma vertical coordinate (m);
∫
0
V
∫
0
V
Xnew = Xold + Udt + fxα
Ynew = Yold + Vdt + fyβ
Znew = Zold + Wdt + fzγ

305
t is time (s);
f is the Coriolis parameter (s-1);
g is gravitational acceleration;
ρ’ = ρ - ρmean before the integration is carried out;
ρmean is generally the initial density  eld which is area
averaged on z-levels and then transferred to
sigma coordinates in the exact same way as the
initial density  eld;
KM is vertical kinematic viscosity (m2·s-1);
Fx, Fy are the horizontal diffusion terms (m2·s-2);
KH is vertical diffusivity (m2·s-1);
q2 is twice the turbulence kinetic energy (m2·s-2);
l is turbulence length scale (m).
Pollutant Dispersion – A Random Walk Model
The Random Walk model is based on the particle
tracking approach, which follows the concept of the
random movement of particles. Speci cally, particles
are represented as real entities spread across the
computational domain rather than as concentrations.
The ef uent discharge is represented by placing a  xed
number of “particles”, converted from the discharge
rate and concentration, at the outfall position at each
timestep (Riddle 1998). The POM is implemented to
seamlessly provide the velocity components at each
coordinate. These particles are therefore moved during
each subsequent timestep (Webb 1982):
Xnew = Xold + Udt + fxα
Ynew = Yold + Vdt + fyβ
Znew = Zold + Wdt + fzγ
where:
X, Y and Z represent the position of a particle and the
subscripts “old” and “new” represent the positions
at the start and end of a model timestep;
dt is the timestep, and U, V and W are the horizontal
and vertical velocity components at time t from the
POM model and the effect of wind, respectively;
The functions fx, fy and fz de ne the mixing process;
α, β and γ are random numbers from a standard
normal distribution.
Each particle represents a  xed mass of ef uent, and it is
assumed that no reaction takes place.
A constant diffusion coef cient based on the Fickian
equation is used to characterize the horizontal and
vertical diffusion as follows:
(6)
fx = fy = 2Khdt
«
fz = 2Kzdt
«(7)
where
Kh and Kz are the horizontal and vertical mixing
coef cients (m2·s-1).
Conversion of particle numbers and locations into
concentrations is straightforward. The concentration
distribution of a pollutant in the water is quanti ed using
a counting cell. The number of particles in a grid cell
over a depth interval from the water surface down to a
speci ed depth is counted, giving the mass of the pollutant
in a known volume, and therefore the concentration is
computed. We can write the following expression for
the concentration calculation under the assumption that
each particle has the same mass (Suh 2006):
C = mP
Ah (8)
where:
C is the average concentration in a cell (Pg·L-1);
m is the mass of a particle in mg (i.e. total mass of the
system divided by the number of particles);
P is the number of particles in the cell;
A is the area of the cell (m2);
h is the average depth of the cell (m).
Application of the POM-RW Approach
The developed POM-RW approach was validated with
data collected around an offshore platform facility
located in the Atlantic Ocean off the east coast of Canada.
A large-scale area for the ocean current simulation
has been con gured to eliminate the in uence of open
boundaries on the study area. Within the simulations, the
concentrations of Pb were used to track the 3D discharge
pattern of the produced water. Corresponding 3D  eld
monitoring data were provided from a  eld based
environmental effects monitoring program to validate
the POM-RW approach.
Overview of the Study Site
The Hibernia platform is located at 46°75’N, 48°78’W
off Canada’s east coast, on the Grand Banks of
Newfoundland, 315 km off the coast of Newfoundland
(Fig. 2). It is situated in relatively shallow water,
approximately 80 meters deep. The Hibernia oil  eld was
discovered in 1979. It began producing oil in November
1997. Figure 2 presents the Hibernia platform location
and the chosen modeling area. The small inside square
around the Hibernia site is the study area for the present
research. The area measures 50 km by 50 km with the
Hibernia platform in the centre.
The major issue involved in the ocean current
simulation in the present research is that the Hibernia
platform is located in an open sea; four lateral boundaries
are completely unbounded in the study area as shown in
Fig. 2. There are no existing current monitoring stations (or
existing  eld observation data) for each lateral boundary.
Thus, the situation leaves no choice but to use numerical
open boundary conditions for each lateral boundary.
Modeling of Produced Water Discharges

306
However, no matter which kinds of open boundary
conditions have been chosen, numerical errors will exist
and may create an unrealistic  ow across the boundary,
consequently affecting the simulation results. Therefore,
in order to eliminate the numerical errors for the study
area, simulating ocean current on a larger scale covering
the study area at the centre is proposed in the present
paper. A large-scale area was chosen from 60°W, 44°N
to 45°W, 45°N as shown in Fig. 2. The left boundary is
along the shore of Canada’s east coast. Only the portion
of ocean current modeling results related to the study
area was used for pollutant dispersion simulation, which
is from 49°135’W, 46°54’N to 48°475’W, 47°02’N.
Fig. 2. Study site and modeling area.
The model grid and bottom topography are shown
in Fig. 3. The solution of the horizontal grid is modi ed
into Cartesian coordinate grids, which have 90 by 93
nodes for the large-scale area. The size of the model grids
is generated as Δx = Δy = 2 km in the study area. Outside
the study area, the size of the model grids is designed to
be larger than the inside study area, where the grids vary
between Δx ≈ 8 km to Δx ≈ 50 km, Δy ≈ 12 km for the
irregular mesh as shown in Fig. 3.
The constructed sigma coordinate for the study site
has 21 vertical layers, σ = (0.0, -0.0263, -0.0526, -0.1053,
-0.1579, -0.2105, -0.2632, -0.3158, -0.3684, -0.4211,
-0.4737, -0.5263, -0.5789, -0.6316, -0.6842, -0.7368,
-0.7895, -0.8421, -0.8947, -0.9474, -1.0) and σ = (z-η)/
(H+η). The vertical resolution is higher near the surface.
For example, for a grid point where the water depth is 80
m, Δz is around 2 m at the surface and 4 m in the other
layers.
The current model was initialized by mainly using the
climatological data of June 2005 and was run for 30 days.
The data set includes sea surface temperature obtained
from the Fisheries and Oceans Canada Oceanographic
database and includes the hourly averaged wind speed
and directions of June 2005 from the Environment
Canada climatic database, the National Data Buoy Centre
database, and the Hibernia Annual Environmental Data
Summary Report in 2005 (Lee et al. 2005). The wind
data were collected from 28 locations, including the
Hibernia platform. Most of the wind monitoring stations
are distributed along the west and south boundaries of
the large-scale area (Fig. 2).
Samples of produced water and ambient sea water
at 3 depths from the surface to the ocean bottom were
collected by the Bedford Institute of Oceanography
research cruise during the period of 27 June 2005
to 7 July 2005. The analysis of the sea water samples
was conducted by the Centre for Offshore Oil and
Gas Environmental Research at the Bedford Institute
of Oceanography. The Pb concentration in produced
water was analyzed by the Trace Analysis Facility at the
University of Regina.
Among those contaminants in the produced water,
the dispersion of Pb was used as a tracer in this study
to validate the POM-RW model due to its conservative
nature. The background dissolved Pb concentration in
seawater was 0.001 μg·L-1 based on the measurement,
and a continuous point discharge of produced water at a
depth of 40 m below the surface at the Hibernia platform
was identi ed and considered for dispersion modeling.
The emission rate of produced water was 882 m3/hr at
456.7 μg·L-1 of Pb, assuming that Pb is conservative.
Based on the comparison with the  eld observation data
and the values published in the literature (Riddle 1998;
Riddle et al. 2001), the horizontal mixing coef cient of
50 m2·s-1 and vertical coef cient of 1 × 10-3 m2·s-1 were
adopted in this paper.
3D Current Simulation and the Comparison with
Field Data
The  rst step of the current simulation was to generate
the model grid with a set of 90 by 93 nodes for the larger-
scale area as shown in Fig. 3, which contains the Hibernia
site from 49°30’W, 46°40’N to 48°20’W, 47°20’N. The
topography, temperature, salinity, and hourly wind data
for the larger domain containing the study site were
interpolated into Cartesian horizontal grids and vertical
sigma coordinate layers as the input conditions. At the
four lateral open boundaries (the locations where the
water depths were lower than 10 m were considered
Fig. 3. Model grid and bottom topography contour map (The
diamond point is the location of Hibernia, the square around
the Hibernia platform is the study area).
Chen et al.

307
as closed boundaries in the model), Sommerfeld-type
radiation conditions were used (Mellor 2004; Palma and
Matano 1998).
The current modeling results were obtained as daily
averaged velocities and visualized through vector  elds.
Comparisons with the observed current vector data were
conducted at three depths: the surface, 9 meters from the
surface, and 42 meters from the surface. Figures 4a and
b show the surface modeling results of the current vector
 eld after a model run of 5 days and 15 days, respectively.
Corresponding to each day, the  eld observations are
real-time velocities, which were measured by a MIROS
Directional Wave and Current Radar installed on the
Hibernia Platform (Oceans Ltd. 2006). Figures 4a and
b, with a comparison of both magnitude and direction,
indicate that POM can provide a reasonable simulation
of the surface current in the Hibernia area.
Figures 5a and b give the velocity vector comparisons
at 9 m of depth in the water after a model run of 16 days
and of 23 days, corresponding to the observed current
velocity data that occurred during the period from 16
June 2005 to 24 June 2005 at locations indicated in
Fig. 5. Figures 6a and b give the current velocity vector
comparisons at 42 m of depth after a model run of 16
days and 23 days, corresponding to the  eld data that
occurred during the period from 16 June 2005 to 24
June 2005 for this depth measured by the Oceans Ltd.
in 2005 (Oceans Ltd. 2006). The comparisons between
simulation and monitoring results in 3D indicate that
the modeling of ocean currents in the Hibernia area
is satisfactory using POM, which accounts for local
hydrodynamic effects and is in direct support of assessing
the dispersion of pollutants resulting from the coastal
petroleum production process.
Pb Dispersion Modeling Results and a Comparison
with Field Monitoring Data
The POM-RW method was formulated to simulate the
dispersion of Pb in the produced water ef uent in the
present study. The model ran for 30 days with a timestep
Fig. 4. Modeling result of surface  ow velocity  eld for (a) June 5th, 2005 (the observed magnitude and direction of current
velocity at the Hibernia site on the June 5th, 2005 is in bold) and for (b) June 15th, 2005 (the observed magnitude and direction
of current velocity at the Hibernia site on the June 15th, 2005 is in bold).
(a) (b)
of 180 s and a release of 200 particles per timestep. The
Pb dispersion results compared with  eld data at 10, 35,
and 60 m are shown in Fig. 7a, b, and c, respectively.
The modeling results are the distribution of average
concentration for the model run from 21 days to 30 days.
It shows that the model results have good agreement
with the  eld observations at the depth of 35 m, which is
the closest layer to the emission source point. Figure 7b
also clearly shows the emission source location with the
highest concentration in the resulting plume at that layer.
The  ow modeling results for the layer at the depths of
10 and 60 m con rm that the effects of the turbulent
currents have been quanti ed to support a  eld modeling
of pollutant dispersion. This explains why the dispersed
pollutants move slightly to the north of the Hibernia site
as indicated in Fig. 7a and c.
The predicted concentrations for  eld locations far
away from the emission source are generally lower than
the sample concentrations as shown in Fig. 7a and c. This
could be explained as follows: i) the computational grid
cells were set at 2 km by 2 km by 4 m for the study
region, which can be re ned with high performance
computational facility; ii) there are uncertainties
associated with the natural marine condition as well
as the possible operational changes of produced water
discharges from the source; iii) the model ran for only 30
days; most of the particles could still accumulate in the
near  eld and possibly only a small number of particles
reached the surface and the bottom; and iv) the mixing
coef cients were assumed constant in this study; different
values of the coef cients will affect the dispersion pattern
(Chen and Huang 2003).
Discussion and Uncertainty Analysis
Determination of boundary conditions is critical for
a successful simulation of the coastal current  eld.
Modeling and veri cation results in this study con rm
that the development of a radiation-type open boundary
condition is appropriate for modeling the ocean current
 elds in the study area. Additionally, a much larger and
Modeling of Produced Water Discharges

308
wider area containing the study region (Fig. 2) is considered
to minimize the in uence of boundary conditions for the
study region. An integrated effort was made in this study
for 3D  eld sampling and measurement, which directly
supported the  eld validation of the developed POM-
RW. More regular monitoring of the local ocean current
conditions will further help to con gure the complex
model boundary conditions.
Field validation indicates that the developed POM-
RM approach can provide better prediction of pollutant
concentration close to the emission source (Fig. 7b), but
modeling outputs for locations near to the surface and
the ocean bottom do not match with monitoring data
very well (Fig. 7 b and c). This can be further attributed
to the following: (i) the Random Walk approach provides
better results in the near- eld region, and it might result in
erroneous particle distributions in the far- eld locations
(Suh 2006); (ii) the tide was not considered in this study,
which could contribute to more dilution and to carrying
pollutants to different locations from the predicted results;
and (iii) instantaneous changes of current in the study
(a) (b)
Fig. 5. Modeling result of  ow velocity  eld at the 9-meter depth from surface for (a) 16 June 2005 and for (b) 23 June 2005. The
measured data at locations around Hibernia at the 9-meter depth are in bold for the period of 16 June 2005 to 24 June 2005.
(a) (b)
Fig. 6. Modeling result of  ow velocity  eld at the 42-meter depth from surface for (a) 16 June 2005 and for (b) 23 June
2005. The measured data at locations around Hibernia at the 42-meter depth are in bold for the period of 16 June 2005 to 24
June 2005.
area due to aquatic life activities, sailing ships, and oil and
gas production and transportation activities would also
change the pattern of dispersion. Nevertheless, this study
shows that the developed POM-RW approach is capable
of examining both regional circulation conditions and
pollutant dispersal for the study site.
Additionally, determination of key dispersion
model parameters was a dif cult task during the model
application study. Especially, the horizontal and vertical
mixing coef cients, Kh and Kz given in equation 7, are
among the most important factors to determine the
concentrations of pollutants in the environment. A
thorough analysis of the model and site uncertainties is
suggested in future studies (Chen and Huang 2003).
Conclusions
A POM-RW approach has been developed in this study
based on a Princeton Ocean Model and a Random
Walk simulation. Notably, the effects of ocean current
on the dispersion of pollutants in the natural marine
Chen et al.

309
(a) (b)
(c)
Fig. 7. Modeling results for the dispersion of Pb with a comparison with monitoring data at (a) a 10-meter depth (μg/L), (b) a
35-meter depth (μg/L), and (c) a 60-meter depth (μg/L).
environment can be fully considered for addressing
potential environmental impacts associated with large
waste ef uents from offshore oil production activities.
Based on the full consideration of boundary
conditions, the modeling results of the  ow  eld indicate
that POM can provide satisfactory current simulations
for the study region. Therefore, it not only helps to
understand the ocean current circulation pattern in the
Atlantic Ocean off the east coast of Canada, but also
provides hydrodynamic inputs to the model of pollutant
dispersal.
A  eld program has been conducted to supply
monitoring data of the ambient ocean water quality.
Comparing the  eld data with the modeling results shows
a relationship that the developed POM-RW approach can
provide an environmental assessment of the produced
water discharge activities near its source. Although
Pb was used in this research as a model contaminant
Modeling of Produced Water Discharges

310
tracer, the dispersion and risks of other contaminants
to the regional marine environment may be examined
using the developed modeling approach. This research
will contribute to the development of effective decision
tools for the long-term management of produced water
discharges in the ocean environment.
Acknowledgments
We would like to acknowledge the professional sample
analysis work by Renata Bailey at the University of
Regina, and by Susan Cobanli from Fisheries and Oceans
Canada. This study was funded by the 2005-2006
PetroCanada Young Innovator Program, Natural Science
and Engineering Research Council Canada Discovery
Program, Fisheries and Oceans Canada, and the Program
of Energy Research and Development (PERD).
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Received: 21 February 2007; accepted: 30 October 2007
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