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http://www.thermopedia.com/content/668/CORROSION, PREDICTION
METHODS FOR
Introduction
This article deals with the prediction of corrosion inside
carbon steel pipes carrying unprocessed hydrocarbons and in pipes
used for injection of water into reservoirs (the injected water
will maintain the pressure in the reservoir).
Several forms of corrosion may occur in such systems. Depending
on the form of corrosion, the predictions may result in: a) "yes"
or "no" rating of a material; or b) a predicted corrosion depth
after a certain length of service. An example for a) is if the
partial pressure of H2S is larger than 0.003 bar and the pH and
temperature are smaller than certain magnitudes, stress corrosion
cracking of carbon steel may occur. A carbon steel with a specified
heat treatment and hardness will then obtain a "yes" rating.
For b), an example is general CO2 corrosion. This form may allow
operation in an environment which induces significant corrosion of
the carbon steel. The expected lifetime is now compared with a
predicted cumulative corrosion depth. In order to preveni reduction
of the operating pressure in the pipe, the predicted corrosion
depth must be equal to or smaller than the corrosion allowance.
i.e., the extra thickness of pipe which may be consumed by
corrosion.
Prediction of corrosion depth in carbon steel relies largely or
experiments. Based on experience, present-day mechanistic models do
not allow estimates of corrosion depth outside the parameter range
covered in experiments. One reason is the inability to predict how
protective a corrosion product will be i.e., its porosity and
strength without experiments. No mechanistic model can simulate how
a film-forming inhibitor will influence the corrosion process. If a
film-forming inhibitor is added to water, the inhibitor may, for
example, modify the characteristics of the corrosion product in a
manner specific for the given inhibitor. It is even possible that
certain inhibitors may prevent formation of this product. Further
partial filming may induce pitting. Thus, mechanistic models are
limited to the estimation of how, for example, certain additives to
the water can modify the pH and hence the corrosivity of a
fluid.
Below, two important forms of corrosion which can be predicted
by mechanistic models will be demonstrated. These are:
Production systems CO2 corrosion of carbon steel Injection
systems O2/Cl2 corrosion of carbon steel The laminar flamelet
model, with assumed probability density functions (PDFs)
which are functions of the reaction progress variable and the
stretch rate, appears to be valid over a wide range. It has been
used successfully to predict lift-off heights of turbulent
diffusion flames, the combustion field in premixed swirling flow,
and flame blow-off.
Corrosion of carbon steel in a CO2 environment (production of
hydrocarbons) and of such steel in an O2/Cl2 environment may serve
as examples of corrosion processes when mass transfer of the
corrosion species through electrolytes may partly or completely
control the corrosion rates.
Production Systems - Carbon Dioxide Corrosion of Carbon
Steel
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http://www.thermopedia.com/content/668/In practice, a model is
used for prediction if the corrosivity of the environment allows
the use of carbon-steel when an effective inhibitor is applied. An
effective inhibitor should reduce the general corrosion rates by
80-90% and should not induce pitting in the steel.
The next step is to verify the corrosivity and select the
inhibitor by realistic experiments, i.e., in high-pressure
hydrocarbon gas/liquid flow loop [Gramme (1994)]. Later, inhibitor
effectiveness should be verified during production for actual field
application.
Here, however, only the description of a mechanistic model will
be given. The model described by Nordgaard and Soendvedt (1994)
will serve as a basis.
Mechanistic corrosion model
Kinetics of surface reactions
The corrosion rate of steel in CO2 environment appears to be
mainly controlled by cathodic reaction, which most probably is the
hydrogen evolution reaction [Smith and Rothmann (1979)].
There are discrepancies in the literature as to the species
reacting at the electrode to form hydrogen atoms. The applied
cathodic reaction mechanism is based on the work by de Waard and
Milliams (1975) who suggested that the undissociated acid plays a
catalytic role in the cathodic process
(1)
(2)
with Eq. (1) as the rate-determining step. The anodic reaction
is as follows:
(3)
From these reactions, it can be seen that H2CO3 is consumed and
Fe2+ and HCO3 are generated by the reaction.
According to the electrochemical theory of corrosion, the
corrosion process takes place at a mixed potential Ecorr. It is
assumed that the Bulter-Volmer expression can be applied to the
kinetics of system reactions [Newman (1973)]. Based on experimental
data from de Waard and Milliams, the reactions flux can then be
given by
(4)
(5)
(6)
where
jr = reaction flux at the surface; A = constant describing the
pH dependence of surface reaction;
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http://www.thermopedia.com/content/668/PH6 = pH at surface; T =
bulk fluid temperature; and Cs,i= concentration of species i at the
surface.
Thermodynamic calculations
The thermodynamic model is based on a work by Liu and High
(1992). The bulk concentrations are calculated, assuming that the
solution is saturated with CO2 and chemical equilibrium is
established for the system, by
(7)
(8)
(9)
If the system satisfies the equation involving the solubility
product criterion, an additional equation is required,
(10)
At present, the species involved are H2CO3, H+, Fe2+, Na+, OH,
HCO3 and CO32, and electroneutrality can be expressed as:
(11)
The equilibrium constants are taken from the work by Edwards et
al. (1978). The concentration of H2CO3 can be obtained from Henry's
law
(12)
where PCO2 is the partial CO2 pressure and HCO2 is the Henry
constant.
In order to calculate the bulk concentrations, the activity
coefficients need to be evaluated. The calculations are the same as
in SOLMINEQ88 [Kharaka et al. (1988)].
Convective diffusion in liquids, including passage of current
through electrolytic solutions
General formulation. The corrosive gas, CO2, will dissolve into
the liquid phase, H2CO3. H2CO3 will disassociate into its
corresponding ions, HCO3 and CO32. Ions and H2CO3 are transported
to the pipe wall where corrosion will occur. In the corrosion
process, surface electrochemical reactions will set up an electric
field. A feature of ions transfer in a moving solution that
differentiates it from the transfer of dissolved neutral particles
is the fact that the motion of ions is affected by the electric
field in the solution. Ion transfer in the solution is produced by
convective diffusion and by the migration of ions in the electric
field. Convective diffusion in the solution is governed by two
quite different mechanisms.
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http://www.thermopedia.com/content/668/Molecular diffusion is
the mechanism of transport of species to the electrode as a result
of concentration differences causing a diffusional flux
(13)
where Dmdi is the molecular diffusion coefficient for species i
and ci is the concentration of species i. ci is given by
(14)
In a moving liquid, the solute is entrained and transported by
the flowing stream, causing a convective flux
(15)
where the velocity field, u, is defined as:
(16)
The migration of i-type ions can be written in the form
(17)
where R is the universal gas constant, F is the Faraday constant
and zi is the valency of ion i. The electric field, E, is given
by
(18)
where is the electric potential. The total flux of particles of
the species i in the moving medium, ji is equal to
(19)
Diffusion in turbulent flow in a pipe Levich (1962) has shown
that turbulent flow has a four-layered structure. Far from surface,
there is a zone of developed turbulence in which the concentration
remains constant. Closer to the surface, in the turbulent boundary
layer, both average velocity and average concentration decreases
slowly according to a logarithmic law. In this zone, neither
molecular viscosity nor diffusion play a noticeable part. Both
momentum and matter are transferred by means of turbulence eddies.
Still closer to the wall, in the viscous sublayer, turbulence
eddies become so small that the momentum transferred by molecular
viscosity exceeds that transferred by turbulence eddies. However,
the molecular diffusion coefficient is 1,000 times smaller than
kinematic viscosity, Sc >> 1, and the remaining turbulence
eddies still transfer substantially more solute than molecular
diffusion.
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http://www.thermopedia.com/content/668/The coefficient of
turbulent diffusion (eddy diffusivity) in the viscous sublayer is
proportional to y4 and decreases rapidly as the wall is approached.
At a certain distance from the wall, dl, eddy diffusivity must
equal the coefficient of molecular diffusion. (20)
where
D, i = eddy diffusivity; = constant; u* = friction velocity; dl
= diffusion layer thickness; anddl = viscous sublayer
thickness.
The viscous sublayer thickness can be expressed as:
(21)
where is the kinematic viscosity. Solving for the diffusion
layer thickness gives (22)
where = 1 and a = . The friction velocity is given by the
following relation (23)
where
wi = wall shear stress; = liquid density; and U = pipe
velocity.
The skin-friction coefficient, Cf, (f = 4 Cf) is a function of
the Reynolds number and pipe roughness, k. An equation by Colebrook
and White encompasses all flow regimes encountered in a Moody
chart. This equation is:
(24)
The molecular diffusion coefficients are obtained from dilute
electrolyte theory
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where i is the limiting ionic conductance of species i in water
at 298 K. In the innermost portion of the viscous sublayer at y
< dl, the molecular mechanism predominates over the turbulence
mechanism. (See also Boundary Layer; Friction Factors for Single
Phase Flow; Turbulent Flow.)
Mass Transfer and Ion Migration in Diffusion Layer
Flux and mass balance equations. At present, it is assumed that
the diffusional layer provides all the resistance to mass transfer.
Therefore, outside this layer, the concentration is uniform for all
species and equal to the bulk concentration. A one-dimensional
problem is considered. Equation (19) can then be simplified to
yield
(26)
and the mass balance is reduced to
(27)
These equations involve an electrical potential term. Then, one
more equation is necessary to completely specify the system. For a
corrosion system, the assumption that the net current flow is zero
(open-circuit condition) is always true [Levich (1962)]
(28)
From the latter, the distribution of the field in the solution
can be derived
(29)
Boundary conditions. At pipe wall surface (y = 0):
The total reaction flux of species i in the moving medium in the
diffusion layer is equal to
(30)
If the species are nonreactive at the wall, jr, i is zero.
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http://www.thermopedia.com/content/668/The diffusion layer
boundary (y = ): At the interface of the diffusional layer and the
turbulent layer (outer part of the viscous sublayer), ci = c, i =
cb, where c, i is the concentration of species i at the diffusion
layer boundary and cb, i is the concentration of species i in the
bulk.
Calculation procedure
The model needs bulk temperature, CO2 partial pressure, bulk
velocity, bulk iron concentration and added sodium bicarbonate as
input. Initial concentration values for all species in the bulk is
calculated by assuming the activity coefficients to be unity. Based
on these initial values, the actual concentrations are calculated.
After calculating the physical properties (viscosity, density and
diffusion coefficients), the diffusion layer and flow condition are
calculated.
The diffusion layer is divided into grids, and initial values
for all the grid points are calculated. The surface reaction fluxes
are calculated for the given initial values. The grid point
concentrations throughout the diffusion layer are calculated by a
finite difference technique [Patankar (1980)].
Because ordinary differential equations are highly nonlinear and
coupled, they are solved one by one. The specific equation
generally converges in two or three iterations. When all the
equations are solved, the concentration of the species are updated.
As a convergence criteria, the total number of iterations are used.
The program checks if convergence really occurred. If not, more
iterations need to be performed.
Comparison with experimental data
In order to test out the model, experimental results from
Kjeller Sweet Corrosion have been used. These experiments are
documented elsewhere [Dugstad and Videm (1990)]. Simulation results
of the pH and the resulting corrosion rate along with the measured
values are given in Table 1.
Table 1. Comparison between IFE data and mechanistic corrosion
model
Experiments with temperatures up to 60C have been applied. Above
this value, the formation of protective layers is seen to lower the
corrosion rate. The pH calculations agree very well with the values
given for the experiments. The corrosion rate simulations are
within 20% of the experimental results, which is regarded as a very
good agreement.
Corrosion in Seawater Injection Systems
Model formulation
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http://www.thermopedia.com/content/668/Seawater used for
injection into the reservoir is treated to avoid microbiological
activity, corrosion and reservoir formation blockage. The need for
both microbiological and corrosion control can be in conflict
because chlorine, which is corrosive, is one of the chemicals used
for microbiological control. Typical chlorine concentrations are
0.3-0.5 ppm [Hudgins (1971) and Mitchell (1978)].
Chlorine can be produced by electrochlorinators or added as
hypochlorite. When chlorine is added to seawater, an equilibrium
between chlorine (Cl2), hypochlorous acid (HOCl) and hypochlorite
(OCl) is established. At pH > 7.5, hypochlorite predominates
whereas at pH 6.5, OCl is present with considerable quantities of
HOCl [Mitchell (1978)]. Another complicating factor is the presence
of approximately 70 mg/l bromide in seawater. The bromide will have
the effect of reducing the added hypochlorite to Cl while Br is
oxidized to hypobromite (OBr) [Gundersen et al. (1989)].
Several cathodic reactions can take place in chlorinated
seawater.
Reduction of hypochlorite:
(31)
Or hypobromite:
(32)
Reduction of oxygen:
(33)
Reactions (31), (32) and (33) are flow-dependent. Flow
dependence will not only include the velocity, but also the
geometry (i.e., obstacles with local enhanced mass transfer and
wall shear stress). Corrosion rates have been measured in a
simulated water-injection system where seawater has been
chlorinated and deoxidized [Andersen and Soendvedt (1993)]. The
influence of chlorine, oxygen, flow velocity and geometry have been
investigated.
The following conclusions were made from the experiments:
Oxygen alone is more corrosive than in combination with
chlorine. In injection systems with chlorinated seawater, two types
of layers are formed on the
steel surface. In seawater with low oxygen concentrations,
magnetite will be the corrosion product. It was also observed that
the pipes were covered with a layer of organic matter when chlorine
was added to seawater.
The corrosion rate seems to be controlled by mass transfer of
oxygen and chlorine to a protective layer, and through this layer
to the metal surface.
The corrosion rate is mainly controlled by the concentration of
oxygen and chlorine and local mass transfer of corrosive species.
The corrosion rates at flow disturbances are much larger than on
smooth sections.
It is assumed that the corrosion rate is limited by transport of
chlorine and oxygen through a protective layer. The flux density of
each corrosive species through the diffusion boundary layer and
through pores in the protective layer with thickness H and
permeability Kp is given as follows:
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where
m = local mass transfer coefficient to the protective layer;H =
height of layer made by both oxygen and chlorine;
= bulk concentration of species; Dmd, i = molecular diffusivity;
and Kp = porosity of layer.
The total corrosion rate:
(35)
where
K2 = corrosion rate corresponding with unit cathodic diffusion
limited current; z = valency change; and F = Faraday constant.
It can now be assumed that the thickness of the protective layer
(H) is increased by mass transfer of each species to the layer (m)
and is decreased by wall shear (W) from the liquid. In
steady-state, this gives H equal to
(36)
where K is a constant.
Apparently the porosity of magnetite can be constant as
described by Surman and Castle (1969) and Sanchez-Caldera (1984).
The porosity is set equal to 0.3. For turbulent flow with a
moderate flow normal to the wall, the wall shear is related to the
mass transfer coefficient by:
(37)
When two pipes with different diameters have the same friction
velocity, the wall shear on the pipe walls are identical. From the
above relations, it follows that the height of the protective layer
is given as
(38)
where K4 is a constant for a given liquid density;
(39)
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http://www.thermopedia.com/content/668/where is the density of
the fluid. A main variable, if the corrosion process is
diffusion-controlled, is the local mass transfer distribution on a
specific section of the piping. This local mass transfer can be
very different from smooth-section magnitudes. This, in turn,
governs the velocity dependence by enhanced transport to the
protective layer and the equilibrium height (or porosity) of the
protective layer.
Figures 1-2 contain estimated magnitudes of the mass transfer
expressed as Sherwood number (Sh) for geometries used in the
corrosion tests [Soendvedt (1991)].
Figure 1. Geometry A - flush mounted specimens.
Figure 2. Geometry B - cross-over (diameter reduction).
The main unknown in this model is the height of the protective
layer. This must be determined by correlation with experiments.
Derivation of apparent height characteristics for different
geometries follows below.
Correlation with Experiments
Smooth Pipe
The model presented above has been correlated with several
experimental points.
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http://www.thermopedia.com/content/668/If no chlorine is
present, the calculated limiting corrosion rates fit with the
recorded corrosion rates, i.e., no protective layer is found on the
smooth sections.
To correlate with the experiments when chlorine is present, a
protective layer must be introduced in the simulation of the
experiments. The derived layer thickness is large and given as
follows:
(40)
Sudden reduction in diameter:
The geometry considered is illustrated in Figures 3 and 4. The
results are included in Table 3. The corrosion rates are
significantly smaller than the limiting value.
Figure 3. Geometry C cross-over (diameter increase).
Figure 4. Geometry D - concentric reducer.
Table 2. Smooth pipeTest conditions and results from
measurements and calculations
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Table 3. Cross-over (reduction in diameter)test conditions and
results from measurements and calculations
Analysis of the experiments reveals that the effective
protective layer height varies with friction velocity as
follows:
(41)
It has been observed that H is reduced as u* increases with an
exponential of similar value to that given by Eq. (38) (i.e., u* to
a power of 1.1).
Bends
The results are presented in Table 4.
Table 4. BendTest conditions and results from measurements and
calculations
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The correlated protective layer height is described with the
same type of formula as for sudden reduction in diameter:
(42)
H is zero when no chlorine is present. Again, the corrosion
rates with Cl2 present are significantly smaller than the limiting
values.
Welds
The geometry considered is sketched in Figure 5. The correlation
for thickness of the protective layer is given by:
(43)
This leads to corrosion rates much smaller than magnitudes
corresponding with no/inefficient protective layer (see Table
5).
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http://www.thermopedia.com/content/668/Figure 5. Geometry E -
smooth pipe + weld.
Table 5. WeldTest conditions and results from measurements and
calculations
Sudden Increase in Diameter
The geometry in question is sketched in Figures 4 and 6.
Figure 6. Geometry F - narrow pass.
In the reversed flow zone, die increase of Sh/Sh0 is given as
follows:
(44)
The high wall shear stress fluctuations in this region seem to
give a thinner protective layer, H,
(45)
H is zero when no chlorine is present.
For the edge before the enlargement, the significant corrosion
rates indicate a local high increase of mass transfer on the edge
while the wall shear stress fluctuations should be small. To fit
the data, Sh/Sb0 is given as follows:
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Nomenclature
A Constant describing the pH dependence of surface reaction
(-)
Bulk concentration of species (mol/m3)
cb, i Concentration of species i in the bulk ()
c, i Concentration of species i at the diffusion layer boundary
(-)
Cf Skin-friction coefficient
cs, i Concentration of species i at the surface ()
CR Corrosion rate (mm/year)
D Pipe diameter (m)
Dmd, I Molecular diffusivity (m2/s)
E Electric field (V/m)
F Faraday constant (C/mol)
f Friction factor ()
H Protective layer (m) HCO2 Henry constant
Ji Flux density of corrosive species i (mol/m3s)
Jconv, i Flux due to convective diffusion of species i (m/s)
ji Total flux of species i (m/s)
jmd, i Flux due to molecular diffusion of species i (m/s)
jmigr, i Flux due to migration of species i (m/s)
jr Reaction flux at surface (m/s)
K Constant ()
Kp Permeability of protective layer ()
K2 Corrosion rate corresponding with unit cathodic diffusion
limited current (A/m2)
PCO2 Partial CO2 pressure (N/m2)
pHs pH at surface ()
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http://www.thermopedia.com/content/668/R Universal gas constant
(J/K mol)
Re Reynolds number ()
Sh Sherwood number ()
Sh0 Sherwood number for smooth pipe ()
T Bulk fluid temperature (C)
U Pipe velocity (m/s)
u Velocity field (m/s)
u Velocity component in x-direction (m/s)
u* Friction velocity (m/s)
v Velocity component in y-direction (m/s)
w Velocity component in z-direction (m/s)
x x coordinate (m)
y y coordinate (m)
z z coordinate (m)
zi Valency of ion i ()
Greek Symbols
m Mass transfer coefficient (m/s) D, i Eddy diffusivity (m2/s)
dl Diffusion layer thickness (m) vl Viscous sub layer thickness (m)
Constant i Limiting ionic conductance of species i in water at 298
K (m2C2/J mol s) Electric potential (V) Liquid density (kg/m3)
Kinematic viscosity (m2/s) W Wall shear on the layer (N/m2).
References
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http://www.thermopedia.com/content/668/1. Andersen, T. R. and
Soendvedt, T. (1991) The influence of chlorine, oxygen and flow
on corrosion in seawater injection systems, UK Corrosion
Manchester Conference 22-24 Oct.
2. DeWaard, C. and Milliams, D. E. (1975) "Carbonic Acid
Corrosion of Steel". Corrosion, 31, 177-181.
3. Dugstad, A. and Videm, K. (1990) Kjeller Sweet Corrosion-II
Final Report IFE/KR/F-90/008.
4. Edwards, T. J., Maurer, G., Newman, J., and Prausnitz, J. M.
(1978) Vapor-liquid Equilibrium in Multicomponent Aqueous Solutions
of Volatile Weak Electrolytes, AlChE Journal, 24, 996-976. DOI:
10.1002/aic.690240608
5. Eriksrud, E. (1980) Internal Corrosion of Offshore Pipelines,
Veritas Report No. 80-0517.
6. Fischer, W. and Siedlarek, W. (1978) "Werkstoffe und
Korrosion" 28, 822. 7. Gundersen, R., et al. (1989) The effect of
sodium hypochlorite on the electrochemical
properties of stainless steel and on the bacterial activity in
seawater. NACE Corrosion 89, Paper no 108, New Orleans, Louisiana,
April 17-21.
8. Henriksen, N. et al. (1987) Efficient new processing system
for water deoxidation. Off-shore Technology Conference, Paper no.
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9. Horner, R.A. et al. (1994) The Forties Water Injection
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10. Hudgins, C. M. (1971) The Oil and Gas Journal, February 15,
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H., and DeBraall, F. D.
I. (1988) "SOLMINEQ88: A Computer Program for Geochemical
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12. Levich, V. G. (1962) Physicochemical Hydrodynamics. Prentice
Hall, Inc. 13. Liu, G. and High, M. S. (1992) Final Report: Down
hole Corrosion Modelling. A
report to Norsk Hydro a.s. School of Chemical Engineering,
Oklahoma State University.
14. Manner, R. and Heitz, E. (1978) Werkstoffe und Korrosion 29,
783. 15. Mitchell, R. W. (1978) Journal of Petroleum Technology,
June, 887. 16. Newman, J. S. (1973) Electrochemical Systems.
Prentice Hall, Engellewood Cliffs,
N.J. 17. Nordgaard, A. and Soendvedt, T. (1994) Mechanistic CO2
corrosion modelling.
Model formulation and comparisons with experiments up to 60 C.
Norsk Hydro Publication, Oil and Gas Division, Stabekk, Norway.
18. Patankar, S. V. (1980) Numerical Heat Transfer and Fluid
Flow, Hemisphere publishing corporation, McGraw-Hill book
company.
19. Sanchez-Caldera, L. E. (1984) The mechanism of
corrosion-erosion in steam extraction lines of power plants,
Massachusetts Institute of Technology.
20. Schmitt, G. and Rothmann, B. (1978) Werkstoffe und Korrosion
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in deoxidized and chlorinated sea
water. Development of model. Prod. Technology, U&P Division,
Norsk Hydro.