Volume 1 Paper 3
Superposition of Diffusion and Chemical Reaction Controlled Limiting Currents - Application to CO2 Corrosion
Srdjan Nesic, B.F.M. Pots, John Postlethwaite and Nicolas Thevenot
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JCSE Volume 1 Paper 3
Submitted 22 June 1995, revised version submitted 9 November 1995
Superposition of diffusion and chemical reaction controlled limiting currents - Application
Srdjan Nesic¤, B.F.M. Pots#, John Postlethwaite* and Nicolas Thevenot¤
Institute for Energy Technology (IFE), P.O.Box 40, N-2007 Kjeller, Norway,
Koninklijke/Shell-Laboratorium, Amsterdam (Shell Research B.V.), P.O.Box 38000,
1030 BN Amsterdam, The Netherlands, e-mail: mailto2('pots1','ksla.nl')
IFE, on sabbatical leave from the University of Saskatchewan, Saskatoon,
Canada, e-mail: mailto2('John_Postlethwaite','engr.USask.Ca')
Institute for Energy Technology (IFE), P.O.Box 40, N-2007 Kjeller, Norway
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It was observed
experimentally that a chemical reaction limiting current can be affected by flow. In the present study a new more general expression
than the one found in literature was derived for the superposition of the
diffusion and chemical reaction controlled limiting currents. It was found that their interaction in the
case of CO2 corrosion is
significant at temperatures lower than 40°C and velocities higher than 1 m/s when the mass transfer layer is of the
similar thickness as the reaction layer.
The corrosion of steel in water
containing dissolved CO2 gas is a topic of considerable interest with practical
applications and substantial economic impact in the oil and gas production and
When dissolved in water, the CO2 is hydrated to give carbonic acid:
§3 This weak, partly dissociated
acid is responsible for high corrosion rates of steel in water CO2
solutions. The electrochemistry of CO2 corrosion is
still not certain although a number of good studies exist in this field.2-8 One of the simplest assumptions is that the
dominant cathodic reaction is the reduction of hydrogen ions, where the
hydrogen ions are supplied by dissociation of carbonic acid:
§4 The other possibility is the
direct reduction of carbonic acid:2
§5 When conducting potentiodynamic
sweeps on steel in CO2
solutions, it is difficult to identify a pure Tafel region for the cathodic
reaction as a limiting current is reached for relatively small
overpotentials. The origin of this
limiting current has been investigated 3,4 previously and is the topic of the
Experiments were conducted at atmospheric pressure in a glass cell. Gas (CO2 or N2) was
continuously bubbled through the cell. A three electrode set-up (Figure 1) was used in all
electrochemical experiments. A rotating
cylinder electrode with a speed control unit (0-5000 rpm -
5000 rpm for our cylinder corresponds to a peripheral velocity of 2.61
m/s, a shear stress of 25 Pa., and a Reynolds number of 26175) was used as
the working electrode. A concentric platinum ring was used as a counter
electrode. A saturated Ag/AgCl
reference electrode was used externally connected to the cell via a Luggin
capillary and a porous wooden plug. The
speed of rotation of the working electrode was controlled with the aid of a
stroboscope. The pH was followed with an electrode directly immersed into the
electrolyte. The temperature was followed with a Pt-100 probe which also served
as an input for the temperature regulating system - a hot plate combined with a magnetic stirrer. Oxygen concentration was monitored with an
Orbisphere oxygen meter. The
concentration of Fe++ was measured
occasionally using a photospectrometric method. The concentration of CO2 in the water
was also measured in selected experiments. Electrochemical measurements were
made with a Gamry Instruments Inc. potentiostat connected with a PC 486/25
construction carbon steel St52 was tested (corresponding to ASTM A537 Grade
1). Chemical composition of the steel
is given in Table 1. The working electrode was machined from the parent material into
a cylinder 10 mm in diameter and 10 mm long.
The exposed area of the specimen was 3.14 cm2.
§8 Table 1. Chemical composition of the St52
steel used for the working electrode (mass%)
§9 Figure 1.
Schematic of the experimental test cell: 1-reference electrode, 2-gas
in, 3-gas out, 4-Luggin capillary, 5-platinum counter electrode, 6-rotating
cylinder, 7-temperature probe, 8-pH electrode, 9-working electrode.
The glass cell
was filled with 3 litres of electrolyte: distilled water + 1 mass% NaCl. In
different experiments CO2 or N2 gas were bubbled through the electrolyte (min. 60 min.) in
order to saturate or deaerate the solution.
Monitoring of pH and O2 concentration
was used to judge when the solution was in equilibrium. When needed, HCl or NaHCO3 were added to adjust the pH. The temperature was set and
maintained with an accuracy of 1oC in all experiments.
§11 Before each
polarisation experiment, the steel working electrode surface was polished with
500 and 1000 grit silicon carbide paper, washed with alcohol, mounted on the
specimen holders and immersed into the electrolyte. The free corrosion potential was followed immediately after
immersion. Depending on the conditions,
the potential stabilised within ±1 mV in 1 to 10 min.
§12 The cathodic
and anodic sweeps were conducted separately starting from the free corrosion
potential. Typical scanning rate used was 0.1-0.2 mV/s. The cathodic sweeps were sometimes repeated
by sweeping in the opposite direction, without significant difference in the
result. In each experiment the anodic
sweeps were conducted only once for a single working electrode specimen and a
given electrolyte (starting from the free corrosion potential) since they
altered the specimen surface and contaminated the electrolyte with significant
amounts of dissolved iron (Fe++>3
ppm). Typically the Fe++ concentration was kept below 1 ppm.
§13 Table 2. Experimental conditions
water + 1
1 bar N2 or CO2
0.1 - 0.2
from -600 to
+200 mV vs. Eoc
When conducting cathodic
potentiodynamic sweeps in strong acids, limiting currents found are clearly
flow dependent (Figure
2). It was shown previously9
that the rate of the hydrogen evolution reaction in the limiting current region
proceeds only as fast as the hydrogen ions can diffuse from the bulk to the
§15 Figure 2.
Potentiodynamic sweep conducted in HCl solution at pH 4 purged with N2 , t=22 °C, 3%
NaCl, using a rotating cylinder electrode d=1 cm.
§16 Figure 3. Potentiodynamic sweep conducted in
solution at pH 4, t=22 °C, 3% NaCl, using a rotating cylinder electrode d=1 cm.
§17 In CO2 solutions it was found3
that the current limitation partly comes from a slow chemical step preceding
the charge transfer step (see also Figure
3). It was assumed that the slow
hydration step (1) preceding the direct
reduction of carbonic acid (5) is the cause for the
observed limiting currents.
§18 In the present study limiting
currents were measured over the range of 500 - 10000 rpm
in both HCl and CO2
solutions using potentiodynamic sweeps.
The correction was made for the contribution of the direct water
reduction and the resulting limiting currents as a function of rotation speed
are shown in Figure 4. The gap between the two curves which exists
over the whole velocity range confirms the assumption of Schmitt and Rothman3 and Eriksrud
and Søntvedt4 that there is
a flow independent component of the limiting current in CO2 solutions which is
probably controlled by a chemical step: the hydration of CO2 into H2CO3.
§19 If we assume that in CO2 solution at pH 4, both the H+ ions and H2CO3 are reduced at the surface, then at a
given flow rate the limiting current for a CO2 solution can be separated into two components. The first component is related to the
diffusion of H+ ions from the
bulk (the same as in HCl solutions).
The other flow independent (chemical reaction controlled) component
which comes from H2CO3
is actually the gap between the two curves.
Since the gap increases with rotation speed, it is hypothesised that the
chemical reaction limiting current is also affected by the flow. This assumption will be analysed below.
§20 Figure 4. Limiting currents for a CO2 and a HCl
solution at pH4, t=22°C measured potentiostatically using a rotating cylinder
electrode d=1 cm.
Means for calculating the magnitude of
a pure chemical reaction limiting current were first proposed by Vetter:10
was later successfully used to explain observed limiting currents in CO2 solutions (glass-cell experiments).5, 11 However, it was
recently reported12 that by using
(6), limiting currents measured
in loop experiments were underpredicted especially at higher velocities (>1m/s).
Inspection of Vetter’s10
derivation showed that (6) is strictly valid only for
stagnant solutions when the thickness of the so-called “reaction layer” is much
smaller than the thickness of the “diffusion layer”. In that case the reported discrepancy12 can be
explained by assuming that at higher velocities the thickness of diffusion
layer was reduced and at some point became comparable to the thickness of the
reaction layer. This concept is
illustrated on Figure 5 where the
calculated thickness of the two boundary layers are compared.
§22 Figure 5. Thickness of the boundary layers
for pipe flow, t=20°C, pCO2=1 bar, dp=0.1m.
§23 Figure 6. Boundary layer thickness ratio as a
function of velocity and temperature for pipe flow, pCO2=1 bar, dp=0.1m.
§24 The thickness
of the mass transfer (diffusion) layer shown in Figure 5 is estimated by
using the relation:
D is the diffusion coefficient for carbonic acid and km is the mass transfer coefficient for straight pipe
flow calculated using the correlation ofBerger and Hau13 The thickness of the chemical reaction layer
is calculated using
the relation derived by Vetter10 for a first
order chemical reaction:
is the rate of carbonic acid dehydration (described in more
detail below in the text). From Figure 5 it can be seen
that under given conditions at 4 m/s
the two boundary layers are of the same thickness. The ratio
is a strong function
of temperature as shown in Figure 6. It is clear that for lower temperatures
velocities larger than 1 m/s. Thus a
more general expression than (6) is needed for the
reaction-controlled limiting current which accounts for any
ratio and covers a
wider range of applications.
§25 In order to
derive such an expression, we will assume here the following sequence of
reactions in the limiting current region:
chemical reaction (9)
§26 If we further
assume that reaction (9) is a first order chemical reaction,
the rate of change of H2CO3
§27 We can assume
that the concentration of dissolved CO2 is constant
for all practical purposes and denote the rate of hydration with vo =const.. For the sake of simplicity we can drop the
subscript so (11) becomes:
§28 At equilibrium
v=0 , hence:
where is the equilibrium
concentration of H2CO3. Substitution of (13) into (12) gives:
Here u is the nondimensional concentration of
H2CO3 . It is the gradient of u (concentration) at the metal surface that will give us the
desired chemical reaction limiting current.
§29 To obtain the
concentration profile the steady state mass balance (Fick’s second law) for the
case of an accompanying homogeneous chemical reaction has to be solved:
For a steady
state case . We can further
assume that the diffusion coefficient is independent of concentration:and that there are no temperature gradients so
. Finally, by
substituting v from (14) into (15), the nondimensional steady
state mass balance is obtained:
§30 The boundary
at the metal surface, in the limiting current case, the
concentration of H2CO3
is approaching zero, so for
for the bulk of the fluid due to turbulence the fluid is
well mixed so there are no concentration gradients and we can assume that all
reactions are in equilibrium, so for:
§31 Here we have
assumed that the edge of the mass transfer boundary layer at
is the point where
everything is well mixed and all reactions are in equilibrium. At this stage the present derivation departs
from the one in Vetter’s10 book. Vetter 10 assumes that
the fluid is well mixed and in equilibrium only for
that is “very far”
from the metal surface. This is a good
assumption for stagnant solutions or laminar flow, however one can imagine that
for a high enough velocity and turbulent flow the thickness of mass transfer
layer is of the same order
of magnitude as the reaction layer which we are calculating. Of course by setting
derivation follows the one in Vetter’s10 book.
§32 Integration of
(16) with the boundary conditions (17) and (18) yields the nondimensional
interested in the limiting current which is:
When is returned to (20) we obtain:
Vetter’s10 expression (6) is now recovered, however corrected
with the multiplier here called “flow factor”:
into account the effect of flow on the chemical reaction limiting current.
Figure 7. Flow factor as a function of
velocity and temperature for pipe flow, dp=0.1 m, pCO2=1
§33 Assuming a
stagnant solution, so the flow factor f=1
and the solution reduces to the one derived by Vetter.10 The sensitivity of the flow factor to
velocity and temperature is illustrated in Figure 7.
§34 As a rule of
thumb in CO2 applications
one can say that this correction is important for temperatures lower than 40°C and
velocities higher than 1 m/s when
the mass transfer layer is of the similar thickness as the reaction layer.
§35 Another way of
looking at the superposition of the diffusion and reaction limiting currents is
to express it in terms of a pure diffusion limiting current corrected for the
presence of a rate limiting chemical reaction 14 .
By using (7) and (8) together with (21) it is obtained:
Finally, the derived equations can be compared with the
measured limiting currents shown in Figure
4. The result with and without
the derived correction is shown in Figure
8. Although in the measured
velocity range the effect is not large it is clear that the flow factor
improves the agreement of the measurements and the theory.
Figure 8. Comparison of the model prediction
and experimental results. Conditions
the same as in Figure
4. The points represent
measurements, the lines are the model: red solid line - mass transfer limiting current
(Eisenberg et al.15), black dotted line - mass transfer + chemical
reaction limiting current (equation 6), black solid line - mass transfer + corrected
chemical reaction limiting current (equation 21).
It was observed
experimentally that a chemical reaction limiting current can be affected by flow. A new more general expression was
derived for the superposition of the diffusion and chemical reaction controlled
limiting currents. It was found that the their interaction in
the case of CO2 corrosion is
significant at temperatures lower than 40°C and velocities higher than 1 m/s when the mass transfer layer is of the
similar thickness as the reaction layer.
coefficient, m2/s ;
Faraday constant (96490 C/equiv.);
limiting current density, A/m2
reaction rate (CO2hydration reaction), 1/s
reaction rate (H2CO3 dehydration reaction), 1/s ;
transfer coefficient, m/s ;
chemical reaction rate, mol/(s m3);
distance from the metal
surface, m ;
of the mass transfer (diffusion) layer, m;
of the chemical reaction layer, m;
ratio of the diffusion and reaction layers;
1. A. Dugstad, L. Lunde and S.
Nesic, “Control of Internal Corrosion in Multi-Phase Oil and Gas Pipelines”,
Proceedings of the conference Prevention of Pipeline Corrosion, Gulf Publishing
2. C. deWaard and D. E.
Milliams, Corrosion, 31 (1975): p.131.
3. G. Schmitt and B.
Rothman, Werkstoffe und Korrosion, 28 (1977): p.816.
4. E. Eriksrud and T.
Søntvedt, "Effect of Flow on CO2 Corrosion Rates in Real and Synthetic
Formation Waters", Advances in CO2 Corrosion, Vol. 1. Proceedings of the
Corrosion /83 Symposium on CO2 Corrosion in the Oil and Gas Industry, Editors: R. H.
Hausler, H. P. Goddard , p.20, (Houston, TX: NACE, 1984).
5. T. Hurlen, S. Gunvaldsen, R.
Tunold, F. Blaker and P. G. Lunde, J. Electroanal. Chem., 180 (1984): p. 511.
6. L. G. S. Gray, B. G.
Anderson, M. J. Danysh, P. G. Tremaine, “Mechanism of Carbon Steel Corrosion in
Brines Containing Dissolved Carbon Dioxide at pH 4”, Corrosion/89, paper no.
464, (Houston, TX: NACE International, 1989).
7. L. G. S. Gray, B. G. Anderson,
M. J. Danysh and P. R. Tremaine, "Effect of pH and Temperature on
the Mechanism of Carbon Steel Corrosion by Aqueous Carbon Dioxide", Corrosion/90,
paper no. 40, (Houston, TX: NACE International, 1990).
8. M. R. Bonis and J. L. Crolet,
“Basics of the Prediction of the Risks of CO2 Corrosion in
Oil and Gas Wells”, Corrosion/89, paper no. 466, (Houston, TX: NACE
9. M. Stern, J.Electrochem. Soc., 102 (1955): p.609.
10. K. J. Vetter,
Electrochemical Kinetics, Theoretical Aspects, Sections 1, 2, and 3 of
Electrochemical Kinetics: Theoretical and Experimental Aspects, translation
from German, (New York: Academic Press, 1967): pp.235-250.
11. S. Nesic, J. Postlethwaite and S.
Olsen, “An Electrochemical Model for
Prediction of CO2 Corrosion”, Corrosion/95,
paper no. 131, (Houston, TX: NACE International, 1995).
12. S. Nesic, G. Th. Solvi, and J.
Enerhaug, “Comparison of the
Rotating Cylinder and Pipe Flow Tests for Flow Sensitive CO2 Corrosion”, Corrosion/95, paper no. 130, (Houston,
TX: NACE International, 1995).
13. F. P. Berger and K.-F.
F.-L Hau, Int. J. Heat Mass Transfer, 20 (1977): p.1185.
14. B. F. M. Pots, “Mechanistic Models for the Prediction
of CO2 Corrosion
Rates under Multi-Phase Flow Conditions”, Corrosion/95, paper no. 137,
(Houston, TX: NACE International, 1995).
15. M. Eisenberg, C. W.
Tobias and C. R. Wilke, J. Electrochem. Soc., 101 (1954): p. 306.