Volume 20 Paper 84
An experimental and theoretical investigation of the influence of surface roughness on corrosion in CO2 environments
Mohammed Al-Khateeb, Richard Barker, Anne Neville, Harvey Thompson
Keywords: Electro-chemical modelling, experiments, surface roughness
The influence of surface roughness on the rate of corrosion in CO2 environments in the absence of protective film formation is investigated both experimentally and theoretically. The former measurements are obtained using the Linear Polarisation Resistance technique on a Rotating Cylinder Electrode apparatus with four different samples with roughness of 0.5, 6, 20 and 35Î¼m. Experimental measurements of corrosion rate for smooth and rough surfaces are compared against predictions from a modified form of a CO2 corrosion model , where mass transfer coefficients are specified using a new correlation for rough surfaces , which accounts for both the influence of the total surface area and enhancement of the mass-transfer process. Test conditions selected for comparison consisted of a CO2-saturated 1 wt.% NaCl brine at 25oC covering pH values between 4 and 6. X65 carbon steel samples were used as working electrodes, with rotational rates varying from 1000 to 4000 rpm. Agreement between experimental and theoretical corrosion rates is very good and demonstrates clearly how increased surface roughness accentuates corrosion rates and the need for considering surface topography when making reliable corrosion predictions when implementing theoretical models.
Because you are not logged-in to the journal, it is now our policy to display a 'text-only' version of the paper. This version is obtained by extracting the text from the PDF or HTML file, and it is not guaranteed that the text will be a true image of the text of the paper. The text-only version is intended to act as a reference for search engines when they index the site, and it is not designed to be read by humans!
If you wish to view the human-readable version of the paper, then please Register (if you have not already done so) and Login. Registration is completely free.
An experimental and theoretical investigation of the
influence of surface roughness on corrosion in CO2
Mohammed Al-Khateeb*, Richard Barker, Anne Neville, Harvey Thompson
Institute of Functional Surfaces, School of Mechanical Engineering, University of
Leeds, Leeds, LS2 9JT
The influence of surface roughness on the rate of corrosion in CO2 environments in
the absence of protective film formation is investigated both experimentally and
theoretically. The former measurements are obtained using the Linear Polarisation
Resistance technique on a Rotating Cylinder Electrode apparatus with four different
samples with roughness of 0.5, 6, 20 and 35μm. Experimental measurements of
corrosion rate for smooth and rough surfaces are compared against predictions
from a modified form of a CO2 corrosion model , where mass transfer
coefficients are specified using a new correlation for rough surfaces , which
accounts for both the influence of the total surface area and enhancement of the
mass-transfer process. Test conditions selected for comparison consisted of a CO2saturated 1 wt.% NaCl brine at 25oC covering pH values between 4 and 6. X65
carbon steel samples were used as working electrodes, with rotational rates varying
from 1000 to 4000 rpm. Agreement between experimental and theoretical
corrosion rates is very good and demonstrates clearly how increased surface
roughness accentuates corrosion rates and the need for considering surface
topography when making reliable corrosion predictions when implementing
Keywords: Electro-chemical modelling, experiments, surface roughness.
CO2 corrosion of steel in oil and gas production and transportation systems is an
important issue of practical and commercial interest. When CO2 dissolves in brines
it permits the formation of carbonic acid which is corrosive towards equipment
made from carbon steel. This process is capable of affecting asset integrity, the
environment and safety of personnel .
In the context of oil and gas pipelines, the surface roughness of steel pipelines
delivered to coating yards can be in the order of 20μm and may even exceed 50μm
, yet laboratory experiments in CO2 environments tend to be with samples which
are wet-ground to sub-micron surface finishes (i.e. 1200 grit SiC paper). This is
despite the fact that the effect of surface roughness is believed to contribute
significantly towards corrosion rates in CO2-containing environments  based on
the notion that surface topography can affect the hydrodynamic and mass-transfer
boundary layer which can influence the electrochemical response of the corroding
A review of the literature reveals that surface roughness is actually believed to
control the rate of mass transfer to surfaces, as opposed to the geometry of the
system itself. These effects have been quantified using several empirical
correlations linking the Sherwood, Reynolds and Schmidt numbers, see e.g. Poulson
. An assessment of the influence of roughness on mass-transfer characteristics
has been conducted on geometries such as rectangular ducts , pipes , the
rotating disk  and the rotating cylinder electrode (RCE) , the latter of which is
the focus of this study. The general consensus of these studies is that rougher
surfaces lead to an accentuation in mass-transfer and hence, the rate of material
dissolution in diffusion-controlled processes.
Research as early as the 1930s by King and Howard  demonstrated that in
diffusion-controlled environments, surface roughness has a major effect on
enhancing the rate of metal dissolution. These observations are also supported by
the work of Ibl  and by Brenan and Trass  in the 1960s who studied the
effect of roughness on the dissolution of crystalline surfaces with different degrees
of roughness. Their results showed that the rate of mass transfer increased fourfold
with the increase in surface roughness height from ~2.5 to 10 µm over a Reynolds
number range from 8,000 to 60,000.
Regardless of initial internal surface conditions of the pipeline, multiphase flow
environments have also been shown to increase pipe wall internal surface
roughness, resulting in an increase in mass transfer . Such behaviour was also
observed by Postlethwaite and Lotz  in erosion-corrosion experiments in aerated
aqueous slurries of sand. Both authors concluded that the mass transfer would be
affected by the surface roughness produced by erosion-corrosion in the presence
of sand particles, accentuating corrosion of carbon steel.
Given that some of the electrochemical processes on carbon steel surfaces in CO2
environments are influenced by mass-transfer (particularly in solutions close to pH
4), and that numerous studies have shown rough surfaces can enhance masstransfer, there is clearly a need for greater awareness and fundamental
understanding of the role of surface roughening on corrosion rates in CO2
environments and how this relates to the transport of species to and from the steel
surface and the impact that this has on material dissolution.
In relation to experimentally observing the effect of surface roughness, the RCE
provides a convenient means of generating a uniform reaction environment for
fundamental and engineering studies of corrosion and mass-transfer under opencircuit, controlled potential or constant current conditions, and is the experimental
apparatus of choice for this study. The recent review by Walsh et al.  provides a
comprehensive summary of the range of applications and previous experimental
studies in RCE geometries.
This present paper utilises the Linear Polarisation Resistance (LPR) technique in
conjunction with the RCE to study the effect of surface roughness on carbon steel
corrosion rate in CO2 environments. It extends the recent experimental study of AlKhateeb et al , who explored the influence of surface roughness and total surface
area on mass-transfer through the application of the limiting current technique for
a range of rotational speeds in NaCl solutions saturated either with N2 or CO2 at
pH=3 and pH=4. The previous paper by Al-Khateeb  provides reliable benchmark
mass-transfer data, which is used in this work to assist in the construction of a
theoretical CO2 corrosion prediction model for rough surfaces which are then
assessed and validated against electrochemical corrosion measurements. This data
will be useful since properly-validated corrosion models can be useful for
improving the design of pipeline networks and infrastructure for oil and gas
production and processing. This is a key consideration informing major design
decisions, such as material selection and pipeline thickness, as well as the need for
corrosion mitigation equipment and strategies.
The recent review of CO2 corrosion models by Kahyarian et al.  identified three
categories: empirical, semi-empirical and mechanistic. Empirical/semi-empirical
ones are simple models, developed when there is limited fundamental
understanding of the physical phenomena, often taking the form of statistical fits
based on experimental data or correlation factors. Although these can be useful for
representative conditions for which they have been designed, they should be used
with caution outside their range of application. Important examples of
empirical/semi-empirical models include those of deWaard & Milliams  and Pots
et al.  A number of useful reviews of such models have appeared in the
literature, see e.g. Olson  and Nesic .
A number of mechanistic models have been developed to provide a physical basis
for corrosion rate predictions and to address the inherent limitations of empirical
and semi-empirical models . Elementary mechanistic models de-couple the
main physicochemical phenomena in corrosion processes, namely mass-transfer,
charge-transfer and chemical reactions, and use parameters which have a sound
theoretical foundation. Examples of these are widely used in corrosion engineering
analyses (see e.g. Sundaram et al. , Han et al. ) but their neglect of
homogeneous chemical reactions is a serious shortcoming.
These limitations have been addressed in more comprehensive mechanistic models
based on the Nernst-Planck equation for mass conservation. Nordsveen et al. 
solved the Nernst-Planck equation to describe the time-dependent mass-transfer
of species in the boundary layer using a computationally expensive multi-node
approach. The computational requirements of their multi-node approach were
alleviated by Remita et al.  who used a simplified, steady-state form of the
Nordsveen et al.  model, which may be sufficient for practical purposes of
corrosion rate estimation. Zheng et al.  recently proposed a novel, and much
more computationally efficient 2-node approach to predicting corrosion rates in
cases of mixed CO2/H2S corrosion, which calculates the surface concentrations and
corrosion rates at corroding surfaces using mass-transfer coefficients and bulk
concentrations of each species. This paper uses a new correlation based on the 2node approach for mass-transfer coefficients in RCE environments with rough
surfaces to predict corrosion rates for comparison with the experimental data
The paper is organised as follows. The experimental methods and RCE experiments
are first described before the corrosion modelling strategy is described and
validated. A series of experimental and computational results are then presented
which explore the effect of surface roughness, RCE velocity and pH on corrosion
rate at a temperature of 25°C in a CO2-saturated 1 wt.% NaCl brine. Finally,
conclusions are drawn.
Four RCE samples with different surface finishes were prepared by machining each
sample on a lathe and applying discrete and carefully controlled pressures on the
tool holder. The electrodes were carbon steel X65 with 1.2 cm diameter and 1 cm
length. The surface texture of the samples was analysed using white light
interferometry, a non-contact optical technique for surface height measurements
which is capable or resolving surface topography down to nanometer accuracy. The
specification of the samples are given in Table 1, with images of the samples and
an example of the profilometry data provided in Figure 1. Where (e) is average
distance from peak to valley and (AR/AP) is ratio of true surface area of rough
electrode projected surface area of electrode.
Table 1 RCE surface properties of the four samples considered in this study.
Figure 1 (a) Images of the RCE samples with different surfaces roughnesses of 0.5,
6, 20 and 35 µm and (b) example 2D output from profilometry analysis of 6 µm
Experiments were conducted in a 1L glass cell at atmospheric pressure and 25ºC.
The three electrode setup shown in Figure 2 was employed for all experiments,
which comprises a working electrode (RCE sample), a reference electrode (Ag/AgCl)
and a counter electrode (platinum). Electrochemical measurements were performed
using an ivium compactstat connected with a computer.
The tests were performed at rotational velocities between 1000 and 4000 rpm in a
1 wt.% NaCl solution saturated with carbon dioxide (CO2) gas for 24 hours prior to
the experiments to ensure that the system was sufficiently free from oxygen.
Bubbling of gas into the electrolyte was also maintained over the duration of each
experiment and temperature was controlled with the aid of a hotplate and
thermocouple. The pH of the system was initially measured using a pH probe
directly immersed into the electrolyte and adjusted to the desired value using
sodium bicarbonate (NaHCO3). The full matrix of test conditions evaluated is
provided in Table 2.
Table 2 Experimental test matrix.
1000 – 4000 rpm
Figure 2 Schematic of RCE three electrode cell.
Prior to each experiment the samples were degreased with acetone, rinsed with
distilled water and then dried with compressed air before mounting onto the RCE
shaft. The open circuit potential of the material was then allowed to stabilise for 10
minutes before starting each experiment. Following stabilisation of the OCP, in situ
corrosion rates were recorded by means of the DC LPR technique. LPR
measurements were conducted by polarising the sample ±15 mV vs. the open
circuit potential, scanning at a rate of 0.25 mV/s to obtain a polarisation resistance,
Rp (Ohm.cm2). LPR measurements were undertaken every 10 minutes over a total
period of 3 h.
In all experiments, the solution resistance, Rs (Ohm.cm2) was determined after LPR
measurements were complete using electrochemical impedance spectroscopy (EIS).
This consisted of polarising the sample ±5 mV vs. the OCP using a frequency range
from 20 kHz to 0.1 Hz. The value of Rs was subtracted from Rp to produce a
charge-transfer resistance, Rct (Ohm.cm2) which was used to determine the
corrosion rate behaviour with time:
Potentiodynamic measurements were also performed on each sample at the end of
the 3 h test. This technique was used to generate Tafel polarisation curves to
determine the anodic and cathodic Tafel constants (βa and βc, respectively in
mV/decade) and ultimately an appropriate Stern-Geary coefficient (B) to enable
calculation of corrosion rates from the values of Rct determined as a function of
time in each experiment.
Tafel polarisation curves were also collected by performing individual anodic and
cathodic sweeps starting at OCP and scanning to either 250 mV or -500 mV vs.
OCP, respectively at a scan rate of 0.5 mV/s. Only one Tafel curve (either anodic or
cathodic) was generated at the end of each experiment as significant polarisation
can alter the surface characteristics and/or result in contamination of the test
From the polarisation curves produced, it was possible to determine βa and βc by
measuring their respective gradients over regions were linearity was observed
between the applied voltage and the natural log of the measured current. The Tafel
slope measurements were used to determine the Stern-Geary coefficient (B), and
the corrosion current density, icorr (mA/cm2):
where βa and βc are the coefficients which characterize the anodic and cathodic
Tafel slopes of corrosion process in (V). The icorr value obtained was used in
combination with Faraday’s Law and the measured values of Rct to determine the
corrosion rate (CR) in mm/year
Where 3.27 is a conversion factor (mm.g/(mA.cm.year)), MFe is the atomic mass of
iron = 55.845 g/mol, n=2 is the number of electrons generated in the anodic
reaction and ρ the density of iron (g/cm3).
Each experiment was repeated at least twice and the values of corrosion rate
reported in this work reflect the average of multiple LPR measurements over both 3
hour tests complete with errors bars which indicate the maximum and minimum
corrosion rates determined from the individual measurements across all
The experimental measurements of the effect of surface roughness on corrosion
rate are compared with predictions based on the computationally-efficient 2-node
approach, proposed recently by Zheng et al. , which calculates species
concentrations at the corroding surface in a thin surface water film of thickness Δx
by accounting for homogeneous chemical reactions, mass-transfer of species and
electro-chemical reactions at the corroding surface. This leads to the equation
where cs,j is the surface concentration of species j, Nin,j is the flux of species j from
the bulk into the surface water film, Nout,j is the flux of species out of the surface
water film due to the electro-chemical reactions and Rj is the rate of chemical
reaction of species j in the surface water film, see Figure 3. There are 7 species to
be accounted for, namely CO2, H2CO3,
A thin surface water layer, ∆x
Nin.j Mass transfer from bulk to
Fluxes due to
Figure 3 A schematic diagram of two-node model.
Mass Transfer Fluxes
The mass transfer fluxes, Nin,j are given by
where km,j (m/s) and cb,j (mol/m3) are the mass-transfer coefficient and bulk
concentration of species j respectively. Mass-transfer coefficients are generally
functions of the geometry and of the Reynolds, Schmidt and Sherwood numbers.
Thus, the mass-transfer coefficient for turbulent single phase flow inside a pipe can
be calculated using the Berger and Hau  correlation:
where the Sherwood number Sh=(kd)/D, in terms of the mass-transfer coefficient, k
(m/s), RCE diameter, d (m), and diffusion coefficient D (m2/s), the Reynolds number
Re=(URCE d)/ν, where ν is the kinematic viscosity (m2/s) and the Schmidt number
For an RCE the following Eisenberg correlation  has been shown to be accurate
for smooth surfaces
However, for rough surfaces the recent experimental study of Al-Khateeb et al. 
has shown that the total surface area of the rough surface must be accounted for.
They proposed the following correlation for mass transfer for rough samples:
where ShR is the Sherwood number corrected with the total surface area and
The properties of the species depend on temperature and viscosity, and are
provided in Tables A.1, with reference diffusion coefficients provided in Table A.2.
The rate of the electrochemical reactions at the metal surface depends on the
surface concentrations of species involved in electrochemical reactions and on the
temperature . The cathodic reactions are given by the reduction of hydrogen,
carbonic acid (via a buffering effect) and water given respectively by
It is important to stress that carbonic acid has been shown to contribute to the
cathodic reaction via a buffering effect whereby it is transported to the steel surface
and dissociates , resulting in the reaction shown in equation (12), hence there is
a distinction in the pathway, but the ultimate hydrogen evolution reaction is the
The anodic reaction is given by equation (14), although this is a simplification and
is actually believed to occur through a number of complex, intermediate reactions
as described by Nesic et al .
Since the electrochemical reactions involve exchange of electrons, the reaction rate
represents the rate at which electrons are released or consumed. These exchange
current densities can be calculated using the following formula:
where io is the exchange current density (A/m2), E is the potential of the corroding
surface (V), Erev is the reversible potential of a specific reaction (V) and b is the Tafel
slope (V). A positive sign refers to the anodic reaction and a negative sign refers to
a cathodic one. The exchange current densities take the general form
where the reference parameter values and exponents a1, a2 and a3 for each of the
reactions are given in Table A.3 in the Appendix.
For the hydrogen reduction reaction the total current density iH+ is given by the
harmonic mean of the charge transfer-controlled exchange current, i0,H+, and the
mass-transfer limited current
, , namely
The total current density for carbonic acid is calculated similarly, with
F=96485 C/mol is Faraday’s constant and fo is the flow factor for the limiting
current of carbonic acid. The latter is defined by:
is the ratio of thickness of mass transfer diffusion layer to reaction layer (
For spontaneous corrosion the potential, E, at the corroding surface can be found
by equating the total cathodic and anodic current densities:
Once E is determined, the electrochemical fluxes of species can be calculated from
equations (15) and (16) to yield
where ni is the number of moles of electrons created per mole of species in the ith
electrochemical reaction: ni=1 for all cathodic reactions and 2 for the anodic
reaction. A positive or negative sign is taken for cathodic and anodic reactions,
For CO2 corrosion, the water chemistry is determined by the combined effects of
CO2 dissolution, carbonic acid hydration, carbonic acid dissociation, bicarbonate ion
dissociation and water dissociation. These reactions are respectively
The rates of each of these reactions depend on temperature, CO2 partial pressure
and ionic strength . The reaction rate constants used here are given in Table A.4
in the Appendix.
In the bulk, the equations for the 6 different species (CO2, H2CO3,
) are created as follows. Firstly, CO2 molecules are created by carbonic
H2CO3 is created by carbonic acid hydration and carbonic acid dissociation:
ions are created by carbonic acid dissociation and bicarbonate ion
ions are created by bicarbonate ion dissociation:
OH- ions are created from water dissociation:
H+ ions are created by carbonic acid dissociation, bicarbonate ion dissociation and
Equations (29-34) for the 6 different species (CO2, H2CO3,
in the bulk are solved using an efficient Newton-Raphson numerical scheme
implemented in Python.
Steady-state Corrosion Model
This study investigates the effect of surface roughness of corrosion rates in nonfilm-forming conditions where corrosion rate attains a steady-state. In this case it
can be shown, , that the 2-node model can be re-cast into the following
These 7 equations are solved using a Newton-Raphson numerical scheme
implemented in Python. Once
mm/year is 1.16×
(A/m2) has been determined the corrosion rate in
Experimental and Theoretical Results
The chemical solver is validated first. Solutions of equation (29)-(34) for the bulk
chemistry are validated against the experimental results of Meyssami et al.  and
Tanupabrungsun et al. . These are shown in Figure 4. Agreement is excellent in
Figure 4 Validation of bulk chemistry predictions against Meyssami et al.  and
Tanupabrungsun et al. .
The corrosion rate predictions obtained here are now compared with the pipe flow
loop experiments for smooth surfaces and corrosion model predictions for different
pH values and flow speeds from Zheng et al.  in Figure 5, using the Berger & Hau
correlation for mass-transfer coefficient.
Figure 5 Comparisons between the present model predictions for pipe flow against
experiments and predictions of Zheng et al.  at 1 bar CO₂, 20°C, d=0.01m, for a
range of pH values and velocities.
The present corrosion model predictions agree reasonably well with both the
experimental and theoretical results of Zheng et al. . The prediction that
corrosion rates are independent of flow speed for pH=6 indicates that the process
is predominantly activation-controlled rather than mass-transfer controlled in these
A new series of experimental measurements and theoretical predictions of
corrosion rate for RCE systems in aqueous CO2 solutions, with both smooth and
rough surfaces, is now presented. For smooth RCE samples, corrosion rate values
from the RCE experiments were compared with the model’s predictions by varying
the solution pH and the rotational speed of the RCE. The effect of velocity was
studied at pH=4, 5 and 6. The rotation speed started with 1000 rpm (0.628 m/s)
and increased up to 4000 rpm (2.512 m/s).
Figure 6 Comparisons between experimental and theoretical corrosion rates at 1
bar total pressure, 25°C, various pH, and different rotation speeds for a smooth
Figure 6 shows that for pH=4 corrosion rate increases with rotational speed,
indicating that mass-transfer from the bulk is important, whereas for the higher pH
values, where the bulk concentration of H+ are orders of magnitude smaller, mass
transfer of H+ ions is far less important. This leads to a reduction in the cathodic
consumption of H+ ions and a corresponding reduction in corrosion rate. Good
agreement was obtained between the model predictions and the experimental
results for all cases considered. The average difference between the model and the
experiments is about 14, 10 and 18 % for pH=4, 5 and 6 respectively.
It is generally accepted that an increase in surface roughness leads to higher
corrosion rates, since rough surfaces have a larger interfacial area with the
corrosive environment and can induced localised mass transfer between surface
peaks . However, few studies have quantified the effect of the increase in
surface area on the values of corrosion rates in CO2 environments. The work of
Asma et al.  studied the effect of surface finish on corrosion rates at room
temperature. Their results revealed that the increase in degree of roughness leads
to increase in corrosion rate. This was attributed to the larger surface which is in
contact with corrosion environment. However, they did not correct for the actual
surface area nor was the effect of surface roughness on mass-transfer quantified as
experiments were performed in static conditions.
The first series of experiments on rough surfaces in this work were also carried out
in static conditions and normalised based on their actual surface area determined
by profilometry, as opposed to their projected area. The purpose of this analysis
was to confirm that the machining of the test samples did not modify or cold work
the surface such that the corrosion rate of the material was enhanced. Tests were
performed with four samples of different surface finishes of X65 carbon steel in a 1
wt.% NaCl solution saturated with CO2. The pH and temperature were 4 and 25°C
respectively. Figure 7 presents the corrosion rate results after correcting with the
real surface area. It is clear that correcting for area leads to no significant change in
corrosion rates across all rough surfaces, indicating that the machining process
does not influence the dissolution behaviour of the steel.
Figure 7 Static corrosion rate experimental results at 1 bar total pressure in a CO2saturated 1 wt% NaCl solution at pH=4, 25°C, for different surface finishes after
correcting for total surface area. Note: area ratios are shown in Table 1.
These tests were then extended to cases of turbulent flow over rough carbon steel
X65 surfaces. The mass-transfer coefficients used in the 2-node corrosion model
are calculated using the new correlation for mass-transfer to rough RCE surfaces
proposed by Al-Khateeb et al. , (equations (9) and (10)). All current densities, and
hence the corrosion rate, were scaled with respect to the total surface area
measured using white light interferometry. Figure 8 shows the experimental and
theoretical corrosion rate results as a function of RCE velocity for each of the four
different roughness values. It is very clear that the corrosion rate increases with the
surface roughness. For example, at 3000 rpm the corrosion rate increases by
roughly 12, 22 and 31 %, compared to the smooth sample, as the surface
roughness increases. The modified 2-node model also agrees very well for all
roughness cases with average discrepancies of 10, 12, 5 and 6.5 % in comparison
with the experiments for the four roughness cases. The average difference between
the model and the experiments is around 8.5% and the maximum deviation is 17%.
Figure 8 Comparisons between model results and experiment results at 1 bar total
pressure, 25°C, various pH, and different rotation speed for different surface finishes.
Several explanations for the effect of surface roughness on increasing corrosion
rate has been discussed in the literature. It is generally assumed that the roughness
peaks disturb the viscous layer and the turbulence generated reduces the resistance
to mass transfer across the concentration boundary layer and in the valleys between
the roughness peaks . The analysis of mass-transfer intensification is based on
behaviour of turbulent eddies. These eddies penetrate into a cavity on a wall
causing deceleration in their motion due to viscous friction with the surface. The
process of deceleration is non uniform and causes the formation of areas where
turbulence fluctuations have relatively high kinetic energies at distances from the
surface which are significantly smaller than the diffusive layer thickness. These
fluctuations in turn cause localised regions of high mass-transfer .
The RCE experiments have shown that surface roughness is very influential and
leads to a monotonic increase in corrosion rate as surface roughness increases.
Results presented here have shown that it is very important to measure the total
surface area of rough surfaces since this is the appropriate area for calculating
corrosion current densities for comparison with the numerous mass-transfer
correlations in the literature.
Reliable corrosion rate prediction models can be very useful for designing pipeline
networks and critical infrastructure in oil and gas production and nuclear
processing industries. Since pipelines will inevitably have non-negligible surface
roughness which increase corrosion rates compared to smooth scenarios, it is
important to develop understanding and accurate prediction models which can
account for surface roughness. The RCE experiments carried out here have shown
that coupling the well-known Eisenberg mass-transfer correlation into the 2-node
corrosion model proposed recently by Zheng et al.  can predict corrosion rates
accurately for smooth surfaces. For rough surfaces, the Eisenberg correlation is
inadequate, and should be replaced by a correlation which accounts for surface
roughness and total surface area. This study has shown that a new correlation for
mass transfer coefficient, equations (9) and (10), can be used within the 2-node
modelling approach to predict corrosion rate from rough surfaces accurately. In the
present study the discrepancy between experimental and predicted corrosion rates
is typically around 8.5%.
Despite the success of the 2-node model, there is a need for far greater
understanding of the physical mechanisms by which roughness accelerates the
corrosion rate. Recent advances in high fidelity Computational Fluid Dynamics,
Busse et al.  are developing the ability to resolve the important localised flow
features over rough surfaces, and will further aid both the physical understanding
and predictive capability of complex mass transfer processes over rough surfaces.
Table A.1 Species properties as a function of Temperature .
Tref is the reference temperature =20°C ,
Table A.2: Reference Diffusion Coefficients for Each Species in the Model
Diffusion Coefficients (m2/s)
Table A.3 Current density parameters for the cathodic and anodic reaction [5, 26,
The exchange current density is
2 for pH<4
H2 + 2OHFe
0 for pH>5
Table A.4 Chemical reaction rate constants
The chemical constants used here are given below, together with their source
references. Note: Tf is the temperature in degree Fahrenheit, T absolute
temperature in Kelvin, Tc is the temperature in Celsius, I is the ionic strength in
molar, and p is the total pressure in psi.
(molar-1 s-1) 
Zheng, Y. Ning, J., Brown, B., Nesic, S. Advancement in predictive modeling
of mild steel in CO2- and H2S-containign environments. Corrosion, 72(5), 679691, 2016.
Al-Khateeb, Barker, R. Neville, A. Thompson, H.M. The role of surface
roughness on mass transfer in CO2-containing oil and gas environments.
Submitted to Corrosion Journal (under review), 2017.
Kermani, M.B. and Morshed, A., Carbon Dioxide Corrosion in Oil and Gas
ProductionA Compendium, Corrosion 59.8 (2003): 659-683.
Fogg, G. and Morse, J. Development of a new solvent-free flow efficiency
coating for natural gas pipelines. in Rio Pipeline 2005 Conference and
Exposition, IBP1233. 2005.
Nordsveen, M., Nesic, N., Nyborg, R., Stangeland, A. A mechanistic model for
carbon dioxide corrosion of mild steel in the presence of protective iron
carbonate films-Part 1: Theory and verification. Corrosion, 59(5): p. 443-456,
Poulson, B., Mass transfer from rough surfaces. Corrosion Science, 1990.
30(6): p. 743-746.
Tantirige, S. and Trass, O., Mass transfer at geometrically dissimilar rough
surfaces. The Canadian Journal of Chemical Engineering, 1984. 62(4): p.
Postlethwaite, J. and Lotz, U., Mass transfer at erosion‐corrosion roughened
surfaces. The Canadian Journal of Chemical Engineering, 1988. 66(1): p. 7578.
Cornet, I., Lewis, W., and Kappesser, R., Effect of surface roughness on
mass transfer to a rotating disc. Trans inst Chem eng, 1969. 47(7): p. 222226.
Gabe, D. and Makanjuola, P., Enhanced mass transfer using roughened
rotating cylinder electrodes in turbulent flow. Journal of Applied
Electrochemistry, 1987. 17(2): p. 370-384.
King, C.V. and Howard, P.L., Heat Transfer and Diffusion Rates at SolidLiquid Boundaries. Industrial & Engineering Chemistry, 1937. 29(1): p. 75-78.
Ibl, N., Advances in electrochemistry and electrochemical engineering: edited
by P. Delahay and CW Tobias, vol. 1 (edited by P. Delahay) 326 pages, $12,
Interscience, New York 1961. 1962, Pergamon.
Brenan, W.C. and Trass, O., 52nd Nat. Meeting of A. I. Ch. E. (1964).
Walsh, F. C., Kear, G., Nahle, A. H., Wharton, J. A., & Arenas, L. F. The
rotating cylinder electrode for studies of corrosion engineering and protection
of metals—An illustrated review. Corrosion Science.,2017.
Kahyarian, A., Singer, M., and Nesic, S., Modeling of uniform CO2 corrosion of
mild steel in gas transportation systems: A review. Journal of Natural Gas
Science and Engineering, 2016. 29: p. 530-549.
De Waard, C. and Milliams, D., Carbonic acid corrosion of steel. Corrosion,
1975. 31(5): p. 177-181.
Pots, B.F.M., John, R.C., Rippon, I.J., Thomas, M.J.J.S., Kapusta, S.D.,
Grigs, M.M., Whitham, T. Improvements on the deWaard-Milliams Corrosion
Prediction and Applications to Corrosion Management. NACE International,
Paper 235, 2002.
Olson, S. Corrosion prediction by use of the Norsok M-506 model – guidelines
and limitations. NACE International. Paper no. 263, 2003.
Nešić, S., Key issues related to modelling of internal corrosion of oil and gas
pipelines – A review. Corrosion Science, 2007. 49(12): p. 4308-4338.
Sudaram, M., Raman, V., High, M.S., tree, D. Wagner, J. Determinisitic
modelling of corrosion in downhole environments. NACE International. Paper
No. 30. 1996
Han, J., Carey, J.W., and Zhang, J., A coupled electrochemical–geochemical
model of corrosion for mild steel in high-pressure CO 2–saline environments.
International Journal of Greenhouse Gas Control, 2011. 5(4): p. 777-787.
Remita, E., Tribollet, B., Sutter, E., Vivier, V., Ropital, F., Kittel, J. Hydrogen
evolution in aqueous solutions containing dissolved CO2: quantitative
contribution of the buffering effect. Corrosion Science, 2008. 50(5): p. 14331440.
Berger, F. and Hau, K.-F.-L., Mass transfer in turbulent pipe flow measured by
the electrochemical method. International Journal of Heat and Mass Transfer,
1977. 20(11): p. 1185-1194.
Eisenberg, M., Tobias, C., and Wilke, C., Ionic mass transfer and
concentration polarization at rotating electrodes. Journal of the
Electrochemical Society, 1954. 101(6): p. 306-320.
Nesic, S., Thevenot, N., Crolet, J. L., & Drazic, D. M.,Electrochemical
properties of iron dissolution in the presence of CO2 Basics revisited. No.
CONF-960389--. NACE International, Houston, TX (United States), 1996.
Zheng, Y., Ning, J., Brown, B., & Nešić, S., Electrochemical Model of Mild
Steel Corrosion in a Mixed H2S/CO2 Aqueous Environment.
CORROSION/2014, paper, 2014(3907).
Zheng, Y. Electrochemical mechanism and model of H2S corrosion of carbon
steel, PhD thesis, Ohio University, 2015.
Meyssami, B., Balaban, M.O., and Teixeira, A.A., Prediction of pH in model
systems pressurized with carbon dioxide. Biotechnology progress, 1992. 8(2):
Tanupabrungsun, T., Young, D., Brown, B., & Nešic, S., Construction and
verification of pourbaix diagrams for CO2 corrosion of mild steel valid up to
250 C. in CORROSION 2012. 2012. NACE International.
Evgeny, B., Hughes, T., and Eskin, D., Effect of surface roughness on
corrosion behaviour of low carbon steel in inhibited 4 M hydrochloric acid
under laminar and turbulent flow conditions. Corrosion Science, 2016. 103: p.
Asma, R., Yuli, P., and Mokhtar, C., Study on the effect of surface finish on
corrosion of carbon steel in CO2 environment. Journal of Applied Sciences,
2011. 11(11): p. 2053-2057.
Dawson, D.A. and Trass, O., Mass transfer at rough surfaces. International
Journal of Heat and Mass Transfer, 1972. 15(7): p. 1317-1336.
Levich, V.G., Physicochemical hydrodynamics. 1962: Prentice hall.
Busse, A., Lützner, M., and Sandham, N.D., Direct numerical simulation of
turbulent flow over a rough surface based on a surface scan. Computers &
Fluids, 2015. 116: p. 129-147.
Nesic, S., Postlethwaite, J., and Olsen, S., An electrochemical model for
prediction of corrosion of mild steel in aqueous carbon dioxide solutions.
Corrosion, 1996. 52(4): p. 280-294.
Perry, R. and Green, D., Handbook of chemical engineering. pg, 1984: p. 176.
Kvarekvål, J., A kinetic model for calculating concentration profiles and fluxes
of CO2 related species across the Nernst diffusion layer. 1997, NACE
International, Houston, TX (United States).
Fardisi, S., Tajallipour, N., and Teevens, P.J., Predicting General Corrosion
Rates In Sour Environments With the Growth of a Protective Iron Sulphide
Film. NACE International.
Oddo, J.E. and Tomson, M.B., Simplified calculation of CaCO3 saturation at
high temperatures and pressures in brine solutions. Journal of Petroleum
Technology, 1982. 34(07): p. 1,583-1,590.
Kharaka, Y.K., et al., SOLMINEQ., A computer program for geochemical
modeling of water-rock interactions. US geological survey water-resources
investigation report, 1988. 88: p. 4227.
Delahay, P., Implications of the Kinetics of Ionic Dissociation with Regard to
Some Electrochemical Processes—Application to Polarography. Journal of
the American Chemical Society, 1952. 74(14): p. 3497-3500.
Palmer, D.A. and Van Eldik, R., The chemistry of metal carbonato and carbon
dioxide complexes. Chemical Reviews, 1983. 83(6): p. 651-731.