Introduction

With the continuously growing demands in energy consumption, conventional energy sources are suffering from depletion. New sources, such as oil sands, will increasingly be relied upon to make up the difference in future global oil production. The most energy- and cost-efficient manner by which to transport oil sands from excavation site to the extraction plant is that of hydrotransport system (Ref 1). In the hydrotransport process, oil sands and water are mixed to make slurries, which are transported via pipelines from the mining to a bitumen extraction facility.

In oil sands slurry, the presence of water and oxygen, combined with salts containing Cl−, HCO3 −, and SO4 2−, causes corrosion to the carbon steel pipe, which is exacerbated by the flowing slurry and the high content of solid sands. The synergistic effect of corrosion and erosion can generate material loss much greater than that caused by either of them individually (Ref 2-8). Erosion-corrosion (E-C) has constituted an essential threat to the integrity of the oil sands slurry hydrotransport system.

In the previous studies (Ref 9-11), the authors used rotating disk electrode (RDE) technique to investigate the effect of fluid hydrodynamics on corrosion of X-65 pipe steel in the simulated oil sand slurry. Furthermore, the synergism of erosion and corrosion and the steel E-C rate were determined by weight-loss testing and electrochemical corrosion measurements through an impingement jet system. It has been demonstrated that, with the increase of the content and size of sands as well as the slurry flow velocity, the steel E-C is enhanced. Moreover, E-C of the steel is dominated by erosion, which accounts for >80% of the total E-C rate.

In this study, the authors continue further the relevant research to investigate the roles of fluid mechanics and solid impact in the steel E-C. Weight-loss testing and computational fluid dynamic (CFD) simulation were combined to study E-C of X-65 pipe steel in oil sands slurry. The distributions of flow field, surface shear stress and normal impact stress on steel were simulated. It is anticipated that this research provides an essential insight into the mechanistic aspects of E-C of hydrotransport pipes in oil sands slurry.

Experimental

Materials and Solutions

Working electrodes for E-C tests were made of a sheet of API X-65 steel, a commonly used steel in oil sands slurry hydro-transportation, with chemical composition (wt.%): C 0.04, Si 0.2, Mn 1.5, P 0.011, S 0.003, Mo 0.02, and Fe balance. The specimens were embedded in epoxy resin, leaving a circular working area of 0.68 cm2. The working surface was subsequently ground with 600, 1000, and 1200 grit emery papers, cleaned by distilled water and methanol.

The test solution simulating the chemistry of oil sands slurry (Ref 12) contained 0.02 M NaHCO3, 0.02 M NaCl, 10% (v/v) paraffin mineral oil, and 0.2% (wt.) dioctyl sulfosuccinate sodium salt as anionic surfactant agent as well as 30 wt.% silicon particles with an average size of 600 μm.

All the tests were performed at ambient temperature (~25 °C) and open to air.

Impingement Jet System

The impingement jet system used previously (Ref 10, 11) consisted of a plastic tank used as reservoir, a high-pressure pump, flow velocity controller, sand concentration controller, stirrer and valves. When the fluid entered the ejector at high speeds, it produced a partial vacuum because of the venturing effect. The sands underneath the valve could be mixed with the flowing fluid by the principle of suction. A speed-adjustable mechanical stirrer was used to insure the homogeneity of the slurry. The ejector, made of stainless steel with 7.6 mm in diameter, was 10 mm away from the testing specimen. The detailed installation of specimen in the test chamber is shown in Fig. 1.

Fig. 1
figure 1

Schematic diagram of the experimental set-up of the steel specimen in the test chamber under fluid impingement

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Weight-Loss Measurements

Prior to and after the E-C tests, the weight of the X-65 steel specimen was measured accurately using an analytic balance with the accuracy of 1 × 10−4 g.

CFD Simulation and the Sand Impact Modeling

The CFD is a numerical analysis technique based on solving the well-known Navier-Stokes equations, which are formulations of mass, momentum and energy conservation laws for fluid flow (Ref 13). The simulation was conducted using a commercial CFD software package COSMOSfloworks 2007 Service Pack. The initial and boundary conditions as well as the input parameters included:

  1. (1)

    Inlet: A flow of oil-water emulsion at the velocity of 3 m/s, a dynamic viscosity of 1.2 × 10−3 Pa s (sand-free fluid) and 1.7 × 10−3 Pa s (sand-containing slurry), and density of 0.99 × 103 and 1.16 × 103 kg/m3 in the absence and presence of sands, respectively. The test temperature was 25 °C. Turbulence intensity was 10%.

  2. (2)

    Outlet: Environment pressure was 101,325 Pa.

  3. (3)

    Solid wall: The wall was approximately considered as an adiabatic wall with roughness of 10 μm, and the roughness of the steel specimen was also set at 10 μm.

  4. (4)

    Flow type: Turbulent flow as calculated, which was shown later.

Results

Weight-Loss Measurements

Figure 2 shows the weight-loss of the steel as a function of the impact angle in oil-water emulsion in the presence and absence of sands. When the impact angle increased from 30° to 45°, the weight-loss is increased. After that, the measured weight-loss reduces. When the impact angle increases to 90°, the weight-loss of the steel is increased again. Furthermore, the addition of sands in the fluid increases the weight-loss of the steel.

Fig. 2
figure 2

Weight-loss of the steel specimen as a function of the fluid impact angle in oil-water emulsion in the absence and presence of sands

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CFD Simulation

Figure 3 shows the CFD-simulated fluid field distribution on the steel electrode at various impact angles in oil sands slurry. It is seen that there are quite different fluid fields established on the electrode surface at the different impact angles. In particular, at the impact angle of 30°, most of the electrode surface is under a fluid flow field of 3 m/s. When the impact angle increases to 45° and 60°, the electrode area experiencing a low-velocity flow of about 1.5 m/s increases. At the impact angle of 90°, the whole electrode surface is under a low flow field of about 1.2-1.8 m/s, and the flow field is dispersed around the electrode center with different directions.

Fig. 3
figure 3

Fluid field distribution on the surface of the steel electrode in oil sands slurry (Color figure online)

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Figure 4 shows the 3D view of the fluid field developed on the electrode surface. It is seen clearly that, with the increase in impact angle, the heave area representing the high fluid flow field decreases.

Fig. 4
figure 4

3D view of the fluid field distribution on the steel electrode surface in oil sands slurry (Color figure online)

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Figure 5 shows the distribution of shear stress on the electrode surface at various impact angles in oil sands slurry. At 30°, a shear stress field of 35-50 Pa is distributed over almost all the electrode surface. When the impact angle increases to 45° and 60°, a zero-shear stress region develops at the edge of the electrode surface, and the area increases with the impact angle. When the impact angle is 90°, the large zero-shear stress region further increases and is concentrated at the center of the electrode, with a low shear stress of about 25-30 Pa around the central area.

Fig. 5
figure 5

Distribution of shear stress on the steel electrode surface in oil sands slurry (Color figure online)

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Discussion

Electrochemical Corrosion of X-65 Steel in Oil Sands Slurry

The cathodic reaction during corrosion of steels in the flowing oil-water and oil-water-sands systems that are open to air is characterized by the reduction of oxygen:

$$ {\text{O}}_{2} + 2{\text{H}}_{2} {\text{O}} + 4{\text{e}} \to 4{\text{OH}}^{ - } $$
(1)

Before reduction, oxygen molecules dissolved in water would diffuse through the solution layer toward the steel surface. The fluid flow accelerates the mass-transport of oxygen.

The anodic reaction of steel in neutral pH solution generally involves multiple-step oxidations of Fe to form a layer of pre-oxide film of Fe(OH)2 by (Ref 14):

$$ {\text{Fe}} + 2{\text{OH}}^{ - } \to {\text{Fe(OH)}}_{2} + 2{\text{e}} $$
(2)

The Fe(OH)2 deposit layer could be further oxidized with the sufficient supplement of oxygen to form Fe2O3 by

$$ 4{\text{Fe(OH)}}_{2} + {\text{O}}_{2} \to 2{\text{Fe}}_{2} {\text{O}}_{3} + 4{\text{H}}_{2} {\text{O}} $$
(3)

The role of fluid flow in corrosion of steel is dual, i.e., it accelerates transport of oxygen to enhance oxidation of the steel, and simultaneously, make thinner, or even completely remove the deposit layer or oxide film from the electrode surface.

Hydrodynamics of Oil-Water Emulsion and Oil Sands Slurry

Dynamic viscosity of fluids, μ, is an essential parameter in CFD simulation. A semi-empirical equation for calculation of the viscosity of two-phase fluid mixtures, e.g., oil-water emulsion, is expressed as (Ref 15)

$$ \begin{gathered} \upmu_{\text{m}} = \frac{{\upphi_{\text{A}} \upmu_{\text{A}} }}{{\uprho_{\text{A}} }}\exp \left( {\upphi_{\text{B}} a_{\text{B}}^{*} } \right) + \frac{{\upphi_{\text{B}} \upmu_{\text{B}} }}{{\uprho_{\text{B}} }}\exp \left( {\upphi_{\text{A}} a_{\text{A}}^{*} } \right) \hfill \\ a_{\text{A}}^{*} = - 1.7\ln \frac{{\upmu_{\text{B}} \uprho_{\text{A}} }}{{\upmu_{\text{A}} \uprho_{\text{B}} }} \hfill \\ a_{\text{B}}^{*} = 0.27\ln \frac{{\upmu_{\text{B}} \uprho_{\text{A}} }}{{\upmu_{\text{A}} \uprho_{\text{B}} }} + \left( {1.3\ln \frac{{\upmu_{\text{B}} \uprho_{\text{A}} }}{{\upmu_{\text{A}} \uprho_{\text{B}} }}} \right)^{0.5} \hfill \\ \end{gathered} $$
(4)

where μm is the dynamic viscosity of fluid mixture, ϕ is the volume ratio, ρ is density of the fluid, and A and B refer to the two phases present in the mixture.

The presence of a dispersed phase in solution makes its hydrodynamic properties more complicated. With a high volume of oil and/or sand particles, emulsion/slurry is often non-Newtonian. In this study, the volume fractions of oil and sands are 10 and 10.3%, respectively. The oil-water-sand slurry could be approximately recognized as a Newtonian slurry. Consequently, the dynamic viscosity of oil-water-sand slurry can be calculated by the following empirical equation (Ref 16):

$$ \upmu_{\text{slurry}} = \upmu_{\text{m}} \left[ {1 + 2.5\upphi_{\text{s}} + 10.05\upphi_{\text{s}}^{2} + 0.00273\exp \left( {16.6\upphi_{\text{s}} } \right)} \right] $$
(5)

where μm is the dynamic viscosity of oil-water emulsion, and ϕs is the volume fraction of sands. In the present study, μm = 1.2 × 10−3 Pa s and μslurry = 1.7 × 10−3 Pa s.

Reynolds number, Re, which is used to define the flow pattern of a fluid, is given by

$$ Re = \frac{{\uprho u_{0} L}}{\upmu } = \frac{{u_{0} L}}{\upnu } $$
(6)

where u 0 is the fluid velocity (m/s), L is the characteristic length (m), ν is the kinematic fluid viscosity (m2/s), and ρ is the density of the fluid (kg/m3). By replacing the parameters and variables in Eq 6 with the present conditions, Re is calculated to be about 4.5 × 104 for the fluid flow velocity of 3 m/s. The calculated Re value is much higher than the threshold value of 2300 for laminar flow (Ref 9). It is thus apparent that the impingement jet system generates a turbulent flow, i.e., the actual flow pattern observed in oil sands slurry hydrotransport system.

The fluid impingement on the steel specimen generates a shear stress, τ, which is the measurement of the viscous energy loss within the turbulent boundary layer, and is related to the turbulent intensity acting on the electrode surface. The shear stress is expressed as

$$ \uptau \approx 0.5f \cdot u^{2} \cdot \uprho $$
(7)

where f is the friction factor that is a function of Re and the roughness of the solid surface, and u is time-average fluid velocity. Apparently, the shear stress is primarily dependent on the fluid velocity.

Fluid Hydrodynamics and the Sands Impact as well as E-C of Steel

Shear stress generated on specimen by fluid flow would contribute to E-C of steel. At a small impact angle such as 30°, the whole electrode surface is under a uniform flow field with a high velocity of about 3 m/s. The resulting shear stress is high and distributes uniformly over the electrode surface (Fig. 6). Shear stress, representing a mechanical effect, would thinner and remove the deposit or film, enhancing the corrosion activity of the steel. With the increase of impact angle, the electrode area that is under the high-velocity flow field decreases, and the low-velocity flow field with the value of about 1.2-1.8 m/s dominates the electrode surface, which is clearly shown in Fig. 3 and 4. As a consequence, the electrode area with small shear stresses (0-15 Pa) increases and that with high shear stresses (up to 50 Pa) decreases with the increasing impact angle, as shown in Fig. 5. When the impact angle increases to 90°, the electrode is under a low-velocity flow field with the value of about 1.5 m/s (Fig. 3). The resulting shear stress has the lowest value, and there is the smallest mechanical effect due to fluid hydrodynamics on the electrode state. Therefore, an increase of impact angle would decrease the hydrodynamic shear stress exerted on the steel surface, and thus the activity of the steel specimen.

Fig. 6
figure 6

The sand particle collision model with impact angles of 30° and 90°: (a) the stress distribution; (b) the deformation (Color figure online)

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In addition to fluid hydrodynamics developed on the electrode surface, the mechanical impact of sand particles on specimen and the resulting effect on the steel E-C should not be ignored. Figure 6 shows a single sand particle collision model to illustrate the effect of sand impact on the electrode state under impact angles of 30° and 90°. When the impact angle is 90°, the mechanical stress (van Mises stress) due to the sand impact, i.e., 45.83 N/m2, is approximately twice that generated under 30° impact, i.e., 25.00 N/m2. The resulting deformation, i.e., the displacement into the steel substrate, at 90° of impact is 4 × 10−12 m, twice the one resulting from the impact at 30°. Thus, the displacement-induced steel activity due to impact of sands is expected to increase with the impact angle.

Undoubtedly, E-C of steel is resulted from the combined effect of hydrodynamic shear stress and mechanical sand impact stress. Consequently, a competition between shear stress and the impact normal stress exists in enhancement of E-C rate as a function of the impact angle. When the impact angle is low, shear stress is dominant; and the mechanical impact stress becomes dominant at a relatively high angle. A balanced effect of the two stresses results in the highest E-C rate at about 45° of the slurry impact.

Conclusions

The steel E-C is resulted from the combined effect of hydrodynamic shear stress and the mechanical impact stress developed on the steel surface. At a low impact angle, i.e., 30°, shear stress is dominant. The mechanical impact stress becomes dominant when the angle increases to a high value, i.e., 90°. It is determined that the maximum of E-C rate of the steel occurs at approximately 45° of the slurry impact.