Review of CO₂ Corrosion Modeling for Carbon Capture, Utilization and Storage (CCUS) Infrastructure

Abstract

CO₂ corrosion remains a critical challenge for the safe and reliable operation of Carbon Capture, Utilization, and Storage (CCUS) infrastructure. This review summarizes CO₂ corrosion implications from material selection, exposure time, CO₂ phase behavior, flow conditions, and impurities such as H₂O, O₂, SO_x, NO_x, and H₂S. CO₂ corrosion modeling has, since early works by de Waard in 1975, expanded to a wide range of models and software tools, many of which have already been reviewed and compared. This work provides a historical timeline and a comparative summary of models and software tools to assist in selecting models for CCUS applications. Modeling approaches are classified into empirical, semi-empirical, and mechanistic categories, with their assumptions, strengths, and limitations. CO₂ corrosion modeling has persistent challenges relating to data quality, data quantity, and parameter interactions, which reduce model accuracy, especially for machine learning approaches. The provided perspective emphasizes that machine learning and hybrid modeling approaches for CO₂ corrosion prediction are gaining popularity, and their effectiveness is currently limited by the quality and quantity of available corrosion data. The provided opportunities include recommendations for standardized experimental procedures and hybrid modeling strategies that combine physics-based insights from mechanistic modeling approaches with data-driven machine learning approaches.

1. Introduction

Carbon dioxide (CO₂) is a major greenhouse gas, and large-scale carbon capture, utilization, and storage (CCUS) is essential to mitigate its impact on climate change [1,2,3]. In CCUS, CO₂ is captured from industrial sources or from the atmosphere and then generally transported by ship or pipeline for storage or utilization [4,5]. However, the captured CO₂ often contains impurities such as H₂O, NO_x, SO_x, H₂S, and O₂, where the concentration and type of impurity depend on the capture technology and the source from which the CO₂ is captured [6,7]. These impurities can compromise the infrastructure’s integrity by creating a corrosive environment [8,9]. Enhanced oil recovery (EOR) has been used since the 1970s by injecting CO₂ into oil wells to extract more oil from reservoirs [10]. The pipelines used for these have been constructed of carbon steel, which makes it crucial to understand the risks of impurity-induced corrosion [7,10]. Studies have examined CO₂ corrosion and its mechanisms in depth [11,12]. Studies have also analyzed corrosion from impure CO₂, as demonstrated by Simonsen et al. in their review study [13]. Additionally, studies have shown that various factors, such as temperature, pressure, impurity type, impurity concentration, flow rate, and exposure time, can significantly influence corrosion behavior [12,14,15,16,17,18,19,20]. Other studies show synergistic effects between impurities such as NO₂ and SO₂, where NO₂ catalyzes the reaction with SO₂ and H₂O, posing further challenges for the occurrence of corrosion [21].

The primary challenges for CO₂ transportation are to balance the cost of pipeline materials, including maintenance, and potential corrosion. Failure to strike the right balance relates to unnecessary expenses and safety risks. The benefits of corrosion modeling are a common initiative to make informed decisions on this balance, which, in the case of CO₂ corrosion, includes the following:

• Risk assessment: Modeling enables the assessment of corrosion risks under various operating conditions, allowing engineers to identify potential trouble spots and take preventive measures [13,22].
• Material selection: Engineers can use models to evaluate the performance of different materials under specific conditions and choose materials that are more resistant to CO₂ corrosion. Material challenges for CO₂ transport related to CCUS are investigated in [22,23].
• Corrosion control strategies: Modeling helps in the development and optimization of corrosion control strategies, such as the use of inhibitors or coatings, to mitigate the impact of CO₂ on equipment and pipelines [22,24].
• Cost reduction: By predicting corrosion rates and understanding the factors influencing corrosion, engineers can implement more targeted and cost-effective corrosion management practices, reducing maintenance and replacement costs [11,13,25].
• Transport type: CAPEX and OPEX costs related to CO₂ varies on the transportation type. Fluid regime, pressure, and temperature are very different between CO₂ transport by train, truck, or pipeline. Here, corrosion modeling helps engineers select the appropriate type of transportation [25,26,27].

The area of corrosion modeling has been investigated since 1975 [28], while corrosion modeling using neural networks has been studied as early as 2001 [29], although recent focus on machine learning has substantially increased the research focus [30,31,32,33,34].

Different review studies on CO₂ corrosion modeling have been conducted, presenting various corrosion models, including de Waard, Norsok M-506, Hydrocor, Corplus, Cassandra, KSC, Multicorp, ECE, Tulsa, ULL, OLI, and SweetCor [35,36,37,38]. They discuss the effect of impurities such as H₂O, O₂, SO₂, H₂S, NO₂, and the effects of acids, alkali, and salts. Furthermore, the effects of pressure and temperature, electrolyte composition, electrochemical reactions, and the influence of corrosion products [13]. However, these studies do not consider the broader trends in CO₂ corrosion modeling, which may lead to solution overlap or to the modeling approaches encountering the same limitations or challenges. In addition, although there is an increasing tendency to use machine learning for CO₂ corrosion models, challenges related to the quality and quantity of data from corrosion experiments remain. Thus, the motivation and the contributions of this work are summarized as follows:

• A historical overview of CO₂ corrosion models and software tools, illustrating the major trends, with the recent popularity of machine learning approaches.
• An overview of CO₂ corrosion models with their respective strengths, assumptions, and limitations.
• Identification of challenges in CO₂ corrosion modeling, with emphasis on data-related problems when applying machine learning approaches to predict CO₂ corrosion rate.
• Proposed opportunities given these challenges, through gathering data and increasing the quality of new data by more unified experimental approaches.

This study does not present the mathematics or theoretical approach of the different models, as these have already been presented in various studies [39,40,41,42,43]. Instead, this study focuses on CCUS applications and the current trends in corrosion modeling.

The remainder of the study consists of Section 2, which discusses the factors that influence CO₂ corrosion, including the presence of impurities and flow conditions. Section 3 then presents the various modeling approaches, including empirical, semi-empirical, and mechanistic models, along with a historical overview and the direction of corrosion modeling. Then, Section 3.4 presents the challenges and opportunities in CO₂ corrosion modeling, before concluding in Section 4.

2. Properties of CO₂ Corrosion

This section summarizes the properties of CO₂ that can affect corrosion, which have been investigated in several studies previously [44,45,46,47,48] and reviewed by [7,11,13,20].

When discussing CO₂ corrosion, it refers to the electrochemical process that occurs between CO₂ and iron (Fe) in an aqueous environment. The CO₂ dissolves in water (H₂O) to form carbonic acid (H₂CO₃), which facilitates the oxidation of iron to its ferrous state (Fe²⁺). The process can be expressed as redox reactions:

$$\begin{array}{cc}\hfill C{O}_2+H_{2}O& \to H_{2}C{O}_3\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill Fe+2H_{2}C{O}_3& \to F{e}^{2+}+HC{O}_3^{-}+H_2\hfill \end{array}$$

(2)

$$\begin{array}{cc}\hfill F{e}^{2+}+C{O}_3^{2-}& \to FeC{O}_3\hfill \end{array}$$

(3)

In the following subsections, the properties that influence corrosion, including the phase of CO₂, the presence of impurities, flow, material, and time after exposure to a corrosive environment, are summarized, along with their relevance to incorporating them into corrosion prediction models.

2.1. CO₂ Phase Conditions

CO₂ can exist in different phases, depending on the temperature and pressure conditions, including solid, gaseous, liquid, and supercritical phases [8,49]. The supercritical phase occurs when CO₂ surpasses its critical temperature and pressure, which is 30.98 °C and 73.77 bar [49]. However, the critical condition of CO₂ can be impacted by impurities, such as the non-condensable gases (CO, H₂, O₂, and N₂) [50,51]. For corrosion, different phases can have significant differences in corrosion rate, which are important when modeling corrosion.

The phase of matter of CO₂ is typically chosen based on the transportation mode, which generally is within its gaseous, liquid, or supercritical phase [52,53]. CO₂ can be transported by pipeline in the gaseous, dense, or supercritical phase, while stationary transportation modes such as truck, ship, and train generally are in the liquid phase [13,53,54,55]. For pipeline transportation, CO₂ is first compressed, raising its pressure and temperature, pushing it into the supercritical state. Along the pipeline, where ambient temperatures are generally 5–20 °C, the CO₂ transitions from supercritical to dense phase as it cools [13,55]. The exact phase depends on both the operating pressure and whether the system is designed for dense phase or gaseous transportation [55]. For stationary transportation, CO₂ is maintained in the liquid phase at approximately −28–−50 °C and 7–18 bar, with no continuous flow during storage or transfer [56].

The amount of CO₂ that can be packed into a given space depends heavily on its phase. As a gas at standard pressure and room temperature, its density is relatively low at around 1.8 kg/m³; however, when cooled and pressurized into a liquid, its density can reach about 1150 kg/m³ [57,58]. Transporting CO₂ in liquid or supercritical form is usually more efficient because it allows much more mass to be transported in the same volume. This has a significant impact on transport costs and system design, especially since changes in phase affect energy use and can lead to operational challenges, such as phase separation [59,60,61]. In addition, supercritical CO₂ has a higher solubility for H₂O, which means that the CO₂ can contain a greater amount of H₂O before water droplets form, which would lead to an accelerated corrosion rate [62]. Phase behavior of impure CO₂ has been studied by Sun et al. [63], where H₂S was found to increase water precipitation by reducing the H₂O solubility in CO₂.

When modeling the corrosion rate, it is essential to consider the phase of CO₂, as a change in phase can alter the solubility of impurities such as H₂O, H₂SO₄, and HNO₃ [11,50]. Pressure and temperature influence the corrosion rate but also affect the CO₂ phase and the solubility of H₂O and corrosive species, such as HNO₃ and H₂SO₄. Corrosion tends to increase between 80 and 100 °C, but at temperatures above 120–150 °C, it may decrease due to protective surface layers forming [64]. As Brown et al. [65] showed, an increase in temperature from 4 to 50 °C at 10 MPa resulted in a corresponding increase in the corrosion rate, from 0.017 to 0.088 mm/y. Additionally, higher pressure accelerates corrosion by enhancing internal stress and increasing chemical reactivity [19,64].

2.2. Presence of Impurities

This section provides a brief overview of the impact of impurities present in CO₂, as other studies have already conducted in-depth research on this, as well as the chemical reactions and reaction products that the impurities can form [11,50,66]. The types of impurities present in CO₂ depend not only on the source of the CO₂ but also on the capture process [6,62]. These can include H₂O, O₂, SO₂, NO₂, and H₂S. The impurities can be roughly divided into two groups: corrosion-inducing impurities and non-condensable gases [50]. The non-condensable gases, such as Ar, N₂, H₂, and CH₄, reduce the density while also increasing the pressure loss, resulting in greater energy requirements for compression [59]. In particular, H₂ increases the vapor pressure of CO₂, which is the pressure where a liquid tends to evaporate at a given temperature. Even at concentrations as low as 500 ppm H₂, can significantly increase the vapor pressure, thereby reducing the efficiency of liquefaction and compression [50,58]. The solubility of H₂O in CO₂ is influenced by the presence of non-condensable gases, where the presence of 2.5 mol% O₂, N₂, or CH₄ decreases the H₂O solubility in dense and supercritical CO₂ by 75 to 200 ppm [50,67].

The corrosion-inducing impurities, such as H₂S, SO₂, NO₂, O₂, and H₂O, significantly increase the material costs of the pipeline, due to a need for a higher material grade to withstand corrosion [16]. The presence of water is a prerequisite for electrochemical corrosion processes [11]. Even trace amounts of water increase the possibility of corrosion [11,50]. Studies have examined the impact of water content in CO₂, spanning a wide range from 50 ppm to saturated levels of around 50,000 ppm, as reviewed by Simonsen et al. [13]. Impurity type and concentration, particularly H₂O, NO₂, H₂S, and SO₂, have a strong impact on the corrosion severity. These compounds can interact to form strong acids like H₂SO₄ and HNO₃, which aggressively oxidize exposed materials [12,21]. Among these, water is especially problematic due to its role as a reactant in most impurity-driven reactions. Corrosion risk remains relatively low when water is kept below its solubility limit in CO₂ [68].

In addition, amines such as monoethanolamine (MEA) or methyldiethanolamine (MDEA) can be present in the CO₂ after flue gas treatment [50]. When these amines are combined with CO₂ and H₂O, they can create a corrosive environment. However, at low amine concentrations, they have been reported to inhibit corrosion, suggesting that their influence on corrosion depends on concentration [19,50,69].

The presence of multiple impurities has been shown to amplify corrosion through synergistic interactions. For example, NO₂ accelerates reactions between other impurities, such as the conversion of SO₂ and H₂O into sulfuric acid [11,45,50,70]. Even a few ppm of NO₂ can initiate reactions that can lead to the formation of acid [50]. Similarly, H₂S can react with oxidants like O₂, SO₂, or NO₂ to generate water, which in turn increases the risk of condensation and enhances corrosive effects [65]. At concentrations exceeding 5 ppm, H₂S can also promote acid drop out depending on the impurity composition [50]. Likewise, the presence of both O₂ and H₂S will lead to H₂ oxidation, producing SO₂ and elemental sulfur, and causing additional pitting corrosion [11,14,20,50].

2.3. Flow Conditions

Flow conditions also affect CO₂ corrosion of pipelines. Typically, pipeline flow velocities range from 0.9 to 2.6 m/s [53]. Flow velocity affects the exchange of reaction products at the metal surface. Higher flow velocities increase corrosion because they remove protective layers of reaction products and bring fresh corrosive species to the steel surface [71]. This keeps the metal exposed and active, leading to higher corrosion. Once a stable protective layer forms, however, the effect of flow velocity decreases because the layer protects the steel and reduces the impact of fluid movement [20]. Flow conditions can significantly promote erosion, thereby increasing corrosion rates, as observed by Dugstad et al. [17] and Xiang et al. [72], where a higher flow rate corresponded to a higher corrosion rate. In addition, the presence of solid particles introduces further risks related to erosion, equipment damage, and reduced injectivity [50]. Moreover, CO₂ multiphase flow can increase corrosion and erosion mechanisms due to phase interactions and localized shear stresses [30,73].

2.4. Materials

Material selection is important in ensuring durability and performance, as different materials exhibit varying levels of resistance to the environment. For example, carbon steel is a cost-effective option but offers limited corrosion resistance [16,23]. Enhancing the material by alloying with chromium (Cr) and nickel (Ni) significantly improves its resistance to corrosion but comes with an increased cost [20,23]. In addition to material selection, certain corrosion products can form a stable, protective layer on the surface, which helps decrease or prevent corrosion of the underlying material [11,20]. The corrosion product formed on carbon steel material during CO₂ exposure with impurities is typically FeCO₃; however, it depends on the other impurities. For instance, if SO₂, O₂, and H₂O are present, the main corrosion product formed is FeSO₃ [16,19,74,75,76]. On the other hand, at water saturated conditions and O₂ concentration of <1000 ppm, FeSO₄ was the main corrosion product observed [16]. Materials with higher content of mangan (Mn) and silicium (Si) are known to enhance the corrosion resistance, by forming more protective and stable corrosion films, where the formation of FeCO₃ is protective for the material, causing a decrease in corrosion rate [16,77]. In addition, the application of corrosion-resistant coatings provides an effective strategy to further improve the material against corrosion [78]. While corrosion-resistant alloys offer improved tolerance to impurities in CO₂, their higher material and fabrication costs limit large-scale deployment in CCUS infrastructure. Therefore, carbon steel remains the preferred material for CO₂ transportation due to its lower cost [25,78].

2.5. Time

The exposure time of the experimental conditions affects the calculated corrosion rate, based on the material loss, as shown in Equation (4) [79,80].

$$CR={\displaystyle \frac{K·W}{A·T·D}},$$

(4)

where K is a constant, W is the mass loss in grams, A, is the exposed area, T is the time of exposure in hours, and D is the density of the material exposed in g/cm³. A corrosion experiment based on mass loss can give a misleading impression of the corrosion rate; the accumulation of corrosion products on the metal surface can lead to a decline in the corrosion rate, due to acting as a passivating layer that limits interaction between the metal and the corrosive environment [25]. This was observed by Elgaddafi et al [81], who investigated the corrosion rate using linear polarization resistance (LPR), rather than the mass loss method. LPR offers the advantage of real-time observation of the corrosion behavior throughout the experiment [82]. In their study, the corrosion rate reached its maximum after ∼25 h of exposure to the corrosive environment, and then the corrosion rate decreased until the end of the experiment. The authors attributed this reduction in corrosion rate over time to the formation of a passivating layer on the metal’s surface, which inhibited further corrosion. Another study by Xiang et al. [72] conducted supercritical CO₂ corrosion testing using the mass loss method over exposure times of 1, 3, 5, 10, and 20 days under stagnant conditions in the presence of H₂O, SO₂, NO₂, and O₂. The results showed a very high initial corrosion rate of ∼17 mm/y after the first day of exposure, followed by a sharp decrease between 1 and 3 days. Beyond this period, the corrosion rate continued to decline more gradually with increasing exposure time, reaching a considerably lower value after 20 days. This behavior was attributed to the formation of a protective surface scale on the material.

3. Modeling Approaches

Modeling methodologies can be categorized into three main types: mechanistic, semi-empirical, and empirical [83]. The three model types are complementary, such that empirical models enable fast input/output correlation; semi-empirical models add knowledge of behavior to reduce the number of tuning parameters to provide better predictions outside of the training data range; and mechanistic models provide explanatory power and improved extrapolation when chemistry, flow, and film formation are coupled and time-dependent.

Several studies have provided a review of CO₂ corrosion modeling, including historical progression and modeling types [39,83,84,85,86]. This paper extends these review studies by summarizing the empirical, semi-empirical, and mechanistic CO₂ model types, while focusing on the recent machine learning (ML) models.

In this work, the model types are defined as follows:

• Empirical model type is defined by arbitrary mathematical expressions, where parameters are found by fitting the expression to corrosion data.
• Semi-empirical model type is defined by a mathematical expression informed by at least some electrochemical or physical principles, where parameters are found by fitting the expression to corrosion data.
• Mechanistic model type is defined by electrochemical and physics-based equations that generally require more inputs but little to no experimental data.

The literature generally agrees on the broad definition; however, semi-empirical is sometimes sub-grouped into empirical. An example of this is that other works refer to de Waard’s early works and Norsok M506 as either empirical [87,88] or semi-empirical [37,40,84,89] or mechanistic [84].

This difference in model type classifications results from different definitions of what is meant by semi-empirical and mechanistic. In some works, a model is mechanistic if some of its structure is merely inspired by physics, whereas in other works, a model has to have elaborate electrochemical and physics-based equations.

To visualize the progression of CO₂ corrosion models and software tools, a historical timeline is constructed in Figure 1, summarizing the development of key models since 1975. This timeline captures the transition from early empirical models based on correlations from experimental data to more sophisticated semi-empirical approaches and, ultimately, to fully mechanistic and hybrid models. Each model is positioned chronologically to illustrate how earlier work, such as the foundational de Waard–Milliams model, provided the basis for subsequent models. In addition to Figure 1,

Table 1. Comparison of selected CO₂ corrosion models with their scope and limitations.

Model	Type	Temp. Range	Pressure Range	Inputs	Limitations	Assumptions	Source
De Waard-Milliams (1975)	Semi-empirical	<90 °C	-	CO2 partial pressure and temperature.	Does not include bicarbonate or hydrogen ions. pH only defined by CO2 equilibrium. Disregard reactions with carbonate.	Relationship between temperature and CO2 partial pressure. Linking potential to corrosion current with pH-dependent expressions.	[28,88,107]
LIPUCOR (Total) (1979)	Semi-empirical	20–150 °C	<250 bar, <50 bar CO2	H2S in mole%, total pressure, temperature, diameter, water chemistry, and production rate.	-	Based on lab and field data. Calculates pH from CO2 concentration, water chemistry, and temperature.	[20,88,101]
CORMED (Elf) (1989)	Semi-empirical	<120 °C	-	-	Does not include oil wetting or liquid flow velocity.	Accepts higher temperatures and ionic strengths but displays a warning, as the pH calculation becomes uncertain. The corrosion risk prediction is still valid. pH calculated from pressure, CO2 concentration, temperature, water chemistry, and free acetic acid.	[20,88,101]
De Waard-Lotz-Milliams (1991)	Semi-empirical	-	-	-	No flow velocity.	Correction factors for the effect of corrosion product formation and pH were added.	[99]
De Waard-Lotz (1993)	Semi-empirical	-	-	pH, effect of corrosion product film fugacity of CO2, temperature.	No flow velocity.	Builds on top of the de Waard-Milliams equations. The correction factors were adjusted from the 1993 version. Uses correction factors to avoid overestimation of corrosion.	[105]
De Waard-Lotz-Dugstad (1995)	Semi-empirical	0–140 °C	<10 bar CO2 partial pressure	pH, temperature, velocity, CO2 partial pressure.	-	The effects of fluid velocity, mass transport, and composition of the steel were added. This model often gives a lower corrosion rate than the 1991 and 1993 models at low flow rates.	[88,104]
NORSOK (1995)	Semi-empirical	20–150 °C	<1000 bar, <10 bar CO2	Temperature, total pressure, CO2 concentration, wall shear stress, glycol concentration, and pH.	pH between 3.5–6.5.	Spreadsheet that is open access. Fitted to data from IFE.	[20,88,101]
HYDROCOR (Shell) (1995)	Mechanistic	0–150 °C	<200 bar, <20 bar CO2	Multi-phase flow. Pressure, temperature, diameter, concentration, H2S, and CO2 in mole%, organic acid, glycol, and bicarbonate concentration, and production rate.	-	The LCR model by Pots is used for the prediction of corrosion. Determines the corrosion rate along the pipeline. Calculation of pH takes the iron and bicarbonate production into account.	[20,88,101]
TULSA (1995)	Mechanistic	38–116 °C	<17 bar CO2 partial pressure	Temperature, liquid flow velocity, pipe diameter, CO2 partial pressure, and pH.	Single-phase flow. Does not take effect from oil wetting.	Electrochemical reaction kinetics and mass transfer. It can be used in straight and elbow pipes. pH can be input directly or calculated from water chemistry.	[20,88,101]
PREDICT (InterCorr) (1996)	Semi-empirical	20–200 °C	<100 bar CO2 partial pressure	Temperature, H2S and CO2 partial pressure, and flow velocity.	pH between 2.5–7. Does not give any limits, either in the software or in the manual.	Based on the de Waard model, with other correction factors. Calculates CO2 partial pressure from the pH. pH can be input directly or calculated from water chemistry or from bicarbonate concentration and ionic strength.	[20,88,101]
Dream (1996)	Semi-empirical	-	-	Temperature and pressure at wellhead, separator, and bottomhole, well depth, diameter, water chemistry, gas composition, gas and water production rates.	Does not include hydrocarbon condensates.	Corrosion prediction in annular flow gas wells. Includes effects from protective corrosion films.	[88]
Ohio model (1997)	Mechanistic	10–110	<20 bar	Temperature, pressure, CO2 concentration, flow rate, pipe diameter, water chemistry.	Protective film formation is not predicted.	pH is either an input or calculated from water chemistry.	[88,93,101]
Cassandra (BP) (1998)	Semi-empirical	<140 °C	200 bar, <10 bar CO2	Water chemistry, total pressure, temperature, velocity, CO2 in mole% Glycol concentration, oil type, diameter.	-	Implements the de Waard model and BP’s own experience. pH calculated on CO2 content, water chemistry, and temperature. Accepts input outside these values but displays a warning.	[20,88,101]
KSC (IFE) (1998)	Mechanistic	5–150 °C	<250 bar, <50 bar CO2	Temperature, pressure, partial pressure of CO2, liquid flow velocity, and pH.	Flow velocity between 0.2 and 30 m/s. Does not take oil wetting into account.	Based on electrochemistry. Calculates corrosion rate with and without protective film formation. pH calculated on ionic strength and bicarbonate.	[20,88,101]
SweetCor (Shell) (1998)	Empirical	5–121 °C	0.2–170 bar CO2 partial pressure	Temperature, pressure, pipe diameter, CO2 mole%, water chemistry, and gas/liquid superficial velocities.	-	Large corrosion dataset from laboratory and field data. Data is grouped using statistics to make correlations and predict the corrosion rate, or by filtering data that closely matches the conditions. pH and corrosion rate are calculated from inputs.	[20,88,90,101]
Corpos (CorrOcea) (1999)	Semi-empirical	-	-	Needs calculations of pH, probability of water wetting, and an external fluid flow model.	-	Norsok model is used to calculate corrosion rate at several points along the pipeline.	[88]
OLI model (1999)	Mechanistic	-	-	Temperature, pressure, molar composition, flow velocity.	Does not account for oil wetting.	Combines thermodynamic and electrochemical corrosion modeling. Modeling of formation and dissolution of sulfide and carbonate scales. Scale formation has been calibrated from laboratory data.	[88]
Electronic Corrosion Engineer (ECE) (early 2000s)	Semi-empirical Software	-	-	O2, H2S, and CO2, and NaCl concentration, water density, liquid density, and length of tubing.	Quantitatively assess corrosion by using thermodynamic simulations to predict free water content for dense phase or supercritical CO2 systems.	Based on de Waard 95 model. Calculates pH from bicarbonate and water chemistry.	[88,100]
ULL (2002)	Semi-empirical	-	-	Temperature and pressure at wellhead, separator, and bottomhole, well depth, diameter, water chemistry, gas composition, condensate density, gas, condensate, and water production rates.	-	Developed for gas condensate wells, predicting corrosion rate along the well. Predicts corrosion only when water condenses.	[88]
Freecorp 1.0 (2008)	Semi-empirical	1–120 °C	-	Concentration of H2S, acetic acid, O2, Fe2+, temperature, pressure.	Pipe diameter: 0.01 to 1 m Liquid velocity: 0.001 to 20 m/s Fe2+: 0 to 100 ppm acetic acid: 0 to 1000 ppm pH: 3 to 7, O2: 0 to 10,000 ppm.	Point model: predicts corrosion at a single location with known conditions. Single-phase flow only. Uniform corrosion only. Ideal water chemistry (infinite dilution assumed). No interaction between diffusing species. Salinity effects are ignored. Iron carbonate film growth based on simple supersaturation correlation. The dominant mechanism between CO2 and H2S corrosion is chosen based on the higher predicted corrosion rate. Fe2+ is required for FeCO3 film growth kinetics. Total time must be provided if H2S is present.	[91]
Freecorp 2.0 (2018)	Semi-empirical	-	-	H2S, organic acids, flow rate, time.	Ignore effects of high salinity, oxygen, elemental sulfur, etc.	Includes formation and protection by corrosion product layer. Uniform corrosion only. Bulk water chemistry is used, which may differ from surface conditions. No corrosion product layer formation included. Steady-state model, no time-dependent effects. Ideal water chemistry (infinite dilution assumed). Single-phase flow only, uses empirical mass transfer correlations.	[97]
OLI Corrosion analyzer (2019)	Mechanistic	-	-	Temperature, pressure, impurity concentration, salt concentration.	Aqueous systems only, not valid for concentrated acids, alcohols, etc. No film shear removal, erosion-corrosion is not modeled. Thin films are not fully included. Transport and gas/liquid equilibrium are simplified.	Thermophysical and electrochemical simulation showing effects of temperature, pressure, pH, concentration, and velocity on corrosion. Inclusion of half-reactions for elements, alloys, and solution species. Electrochemical parameters such as the Tafel slope and the exchange current density are calibrated from the literature. Rigorous transport predictions include diffusion, electrical conductivity, and viscosity. Supports many alloys, including carbon steel, nickel alloys, stainless steel, and aluminum.	[98]
Tubular Corrosion Desktop (TCD) (2022) (Bandung Institute of Technology)	Semi-empirical Software created in C++.	-	-	O2, H2S, N2, bicarbonate, CO2, and NaCl concentration, water density, and liquid density.	-	Based on work by de Waard, Liane Smith, and Mike Billingham.	[100]
Yang et al. (2023) (Shell)	Machine learning model	-	-	CO2 and O2 partial pressure, pH, and temperature.	-	Uses data generated from CFD simulations. A total of 1122 data points for training and testing of the LightGBM model. The hybrid model is 106 times faster than CFD simulations alone.	[34]
Dong et al. (2024)	Machine learning model	0–200 °C	-	Material, chromium content, H2O, O2, SO2, NO2, and H2S concentration, pressure, temperature, and time.	-	Six different models using SVM, LightGBM, XGBoost, GBDT, KNN, and RF made on 248 data points.	[31]
Juian Cui (2025)	Deep learning model	-	-	Temperature, pressure, pH, material, flow rate, water content, carbonic acid concentration, and CO2 concentration.	-	Deep confidence network model optimized with Adam algorithm, made on 75 sets of data.	[33]

compares selected corrosion models, including Freecorp, OLI, Predict, NORSOK, and de Waard.

3.1. Empirical Models

Empirical models correlate measured corrosion rates to operating variables, such as temperature, CO₂ partial pressure, flow, pH, impurity concentrations, with mathematical functions [37,89]. These mathematical functions are arbitrary and do not correspond to any real physical meaning [37,39]. Additionally, the models are also limited to the experimental conditions used in the calibration, which reduces the accuracy when extrapolating, due to the absence of theoretical principles [37,39]. Examples of empirical models include the Copra, Dugstad’s earlier work, and Sweetcor, as illustrated in Figure 1 and Table 1. Sweetcor by Shell (1998) uses a large laboratory and field database of steel corrosion in water and CO₂, grouping data by ranges of CO₂ partial pressure, temperature, and flow conditions [20,90,101].

Recent approaches to empirical modeling have expanded to use machine learning techniques. The premise of these methods is to utilize large datasets to identify complex, non-linear relationships between variables without requiring explicit mechanistic assumptions [31,32,33,34]. The following subsection explores machine learning models in greater detail.

Machine Learning

The complexity of CO₂ corrosion, especially under CCUS conditions, has motivated the use of ML as a complementary approach to traditional models [31,32,33,34]. ML models learn patterns directly from data, unlike empirical or mechanistic models, making them well-suited for systems influenced by multiple interacting variables such as temperature, pressure, impurities, flow conditions, and inhibitor performance.

Table 2. Comparison of model types for CO₂ corrosion prediction [33,37].

	Empirical	Machine Learning	Semi-Empirical	Mechanistic
Basis	Data correlation	Data-driven	Physics-informed	Physics-based
Interpretability	Low	Low	Medium	High
Extrapolation	Poor	Dependent on training	Poor to reasonable	Good
Computation time	Low	Low after training	Low	Moderate to high
Data need	High	High	Moderate	Little or none
Number of Inputs	Few	Moderate	Moderate	Many

shows a comparison between traditional model types and ML models for CO₂ corrosion prediction.

The idea of using ML for corrosion prediction is not new, as one of the earliest applications was by Nesic et al., in 2001, who employed neural networks to model CO₂ corrosion laboratory data [29]. They demonstrated that data-driven approaches could capture complex relationships in corrosion processes, even when mechanistic understanding was incomplete.

Traditional models often struggle with non-linear interactions and data variability, particularly when impurities and phase changes are involved [11,30,37,64]. ML has the potential to capture these relationships without requiring explicit assumptions about reaction mechanisms. For predicting corrosion using ML, several different methods have been used, such as random forest (RF), AdaBoost, CatBoost, XGBoost, decision tree (DT), multilayer perceptron (MLP), support vector regression (SVR), and K-nearest neighbors (KNN) [31,32,33].

Modern ML applications in CO₂ corrosion modeling have expanded significantly. Aghaaminiha et al. [32] applied supervised ML algorithms, including RF, Artificial Neural Networks (ANNs), SVR, and KNN, to model time-dependent corrosion rates of carbon steel in the presence of inhibitors. RF achieved the best performance, predicting the entire corrosion-rate profiles with mean squared errors as low as 0.002, and provided useful sensitivity analyses for variables such as CO₂ partial pressure and temperature [32]. However, the authors emphasized the risk of extrapolation beyond the training domain and the need for expert oversight when interpreting ML predictions.

Recent studies have extended ML applications to CO₂ corrosion in multiphase pipelines and CCUS environments. Dong et al. [31] compared RF, XGBoost, and LightGBM for corrosion rate prediction and reported R² values above 0.9, outperforming traditional semi-empirical models. Beyond purely data-driven regressors, some hybrid approaches now integrate physics explicitly by using computational fluid dynamics (CFD) or transport models or first-principles electrochemical simulators to generate training data and features, or by embedding physics constraints within the learning algorithm, achieving higher computational speeds over high-fidelity solvers while maintaining accuracy [34].

Qu et al. [108] employed principal component analysis (PCA), particle swarm optimization (PSO), and SVR. The authors concluded that the PCA identified the key parameters influencing the corrosion rate while reducing redundant information. The PCA-PSO-SVR model demonstrated higher accuracy and robustness, indicating its potential application in corrosion protection of offshore pipelines.

ML models require large, high-quality datasets, which are often inconsistent in corrosion research [13,20,68]. They also lack inherent physical interpretability and can fail when applied outside their training range [32]. Future work should explore the potential of physics-informed ML and use more standardized experimental protocols to improve data quality. Machine learning is not a replacement for mechanistic understanding but a complementary tool that can accelerate model development and decision-making in CCUS applications.

An issue with using methods such as deep learning is that the available data is not comprehensive enough [33]. However, if more standardized data become available, the applicability of ML-based models is expected to increase.

3.2. Semi-Empirical Models

In contrast to empirical models, semi-empirical models include physics-informed equation structures, from either experience with CO₂ corrosion or physics-based equations with unknown parameters [37]. Additionally, like the empirical models, the semi-empirical models are limited to their calibration range, and extrapolation may lead to physically unrealistic predictions [37,39].

The early de Waard Milliams model, which is also the first semi-empirical CO₂ corrosion model, was based on the corrosion current on a linear correlation of pH [20,28,37,40]. They subsequently adapted to relate the corrosion rate to CO₂ partial pressure and temperature by implementing the cathodic reaction of hydrogen evolution, a relationship that continues to be applied in current practice [37,84]. Later, versions of the model by de Waard et al. accounted for effects such as flow rate, protective scales, glycol, pH, and the microstructure of the steel [28,37,99,104,105]. These additional effects were introduced by implementing empirical correction factors to the original de Waard–Milliams model.

Several companies have developed software tools based on semi-empirical models to predict CO₂ corrosion rates. These semi-empirical software tools include Cormed, Corpos, Predict, Corplus, and early Freecorp. Cormed by Elf (1989) started as a semi-empirical model, but was later merged with Total’s Lipucor, which resulted in Corplus [20,36].

Freecorp 1.0 (2008), from Ohio University, was exclusively based on publicly available data, with all its code, including equations, assumptions, and limitations, available to its users. The first version of Freecorp used a semi-empirical structure to predict the uniform corrosion rate of carbon steel [91]. Later versions of Freecorp shifted into mechanistic modeling.

3.3. Mechanistic Models

Mechanistic models describe CO₂ corrosion by explicitly formulating the related electrochemical and transport processes rather than relying on empirical correlations [37,84,109,110,111]. The mechanistic modeling approach offers interpretability and allows better extrapolation outside the range of calibration [83,84].

Kahyarian et al. [83] divided mechanistic models into two main categories: elementary mechanistic models, focusing on basic electrochemical reactions, and comprehensive mechanistic models, which include multiple processes such as mass transport, surface film formation, and flow effects. The comprehensive mechanistic models are considerably more complex to develop and apply, which is why simpler elementary mechanistic models remain the preferred choice among corrosion engineers and academic researchers [83]. The theoretical background for the inputs for mechanistic models has been extensively examined in prior research [37,39,84,109,110,111].

Examples of mechanistic models include the Freecorp 2.0 model developed by Nesic et al. [97], which accounts for multiple species, including H₂S and organic acids. It allows users to include or exclude specific reactions, providing insight into the contribution of each species to the overall corrosion rate. Freecorp 2.0 improves upon version 1.0 by replacing empirical predictions of formation and protection of corrosion layers with a mechanistic approach [97].

Another example is the Hydrocor model developed by Shell, which estimates CO₂ corrosion in aqueous systems by using electrochemical kinetics, mass transport, and protective layer formation under varying pressure and temperature conditions [20,101].

Ref. [95] propose a modeling approach for predicting corrosion rates in supercritical CO₂ pipelines, under thin water film conditions. The model divides the process into six layers: the supercritical CO₂ mixture, the interface region, the water film region, the deposition region, the electrodic region, and finally the pipeline steel itself. Mathematically, it is prepared by setting initial and boundary conditions, and then solving several partial differential equations. The authors refer to this model as mechanistic, as it uses physics-based equations, even though it requires empirical coefficients to be known.

3.4. Challenges and Opportunities

Since 1975, multiple companies and authors have advanced corrosion modeling by extending or modifying previous models, as seen in Figure 1, or contributing datasets for training. The result is a broad range of models, some of which are created to suit specific ranges for parameters such as temperature and pressure. The modeling approach needs to be more advanced than linear regression, as there are many non-linear behaviors between the input parameters, such as the combination effects of the concentration of various impurities, temperature, pressure, pH, and time [11,16,37,97,112].

An increased number of recent studies have used machine learning for corrosion prediction [30,31,32,33,34,108]. While machine learning approaches have great potential for CO₂ corrosion modeling, they generally require a large amount of data to produce a reasonably accurate model for CO₂ corrosion, but the needed data are normally not available [31,32].

For corrosion prediction software tools, it is also common for the underlying data to be restricted due to competitive or legal reasons or a strategic choice of the owners [31,32]. However, for training models, it is a barrier, as it limits the quantity of publicly available data for training. The study by Qu et al. [108] presented a hybrid model, along with the 178 data points used to train and validate the model, which can be used by others. The data points had 14 different input parameters, such as CO₂ partial pressure, temperature, pH, flow rate, and ion concentration. Data contributions are valuable for future machine learning approaches to reach the data quantities where the methods are effective [113].

Data already publicly available from various studies investigating corrosion in CO₂ with impurities presents significant challenges due to inconsistencies in experimental procedures across studies [13]. The result of this problem is varying data quality, which is known to cause poorly performing data-driven models [14]. Initiatives to reduce the inconsistencies are described in [13]. Here, suggestions are presented for the experimental procedures, which include the following:

• Follow the standard cleaning process of corrosion coupons.
• Verify concentration of impurities.
• State flow conditions, rather than flow versus no flow.
• Consider obtaining samples with different exposure times.

In addition to addressing data quantity and quality challenges, a promising possibility is to use a hybrid ML approach, as demonstrated in [34], where the ML model structure is informed by physics to reduce the data requirements. Generally, the mechanistic knowledge can help provide boundaries for complexity to make sure the model has an advanced enough structure to capture the corrosion behavior, but not too advanced a structure that it is prone to overfitting, which is especially a challenge in the field of CO₂ corrosion, where public data are limited.

From an engineering perspective, current approaches benefit from increasing methodological maturity. However, their practical deployment is still constrained by limited quality field data, challenges in transferability across operating conditions, and uncertainty under different CO₂ compositions and flow regimes. These limitations highlight clear research opportunities in hybrid physics-informed models, standardized datasets, and validation under realistic pipeline and storage conditions.

4. Conclusions

This study examined the current state of CO₂ corrosion modeling with a focus on its relevance to CCUS applications. The motivation for this work originates from the growing global emphasis on CO₂ sequestration and the need to ensure the integrity of transport and storage infrastructure. For this infrastructure, impure CO₂-induced corrosion represents a challenge.

Key factors influencing CO₂ corrosion have been summarized, including the presence of impurities such as H₂O, O₂, SO_x, NO_x, and H₂S. This work also summarizes the effect of transportation mode, such as transportation by pipeline or truck, material selection, exposure time, CO₂ phase, and flow regime, to provide an overview. Empirical, semi-empirical, and mechanistic models were compared, with an emphasis on their respective advantages and limitations.

This study illustrates the progression of CO₂ corrosion models and software tools. The historical timeline provided in Figure 1 illustrates how models, such as de Waard-Milliams, inspired subsequent developments, including ECE, Predict, Norsok, and Corpos. This chronological perspective highlights the gradual shift from semi-empirical correlations to physics-based mechanistic models and, more recently, to data-driven machine learning models. One of the key contributions is the comparative table (Table 1), which summarizes CO₂ corrosion models and software tools, supports engineers and researchers in making informed selections and applications of models under specific operating conditions. This work also highlights challenges, including inconsistencies in experimental data, and the need to account for multiple interacting factors, such as impurities, flow regime, and temperature. For data-driven CO₂ corrosion models, this challenge involves selecting which inputs to include and preparing the training and validation datasets. As the typical datasets originate from a broad range of researchers, the conditions stated in the experiments vary. Therefore, future opportunities include the development of standardized experimental protocols to reduce data variability. Additionally, integrating mechanistic principles into ML models to improve interpretability and predictive accuracy, enabling robust corrosion management strategies for CCUS pipelines and storage systems.

CO₂ corrosion modeling remains a dynamic research field at the intersection of materials science, electrochemistry, and computational modeling. The progress summarized in this work provides an overview of current research trends that aim to improve corrosion predictions through ML approaches supported or informed by physical and chemical behavior. The continued advance in CO₂ corrosion modeling ultimately supports the CCUS industry by enabling more informed material selection, defining purification demands, and predicting maintenance needs. The recent machine learning approaches further call for more open CO₂ corrosion data availability with shared interests instead of competitive and restrictive commercial interests.