A numerical feasibility study of CO₂ foam for carbon utilization and storage in a depleted, high salinity, carbonate oil reservoir

Abstract

Carbon Capture, Utilization, and Storage (CCUS) offers a viable solution to reduce the carbon footprint in the petroleum industry, and foam injection presents a promising method to achieve this while simultaneously increasing oil recovery. In this work, we studied the feasibility of CO₂ foam for co-optimizing enhanced oil recovery and CO₂ storage in a high-salinity carbonate formation. The simulated hydrodynamic model is a depleted formation containing 30% residual oil, with three mechanisms for CO₂ storage: solubility, residual, and mineralization trapping mechanisms. The results showed that after 20 years, oil recovery during foam injection was 2.7 times higher than CO₂ injection, and the CO₂ stored during foam flooding was 38% higher than CO₂ injection. Notably, foam injection also increased CO₂ storage capacity by 2.6 times, indicating the potential to store around 2 gigatons of CO₂ in the simulated model. This was attributed to the ability of foam to significantly reduce gas mobility and thus form isolated bubbles through its Jamin effect. Residual trapping was the dominant trapping mechanism, contributing to over 70% of the total CO₂ trapped, attributed to the reduction in the dissolution of CO₂ in brine due to the high salinity of the aqueous medium. CO₂ mineralization was also studied, showing the least trapping efficiency and the dissolution trend of all the carbonate minerals. This study illustrates a novel CO₂ utilization and storage technique in which CO₂ is concurrently sequestered while enhancing oil recovery in a depleted oil reservoir by injecting CO₂ as foam. The relevance of this study lies in its potential to provide a dual benefit of reducing greenhouse gas emissions and boosting oil production, offering a sustainable approach for the petroleum industry.

Introduction

The oil and gas industry has been a significant contributor to the increasing levels of anthropogenic CO₂ emissions, primarily due to the combustion of fossil fuels for energy production^1,2, accounting for around 15% of total energy-related emissions globally³, as well as 45% of anthropogenic greenhouse gas emissions⁴. As the demand for energy continues to rise, finding sustainable solutions to mitigate CO₂ emissions becomes imperative. One approach to addressing this challenge is through carbon capture, utilization, and storage (CCUS), where CO₂ is captured from industrial processes and power plants, then transported and stored underground to prevent its release into the atmosphere³. This approach does not only provide a means of CO₂ storage but also improves the economic viability of oil production^5,6. However, injecting CO₂ into reservoirs comes with its challenges, primarily related to the buoyancy of CO₂ compared to the reservoir fluids. CO₂, being lighter, has a propensity to escape back into the surface, leading to less effective oil recovery and potential environmental consequences^7,8. Overcoming these challenges is crucial to ensuring the success of CO₂ injection as a sustainable and efficient technique.

Conventional CO₂ injection is quite effective in recovering oil and still stores some quantity of CO₂ since some CO₂ gas will be trapped and can be dissolved in the reservoir brine, oil, and minerals^9,10. However, if we are considering gigaton level of CO₂ storage, effective strategies should be implemented. Foaming the injected CO₂ poses as a promising solution to address these challenges. By generating foam with CO₂ gas in a foaming liquid containing surfactants, the buoyancy issue can be mitigated. This foaming process transforms the gaseous CO₂ into a stable foam, which not only improves its mobility in the reservoir but also prevents its escape back into the atmosphere^11,12.

Depleted oil reservoirs are considered practical sites for this purpose since they have already been exploited for hydrocarbon production and have reached their economic limit. These reservoirs offer several advantages for storing CO₂, such as their large storage capacity, proven sealing integrity, existing infrastructure, and potential for enhanced oil recovery (EOR)^13,14,15. According to Hong (2022)¹⁶, depleted oil and gas reservoirs have been estimated to have a global storage capacity of between 675 to 900 Gt CO₂, which is equivalent to more than 200 years of current global CO₂ emissions. These sites are promising as they are well characterized from previous oil and gas operations, and they have large pressure margins for safe storage. Furthermore, the infrastructure required for CO₂ injection is already in place, which reduces the cost of implementing CCUS projects. Additionally, depleted oil reservoirs can enable the recovery of residual oil through CO₂ injection, which can improve the economic viability and environmental performance of CCUS projects¹⁴. Callas et al. (2022)¹⁷ reported that CO₂-EOR can produce hydrocarbons with a neutral or negative carbon impact, depending on the source and transport of CO₂. Therefore, depleted oil reservoirs are an effective and practical CCUS method in the oil and gas industry.

Injecting CO₂ as foam rather than gas is better for CO₂ storage because foam can reduce the mobility of CO₂ and increase the sweep efficiency of the injected fluid¹². This can help to improve the storage capacity of the reservoir and reduce the amount of CO₂ required for injection. An experimental study was conducted in Foyen et al. (2020)¹⁸ where the authors mentioned that injecting CO₂ as foam rather than gas can lead to significant improvements in CO₂ storage. In the numerical study by Lyu et al. (2021)¹⁹, CO₂ foam increased oil recovery by 32% compared to pure CO₂ injection and 27% compared to Water Alternating Gas (WAG). In addition, CO₂ storage capacity increased from 12% during pure CO₂ injection up to 40% during Surfactant Alternating Gas (SAG) injections. The results show that foam-assisted CO₂ injection can reduce gas mobility effectively by trapping gas bubbles and inhibit CO₂ from buoyancy-driven migration upward, thus enhancing storage efficiency.

The mechanisms of foam generation, propagation, and stability in porous media depend on various factors, such as the injection scheme, the surfactant formulation, the reservoir heterogeneity, the presence of oil, and the temperature and pressure conditions⁷. However, foam can improve $\text {CO}_{2}$ sequestration by increasing the apparent viscosity of the gas phase, which reduces the mobility ratio between the gas and the liquid phases. This reduces the fingering and channeling of the gas phase and improves the displacement efficiency^20,21. Additionally, foam reduces the density difference between the gas and the liquid phases, which reduces the gravity segregation of the gas phase. This increases the vertical sweep efficiency of the foam flood and prevents the gas from accumulating near the top of the reservoir. In the experimental work of Chaturvedi and Sharma (2021)²², foam increased the residual gas saturation in the swept zone, which enhanced the capillary trapping of $\text {CO}_{2}$. This is a result of the snap-off and blocking mechanisms of foam in the pore throats, which prevented the gas from flowing back when the pressure gradient is reversed.

Mineral trapping is key to $\text {CO}_{2}$ storage as it is the safest mechanism of $\text {CO}_{2}$ storage and can help to store $\text {CO}_{2}$ for longer periods of time^23,24. Mineral trapping involves the transformation of $\text {CO}_{2}$ into solid minerals through chemical reactions with minerals present in the reservoir rock. However, these reactions can take an extensive amount of time and are often difficult to replicate accurately in a laboratory setting. To address this challenge, the development and application of numerical simulators have become essential tools in predicting $\text {CO}_{2}$ storage over extended periods. These simulators integrate geologic, hydrodynamic, and geochemical factors to model the behavior of $\text {CO}_{2}$ in the reservoir over time accurately. With these simulators, 2D and 3D models can be developed to examine the mechanisms occurring during mineral trapping and how they affect its efficiency^23,25,26,27.

Therefore, in this work, we have conducted a numerical simulation of foam injection for combined EOR and $\text {CO}_{2}$ storage in a depleted carbonate oil formation characterized by high salinity. The objective is to understand how foam can improve storage capacity. The novelty of this study lies in its focus on depleted oil reservoirs, unlike numerous studies that have previously explored $\text {CO}_{2}$ sequestration mechanisms in saline aquifers. Additionally, this work analyzes three $\text {CO}_{2}$ trapping mechanisms (residual, solubility, and mineralization) for both $\text {CO}_{2}$ and foam injections in relation to $\text {CO}_{2}$ utilization and storage. Depleted oil formations present unique challenges and opportunities, particularly for simultaneous EOR and $\text {CO}_{2}$ storage. Furthermore, we aim to study how these processes mutually enhance each other. A storage capacity function introduced earlier by Bello et al. (2023)¹² has been applied to better understand these dynamics.

Simulation Materials and Methodology

Reservoir model description

The reservoir model, shown in Fig. 1, is characterized by a grid structure of 38x45x13 dimensions. This model has been used in Bello et al. (2023)²³ for sensitivity analysis of parameters affecting mineralization trapping. The porosity of the reservoir varies between 25.5% and 40.2%, averaging at 34.96%, while the mean permeability is 158 mD. The distribution of the porosity and permeability values is presented in Fig. S1 in the supplementary information document to show the degree of heterogeneity in the geological model. A summary of the model parameters can be found in Table 1.

Figure 1

Hydrodynamic geological model used in this study.

Table 1 Basic parameters of reservoir simulation model.

Fluid model

In our study, we consider a depleted oil reservoir with a residual oil saturation of 0.3. The reservoir oil is represented by a 13-component PVT model based on the Peng-Robinson equation of state. The dissolution of $\text {CO}_{2}$ into oil is also modelled based on this PVT model. The relative permeability curves can be seen in Fig. S2 in the supplementary information document. The composition of the oil model is presented in Fig. 2

Figure 2

Composition of the reservoir oil model used in this study.

Assumptions and governing equations

The governing equation for the combined process is based on the principle of mass conservation, which applies to every component present in the fluids. The mass conservation equation describes the changes in fluid saturation over time within the reservoir. For each fluid phase, the equation can be written as^28,29:

$$\begin{aligned} \ \frac{\delta (\phi p_i S_i)}{\delta t} + \nabla \cdot (p_i S_i v_i) = Q_o \ \end{aligned}$$

(1)

where $\phi$ is the porosity of the reservoir rock; $\rho$ is the density of phase i; $\hbox {S}_i$ denotes the phase saturation; v is the Darcy velocity, and Q represents any source/sink terms, depending of the phase, i could be o, w or g, representing oil, water and gas, respectively³⁰.

$$\begin{aligned} \ v_i = -\frac{k_{ri}}{\mu _{ri}} \nabla P_i\ \end{aligned}$$

(2)

Here, $\hbox {k}_{ri}$ is the relative permeability of phase, i, $\mu _{ri}$ is the viscosity of phase i, and $\hbox {P}_i$ is the pressure gradient of phase, i.

Modelling of $\text {CO}_{2}$ trapping mechanisms

In our study, we employed a compositional simulator (CMG-GEM) to represent the displacement and sequestration processes. Compositional simulators rely on equations of state (EOS) with theoretical parameters capable of forecasting the fluid behavior of typical hydrocarbons found in oil and gas reservoirs^19,31

. Specifically, the $\text {CO}_{2}$ module within this simulator was employed to simulate $\text {CO}_{2}$ injection and sequestration into a depleted oil formation, as well as oil production, alongside aqueous phase chemical reactions, mineral precipitation, and dissolution processes. Modeling $\text {CO}_{2}$ storage involves solving component transport equations, equations governing thermodynamic equilibrium between gas and aqueous phases, and geochemical equations accounting for reactions between aqueous species and mineral precipitation/dissolution. In this work, the $\text {CO}_{2}$ sequestration mechanisms modeled include solubility, residual, and mineralization trapping mechanisms.

The solubility mechanism was modeled using the equality of $\text {CO}_{2}$ fugacities in the gas and aqueous phases. This is because the dissolution of gases in a liquid proceeds very fast and the phases are assumed to be in thermodynamic equilibrium which is governed by the equality of fugacity in both phases. Upon injection, $\text {CO}_{2}$ dissolves in the aqueous phase and can be represented by Eq. 3

$$\begin{aligned} \ f_{CO_2, g} = f_{CO_2, aq}\ \end{aligned}$$

(3)

where $\hbox {f}_{CO_2, g}$ is the gas fugacity from PR-EOS and $\hbox {f}_{CO_2, aq}$ is the fugacity of the aqueous phase obtained from Henry’s law

$$\begin{aligned} \ f_{CO_2, aq} = y_{CO_2, aq} \cdot H_{CO_2, aq} \ \end{aligned}$$

(4)

where $H_{CO_2, aq}$ is the Henry’s constant for $\text {CO}_{2}$ solubility in brine and $y_{CO2, aq}$ is the mole fraction of $\text {CO}_{2}$ in brine.

Residual trapping is another important sequestration mechanism, as it converts $\text {CO}_{2}$ into an immobile phase in the pores through capillary effect and imbibition because $\text {CO}_{2}$ is first injected displacing the wetting phase (oil/water), hence the mechanism is considered a drainage process. After the injection has stopped, the water migrates to the pore spaces where the gas was injected (imbibition process) to generate hysteresis^32,33. Thus, the residual gas saturation is calculated as the gas trapped when the water has imbibed into the rock from a state of irreducible water saturation to a state of zero capillary pressure. Land’s model³⁴ is commonly used to determine the trapped gas saturation as follows:

$$\begin{aligned} \ S_{gt}= & {} \frac{S_{gi}}{1 + C S_{gi}}\ \end{aligned}$$

(5)

$$\begin{aligned} \ C= & {} \frac{1}{S_{gt,max}} - \frac{1}{S_{g,max}} \ \end{aligned}$$

(6)

In these equations, $S_{gt}$ is the residual gas saturation corresponding to $S_{gi}$, and $S_{gi}$ is the gas saturation value ($S_{g}$) when the shift to wetting phase saturation occurs. C is Land’s coefficient, $S_{g, max}$ and $S_{gt, max}$ represent maximum gas saturation and maximum residual saturation/maximum trapped gas saturation, respectively.

In our work, residual gas trapping was simulated by using a value for the maximum residual gas saturation. Holtz (2002)³⁵ and Kumar et al. (2005)³⁶ have validated a theory and developed a correlation (Eq. 7) that porosity ($\phi$) is the petrophysical property that influences the value of maximum residual gas saturation the most. Thus, an average value, calculated based on this correlation, was included in our model.

$$\begin{aligned} \ {S_{gt, max}} = 0.5473 - 0.969 \cdot \phi \ \end{aligned}$$

(7)

When $\text {CO}_{2}$ mixes with water, $\hbox {H}^+$, $\hbox {HCO}_3^-$ and/or $\hbox {CO}_3^{2-}$ ions are released in the chemical reactions, which serve as the basis to model the intra-aqueous chemical reactions for the geochemical reactions. The chemical equilibrium reactions are governed by the following chemical equilibrium constants³⁷:

$\hbox {CO}_2$(aq) + $\hbox {H}_2$O $\longrightarrow$ $\hbox {H}^{+}$ + $\hbox {HCO}_{3}^{-}$

$\hbox {HCO}_{3}^{-} \longrightarrow$ $\hbox {H}^{+}$ + $\hbox {CO}_3^{2-}$

Dissolved $\text {CO}_{2}$ is acidic and can cause the dissolution of various resident rock minerals and can in turn cause the formation of complex cations with the bicarbonate ion, which will react with different metal ions present in the formation to precipitate carbonate minerals. Although this is believed to be a very slow process and can take up to hundreds of years to complete, it is still considered a desirable process because of its safety and long-term storage of $\text {CO}_{2}$.

Geochemical reactions between mineral and aqueous components drive the mineralization trapping mechanism, influencing the sequestration of $\text {CO}_{2}$. Changes in mineral moles are attributed to dissolution or precipitation and they provide insights into the extent of $\text {CO}_{2}$ sequestration via mineralization trapping. We have previously conducted X-ray diffraction (XRD) analysis to determine the mineral composition, and we obtained data on the formation water chemistry for the target formation. These details are outlined in Tables 2 and 3.

Table 2 Mineral composition of formation rock.

Table 3 Brine composition.

Based on these results, the geochemical reactions considered in our simulation model and their reaction kinetic parameters are given in Table 4. Except for the volume fraction, which is based on XRD results, all other parameters are standard values from the compositional simulator. The K-values provided are for $\hbox {25}^0$C but are adjusted by the simulator to the reservoir temperature of $\hbox {41}^0$C during the calculations.

Table 4 Aqueous and Mineral reactions.

The mineral dissolution and precipitation reactions are modeled in the compositional simulator following the rate law equation, given by Nghiem and Li (1984)³⁹:

$$\begin{aligned} \ r_{\beta } = A_{\beta }^{k_{\beta }} \left( 1 - \frac{Q_{\beta }}{K_{eq,\beta }}\right) , \quad \beta = 1, \ldots , R_{mn} \ \end{aligned}$$

(8)

where $r_{\beta }$ is the reaction rate for a given mineral, $\beta$, $R_{mn}$ is the number of mineral reactions, $A_{\beta }$ is the reactive surface area and the $k_{\beta }$ is the rate constant of mineral reactions. $Q_{\beta }$ is the activity product of the mineral reaction.

Foam modelling

The compositional simulator has a foam injection model that uses an empirical approach to interpolate gas relative permeability curves with and without foam. This interpolation is facilitated by a scaling factor, which reduces gas relative permeability when foam is present.

$$\begin{aligned} \ k_{rg}^{f} = k_{rg} \cdot FM \ \end{aligned}$$

(9)

where $k_{rg}^{f}$ is the foam relative permeability and $k_{rg}$ is the gas relative permeability and FM is the mobility reduction factor.

The mobility of $\text {CO}_{2}$ is adjusted by the inverse mobility factor, denoted as FM, which also serves as the apparent viscosity of the foam³⁸. The scaling factor, FM, dictates foam behavior and relies on seven parameters. It is expressed by an equation where its values range from 0 to 1, signifying the absence of foam to the generation of strong foam, respectively. Parameters $F_1$ to $F_7$ account for various factors: foaming agent concentration ($F_1$), oil’s detrimental effect ($F_2$), flow velocity concerning shear thinning ($F_3$) and generation effects ($F_4$), oil composition ($F_5$), salinity effect ($F_6$), permeability dependence ($F_7$). $F_{dry}$ in Eq. 10 represents the foam dry-out effect and can be computed with Eq. 11.

$$\begin{aligned} \ FM = \frac{1}{1 + FMMOB \cdot F_1 \cdot F_2 \cdot F_3 \cdot F_4 \cdot F_5 \cdot F_6 \cdot F_7 \cdot F_{dry}} \ \end{aligned}$$

(10)

$$\begin{aligned} \ F_{dry} = 0.5 + \frac{\arctan (SFBET(S_w - SF))}{\pi } \ \end{aligned}$$

(11)

A detailed description of each dependent F function used in this study and their values are provided in the Supplementary information document.

Simulation Methodology

4 injection wells and 2 production wells were placed in the reservoir. The injectors were placed to inject pure $\text {CO}_{2}$ into the bottom layers, by perforating the last 7 layers. Injection and production were controlled by setting the bottom-hole pressures to 25 MPa and 18 MPa, respectively. This was based on a prior sensitivity analysis to guarantee that some $\text {CO}_{2}$ remains in the reservoir after the wells are shut in. Following 20 years of injection and production, all wells were shut in, and the remaining $\text {CO}_{2}$ in the reservoir model is monitored over an additional 80 years, analyzing various storage mechanisms. In our previous work⁴⁰, we used the same oil model as in this study and determined the minimum miscibility pressure (MMP) to be around 10 MPa. Therefore, this study involves miscible $\text {CO}_{2}$ flooding, as the injection was conducted above the MMP. At the well shut-in time, the oil recovery factor was calculated.

Two scenarios were considered for foam injection. The first involves using the empirical foam model of the simulator, while the second uses Surfactant-Alternating-Gas cycles at a ratio of 1:2, to replicate field conditions. In Bello et al. (2023)¹², various methods of foam generation in both laboratory and field conditions were explained. A cycle ratio of 1:2 is selected to mimic the generation of the same foam quality of 75% as in the empirical foam model of the simulator for logical comparison.

Results and Discussion

Enhanced Oil recovery and $\text {CO}_{2}$ storage

The results in our work show the efficiency of foams for EOR and $\text {CO}_{2}$ storage, as compared to $\text {CO}_{2}$ injection. Fig. 3 below presents ternary diagrams of the simulation model, showing the distribution of the fluids under the injection techniques after 10 and 20 years. The 10-year ternary diagram represents the midpoint of the injection and production period, so we expect to see the dynamics in the fluid phases within the model. The 20-year ternary diagram signifies the end of the injection and production period, and the $\text {CO}_{2}$ left in the reservoir at this point is an important metric for determining the amount of $\text {CO}_{2}$ each injection technique can keep in the geological model after oil production.

Figure 3

Ternary diagrams showing the saturations of fluid phases in the mid layer of the reservoir (Red color represents gas; Green color represents oil; and blue color represents water). (a) Gas injection. (b) Foam model - Simulator. (c) SAG Foam injection.

As it can be seen in Fig. 3a, during gas injection, the gas sweeps a large area but predominantly migrates towards the production zone. By the end of the injection and production period (Fig. 3a, right image), a significant amount of oil remains unproduced with minimal gas available after the shut-in period. This is attributed to the gas primarily channeling through the oil zone and breaking through to the production wells, a phenomenon characterized by the high mobility difference between the gas and oil zones in several studies^41,42,43. Foam significantly mitigates this by enhancing the viscosity and density of the propagation front, thereby controlling gas mobility^43,44. In the scenarios of foam injection (Figs. 3b and 3c), we can see that a higher volume of gas is present in the reservoir post-production (Fig. 3b, right image and Fig. 3c, right image), indicating increased oil production, since the gas will either mix with the oil/water or fill into the pore spaces that were earlier occupied by the produced oil. Therefore, the enhanced oil production during foam injection is at least 2.3 times higher (Fig. 4). As stated in the⁴³, the foam slug effectively redistributes gas mobility within the reservoir. Therefore, compared to gas injection, the gas-dominant channels under foam injection are less noticeable, resulting in $\text {CO}_{2}$ spreading over a larger area in the oil reservoir to increase volumetric sweep efficiency.

A clear difference is observed between the two foam techniques used. The SAG injection presents a more favorable outcome with a significant increase in oil production levels. This is because the SAG process involves the cyclic injection of surfactant solution and $\text {CO}_{2}$ gas, leading to the in-situ generation of foam within the reservoir, which can help mitigate potential issues related to foam instability. By periodically injecting surfactants along with gas, this method ensures a continuous supply of fresh surfactant slugs into the reservoir, aiding in the stabilization of the foam structure over time. This leads to increased oil recovery rates, as opposed to injecting pregenerated foam, where the foam properties may degrade more rapidly over time.

Figure 4

Oil recovery performance: (a) Whole simulation period (b) 20 years.

Fig. 4 shows the oil recovery performance from the different injection strategies. The results show the effectiveness of foam in increasing the oil recovery than the gas injection. The disparity in the results of the two foam injection modes could be attributed to foamability and foam stability, earlier explained. Fig. 4 illustrates the comparative oil recovery performance for the injection techniques, highlighting the higher oil recovery factor of foam over gas injection. By using the simulator’s empirical foam model, it is quite difficult to guarantee the continued stability of foam a few meters into the reservoir⁴⁵. However, generating foam in-situ with surfactant alternating gas ensures a continued presence of foam since both gas and surfactant solutions are consistently introduced, generating foam slugs at regular intervals.

Furthermore, we see in both cases of foam injection that with the surfactant solutions, $\text {CO}_{2}$ was able to mobilize some capillary trapped oil that does not happen during gas flooding alone (Fig. 4b, red and green curves). During gas injection, oil production plateaued around the 16th year even though the producers were still operational (Fig. 4b, blue curve). This is not seen in the foam injection techniques and this suggests an improvement in the fluid properties, which could be attributed to the influence of the surfactant solution in the foaming system, thereby encouraging foam injection to provide mobility control for oil recovery.

In Fig. 3a, we showed how the injected $\text {CO}_{2}$ flows rapidly from the injectors to the producers, which suggests that the $\text {CO}_{2}$ storage might be affected since most of the $\text {CO}_{2}$ injected flows to the producer. Fig. 5 below further explains that and also shows how the various fluid phases tend to mix with $\text {CO}_{2}$ under various injection techniques. These figures represent the moles of $\text {CO}_{2}$ in the fluid phases in the reservoir throughout the simulation period. As it can be seen, during gas injection, more $\text {CO}_{2}$ can be seen in all the phases. With foam, this is reduced and allows $\text {CO}_{2}$ saturation in oil and water.

Figure 5

$\text {CO}_{2}$ component in different fluid phases: (a) in gas phase (b) in oil phase (c) aqueous phase.

It can be seen that a higher mole of $\text {CO}_{2}$ is present in the gas phase during the gas injection (Fig. 5a, blue curve). At the end of the injection period, the amount of $\text {CO}_{2}$ in the gas phase is 6.7 times more than that of the oil phase and 48.2 more than that of the water phase. Although we see similar figures for the foam injection, as the amount of $\text {CO}_{2}$ in the gas phase is 5 times more than the $\text {CO}_{2}$ in the oil phase and 40.9 times more than the $\text {CO}_{2}$ in the water phase, the quantity of $\text {CO}_{2}$ retained after production during gas injection is still lower than during foam injection (Fig. 3). This is because less oil was displaced by $\text {CO}_{2}$ injection, and majority of the gas was produced, however, in the case of foam, the gas mobility was effectively controlled.

Moreover, it appears that the reservoir pressure had already fallen below the bubble point pressure of the oil after the 10th year (Fig. 5b). This is likely why $\text {CO}_{2}$ could not dissolve in the oil as efficiently as possible, leading to a subsequent decline in $\text {CO}_{2}$ volume in the oil phase. Similar results were obtained in Li et al. (2011)⁴³ where the authors stated that the phase behavior of $\text {CO}_{2}$-crude oil mixtures is influenced by $\text {CO}_{2}$ dissolution, which increases saturation pressure and gas-oil volume ratio; and can lead to a reduction in the volume of $\text {CO}_{2}$ in the oil phase, especially when the reservoir pressure falls below the bubble point pressure of the oil.

While these figures provide an overview of the distribution of the $\text {CO}_{2}$ present in the fluid phases, drawing conclusions about how $\text {CO}_{2}$ was stored would seem premature since not all of the $\text {CO}_{2}$ was produced. Thus, in subsequent sections, we will examine in detail the contribution of each trapping mechanism to the total $\text {CO}_{2}$ stored.

At the producer, $\text {CO}_{2}$ can be produced in three forms: gas, oil, and water. The total $\text {CO}_{2}$ produced is therefore calculated by summing the moles of $\text {CO}_{2}$ component in oil, gas, and water phases at the producer. Subsequently, $\text {CO}_{2}$ retention post-production is determined using the formula below, with the results shown in Fig. 6:

$$\begin{aligned} \ \text {{CO}}_2 \text {{ retention}} = \frac{{\text {{total CO}}_2 \text {{ injected}} - \text {{total CO}}_2 \text {{ produced}}}}{{\text {{total CO}}_2 \text {{ injected}}}} \ \end{aligned}$$

(12)

Figure 6

Percentage of $\text {CO}_{2}$ retained the the reservoir after 20 years.

From Fig. 6, we can see that, at the end of the production period of 20 years, 25.68% of the injected $\text {CO}_{2}$ during continuous $\text {CO}_{2}$ injection can still be potentially stored. For the foam injection methods, these values are 29.78% and 50.34%, respectively. This indicates a higher quantity of $\text {CO}_{2}$ storage in the reservoir with foam injection, suggesting that foam injection allows for more $\text {CO}_{2}$ to be retained in the reservoir for $\text {CO}_{2}$ trapping mechanism analysis while maintaining efficient oil production.

As explained in Bello et al. (2023)¹², foam mechanisms for $\text {CO}_{2}$ sequestration can be categorized into three main groups: gas trapping, gravitational segregation reduction, and $\text {CO}_{2}$ leakage pathway blockage. Gas trapping involves the liquid phase within the foam effectively capturing gas through mechanisms such as snap-off, bypassing, and the Jamin effect. The Jamin effect occurs in foams within porous media, where fluid displacement leads to the formation of isolated pockets or bubbles of the displaced fluid^46,47. These mechanisms are crucial for $\text {CO}_{2}$ sequestration in depleted oil formations, and can readily occur during foam flow in porous media due to the fact that foams possess properties that make them conducive for gas trapping such as their variously sized gas bubbles that are sparged throughout a continuous liquid phase. Also, the wetting phase fills the small pores, leaving minimal space for gas bubbles in the non-wetting phase, meaning that they can occupy the center of the large pores.

Contribution of each trapping mechanism

To address the $\text {CO}_{2}$ storage mechanisms in the reservoir, in our model, we simulated and included functions for residual, solubility, and mineral trapping mechanisms. The $\text {CO}_{2}$ trapping efficiencies of the injection mechanisms are presented in Fig. 7.

Figure 7

Cumulative contribution of each trapping mechanism: (a) Solubility trapping (b) Residual trapping (c) Mineral trapping.

Generally, we see that the trapping performance of gas injection is much lower than in foam injection. The higher trapping of the foam SAG injection could also be attributed to the ability of foam to reduce gas mobility in the reservoir.

Solubility trapping involves the dissolution of $\text {CO}_{2}$ into the formation water, which is a function of the interaction of $\text {CO}_{2}$ with the brine. The SAG process enhances this interaction by creating a larger interface between the $\text {CO}_{2}$ and the brine due to the structure of the foam that is generated. The surfactants in the foam can function as co-solvents, potentially increasing the solubility of $\text {CO}_{2}$ in the brine. Additionally, the alternating injection of gas and surfactant solution can induce a mixing effect that promotes the dissolution of $\text {CO}_{2}$ into the formation water, leading to more effective solubility trapping⁴⁸. Similar results found in Adebayo (2019)⁴⁷ and Lyu et al. (2021)¹⁹, were attributed to the ability of foam to control gas mobility and improve sweep efficiency.

Residual trapping is controlled by hysteresis. Hysteresis in capillary pressure and relative permeability can significantly affect the trapping of $\text {CO}_{2}$. During the injection and subsequent imbibition cycles, the trapping characteristics of the reservoir can exhibit hysteresis, meaning that the drainage and imbibition curves do not coincide^49,50. This hysteresis can lead to increased residual trapping because the capillary forces that allow $\text {CO}_{2}$ to enter the pore spaces during injection are not the same as those that release it during imbibition. As a result, some $\text {CO}_{2}$ is left trapped in the pore spaces after the injection process. During SAG injection, the foam generated can increase this hysteresis effect. In Adebayo (2018)⁵¹, the presence of the foam in the pore spaces of carbonate core samples altered the wettability and surface properties of the rock, which changed the capillary pressure relationships and enhanced the hysteresis effect, leading to more $\text {CO}_{2}$ being residually trapped.

In Fig. 7c, we see that the $\text {CO}_{2}$ mineralization was mainly due to dissolution of the minerals and not precipitation (negative vales denote dissolution, while positive values denote precipitation). It is interesting to see a significant increase (about 67%) in the mineralization trapping during the foam injection techniques. This further suggests that surfactant solutions can as well contribute to rock mineralization and further laboratory experiments are needed to assess that.

Table 5 below summarizes the potential of foam injection for oil recovery and $\text {CO}_{2}$ trapping.

Table 5 Contribution of trapping mechanisms.

The simulation results show the effectiveness of foam to increase the oil recovery factor than the continuous $\text {CO}_{2}$ injection technique in a carbonate reservoir. These findings further show that foam injection can improve oil recovery and $\text {CO}_{2}$ trapping mechanisms, which promote $\text {CO}_{2}$ sequestration.

Notably, compared to the high residual trapping values, $\text {CO}_{2}$ solubility trapping accounted for only 24.06% of the total trapping during SAG injection while during gas injection, solubility trapping was 20.68%. In Bello et al. (2024)²³, we have shown how salinity causes a reduction in $\text {CO}_{2}$ dissolution in brine, due to salting-out effects and an increase in aqueous viscosity. Hence, in such a high salinity reservoir like ours, such reduced $\text {CO}_{2}$ solubility trapping efficiency is expected. The residual trapping was the most dominant in all cases and this could be attributed to the capillary forces existing within the reservoir from the residual oil. However, it is evident that solubility trapping would not be the most dominant mechanism in a high salinity, depleted oil reservoir.

Furthermore, the presence of surfactant reduces interfacial tension, allowing $\text {CO}_{2}$ to spread more easily within the pore spaces and come into contact with more of the rock surface area. This increased contact enhances the likelihood of $\text {CO}_{2}$ molecules being left behind as residual bubbles when the foam propagates. The foam has a higher apparent viscosity than the gas alone, which slows down the gas movement, allowing more time for the $\text {CO}_{2}$ to be trapped by residual and solubility trapping⁴⁷.

We also see very low mineralization trapping efficiencies for mineral trapping, corroborating results from previous studies concerning $\text {CO}_{2}$ mineralization happening only after hundreds to thousands of years^23,52,53. The effect of mineralization trapping is further shown in Fig. 8 where we see that all the three minerals simulated show a similar trend of dissolution over a simulation period of 100 years. Negative values signify the dissolution of the minerals. Fig. 8 shows the change in number of moles of the simulated minerals with time.

Figure 8

Mineral mole changes in the reservoir model: (a) Calcite (b) Dolomite (c) Illite.

The dissolution process involves the reaction of the mineral with $\text {CO}_{2}$ and water to form bicarbonate ions and cations of the mineral. The dissolution of calcite can be represented by the following reaction:

$$\begin{aligned}\text {CaCO}_3\text {(s)} + \text {H}_2\text {O(l)} + \text {CO}_2\text {(aq)} \rightarrow \text {Ca}^{2+}\text {(aq)} + 2\text {HCO}_3^-\text {(aq)}\end{aligned}$$

This reaction is driven by the acidity of the $\text {CO}_{2}$-saturated water, which increases the solubility of the calcite. Similar reactions can occur for dolomite, $(\textrm{CaMg}(\textrm{CO}_3)_2)$ and illite $(\textrm{KAl}_2(\text {Si}_3\textrm{Al})\text {AlO}_{10}(\text {OH})_2)$ as well, leading to the release of $Mg^{2+}$, $K^+$, and $Al^{3+}$ ions into the solution.

$$\begin{aligned}\text {Al}_2(\text {Si}_3\text {AlO}_{10})(\text {OH})_2 + \text {H}_2\text {CO}_3 \rightleftharpoons \text {Al}^{3+} + 3\text {SiO}_4^{4-} + 2\text {HCO}_3^- + 2\text {H}_2\text {O}\end{aligned}$$

In each of these reactions, the dissolution of minerals is favored under conditions where the concentration of dissolved $\text {CO}_{2}$ and carbonic acid is high, leading to the formation of soluble bicarbonate ions and dissolved cations⁵⁴. Thus, the preference for dissolution over precipitation in the presence of $\text {CO}_{2}$ can be attributed to the thermodynamic stability of the dissolved species. As stated earlier, when $\text {CO}_{2}$ dissolves into water, it forms carbonic acid, which dissociates into bicarbonate ions. The dissolution of minerals into bicarbonate ions represents a lower-energy state compared to the precipitation of minerals from the solution⁵⁵. Furthermore, Johnston et al. (2021)⁵⁶ reported that the precipitation of carbonate minerals is a much slower process than dissolution which can take hundreds to thousands of years. Therefore, it may not be observed during the timescale of 100 years as in our simulation.

Assessment metrics for $\text {CO}_{2}$ storage in our model

To maximally achieve the purpose of CCUS strategies in the petroleum industry, it is important to co-optimize oil recovery with $\text {CO}_{2}$ storage. This helps to understand what to prioritize during field operations. Previous studies^57,58 have introduced the concept of theoretical storage capacity. This refers to the quantity of $\text {CO}_{2}$ that can be potentially stored in a porous medium and it assumes that the pore spaces previously occupied by the produced fluids can be potentially utilized for $\text {CO}_{2}$ storage. The formula is presented below:

$$\begin{aligned} \ M_t = \rho _{\text {gas}} \left[ RF \times \left\{ Ah\phi (1-S_{wi})-V_{iw}+V_{pw}\right\} + C_{ws} \times \left\{ Ah\phi S_{wi}+V_{iw}-V_{pw}\right\} + C_{os} \times \left\{ Ah\phi (1-RF)+(1-S_{wi})\right\} \right] \ \end{aligned}$$

(13)

where $M_t$ = theoretical $\text {CO}_{2}$ storage capacity in the porous medium, kg; $\rho _{gas}$ = the density of $\text {CO}_{2}$ in reservoir conditions, kg/$m^3$ ; RF = the recovery factor; A = the cross-sectional area of the porous medium, $m^2$ ; h = reservoir thickness, m; $\phi$ = porosity; $V_{iw}$ = the volume of injected water, $m^3$ ; $V_{9w}$ = the volume of produced water, $m^3$ ; $S_{wi}$ = irreducible water saturation; $C_{ws}$ = the solubility coefficient of $\text {CO}_{2}$ in formation water; and $C_{os}$ = the solubility coefficient of $\text {CO}_{2}$ in oil.

Knowing $M_t$, the $\text {CO}_{2}$ storage efficiency can be calculated. Here, the $\text {CO}_{2}$ storage efficiency is different from the percentage of $\text {CO}_{2}$ retained in the reservoir which was earlier presented in Fig. 6. This rather refers to the efficiency of $\text {CO}_{2}$ that can be stored in this particular reservoir. Different studies have assessed ways to calculate this, however, in Bello et al.¹², we have included a modified formula that accounts for the $\text {CO}_{2}$ loss due to surface and subsurface actions. When $\text {CO}_{2}$ is injected, not all of it reaches the target sites. Some volume can be lost due to mechanical issues with the pumps, which may not operate at 100% efficiency. Additionally, some may escape through minor leaks in the injection system, including pipes, valves and fittings. Although in numerical studies, this is not expected to happen. We used a value of 5% for this^59,60. The formula is presented below:

$$\begin{aligned} \ \text {CO}_2 \text { storage efficiency} = \frac{\text {CO}_2 \text { injected} - (\text {CO}_2 \text { produced} + \text {CO}_2 \text { loss})}{\text {CO}_2 \text { theoretical storage capacity}} \ \end{aligned}$$

(14)

These assessment metrics were computed and the results are summarized in the Table 6 below:

Table 6 Assessment metrics for $\text {CO}_{2}$ storage.

From Table 6, it can be seen that foam can be used as a promising alternative to improve the storage capacity of $\text {CO}_{2}$ in the reservoir. This amounts to an almost three-fold and eight-fold increase in storage capacity and $\text {CO}_{2}$ storage efficiency, respectively.

Conclusions

This study presents findings from numerical simulations of foam in a hydrodynamic model that mimics a depleted oil formation with a residual oil saturation of 0.3. $\text {CO}_{2}$ foam was injected with the dual purpose of enhanced oil recovery and $\text {CO}_{2}$ Storage. Solubility, residual, and mineralization trapping mechanisms were modeled, and the results were analyzed. The main findings of this work can be summarized as follows:

• Foam injection resulted in oil production at least 2.3 times higher than gas injection. This increase is due to significant $\text {CO}_{2}$ spreading and enhanced volumetric sweep efficiency. Gas injection primarily channels through the oil zone, leaving significant oil unproduced, while foam mitigates this by enhancing viscosity and controlling gas mobility.

• After 20 years, at the end of the production period with $\text {CO}_{2}$ injection, only 25.68% of the injected $\text {CO}_{2}$ remained in the reservoir, whereas with foam injection, 50.34% was retained.

• During foam injection, the theoretical storage capacity of $\text {CO}_{2}$ was increased by 2.6 times, presenting a potential to store 1.95 gigatonnes of $\text {CO}_{2}$ in the hydrodynamic model simulated.

• Foam mechanisms for $\text {CO}_{2}$ sequestration in a depleted oil reservoir include gas trapping, gravitational segregation reduction, and $\text {CO}_{2}$ leakage pathway blockage.

• The residual trapping mechanism accounted for over 70% of the total trapped $\text {CO}_{2}$, making it the predominant trapping mechanism. Meanwhile, solubility trapping was significantly affected by the high salinity of the brine, resulting in only approximately 20% of the total $\text {CO}_{2}$ being trapped.

• The low efficiency of mineral trapping could be attributed to the relatively short simulation duration of 100 years. Efficient $\text {CO}_{2}$ mineralization processes typically require hundreds to thousands of years to occur.

• There was a 67% increase in mineralization trapping during foam injection compared to gas injection, indicating the significant contribution of surfactants. Further experimental studies should be conducted to investigate the impact of surfactants on rock mineralization.

With underground $\text {CO}_{2}$ storage increasingly becoming a vital strategy in mitigating climate change by reducing atmospheric $\text {CO}_{2}$ levels, foam injection techniques can potentially be optimized and adapted for various types of geological formations beyond depleted oil reservoirs. Furthermore, future works can focus on the long-term behavior of $\text {CO}_{2}$ in these reservoirs, particularly on enhancing mineral trapping mechanisms which require longer periods to become effective. Additionally, a comprehensive assessments of the economic viability and environmental impacts of large-scale foam injection projects should be conducted to ensure that they are sustainable and cost-effective.