Effect of Salts on Interfacial Tension and CO₂ Mass Transfer in Carbonated Water Injection

Abstract

Carbonated water injection (CWI) is a promising enhanced oil recovery (EOR) and CO₂ sequestration method, which overcomes the problems associated with CO₂ EOR. CO₂ mass transfer and interfacial tension (IFT) are important parameters that influence oil recovery efficiency. This study addresses the impact of MgCl₂ and Na₂SO₄ in carbonated water (CW) on CW/hydrocarbon IFT and CO₂ mass transfer. An axisymmetric drop shape analysis was used to estimate the IFT and the CO₂ diffusion coefficient. It was found that CW+MgCl₂ reduced both the CW/n-decane IFT (36.5%) and CO₂ mass transfer, while CW+Na₂SO₄ increased both the IFT and CO₂ mass transfer (57%). It is suggested that reduction in IFT for CW+MgCl₂ brine is mainly due to the higher hydration energy of Mg²⁺. The Mg²⁺ ion forms a tight bond to the first hydration shell [Mg(H₂O)₆]²⁺, this increases the effective size at the interface, hence reduce IFT. Meanwhile, the SO₄²⁻ outer hydration shell has free OH groups, which may locally promote CO₂ mass transfer. The study illustrates the potential of combining salts and CW in enhancing CO₂ mass transfer that can be the base for further investigations. Furthermore, the contribution and proposed mechanisms of the different ions (SO₄²⁻ and Mg²⁺) to the physical process in carbonated water/hydrocarbon have been addressed, which forms one of primary bases of EOR.

1. Introduction

Recent years have seen an increased interest in carbonated water injection (CWI) as secondary/tertiary enhanced oil recovery (EOR) method. CWI has been projected as a substitute to the CO₂ EOR to overcome challenges such as poor sweep efficiency, and early breakthrough [1]. Low sweep efficiency associated with CO₂ EOR due to gravity segregation and capillary instabilities causes mobility issues [1,2]. For CWI, the CO₂ is dissolved in water and has higher density; this reduces gravity segregation, thereby improving the sweep efficiency. Furthermore, for CWI, an increased mobility of oil is observed as a result of a reduction in the viscosity of the oil resulting from the dissolution/diffusion of CO₂, which enhances sweep efficiency [2]. Figure 1 (inspired from [2]) shows the pictorial representation between the comparison between CO₂ EOR and CWI regarding sweep efficiency and sweep profile. Another problem with CO₂ EOR is that in many of the cases, CO₂ is not readily available in the required volumes. Thus, the transportation of CO₂ becomes necessary, which increases the use costs. CWI, which requires less CO₂, partially reduces the costs associated with transport. CWI is also of interest due to its capability of coupling oil recovery and CO₂ sequestration. Dissolved CO₂ in water (carbonated water) has higher density compared to native brine (formation water). Hence, it sinks into the bottom of the reservoir, eliminating the risk of buoyancy-driven leakage of CO₂ [3,4,5,6], thus improving CO₂ sequestration capability.

At pore scale, the rock wettability defined by rock-fluid interaction, capillary pressure through interfacial tension (IFT), and swelling and mobility through CO₂ mass transfer (oil-CW interaction) are the primary mechanisms responsible for governing the oil recovery by CWI. Various ways have been described in the literature (nanofluid, microbial, polymer, and salts) to address the fluid-fluid and fluid-rock interactions as EOR methods. Lately more attention has been directed to low-salinity water studies [7,8], which indicated wettability and interfacial alteration. The potential of saline water to change the wettability of the rock has been well established [9,10], and has been extended to CWI by Manshad, et al. [11]. Previous studies [9,11,12,13] have presented extensive data on the IFT between brine/hydrocarbon and a few studies [7,14] have also been dedicated to carbonated brine/hydrocarbon [15].

Table 1. IFT obtained by different studies for brine/hydrocarbon and carbonated brine/hydrocarbon systems.

References	Type of Aqueous Systems	Experimental Conditions	Observations
Reduction in IFT
Gomari and Hamouda [9]	n-decane/brine with MgCl2 and Na2SO4	82.4 to 158 °C, atmospheric pressure	IFT reduction in the presence of MgCl2 and Na2SO4 compared to distilled water
Serrano-Saldaña, et al. [16]	n-dodecane/brine with sodium dodecyl sulfate (SDS) and NaCl	25 °C, atmospheric pressure	The presence and rising surfactant concentration leads to a reduction in the IFT
Hosseini, et al. [20]	Crude oil/brine with Na+, K+, Cl, Mg2+, and Ca2+ ions	25 °C, atmospheric pressure	The presence of divalent ions (Ca2+ and Mg2+) decreases the oil/brine IFT. At a given concentration Mg2+ shows a lower oil/brine IFT than Ca2+
Increment in IFT
Ikeda, et al. [17]	n-hexane/water with NaCl	25 °C, 0 to 100 Mpa	Increment in IFT due to the presence of NaCl in water
Cai, et al. [13]	normal alkane + water/brine with NaCl, CaCl2, MgCl2	25 to 80 °C,1 to 300 bar	Increase in IFT due to the presence of salt. Weakly dependent on pressure and salt species
Badakshan and Bakes [21]	Toluene, n-hexane and cyclohexane/brine with NaCl, NaHCO3, Na2SO4	20 °C to 75 °C, atmospheric pressure	For all the salts an increment in IFT was observed
Salt-dependent IFT variation
Lashkarbolooki, et al. [19]	Crude oil/brine with NaCl, KCl, Na2SO4, MgSO4, CaSO4, CaCl2, and MgCl2	Ambient temperature and pressure	Reduction in IFT at high salinity conditions especially for MgCl2. The increment in IFT for monovalent salts such as NaCl and KCl is used
Aveyard and Saleem [18]	n-dodecane-decane/brine with LiCl, NaCl, KCl, KBr, NaBr, KI, and Na2SO4	20 °C, atmospheric pressure	Reduction in IFT in the presence of KI. An increment in IFT for rest of the salts
IFT of carbonated brine/hydrocarbon system
Manshad, et al. [15]	Crude oil/carbonated water with NaCl, CaCl2, MgCl2, KCl, and Na2SO4	75 °C, pressure up to 137 bar	Presence of salt reduces the IFT and is a function of the type of salt
Nowrouzi, et al. [7]	Crude oil/ carbonated brine with NaCl, CaCl2, MgCl2, KCl, MgSO4, K2SO4, and Na2SO4	75 °C, up to 140 bar	Salts are able to reduce the IFT. Addition of CO2 further enhances the reduction in IFT. Minimum IFT was obtained for MgCl2+K2SO4 combination
Isdahl [21]	n-decane/ carbonated synthetic sea water with silica nanofluid	25 °C and 45 °C, 10 to 90 bar	Marginal reduction in IFT for the combination of salt and CO2 in water

gives a summary of work done in the literature on the effect of salts on IFT. Table 1 has been divided into different sections (increasing IFT, decreasing IFT, salt-dependent IFT variation, and IFT of carbonated brine/hydrocarbon systems) depending on the investigations made by the various studies. It may be observed from Table 1 that there are controversial trends of the IFT trend. For example Gomari and Hamouda [9] and Serrano-Saldaña, et al. [16] showed that salts reduced the IFT. However, Ikeda, et al. [17] and Cai, et al. [12] observed that salts increased the IFT. Furthermore, Aveyard and Saleem [18] and Lashkarbolooki, et al. [19] have observed both an increase and decrease in IFT, and concluded that the variation of IFT is a function of the composition of the brine. Additionally, the increase or decrease in IFT was also found to be the function of concentration of salt [16,20]. Not all the salts will have same effect on the IFT; there may be certain types of salts which would have more prominent effects on reducing the IFT than others. Gomari and Hamouda [9], Hosseini, et al. [20], and Lashkarbolooki, et al. [19] observed that MgCl₂ specifically Mg²⁺ ions leads to lower IFT compared to other salts or ions present in their study. Aveyard and Saleem [18] showed that out of seven different salts only KI was able to lower the IFT of n-dodecane and n-decane/brine while other lead to an increase in IFT. Cai, et al. [12] observed the IFT of normal alkane+brine is weakly dependent on slat species. Therefore, there is a contrasting observation for IFT. Hence, there is a need for further investigations. For CW+salt/hydrocarbon system, there are a limited number of studies available [7,14]. Unfortunately, there is insufficient data to understand the critical interfacial phenomena occurring between brine CW/hydrocarbon. This has motivated this work to thoroughly investigate the influence of salts on the CW/hydrocarbon interfacial tension.

The mass transfer of CO₂ and the resulting mechanisms, such as swelling and enhanced mobility of the oil, dictate the degree of oil recovery in CO₂-based EOR methods [4,22]. From the above discussion and Table 1 it may be said that thus far, most of the studies have concentrated on examining interfacial and wettability aspects of CO₂/oil, CW/oil, water/oil, and carbonated smart water/oil systems. However, there is a lack of understanding of CO₂ mass transfer, and factors influencing CO₂ mass transfer, especially when it comes to CW/hydrocarbon systems. The diffusive mass transfer of gases, especially CO₂ into oil, is of primary importance when it comes to CO₂ and CW flooding. Diffusion of CO₂ into oil results in the reduction of viscosity, and displacement of oil (including heavy oil) from reservoirs to surface. Few studies have looked into the aspect of CO₂ mass transfer, and most of these studies are related to CO₂/hydrocarbon [23,24,25] or CO₂/water [26] systems. The number of studies diminishes when it comes to CW/hydrocarbon systems [27]. Furthermore, there may be a significant neglect of the application of salts as a CO₂ mass transfer enhancement tool for CW/hydrocarbon system. Zhu, et al. [28] in their study on syngas and fermentation have experimentally shown that salts in water may enhance mass transfer of gas in water. Zhu, et al. [28] showed that the ions of dissolved salts in water stopped the coalesces of CO bubbles, thereby increasing the surface area between CO and water. Collins [29] showed that salts in water increased the entropy of the solution, which enhances the mobility leading to a convective movement in bulk liquid, and may enhance the mass transfer. Conventionally, salts in water have been viewed as wettability and IFT modifiers; however, salts may have more valuable potential and may also be used as CO₂ mass transfer enhancement tool, and this widens the scope of applicability of salts. Therefore, investigations are needed to establish if salts can improve the CO₂ mass transfer in CW/hydrocarbon systems.

Previous studies have developed various methods to understand the CO₂ mass transfer by estimating the diffusion coefficient of CO₂ in bulk liquids. These methods may be put into two groups, compositional analysis [30,31], and pressure decay [32,33] methods. In compositional analysis, errors will be caused in the extraction of the sample from the setup and carrying out gas chromatography, especially at high pressures and temperatures, which may affect the estimation of the diffusion coefficient [25]. Furthermore, the compositional method is time-consuming, complicated, and expensive [34]. The pressure decay method solves the problems associated with the compositional analysis. However, it requires long experimental time (20–100 h or more). Additionally, the diffusion coefficient obtained by pressure decay method is not for a particular pressure but a range of pressures [25,35]. Hence, there is a requirement for a well-established, reliable, quicker, and simple method for estimating the diffusion coefficient of CO₂ in hydrocarbon, which may be used for both gas-liquid and liquid-liquid systems. Of late, Axisymmetric Drop Shape Analysis (ADSA) using pendant drop equipment coupled with a computational scheme has been used to estimate the diffusion coefficient of gases into liquids [23,24]. The experiments using ADSA can be carried out at high temperature and pressure (up to 60 MPa and 180 °C) [27]. Furthermore, unlike the pressure decay method, the experiments using the ADSA pendant drop technique can be carried out at isothermal and isobaric conditions. The flexibility, simplicity, lesser time, and no human interference makes the ADSA method suitable for calculating the diffusion coefficient of gases into the bulk liquids. The ADSA pendant drop technique is also widely used to estimate the IFT between two fluid at elevated pressure and temperature [36]. The ADSA method has an accuracy of ±0.05 mN/m² when estimating the IFT [36,37]. Therefore, by using the ADSA method, both mass transfer and interfacial studies may be carried out using the same experimental setup and with higher accuracy.

From the above discussion on literature studies, two crucial points may be made. First, the studies and knowledge of the influence of salts on the CW/hydrocarbon IFT are insufficient. Dynamic IFT analysis has been entirely neglected, and there are some opposing trends on the influence of salts on brine/hydrocarbon IFT. Second and importantly, there is significant overlooking of the effects of salts on CO₂ mass transfer. Therefore, there is a lack of understanding of CO₂ mass transfer, and factors influencing CO₂ mass transfer, especially when it comes to CW/hydrocarbon systems. The present work tries to address these issues. As a result, the objective of the present study is to investigate the impact of salts in CW, particularly Na₂SO₄ and MgCl₂ in altering the CW/hydrocarbon IFT and enhancing the CO₂ mass transfer. In fulfilling these objectives, the study adds four major contributions to the existing knowledge of CW/hydrocarbon systems. First, the experiments were designed to analyze both dynamic and equilibrium IFT, and simultaneously carry out mass transfer studies. Second, the experimental pressure range (50–100 bar) was chosen to study the influence of the phase of both gaseous and supercritical phase of CO₂ on the mass transfer and IFT. Third, to the best of authors knowledge, this would be the first time the impact of salts on the CW/hydrocarbon as a combined mechanism of IFT and the mass transfer enhancement tool will be addressed. Fourth, a relatively new and advanced numerical model, which couples with experimental results to estimate the CO₂ diffusion coefficient at-large range of pressure and temperate, has been developed. The present study, through experimental, theoretical, and numerical models, analyzes the influence of salts on the interfacial and mass transfer aspects of CW/hydrocarbon system. ADSA pendant drop experiments have been carried out for a pressure range of 50–100 bar at 45 °C. The study will focus on the effect of MgCl₂ and Na₂SO₄ on IFT and diffusion coefficient.

2. Experimental and Numerical Study

Figure 2a shows the cross-section of the see-through high-pressure cell (PVT cell) where the experiments were carried out. The pendant hydrocarbon drop (HD) consisting of n-decane will be known as drop phase, and the drop phase is surrounded by environmental fluid consisting of salts dissolved in carbonated water known as carbonated brine (CB). The mass of the CO₂ in the brine surrounding the drop phase is always monitored and maintained at the saturation limit. The solubility of CO₂ is higher in hydrocarbons compared to water or brine; therefore, when the hydrocarbon contacts the CB, the CO₂ from the CB diffuses into the drop phase. The resulting mass transfer of CO₂ is driven by the concentration gradient between the drop phase and the environmental fluid. The mass transfer of CO₂ depends on the IFT, CO₂ solubility, density gradient, and experimental conditions. When salts are dissolved in water, they release ions. Depending on the type of salts these ions may be surface active or interface repelling. The ions are responsible for altering the IFT of the CW/oil system. Since salts in water can alter the IFT, there may be a possibility that they may also influence the mass transfer occurring across the interface.

2.1. Materials

The n-decane light hydrocarbon forms the pendant drop phase (Merck KGaA (purity 99%)). As discussed in the introduction, most studies fail to address fundamental phenomena such as CO₂ mass transfer, IFT, and hydrocarbon property alterations, which are critical in understanding and optimizing the process of recovery by CO₂-saturated water. Hence, the first step would be to start with light and homogeneous hydrocarbon. Once the knowledge of fundamental physics for CW-n-decane system has been acquired, then it would easy and meaningful to move to a more complex multicomponent hydrocarbons such as crude oil and synthetic oil. CO₂ with purity of 99.9% (PRAXAIR) was used to prepare the CW/CB. NaCl, MgCl₂, Na₂SO₄, CaCl₂, KCl, and NaHCO₃ salts were used to prepare the brine by dissolving them in deionized water (DIW). The composition of each of these was maintained according to the synthetic seawater (SSW) as given by Hamouda and Maevskiy [38]. The focus of the present study was to identify the feasibility of salts as IFT reduction and mass transfer enhancement option in a CW/hydrocarbon system. Therefore, only the composition of the brine has been altered, and the study of the influence of varying the concentration of salts has been left for future studies. SSW formed the base brine solution and out of this, four more brine types were created either by retaining only MgCl₂ (DIW+MgCl₂) and Na₂SO₄ (DIW+Na₂SO₄) or by removing MgCl₂ (SSW-MgCl₂) or Na₂SO₄ (SSW-Na₂SO₄). This variation in brine composition was done to investigate the influence of Mg²⁺ and SO₄²⁻ ions on the IFT and CO₂ mass transfer.

Table 2. Types of brine, compositions, and the purpose of forming each brine types.

Brine	Composition (g/L)						Purpose
	NaCl	MgCl2 *6H2O	Na2SO4	CaCl2 *2H2O	KCl	NaHCO3
SSW	23.38	9.05	3.41	1.91	0.75	0.17	Combination of salts on CO2 mass transfer and IFT
SSW-MgCl2	23.38	0	3.41	1.91	0.75	0.17	Combination of salts in the absence of Magnesium on IFT and CO2 mass transfer
SSW-Na2SO4	23.38	9.05	0	1.91	0.75	0.17	Combination of salts in the absence of Sulfate on IFT and CO2 mass transfer
DIW+MgCl2	0	9.05	0	0	0	0	Magnesium on CO2 mass transfer and IFT
DIW+NaSO4	0	0	3.41	0	0	0	Sulfate on CO2 mass transfer and IFT

gives the types of brine, compositions, and the purpose of forming each brine types. The brines presented in Table 2 will be saturated with CO₂, and from now on in this study, the combination of CO₂+SSW, which is carbonated SSW, will be abbreviated as C_SSW. Similarly, C_SSW-MgCl2 (CO₂+SSW-MgCl₂), C_SSW-Na2SO4 (CO₂+SSW-Na₂SO₄), CW_+MgCl2 (CO₂+DIW+MgCl₂), and CW_{+ Na2SO4} (CO₂+DIW+Na₂SO₄). Collectively, the combination of CO₂+brines will be termed as CB in the present study. The fluid properties such as density and viscosity of water, CO₂, and n-decane at experimental pressure and temperatures, have been obtained from NIST Chemistry Web Book [39]. Aqion Version 6 software was used to obtain the pH of the each of these brines with and without CO₂, to which the concentration of salts in brine is provided as an input.

2.2. Experimental Setup and Procedure

The equipment and design of the experimental setup are similar to that presented in Bagalkot and Hamouda [27]. The schematic of the experimental setup is shown in Figure 2b. The pendant drop equipment manufactured by EUROTHECHNICA and KRUSS consists of a cylindrical high-pressure cell (PVT cell). The PVT cell is see-through and placed between a high-resolution camera and light source. The capacity of PVT cell is 25 mL, and it can withstand a maximum pressure and temperature of 68.9 Mpa and 180 °C, respectively. A pump (maximum pressure of 32 MPa, GILSON) linked to a piston-cylinder containing CO₂ maintains the pressure in the PVT cell. Furthermore, details of the procedure and experimental setup may be obtained from Bagalkot and Hamouda [27]. Additional experiments were carried out using gas flow meter at 25 °C to estimate the saturation of CO₂ in brine at different pressures, and the result obtained was compared with the model presented by Duan and Sun [40]; there was a maximum error of 3% in the mass of CO₂. The experiments were carried out for a pressure range of 50 to 100 bar, at 45 °C. For these pressures and temperatures, CO₂ is in a gaseous state for P<74 bar at 45 °C and P>74 bar CO₂ is in the supercritical phase. Hence, the experiments will cover the effect of both gaseous and supercritical CO₂. Therefore, there may be a possibility of observing the behavior of various properties (IFT, CO₂ mass transfer, and diffusion coefficient) near to the phase change pressure of CO₂ (74 bar).

2.3. IFT Measurement

The dynamic and equilibrium IFT between CB/n-decane was measured using the ADSA method. The pendant drop method employed in the present study is a practical, accurate, and popular method to measure the IFT of the fluid-fluid system, the method applies Equation (1) to measure the IFT.

$$IFT=\frac{\Delta \rho g{d}^2}{B},$$

(1)

where ∆ρ (kg/m³) is the density difference between the drop and environmental phases; g (m/s²) is the acceleration due to gravity, and d (m) is the maximum horizontal diameter of the unmagnified pendant drop. In Equation (1) three parameters are of significance, B, d, and ∆ρ. Among these B and d are calculated by the drop analysis software, while the densities of both drop phase and environmental phases must be input in the software. When the drop phase (HD, n-decane) contacts the CB, CO₂ diffuses from CB into the HD, which alters the HD density and viscosity. Therefore, for accurate measurement of IFT (dynamic and equilibrium), it is essential to know the density changes of the HD due to the CO₂ mass transfer. The present study adopts the dynamic and equilibrium IFT measuring technique developed by Bagalkot, et al. [41] for the fluid-fluid system. In case of the CO₂-hydrocarbon system, the measurement uncertainty is ±0.3 mN/m. If water is present, uncertainties rise to ±0.5 mN/m [42]. The uncertainty depends on the absolute value of the density difference and becomes greater as the density difference decreases [43].

2.4. Diffusion Coefficient Measurement

2.4.1. Mathematical Model

Molecular diffusion of CO₂ from CB or CW into hydrocarbon pendant drop is a concentration-driven process. In the present study, Fick’s second law (Equation (2)) is employed to represent the diffusive mass transfer process of CO₂ across the interface. The pendant drop is symmetrical about the z-axis (Figure 2a). Therefore, it would be appropriate and convenient to adopt a cylindrical coordinate system (r, θ, z) rather than a Cartesian coordinate system (x, y, and z). Furthermore, details of the model, assumptions/limitations, and its boundary conditions for solving Equation (2) may be found in Bagalkot and Hamouda [27], Bagalkot and Hamouda [44], and Bagalkot and Hamouda [35].

$$\frac{\partial C}{\partial t}=D(t)\{\frac{1}{r}\frac{\partial C}{\partial r}+\frac{{\partial }^{2}C}{\partial r^2}+\frac{{\partial }^{2}C}{\partial z^2}\},$$

(2)

In Equation (2), C is the concentration of CO₂ in the drop phase (kg/m³), and D(t) represents the diffusion coefficient (m²/s). Equation (2) provides the spatial distribution of the concentration of CO₂ in the drop phase as a function of time. The diffusion of CO₂ from CW/CB into the hydrocarbon starts after the HD is formed. At the onset of the experiment (t = 0 s), the concentration of CO₂ in the pendant drop is zero at t = 0 (Equation (3)).

$$C(r,z,t=0)=0$$

(3)

At thermodynamic equilibrium [45], CO₂ concentration at the interface remains constant as long as the pressure and temperature of the system are held constant. On this basis, Equation (4) represents the boundary condition at the interface.

$$C(r=R_D,z=R_D,t>0)=C_o,$$

(4)

where R_D is the radius of the drop, and C_o is the concentration of CO₂ at the interface. A zero (constant) flux boundary condition is employed to address the continuity at the center of the drop (r = 0) (Equation (5)).

$$\frac{\partial C(r=0,z,t)}{\partial r}=0$$

(5)

Equation (2) along with boundary and initial conditions (Equations (3)–(5)) are numerically solvable, to obtain the time and space-dependent concentration of CO₂ in the drop. The volumetric average of CO₂ concertation in the drop phase (C_avg (m³)) is obtained from Equation (6) as a function of time.

$$C_{avg}(t)={\displaystyle \underset{(r,z)\in P_d}{\iint }\frac{C(r,z)}{C_o}rdrdz}$$

(6)

Furthermore, the parameter C_avg is used to calculate the swelling factor (SF) (Equation (7)), which is the ratio of the volume of the CO₂ saturated drop phase to the initial volume of drop phase.

$$SF=1+\frac{{\displaystyle \underset{0}{\overset{T}{\int }}\frac{\left[V_{\exp }(t)-V_o\right]C_{avg}(t)dt}{V_{\exp }{(t)}^2}}}{{\displaystyle \underset{0}{\overset{T}{\int }}\frac{\left[C_{avg}{}^2(t)\right]dt}{V_{\exp }{(t)}^2}}},$$

(7)

In Equation (7), V_exp(t) (m³) is the experimentally obtained volume of drop phase at any instant t (s), and T (s) is the total experimental time; Vo (m³) is the initial volume (t = 0) of the pendant drop obtained from experiments.

At each moment, the volume of the drop phase (HD) is the aggregate of the volume of the hydrocarbon in the drop phase (initial volume of drop) (V_o) and the increment in volume due to by the diffusion of CO₂ in the hydrocarbon (Equation (8)) [44]. The increment in volume is the product of C_avg, and SF-1.

$$V(t)=V_o+(SF-1)\cdot C_{avg}(t)$$

(8)

An optimization function (F) (non-dimensional) as a function of the difference in the experimental (V_exp(t)) and numerical volume (V(t)) is used (Equation (8)) and the minimum of the optimization function (F_min) would give the diffusion coefficient of CO₂ in the hydrocarbon. The lower the F_min, the lower the error in estimating the diffusion coefficient compared to the experimental.

$$F=\sqrt{\frac{1}{T}{\displaystyle \underset{0}{\overset{T}{\int }}\frac{{\left[V_{\exp }(t)-V(t)\right]}^{2}dt}{V_{\exp }{(t)}^2}}}\ast 100\%$$

(9)

3.4.2. Numerical Model

A semi-implicit finite difference numerical scheme was adopted to solve Equation (2) and obtain the CO₂ concentration profiles in the pendant drop. The model assumption/limitations, validation, and description may be found in Bagalkot and Hamouda [35].

2.4.3. Dynamic Interface (Boundary) Method

One of the significant and visible implications of CO₂ diffusion in hydrocarbon is the swelling or the increment in the volume of the hydrocarbon. Therefore, the volume of the pendant drop is not the same as that of initial time, and it increases with time. The increment in the volume indicates a change in the surface area at the CW/oil interface and hence, the movement of the fluid-fluid interface. However, most of the studies carrying out diffusion coefficient measurement using pendant drop experiment assume a quasi-static nature of the fluid-fluid interface, therefore neglecting increase in volume and thus displacement of the interface [25,46]. Such an assumption, especially for CW/oil system where there is a significant increment in volume, would lead to inaccuracy in estimating the diffusion coefficient. Bagalkot and Hamouda [27] showed that error due to the assumption of a static interface is approximately 2% at 10 bar to a significant 36% at 60 bar. Bagalkot and Hamouda [35] developed a simple and effective method to incorporate the dynamic nature of the CW-hydrocarbon interface (boundary). The current study extends the method to CB-hydrocarbon system.

3. Results and Conclusions

3.1. Swelling and Diffusion Coefficient

Figure 3 shows the mass of CO₂ transferred into the n-decane drop (CO₂ mole/ml volume of drop) from the surrounding CB (CW, C_SSW-MgCl2, C_SSW-Na2SO4, CW_+MgCl2, and CW_+Na2SO4) from the start of the experiment until equilibrium is attained. The analysis has been carried out for 50 bar (3a), 70 bar (3b), 80 bar (3c), and 100 bar (3d) at 45 °C. For all the brine types and pressures, the CO₂ mass transfer with time may be divided into two regions. In the first region, the CO₂ mass transfer increases sharply, followed by the second region. In the second region the rate of mass transfer decreases and a plateau is reached, from where the mass transfer increase is negligible, and an equilibrium is approached. The first region of sharp increase takes a shorter time compared to the second region; however, a substantial CO₂ mass transfer occurs in the region of sharp increase. The sharp increase is followed by the gradual increase in mass transfer, which may be explained by the decrease in the CO₂ concentration gradient across the interface as CO₂ diffuses into the n-decane. It may be observed that there is a considerable variation in the profile and amount of mass transfer of CO₂ into n-decane among different brine compositions, indicating that the CO₂ mass transfer across the interface is sensitive to the composition of the brine. For the CBs C_SSW-MgCl2, C_SSW, and CW_{+ Na2SO4} there is a greater CO₂ mass transfer compared to the CW, while a lower CO₂ mass transfer is observed for C_SSW-Na2SO4 and CW_+MgCl2 than CW. Furthermore, a largest CO₂ mass transfer is observed for brine CW_+Na2SO4, and the least mass transfer is observed for brine CW_+MgCl2. Therefore, it may be concluded that the combination of CW and Na₂SO₄ would assist the CO₂ mass transfer leading to a higher mass transfer of CO₂, while the CW and MgCl₂ combination does the opposite.

Figure 4 shows the swelling (ratio of equilibrium to initial volume) of the n-decane pendant drop due to the mass transfer of CO₂ for different CB (CW, C_SSW, C_SSW-MgCl2, C_SSW-Na2SO4, CW_+MgCl2, and CW_+Na2SO4) for a pressure range of 50-100 bar at temperature 45 °C. For a pure hydrocarbon+CO₂ system the higher the CO₂ mass transfer, the more significant will be the swelling of the hydrocarbon. Unsurprisingly, the swelling results in Figure 4 are analogous to the trend in Figure 3 (CO₂ mole). For example, in Figure 3, Na₂SO₄ enhances the CO₂ mass transfer. Therefore, in Figure 4 a larger swelling of drop phase (n-decane) is observed for cases where the brine consisted of Na₂SO₄, while a lower swelling of brine consisting of MgCl₂. Similar to CO₂ mass transfer (Figure 3), the combination of Na₂SO₄ and MgCl₂ resulted in an intermediate swelling.

Figure 5 shows the effective diffusion coefficient of CO₂ into n-decane from CB (C_SSW, C_SSW-MgCl2, CW_+Na2SO4, C_SSW-Na2SO4 and CW_+MgCl2) and CW for pressures 50, 70, 80, and 100 bar at 45 °C. Depending on the phase of CO₂ it may be observed that D_CO2 is both directly and inversely proportional to pressure. For the gaseous CO₂, the D_CO2 is inversely proportional to pressure, whereas when the CO₂ is supercritical, the D_CO2 is directly proportional to the pressure; this observation was common for all the CB types. Similar observations were also made by [27]. Furthermore, it may be observed from Figure 5 that at isobaric conditions, in the presence of salt (CB) the D_CO2 is well scattered above and below that of CW. Therefore, the presence of salt in CW both increases and decreases the rate of CO₂ mass transfer and is a function of the type of salt. The CB containing Na₂SO₄ (CW_+Na2SO4) and absence of MgCl₂ (C_SSW-MgCl2) showed a higher D_CO2 than CW, while the CB containing MgCl₂ (CW_+MgCl2) and absence of Na₂SO₄ (C_SSW-Na2SO4) led to a lower diffusion coefficient than CW. The D_CO2 was highest for CW_+Na2SO4, while the lowest was observed for CW_+MgCl2. On average (average over the pressure) approximately 57% increase in D_CO2 for CW_+Na2SO4 was observed compared to CW_+MgCl2, and approximately 25% increase in D_CO2 for CW_+Na2SO4 was observed compared to CW. The combination of Na₂SO₄+MgCl₂ (C_SSW) led to a reduction in D_CO2 when compared to CW_+Na2SO4; however, it was higher than that of CW_+MgCl2. The D_CO2 for C_SSW was marginally higher than that of CW.

3.2. IFT

Table 3. pH and IFT for different CB at 1, 50, 70, 80, and 100 bar at 45 °C.

Pressure (bar)	IFT (mN/m)
	CW	CSSW	CSSW-MgCl2	CSSW-Na2SO4	CW+MgCl2	CW+Na2SO4
1	50.13	43.18	51.19	31.09	31.82	52.58
50	56.45	54.35	57.31	35.26	32.28	57.95
70	63.90	63.80	67.50	47.85	40.5	62.75
80	62.67	60.49	58.14	50.85	51.97	60.18
100	52.43	50.46	49.56	46.56	30.26	49.73
Pressure (bar)	pH
	CW	CSSW	CSSW-MgCl2	CSSW-Na2SO4	CW+MgCl2	CW+Na2SO4
1	7.00	6.97	7.02	6.61	6.57	7.13
50	3.24	3.27	3.25	3.15	3.19	3.37
70	3.2	3.22	3.21	3.1	3.14	3.33
80	3.18	3.21	3.19	3.09	3.13	3.31
100	3.17	3.19	3.18	3.07	3.11	3.30

shows the equilibrium IFT of brine/n-decane for different brine compositions along with their pH at 45 °C and different pressures. Table 3 shows that initial pH is approximately 7 ±0.2; after saturation of brines with CO₂ at the different pressures, the pH becomes approximately 3.0. The presence of salts in CW slightly alters the pH. IFT of DIW/n-decane (50.13 mN/m) compares well with literature (50.25 mN/m [47]). When brine C_SSW, C_SSW-Na2SO4, and CW_+MgCl2 brines were used, they reduced IFT. The IFT reduction for CW_+MgCl2 (36.5%) and C_SSW-Na2SO4 (30%), followed by C_SSW (13.8%). Whereas when brines CW_+Na2SO4 and C_SSW-MgCl2 were used the IFT increased by 4.9% and 2.1%, respectively.

The dynamic IFTs are presented in Figure 6 for different pressures; 50 bar (6a), 70 bar (6b), 80 bar (6c), and 100 bar (6d) at 45 °C. The influence of CO₂-saturated brines on the dynamic IFT may be divided into two groups. For most of the pressures, the first group (increasing IFT trend) consists of brines C_SSW, C_SSW-MgCl2, CW_+Na2SO4, and CW. The second group (decreasing IFT trend) shows that C_SSW-Na2SO4 and CW_+MgCl2 reduce IFTs’ profiles as a function of time. The IFT reduction occurs with brines containing MgCl₂ (C_SSW-Na2SO4 and CW_+MgCl2), with the highest reduction when the brine contains only MgCl₂ (CW_+MgCl2). Therefore, the presence of MgCl₂ in CW reduces the IFT with time until the equilibrium is reached, while the presence of Na₂SO₄ in CW increases the IFT. At all pressures, MgCl₂ in CW and C_SSW reduces the IFT. Marginal reduction of IFT (about 2 mN/m) for C_SSW-Na2SO4 brine at 100 bar. For better understanding the effect of brines on swelling, diffusion coefficient and IFT, the next section addresses the relation between the IFT and concentration of the diffused CO₂ into n-decane.

3.3. IFT and Concentration of Transferred CO₂ into n-Decane

Figure 7 shows the equilibrium concentration (10⁻⁶ mol/ml) of the CO₂-transferred CB into the n-decane drop against equilibrium IFT (m N/m). The IFT vs CO₂ concentration profiles in Figure 7 may be divided into two regions—higher and lower concentration regions. As shown, the higher concentration trends of the diffused CO₂ correspond to C_SSW, C_SSW-MgCl2, and CW_+Na2SO4 brines. The lower CO₂ concentration trends correspond to CW, C_SSW-Na2SO4, and CW_+MgCl2. CO₂ concentrations (low and high) for the different pressures are as follows; 50 bar (5.7−8.5∗10⁻⁷ and 2.1−2.3∗10⁻⁶), 70 bar (2.1−2.6∗10⁻⁶ and 4.1−6.3∗10⁻⁶), 80 bar (4.5−5.0∗10⁻⁶ and 5.9−8∗10⁻⁶). CO₂ concentrations and the IFT trends are consistent with and support the conclusion where, in general at all the pressures, the presence of Na₂SO₄ increases the diffusion of CO₂, while the MgCl₂ reduces the IFT. For example, in Figure 3 and Figure 4, Na₂SO₄ enhances the CO₂ mass transfer. Larger swelling of drop phase (n-decane) is also observed for cases where the brine contains Na₂SO₄ (CW_+Na2SO4), while lower swelling is observed for brine consisting of MgCl₂ (CW_+MgCl2). In other words, good correlations exist between the mass transfer trends (Figure 3 and Figure 4) and the analytical data of the transferred CO₂ into n-decane (Figure 7), where the lowest diffusion coefficients are related to brines containing MgCl₂ (C_SSW-Na2SO4 and CW_+MgCl2) and the highest diffusion coefficients are related to brines containing Na₂SO₄ (C_SSW-MgCl2 and CW_+Na2SO4). The case of C_SSW, where it contains both salts (MgCl₂ and Na₂SO₄), shows that the diffusion coefficients are between the high (CW_+Na2SO4) and low (CW_+MgCl2). It is also interesting to see that SO₄²⁻ dominates the effect when co-present with Mg²⁺.

3.4. Interfacial Adsorption Isotherm (Surface Excess)

The observed reduction alteration in IFT by SO₄²⁻ (Na₂SO₄) and Mg²⁺ (MgCl₂) ions may be related to the degree of hydration (number of water molecules surrounding an ion) and hydration energy/enthalpy. Among the major ions present in the SSW, Mg²⁻ ion has the smallest ionic radius (0.072 nm), compared to SO₄²⁻ (0.242 nm [2]) and CO₂ (232 nm). However, as a bivalent the Mg²⁻ ions have high hydration energy. They therefore form tight bonds to the first hydration shell [Mg(H₂O)₆]²⁺. Hence, they have a highly effective size leading to lesser adsorption and early saturation at the interface [48]. Higher hydration energy would also mean a higher affinity towards the CW/oil interface [29,49].

When Na₂SO₄ and MgCl₂ are combined as in C_SSW, the IFT reduction is intermediate between that of CW_+Na2SO4 and CW_+MgCl2. The formation of complexes of Mg²⁺ and Na⁺ with SO₄²⁻ due to the combination of Na₂SO₄ and MgCl₂ would reduce the free ions of Mg²⁺ and Na⁺ [50]. Therefore, a lower concentration of Mg²⁺ would mean fewer ions being adsorbed at the CB/n-decane interface and hence, a smaller reduction in IFT. Accordingly, it was observed in Figure 6 and Table 3 that for C_SSW the IFT was intermediate between CW_+Na2SO4 and that of only composed of CW_+MgCl2. O’Brien, et al. [51] in their studies of hydration of SO₄²⁻ ions, reported that they are surrounded by up to 14 hydration ions, where each hydrogen atom interacts with SO₄²⁻ or the oxygen atom of another water molecule. Their studies indicated that the outer-shell water molecules have free OH [51]. It may be suggested that the possible mechanism where the local OH at the interface may slightly reduce the IFT, which then would promote the transportation of CO₂ into n-decane drop. This is in contrast to that for Mg²⁻ ions, where hydrated ions are tightly packed at the interface area, which resist the transportation of CO₂ across the interface and accumulate at the interface. It is interesting that the presence of both ions brings the equilibrium IFT into a level between the two the individual ions.

Figure 7 clearly illustrates and summarizes the brine interaction described above. It is shown that C_SSW-Na2SO4 and C_SSW+MgCl2 restrict the transfer of CO₂; however, they reduce the IFT of the system, compared to the other CBs, C_SSW, C_{SSW- MgCl2} and CW_+Na2SO4.

4. Conclusions

The CO₂ mass transfer and the interfacial phenomena of CW/n-decane are the primary recovery mechanisms of CWI. The impact of salts on CO₂ mass transfer on IFT has rarely been investigated. The present work, through experimental and numerical methods, addresses the impact of MgCl₂ and Na₂SO₄ presence in carbonated water (CW) on the IFT of CW/n-decane and the mass transfer of CO₂. The experimental work was carried out for pressures between 50–100 bar and at 45 °C. The following conclusions were made from the analysis.

Mg²⁺ ion has shown to reduce both the CB/n-decane IFT (36.5%) and the diffusion coefficient of CO₂ into n-decane, in comparison with CW/n-decane system. It is suggested here that since Mg²⁺ has the smallest ionic radius (0.072 nm), and as a divalent ion it has high hydration energy. It therefore forms a tight bond to the first hydration shell [Mg(H₂O)6]²⁺; accordingly, it has high effective size and when it adsorbs at the interface, it reduces the IFT. In the case of SO₄²⁻, the ionic radius (0.242 nm) is larger than that of Mg²⁺ and has lower hydration energy than Mg²⁺. Furthermore, it is reported that SO₄²⁻ ion is surrounded by up to 14 hydration ions, where each hydrogen atom interacts with SO₄²⁻ or the oxygen atom of another water molecule, indicating that the outer-shell water molecules have free OH groups. It is suggested here that a possible mechanism where the local OH groups at the interface may lightly and locally reduce IFT, which then promote the transportation of CO₂ into n-decane drop. The suggested mechanisms for both ions are supported by observation, where in the dynamic IFT, the equilibrium is reached faster in case of Mg²⁺ compared to that with SO₄²⁻.

Brine effects on altering carbonated water physical processes such as diffusion and IFT have been identified. Moreover, the contribution and proposed mechanisms of the different ions (SO₄²⁻ and Mg²⁺) to the physical process in carbonated water/hydrocarbon have been addressed, which contribute to EOR.