Acs Energyfuels 2c03982

pubs.acs.
org/EF Article
Three-Phase Fluid Flow Interaction at Pore Scale during Water- and

Surfactant-Alternating Gas (WAG/SAG) Injection Using Carbon
Dioxide for Geo-Sequestration and Enhanced Oil Recovery
Satyajit Chowdhury, Mayank Rakesh, Srawanti Medhi, Saket Shrivastava, Rajat Dehury,
and Jitendra S. Sangwai*
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sı Supporting Information
ABSTRACT: Sequestration of CO2 in geologic formations such as

depleted oil reservoirs has emerged as one of the lead solutions to
tackle greenhouse gas emissions to reduce pollution and global
warming. Supercritical CO2 (sc-CO2) injection in oil reservoirs has
proven to be useful as an enhanced oil recovery (EOR) technique
along with the benefits of CO2 sequestration. In this study, a
tortuous microscopic pore scale model was used to study and
investigate the phenomena of water-alternating gas (WAG) and
surfactant-alternating gas (SAG) with sc-CO2. The study scrutinizes
the dynamics of the pore-level phenomenon in the multiphase WAG
and SAG flows at the pore level in detail. Transient computational
fluid dynamics (CFD) analysis was used to study the fluid flow
characteristics of oil, water, and sc-CO2 at different reservoir
pressure and temperature conditions in oil-wet conditions. Governing equations were coupled with EOS (Helmholtz free energy
equation) to capture the viscous and intrinsic properties of sc-CO2 due to variations in pressure and temperature conditions. It was
found that higher oil recovery does not necessarily indicate higher sc-CO2 sequestration and that temperature harms the
displacement mechanism due to unfavorable mobility ratios. Comparing WAG and SAG for the first injection cycle, SAG showed a
more diffused interface between displaced and displacing fluid. The additional oil recovery produced in patches was a result of
pressure oscillations near the blind pores. Moreover, high vorticity promotes greater intermixing between the displacing and
displaced fluid by increasing the rate of interface length. In SAG cases, faster sc-CO2 breakthroughs were observed due to reduced
shear stress along the fluid interfaces, which resulted in higher sequestration values in a given time frame. The CO2 sequestration
volume in SAG cases was found to be approximately 40% more than in WAG experiments. The study confirms that lower values of
oil−water interfacial tension aids in faster and more efficient sequestration of sc-CO2 along with additional oil gain from a given
reservoir.
1. INTRODUCTION goal of 1.5 °C. To accomplish climate goals, we need to

The last few decades have witnessed increasing environmental remove 10 billion metric tons of CO2 per year (GtCO2/yr)
challenges that are brought on by the emergence of new from the atmosphere by 2050. 20 GtCO2/yr must be removed
technologies to increase global economic growth. The most after 2050 and thereafter. Governments across the globe have
threatening of these problems is global warming, which is implemented policies and regulations that are aimed at
brought on by the release of greenhouse gases, mostly carbon reducing CO2 emissions, with a focus on carbon capture and
dioxide. The primary greenhouse gas, carbon dioxide (CO2), utilization (CCU). CCU involves capturing CO2 from
can emerge from several sources, including the burning of fossil industrial processes and using it for various applications,
fuels (in cars, trucks, and power plants), the production of such as enhancing oil recovery, generating byproducts, etc.1
biomass energy, large power plants used in industrial processes,
and more. To address the challenges of CO2 emission, various
mitigation strategies have been developed, including carbon Received: November 24, 2022
capture and storage (CCS) processes. CCS involves capturing Revised: February 18, 2023
CO2 from industrial processes and storing it underground to Published: March 13, 2023
prevent its release into the atmosphere. Nearly all countries
have decided to bound global warming to 2 °C above pre-
industrial levels under the Paris Climate Agreement, with a
© 2023 American Chemical Society https://doi.org/10.1021/acs.energyfuels.2c03982

5270 Energy Fuels 2023, 37, 5270−5290
Energy & Fuels pubs.acs.org/EF Article
The rapid increase in the exploitation of fossil fuels as a source method usually leads to an additional recovery of 15−20%.14,15
of energy has posed an environmental challenge.2 Proper However, not all properties of CO2 are favorable for the EOR
treatment of the produced pollutants, especially greenhouse process. Particularly, the low viscosity of CO2 often leads to an
gases is a major concern. Among these, carbon dioxide (CO2) early breakthrough. This can result in poor sweep efficiency
has been one of the main responsible gas for many and eventually, low recovery.16 The problem of low viscosity
environmental concerns. CO2 accounts for 64% of its share can be mitigated by injecting CO2 through liquid−liquid
in polluting the environment due to greenhouse gases.3 dispersion media such as foams and emulsions.17 In water-
Carbon capture, transportation, and storage for a significant alternating gas (WAG) and surfactant-alternating gas (SAG),
period are one of the potential solutions which can largely gas is injected first, which is followed by water or surfactant
contribute to the reduction of global greenhouse gas solution injection. This typical process is termed a single-stage
emissions.4 Three forms of CO2 sequestration methods have WAG in the case of a gas−water system and SAG for a gas−
been identified by the scientific community: surface mineral surfactant system. If the alternate injection pattern is pursued
carbonation, sequestration in geological subsurface, and ocean in a cycle, the method is termed as multistage WAG and SAG
storage.5 The latter method is in the preliminary stage and can for water and surfactant, respectively. The only difference
endanger the marine ecosystem. Sequestration in geologic between WAG and SAG is the dissolved surfactants in the
reservoirs is the most efficient long-term solution for reducing latter case. Foam is generated inside the reservoir rock due to
CO2 emissions to the atmosphere.6 Moreover, discoveries of the contact of surfactant and gas, subsequently increasing the
several naturally occurring CO2 reservoirs have encouraged density and viscosity of the gas. The mobility of gas molecules
researchers to study favorable conditions for CO2 capture and is lowered owing to which the relative permeability of gas is
storage processes.7 On the contrary, after 40 years of research reduced thereby limiting the ill effects of overriding and
and application history, the sequestration processes in channeling. WAG and SAG in single or multiple stages can be
reservoirs and their associated controlling parameters are still adopted to increase displacement efficiency, fluid contact, and
not well understood.6 The injection of CO2 in oil reservoirs for travel time inside the reservoir.18 The application of CCS
enhanced oil recovery methods (EOR) has been recognized as technologies, including SAG/WAG injection, and their impact
a sustainably viable solution for restraining greenhouse on CO2 sequestration have also been explored through
emissions and meeting the global energy demand.8 CO2- computational fluid dynamic (CFD) simulations, experimental
driven injection methods currently contribute about 5% of the studies, and field application investigations. It has been found
total oil production in the United States.9 van Alphen et al.10 that alternating injection of surfactant solution and CO2 may
provide a comprehensive analysis of the development of greatly enhance displacement efficiency and improve the oil
carbon capture and storage (CCS) technologies in the United recovery factor (RF) by 14%.19 A typical pattern for the fields
States between 2000 and 2009. The authors used an under evaluation is an enhancement in oil recovery of between
innovation systems perspective to evaluate the buildup of a 5 and 10% of the oil that was initially present. Another study
national CCS innovation system and to identify the key investigated the effectiveness of different chemical and thermal
determinants of its success. The results show that the United enhanced oil recovery methods, including SAG, WAG,
States has achieved a leading role in the development of CCS surfactant and foam flooding, and carbon dioxide (continuous
technologies and that the extensive knowledge base and and cyclic), on tight oil reservoirs. The results showed that a
networks accumulated over the years have not yet been fully 3.5% surfactant concentration, 0.15 pore volume (PV)
utilized by entrepreneurs. However, the authors recognize that surfactant slug size, and 0.75 PV total surfactant injection
the buildup of the innovation system has entered a critical volume were the optimum parameters for injectivity perform-
phase and simultaneously identified several barriers that need ance. SAG provided the highest oil recovery factor of 54%,
to be addressed to continue positive system dynamics. A policy while WAG had a recovery factor of 46%.20 Likewise, the
strategy consisting of four main elements is proposed to viscosity and mobility of water are increased as a result of
stimulate learning, facilitate integration and collaboration, which piston-like displacement of oil commences that increases
create financial and market incentives, and regulate and breakthrough time and displacement efficiency.21
communicate effectively. The authors conclude that a nation- CO2 is often used as the gaseous component during this
wide cap-and-trade system, along with sound alterations of operation. If the reservoir meets the supercritical conditions for
short-term financial incentives, is crucial for the development CO2, the flow of CO2 turns out to be in a supercritical state.
and commercialization of CCS technologies in the United Figure 1 represents the phase diagram of CO2 for varying
States.10 temperature and pressure conditions.22 CO2 behaves as gas at
Deployment of enhanced oil recovery (EOR) techniques to standard pressure and temperature conditions and transforms
increase the production in depleted reservoirs is one of the to dry ice at low-temperature and high-pressure conditions. At
solutions that is being used to maximize oil recovery and satisfy elevated pressure and temperature conditions, CO2 exists in a
the immediate energy demand. CO2-EOR is one of the most liquid state and with an increase in pressure and temperature
efficient methods to recover oil from the reservoir and help beyond a critical point, supercritical nature dominates (1070.3
CO2 sequestration. It involves three major phenomena;11 the psia and 304.21 K).
dispersal of CO2 into the crude oil trapped in porous reservoir To have a refined understanding of CO2-EOR, one must
rocks, the reaction of CO2 with formation minerals,12 and the understand the properties of CO2 and the principles of
change in pore pressure and its effects on rock mechanics. CO2 flooding techniques. Under conditions of 14.7 psia and 273.15
is considered a favorable fluid for EOR injection methods due K, CO2 is about 1.5 times denser than atmospheric air.23 In
to its low minimum miscibility pressure with hydrocarbons.13 shale and carbonate reservoir rocks, CO2 increases water
Injection of CO2 in a reservoir greater than 7.38 MPa and viscosity by forming carbonate acid and thus increasing sweep
304.21 K renders CO2 in a supercritical state. This technique efficiency.24 In conditions above critical pressure and temper-
of incorporating supercritical CO2 (sc-CO2) as an EOR ature, sc-CO2 behaves as a phase with a density close to that of
5271 https://doi.org/10.1021/acs.energyfuels.2c03982
Energy Fuels 2023, 37, 5270−5290
is injected first, then water, and the process is repeated in a

cycle for a certain number of times. This process is suitable for
most reservoirs with permeability contrasts among various
layers. The primary goal of WAG injection is to increase oil
recovery by improving both macroscopic and microscopic
sweep efficiency, maintaining reservoir pressure, reducing the
viscosity of the oil due to gas dissolution, slowing down the gas
breakthrough, changing fluid composition, and reducing
residual oil saturation by the flow of three phases and reduce
the effects related to relative permeability hysteresis. Drainage
and imbibition must take place in the reservoir either
concurrently or alternately for WAG injection to occur. The
WAG approach also offers better mobility control, extending
the life of gas projects and maximizing oil recovery. Due to its
lower pressure requirements for miscibility and increased
sweep efficiency, carbon dioxide gas is typically used as a
displacing gas.27 Due to the low interfacial tension between the
oil and gas phase, the gas injection has a greater microscopic
displacement efficiency than the water injection efficiency.28
Figure 1. Phase diagram of CO2 under different pressure and
temperature conditions. Several studies have been performed to investigate the total oil
recovery and the effect of control parameters on the sweep
performance in WAG processes. Stern et al.29 investigated the
liquids. Depending upon reservoir geological conditions and multiple-contact miscible CO2 WAG and the effect of injection
reservoir fluid properties, different EOR techniques involving parameters and fluid properties. For water-wet reservoirs,
CO2 have been developed in the past years. These include recovery of oil at high WAG ratios was not significant due to
continuous sc-CO2 injection, sc-CO2 WAG, tapered WAG, and lower sweep efficiencies.29 A study by Khan et al. brings out
WAG followed with gas.9 Several studies and projects have the advantages of the WAG displacement process in stratified
been conducted on the implementation of CO2 EOR for heterogeneous reservoirs having high heterogeneity due to
improving oil recovery. A total of about 60 projects of CO2 permeability and porosity variation. The WAG performance
EOR were there in the USA in 1996 and in Canada, the was calculated in terms of total oil recovery, sweep efficiency,
number was around 40.25,26 gravity effects, hysteresis, uncontacted oil saturation, and gas−
Figure 2 shows a schematic diagram of the water-alternating oil ratio among others using high-resolution compositional
gas sc-CO2 EOR process. In the WAG process, alternating gas simulations. The permeability variation decreases ultimate oil
Figure 2. Schematic representation of sc-CO2 WAG EOR process.
Energy Fuels 2023, 37, 5270−5290
recovery even though showing initially faster oil recovery. simulation of coupled fluid flow and heat transfer in CO2
Hysteresis has an insignificant effect on both homogeneous injection in a microporous domain. The effect of variable fluid
and heterogeneous reservoirs. The simulation overestimates properties was investigated on the performance of sc-CO2
2−3% of overall oil in place (OOIP) for heterogeneous injection under steady-state conditions.48 The effect of
reservoirs as the model does not consider uncontacted oil different capillary and gravity numbers on CO2 EOR in oil-
saturation. Overall, the economic analysis does not recom- wet microporous media below critical point conditions was
mend miscible WAG for homogeneous reservoirs compared to studied by Zhu et al.49 However, it is important to take note
reservoirs with heterogeneity.30 Another study scrutinized the that the supercritical nature of CO2 was not considered in
implementation of CO2 WAG in a heavy oil reservoir and also these studies. Bandara et al.50 studied the capillary trapping
compared its technical viability with N2 WAG.31 The viscosity mechanism of sc-CO2 in geo-sequestration using a smoothed
reduction due to oil swelling was found to be much less for the particle hydrodynamic model. The division trapping mecha-
N2-oil system compared to the CO2-oil system. Jiang et al. nism was found to be the most successful trapping mechanism
examined the effect of salinity on the WAG CO2 process.32 It for CO2 sequestration.50 In another CFD study, the invasion
was found that WAG required less amount of CO2 to reach the profile of CO2 was investigated, where the effectiveness of the
same recovery as a conventional gas injection system. Further, invasion pattern of sc-CO2 was expressed in terms of a new
a laboratory investigation on near-miscible CO2 WAG was dimensionless number (ε) known as stabilizing factor. It was
conducted by Fatemi and Sohrabi. The study showed that observed that ε for light oil was highly affected at lower
WAG had a better performance than continuous water velocities (0.0005 m/s). However, for heavy oil, the relation-
injection and continuous gas injection in both water-wet and ship was reversed that showed sensitivity at lower velocities
mixed-wet systems.33 Larsen et al. first proposed the use of a (0.0005 m/s) compared to higher ones (0.005 m/s).51
micromodel to investigate the three-phase flow process during Furthermore, Chaudhary et al. analyzed the trapping
WAG injection.34 SAG process has a significant effect on mechanism of supercritical CO2 in the sc-CO2 brine system
relative permeability. A combination of alkoxy sulfate and along with the effect of grain wettability and shape.52 Several
olefin sulfonate was used as a surfactant for SAG. The two- more experimental and numerical studies have been performed
phase relative permeability was obtained from Sendra software, by different researchers to understand CO2 displacement in
and JBN/Welge theory by Grader and O’Meara was applied to water and carbonated water system using micromodels.53−56 A
calculate three-phase relative permeability. The relative CFD model developed by Afzali et al. simulates a porous
permeability of each phase in a three-phase flow depends on media with fractures for water-alternating gas injection process
the saturation of all fluids present in the system contrary to a with the help of COMSOL Multiphysics for EOR applications
two-phase flow where relative permeability depends only upon using maroon crude as oil phase, synthetic brine, and CO2 as
the saturation of the corresponding phase. Water relative gas phase. The simulation was carried out at 100 °C and
permeability does not depend upon the presence of surfactant. atmospheric outlet pressure with a WAG ratio of 1:1 and a slug
Surfactant reduces gas viscosity, hence gas relative permeability size of 0.5 PV. The simulation was compared with previously
for SAG compared to WAG. Again the author mentioned that available experimental data, and the maximum absolute error
three-phase relative permeability cannot be predicted by any was observed to be 12% for oil recovery. Hysteresis, increasing
correlations as they do not consider the gas trapping by the fracture aperture, including gravity forces, lowering the IFT
surfactant and interfacial tension (IFT) reduction between oil/ between phases and decreasing permeability increases the
water.35 Recently, chemically enhanced water-alternating gas ultimate oil recovery rate while the effect of fracture inclination
(CWAG) has gained a lot of traction as an EOR technique. angle on recovery rate is insignificant.57 Properties of CO2 are
CWAG injection is a combination of two tertiary oil recovery known to vary greatly due to a small change in pressure and
techniques, i.e., alkaline, surfactant, and polymer additives temperature. Hence, the flow properties even at supercritical
(ASP) as a chemical slug and WAG. This advanced technique conditions are subjected to change at various reservoir
is used to decrease the water-blocking phenomena and increase pressures and temperatures. This sensitivity has not yet been
the WAG mobility with the help of surfactant and polymer captured numerically in any of the recent studies, especially for
respectively. The CWAG method significantly reduces the IFT a multiphase flow regime. It is known that CO2 injections are
and provides more mobility to residual oil in place (ROIP) generally coupled with water or surfactant solution injections
after secondary recovery giving 26.6% more recovery (WAG and SAG, respectively) to improve sweep efficiencies.
compared to WAG. The experimental data was history How the sc-CO2 interacts with water and oil with and without
matched with a commercial simulator to optimize the surfactants is not known, which is vital for enhanced CO2
experiments and sweep efficiency of residual oil.36 sequestration in reservoirs. The effectiveness of this method
Computational fluid dynamics (CFD) has proven to be an can be better understood by conducting a pore scale
effective tool recently to understand flow behaviors. Many investigation which shall allow us to comprehend the
studies have been conducted to characterize flow concerning interfacial dynamics of the fluid displacement phenomenon.
drilling fluids, fracturing fluids, flow in pipelines, and To the best of our knowledge, no research has been conducted
others.37−42 Apart from experimental investigations, pore- to investigate pore-scale flow characterization of sc-CO2 WAG
scale numerical studies have been an evident method to study and SAG through the CFD approach as likewise stated by
multiphase flow behavior in various upstream processes.43−46 Jafari et al.58
Several studies have instated CFD as an efficient technique for This research presents numerical modeling and simulation
CO2 EOR modeling. Safi et al. examined the simulation and of pore scale single-stage CO2-WAG and SAG methods
optimization of CO2 at the macroscale in a Permian basin through a porous path using the CFD technique. A series of
reservoir.47 The effect of injection profiles and parameters like transient numerical simulations have been performed to study
well distance on recovery factor was better understood which is the effect of different pressure and temperature conditions on
vital for optimizing recovery. Choi et al. studied the numerical oil recovery and CO2 sequestration. The investigation also
Energy Fuels 2023, 37, 5270−5290
Figure 3. Natural geological representation of pore geometry where the flow domain is surrounded by unsorted grain distribution.
captures the effect of the dynamic intrinsic property of sc-CO2 between two fluids. An equation of state model was used
(due to changes in reservoir pressures and temperatures) and (described further below) which addressed the changing
its interaction with oil and water (which vastly depends on physical parameters due to changes in pressure and temper-
reservoir pressure and temperature) by coupling an equation of ature of the flow environment. The momentum equation is
state (EOS) with flow governing equations. The study further given by eq 1, as follows59
considers the surface forces generated during a multiphase flow
in a microchannel. Investigation into the flow dynamics of D 1
v
= p+ · T + Fst
these immiscible fluids (oil, water, and CO2) is of utmost Dt (1)
importance, especially for screening injection profiles at a given
reservoir pressure and temperature. A deeper understanding of The mass continuity equation is expressed as eq 2 59
flow patterns at the pore level would offer scope to optimize D
and manage oil production as well as geo-sequestration of CO2 + ( ·v ) = 0
Dt (2)
with better efficiency.
3
where ρ [kg/m ] is density, v [m/s] denotes the fluid flow
2. GEOMETRY AND MODEL CONSIDERATION velocity, ∇·T is the stress deviator tensor, Fst [Pa/m] is the
Figure 3 shows the natural geological representation of pore interfacial tension force term which is modeled by the
geometry used for the study. where the flow domain is Continuum surface force model (CSF),60,61 and p and T
surrounded by unsorted grain distribution. The porous model refer to pressure energy and viscous stress tensor, respectively.
is 190 μm × 31 μm (length × width), which comprised a two- The CSF model is well suited to numerically model surface
dimensional (2D) linear porous network having zones of low forces at fluid interfaces by the Eulerian approach. The
and high permeability in the form of geometric constrictions constraint of explicit treatment for surface tension limits the
(Figure 3). Flow in porous media is a result of effective time step to small values (Δt ∝ (Δx)3/2). Implicit formulation
porosity in the medium that represents interconnected pores. of surface tension would remove this constraint. The interfacial
Along the flow path, the joining interface between adjacent tension force per unit volume is calculated as given in eq 3 62
grains produces blind pores wherein the residual oil generally k1 1
remains trapped. Furthermore, blind pores of different sizes Fst = 1
and depths were assigned at the intergranular junction. These (
2 1
+ 2
) (3)
characteristics considered in this geometry are typically found
in an oil reservoir rock. The study presented in this manuscript Here, σ is the coefficient of surface tension, k1 is the interface
aims to characterize flow in a single pore throat that is curvature, α1 represents the volume fraction of phase 1, and ρ1
nonuniform and tortuous. This geometry consideration is and ρ2 refer to the densities of phase 1 and phase 2,
intended to emulate a micro-dimensional pore that would respectively. Interface curvature k is modeled by (eq 4)63
generate capillary-driven fluid flow.
The flow domain as illustrated in Figure 3 was initially k= ( . n) (4)
completely saturated with oil in the pore spaces surrounded by where n̂ represents unit vector normal to the interface surface.
the rock matrix. Initially, water/surfactant is injected from the This unit normal vector is calibrated by the angle of contact
inlet and then injection of sc-CO2 was commenced. The (θ1) between the solid surface wall and the cell next to it. At
recovery of oil and breakthrough information was made from any live cell next to the wall, the unit vector n̂ is (eq 5)63
the right side of the flow domain, which was assigned as the
outlet. n = n1 cos 1 + t1 sin 1 (5)
3. COMPUTATIONAL MODEL where n̂1 and t1̂ are normal and tangential vectors, respectively.
3.1. Governing Equations. A multiphase model was used The volume of fluid (VOF) model was used to track the
to study the flow behavior of the three fluids; oil, sc-CO2, and interface between the phases. Interface modeling between any
water. Fluid flow was characterized by solving Navier−Stokes two phases is done by solving eq 6 64,65
(N−S) equation for momentum and mass continuity equation. ij 1 yz
Furthermore, the surface/interfacial tension model was jj zz + . (v 1) = 0
coupled with N−S to take account of surface forces existing k t { (6)
Energy Fuels 2023, 37, 5270−5290
Figure 4. (a) Validation of CFD simulations for 4 and 6 mm bubbles; (b) time evolution of 4 mm bubble in the tank;68 (c) position of the
meniscus with time validation from analytical solution; (d) position of the meniscus at three consecutive time steps; (e) movement of gas in liquid
phase, where UG = 0.035 m/s, UL 0.09 m/s surface tension = 0.031 N/m water wall contact angle = 0° (UG and UL are superficial velocities for gas
and liquid, respectively);71 and (f) evolution of liquid−liquid displacement where Vc = Vd = 1.197 mm/s; μc = 44.1 mPa·s, μd = 1.05 mPa·s, Re =
0.00266, Ca = 0.0023 (μc and μd are viscosities of continuous and dispersed phases, respectively, Re is Reynolds number, and Ca is a capillary
number).72 Reproduced with permission from Chowdhury et al.51 Copyright [2022] Publisher Springer Nature.
Energy Fuels 2023, 37, 5270−5290
Here, α1 represents the volume fraction occupied by phase 1 in 3.3. Numerical Validation. This study deals with the
a cell. Furthermore, heat transfer was modeled by the energy interaction of oil, water, and sc-CO2 in a porous micro-path.
equation as given by eq 7 64,65,77 Hence, four validation concerning sc-CO2-liquid (water) and
oil−water are being presented. The first was in form of a gas
( E) + ·( ( E + p)) bubble rising in a water tank wherein the terminal velocity of
t the gas bubble was the validation parameter. This approach
was considered especially due to the tendency of sc-CO2 to
= ·(Keff T hj Jj + ( · )) + S h (7) expand like a gas bubble. Furthermore, the second approach
validates through the position of the meniscus, where a wetting
where Keff is the effective conductivity [S/m]. The terms on phase (water) displaces a nonwetting phase (oil) in a straight
the right side represent heat transfer due to conduction, microfluidic channel representing an imbibition process.
diffusion, and viscous dissipation respectively. Jj⃗ is the diffusion Figure 4a draws comparative results between the analytical
flux of species, Sh is the source term. The change in viscosity model proposed by Krishna et al. and CFD simulations for the
due to pressure work and viscous heating is modeled using eq first validation.68 The analytical model which is validated with
7. experimental results is a modified form of the Mendelson
A new equation of state (EOS) for CO2 was considered for equation.69 The model takes the wall effect into account by
the study which is explicit in the Helmholtz free energy introducing a scale factor (SF). The equation is given by
equation. 66 This equation is considered an accurate
representation of the pressure−density−temperature relation. Vb = 2 / l db + gdb/2 SF; SF = [1 (db/DT )2 ]3/2
Helmholtz energy equation considers two independent
variables density (ρ) and temperature (T). The equation has (11)
two constituents, namely, the ideal gas behavior (Φ°) and where Vb is the bubble rise terminal velocity [m/s], db is the
residual behavior component (Φr). It is expressed as (eq 8)66 diameter of bubble [m], and DT refers to the tank diameter
[m]. The SF underlines the significance of DT on the bubble
A( , T ) r rise velocity. The numerical model in the study is validated
= ( , )= °( , ) + ( , )
RT (8) from eq 11 which takes the bubble radius of 3−17 mm into
consideration. For CFD simulations, a tank diameter of 50 mm
where δ and τ are reduced density and inverse reduced
filled with water and air bubbles of diameters 4 and 6 mm were
temperature, respectively. The ideal gas component is
considered. No-slip boundary conditions were imposed on the
expressed (eq 9)66
bottom and top walls of the tank and free-slip boundary
°( , ) = ln( ) + a1° + a 2° + a3° ln( ) conditions were set up on vertical boundaries. Initially, both
bubbles were set at a height of 10 mm from the bottom of the
8
i°)
tank. Figure 4b represents the contour plots of the transient
+ ai° ln[1 e( ] evolution for the rise of a 4 mm bubble inside the water tank. It
i=4 (9) was observed that as the bubble size increases, the helical
where the coefficients ai° and θi° are taken from Table 27 of pathway followed during the bubble rise vanishes. The
Span and Wagner.66 The residual fluid part of Helmholtz comparative study concluded with an error of less than 5%
energy is given by (eq 10)66 between both models for the two cases.
The second scheme of experimental validation (see Figure
7 34
r di ti di ti ci 4c,d) for liquid−liquid displacement was performed using the
= ni + ni e imbibition equation and fluid properties stated by Guo et al. in
i=1 i=8 a microchannel.70 The equation is given as (eq 12)
39
2
di ti i( i) ( )2 r cos( )
+ ni e i i w n
(x 2 xo2) + n L(x xo) = t
(12)
i = 35 2 6
42
bi Ci( 1)2 Di ( 1)2 where μw and μn are viscosities of the wetting and nonwetting
+ ni e
i = 40 (10) phases, respectively, L denotes the length, r denotes the radius
of the capillary, θ is the contact angle, σ is surface tension, and
where ni, di, ti, ci, αi, ∈i, βi, γi, bi, Ci, and Di are coefficients and t is time in seconds.
exponents. Refer to Table 31 of Span and Wagner for the A horizontal 2D pipe section of length 150 μm and width 10
corresponding values.66 μm was used for the simulation. The wettability conditions
3.2. Simulation Model. The finite volume method (FVM) were set to a 60° contact angle and absolute imbibition
was used to solve the fluid flow equations and energy conditions were simulated. The evolution of meniscus position
equations. The geometry domain was discretized into finite with time was analytically calculated and validated with
nonoverlapping elements.67 The fluid flow equations (PDEs) simulation results. Figure 4d represents the position of the
were integrated over these element volumes and transformed meniscus inside the 2D horizontal pipe sections at three
into algebraic equations. Compared to finite difference (FDM) different time steps.
and finite element method (FEM), the conservative nature of Experimental observations of gas−liquid (G−L) and liquid−
FVM makes it a preferred method for CFD numerical liquid (L−L) immiscible interactions were taken from studies
simulations. Furthermore, FVM is compatible with nontrivial conducted by Guo and Chen, and Li et al.71,72 These
and user-defined boundary conditions because the unknown experiments draw relevance to this research owing to their
variables are calculated over centroid rather than on boundary flow profiles at low capillary numbers through microchannels;
faces. and the fact that CO2 behaves as gas and liquid in a
Energy Fuels 2023, 37, 5270−5290
supercritical state. The simulation results produced a close at the inlet. CO2 and water are injected at the same rate.
match between the advancing interface of the dispersed phase Wettability conditions were set to oil-wet with an oil−water-
of gas in liquid (Figure 4e) and liquid in liquid (Figure 4f). wall contact angle of 60° as supercritical CO2-EOR is more
3.4. Geometry and Meshing. Figure 5 presents the actual efficient in oil-wet media compared to water-wet.73 In the case
flow domain, geometry, meshing, and mesh metrics considered of oil-wet media, after secondary recovery, oil remains in a
continuous phase owing to which, sc-CO2 can directly interact
with the trapped oil. For thermal energy boundary conditions,
walls were set isothermal, the inlet temperature was kept 10 K
higher than the walls, and the outlet temperature was constant
at 306 K.
3.6. Fluid Properties and Phase Interactions. The
broad objective of the study was to evaluate the differences and
mechanisms of oil recoveries in WAG and SAG processes at
different reservoir pressure and temperature condition. The
design of parameters/experiment was taken into account
considering the fact that sc-CO2-EOR is typically more
effective in oil gravities higher than 25° API.23 Hence, viscosity
and density magnitudes of oil considered in the study were
0.091378 Pa·s and 854 kg/m3 which were constant for all of
the cases.74 Supercritical fluid generally behaves as an excellent
solvent. To capture the miscibility of sc-CO2 with oil and water
and to study the interpenetration of liquid−liquid/gas
interfaces, the coefficients of surface tension between sc-CO2
and oil and sc-CO2 and water were considered ultralow
Figure 5. (a) Extraction of flow domain from the naturally (0.0015 N/m).75,76 However, the coefficient of surface tension
represented tortuous geometry and (b) magnified view of free between oil and water was set at finite values (as described in
triangular mesh configuration along with mesh details and qualities. Table 1) depicting realistic scenarios of water and surfactant
solution flooding. Temperature and pressure were set above
for the simulations (Figure 5a,b). A tortuous path was created critical points to keep the CO2 in a supercritical state. Beyond
for the study. A triangular meshing scheme was used for mesh 363 K, the viscosity of sc-CO2 reaches a plateau region. There
generation. A magnified view of generated mesh and mesh are no noticeable changes in viscosity with a temperature rise.
matrices can be found in Figure 5b. Mesh sensitivity study and Hence, we have limited our temperature range to 353 K.
independency are reported in Figure 6. The volume fraction of Helmholtz equation of state for CO2 by Span and Wagner has
oil inside the 2D tortuous surface domain was considered as been used to model the thermodynamic properties of sc-CO2
the parameter for the mesh sensitivity study. that consider alterations in physical properties with changes in
3.5. Boundary Conditions. Velocity inlet and pressure pressure and temperature.66 Table 1 represents all of the cases
outlet boundary conditions are applied to the inlet and outlet considered for the study.
of the flow of water and sc-CO2. For walls, no-slip boundary 3.7. Simulation Strategy. This CFD investigation uses
conditions were adopted. Fluent expression language was used VOF for its simulation to track immiscible interfaces along the
to define the dynamic boundary conditions for volume fraction flow front. Figure 7 summarizes the steps that are followed for
this numerical study. Semi-Implicit Method for Pressure
Linked Equations (SIMPLE) algorithm was implemented for
pressure-velocity coupling. The implicit method was used for
the formulation of numerical solutions. Second order upwind
discretization scheme was used for the spatial discretization of
density, momentum, and energy. A transient simulation
approach was used to study the time-dependent properties.
Second order implicit algorithm was used for time stepping.
The implicit nature of the algorithm helps to stabilize the
solution, particularly for compressible flows, which can exhibit
complex flow phenomena and sudden changes in flow
conditions. Compressible flows often involve high Mach
numbers, where the flow velocity is a significant fraction of
the speed of sound. The Second Order Implicit algorithm is
well suited for handling these high Mach number flows,
providing accurate and stable solutions. Compressible flows
can exhibit shock waves and expansion waves, which can be
difficult to simulate accurately. These phenomena were also
observed and discussed in our study. The Second Order
Implicit algorithm can handle these complex flow phenomena,
Figure 6. Surface integral (area-weighted average) for the volume providing a more accurate and stable solution compared to
fraction of oil with respect to time inside the flow domain at different first-order methods. The solution was initialized from the
mesh refinement conditions. velocity inlet. The flow media was initially 100% saturated with
Energy Fuels 2023, 37, 5270−5290
Table 1. Fluid Properties and Reservoir Pressure and Temperature Conditions Considered in This Studya
oil properties reservoir properties
si. no. representative cases oil viscosity [Pa·s] oil density [kg/m3] reservoir pressure [psi] reservoir temperature [K] IFT [N/m]
1 WAG 1 0.091378 854 3500 323 0.036
2 WAG 2 0.091378 854 5000 323 0.036
3 WAG 3 0.091378 854 3500 353 0.036
4 WAG 4 0.091378 854 5000 353 0.036
5 SAG 1 0.091378 854 3500 323 0.015
6 SAG 2 0.091378 854 5000 323 0.015
7 SAG 3 0.091378 854 3500 353 0.015
8 SAG 4 0.091378 854 5000 353 0.015
a
Sl. No. 1−4 represent WAG, whereas 5−8 represent SAG cases.
Figure 7. Flowchart of VOF method used for this study.
oil. To ensure accuracy time step size of 5 e−5 was set. It is to using sc-CO2. From Figure 8a, it can be observed that water
be noted that VOF is not a stand-alone flow solution technique breakthroughs at the outlet prior to sc-CO2 injection for WAG
but rather an advection scheme that enables tracking the form 1 and WAG 2 are similar. However, a delayed response in
and location of the interface. It is necessary to solve each of the maximum water cut can be seen for WAG 1 compared to
Navier−Stokes equations independently to determine how the WAG 2. For WAG 3 and WAG 4, the water breakthrough time
flow moves. Errors in the estimation of the surface tension is relatively greater than the former two. The fractional flow of
force at the interface lead to front-capturing techniques like the water at the outlet is least for WAG 2 among others. Since, the
VOF and Level-Set (LS) method to create interfacial spurious residence time of water inside the pore geometry is the highest
currents in two-phase flows when the characteristics of the two for WAG 3, the increase in RF with time (see Figure 8b) is less
phases are greatly different. Special handling is necessary to compared to WAG 2 which bears the least residence time for
lessen such spurious currents to solve such flows more water. It is noteworthy to state that the RF is nearly
effectively. In this study, the numerical solution strategy has indistinguishable at the time of maximum water cut for all of
been improved by adding smoothening loops and better the cases. Nevertheless, the RF of oil during sc-CO2 shows a
property averaging techniques. recognizably different trend for all of the cases. WAG 1
displays the highest amount of sc-CO2 (Figure 8c). With a
4. RESULTS AND DISCUSSION higher fractional flow of water, lower RF of oil, and the highest
Simulation studies were conducted under two conditions. The sc-CO2 sequestration for WAG 1; it is fair to state that the
first set of simulations represents a single-stage alternate interaction of sc-CO2 with water is significantly higher than the
injection of water and sc-CO2 (single stage, WAG) while the interaction of sc-CO2 with oil. This can be confirmed by Figure
second set illustrates a single-stage alternate injection of 8d, where the ultimate volume fraction of water inside the flow
surfactant solution and sc-CO2 (single stage, SAG). The domain is less for WAG 1. Figure 8e represents the variation in
environment for the study was defined as oil-wet with an oil− the sc-CO2 cut at the outlet where a highly unsteady and
water surface contact angle of 60°. The study parameters were discrete trend can be noticed.
recovery factor (RF) of oil, water/surfactant solution break- The effect of temperature and pressure can be distinctly
through, recovery factor of water, amount of sc-CO 2 observed on in situ oil viscosity (Figure S1a−d, Supporting
sequestrated, and sc-CO2 breakthrough at the outlet. Information). The viscosity of oil in the case of WAG 2 was
4.1. Single-Stage Water-Alternating Gas. Figure 8 higher than that in WAG 1 (Figure S1a,b) due to an increase
shows the details such as fractional flow, recovery of oil, and in pressure. The least viscosity due to high temperature and
CO2 sequestration during the single-stage WAG injection low pressure was shown by WAG 3 (Figure S1c). WAG 4,
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Figure 8. (a) Fractional flow of water at outlet vs time for water breakthrough, (b) recovery factor of oil vs time, (c) surface integral of sc-CO2
sequestration inside flow domain vs time, (d) surface integral of water volume fraction inside flow domain vs time, and (e) fractional flow of sc-CO2
at outlet vs time for the sc-CO2 breakthrough.
which bears high temperature, shows a greater viscosity the contrary, a stable interface was perceived for WAG 3
compared to WAG 3, which is a result of an increase in (Figure 10c) which generates the desired piston-like displace-
pressure. The change in these viscosity profiles due to ment of oil from the pore spaces.
temperature dominates the mobility of oil and consequently Figure S2 (Supporting Information) depicts the time
the water breakthrough. Hence, an early breakthrough can be evolution of the water−oil interface in WAG 2 (a−d) and
seen for WAG 2 and WAG 1 compared to WAG 3 and WAG WAG 3 (e−h). The change in interface shape can be observed
4. Furthermore, this can also be visualized in the oil recovery as the waterfront passes through different geometrical
curves where WAG 3 and WAG 4 have a delayed ultimate boundaries. Although, the mechanism of displacement bears
recovery during the water injection step (Figure 8b). crucial distinction among the four WAG cases; water flooding
Figure 9a−d represents the microscopic displacement in had no significant impact on additional recovery (∼63%) at
front of a water flood. An oil having similar physical and the end of the water flood. Once a stable trend was achieved in
chemical properties exposed to different pressure and temper- the oil recovery factor, water injection was terminated (Figure
ature conditions will yield dissimilar positions of waterfront at 8b) and injection of sc-CO2 was commenced.
any given time and space. Here, the resident time of water was The compressibility of sc-CO2 is higher than that of oil
least for WAG 2 (Figure 9b) compared to other cases (Figure owing to which the effect of pressure is significantly greater for
9a,c,d). It also appears to have an elongated viscous front the former case. In WAG 2, the reservoir pressure was higher
(viscous fingering) compared to other cases in which there was than that of WAG 3. Consequently, the viscosity of sc-CO2 was
a thick interface within which the water volume fraction considered to be substantially greater for WAG 2. This
changes from maximum to minimum (Figure 10b). This condition provides better mobility as the viscosity contrast is
phenomenon was characterized by a large amplitude of viscous more favorable for WAG 2 compared to WAG 3 which has
fingers. Similar circumstances can also be observed for WAG 1 been subjected to low pressure and high temperature. This
and WAG 4 with less intensity of fingering (Figure 10a,d). On effect is visualized in the magnified view of the lower isolated
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Figure 9. Water injection front at an instantaneous time of 0.008 s for (a) WAG 1, (b) WAG 2, (c) WAG 3, and (d) WAG 4.
Figure 10. Viscous fingering (advancing waterfront) at the start of water injection for (a) WAG 1, (b) WAG 2, (c) WAG 3, and (d) WAG 4.
pore in Figure 11a,e. Here, due to the favorable mobility ratio, temperature. WAG 3 simulating under higher reservoir
the interaction between sc-CO2 and oil was greater for WAG 2. temperature conditions has lesser viscosity of water than that
The effect of reservoir pressure on water viscosity was in WAG 2. This leads to a more blunt viscous finger interface
insignificant due to its incompressible nature. Hence, the in WAG 3 compared to WAG 2 (Figure 11a,b,e,f). Another
driving factor for the viscosity change of water is the reservoir parameter relating to interface mixing is the vorticity
Energy Fuels 2023, 37, 5270−5290
Figure 11. Evolution of sc-CO2, oil, and water interface with time (0.014−0.017 s) after the completion of water injection: (a)−(d) for WAG 2 and
(e)−(h) for WAG 3 cases. Blue signifies water, green indicates trapped oil, and red represents injected sc-CO2 as indicated by phase-id contours.
Figure 12. Final phase distribution of oil, water, and sc-CO2 at t = 0.032 s (end of simulation) for (a) WAG 1, (b) WAG 2, (c) WAG 3, and (d)
WAG 4. Blue signifies water, green indicates trapped oil, and red represents injected sc-CO2 as indicated by phase-id contours.
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Figure 13. Residual oil stripping mechanism trapped in the pores spaces due to the injection of sc-CO2 for WAG 4 at (a) 0.016, (b) 0.017, (c)
0.018, (d) 0.019, and (e) 0.020 s.
magnitude which heuristically measures the local rotation of Mach number was considered as a parameter to study the
the fluid parcel. A higher magnitude of vorticity increases the fluid parcel velocity profile and intermixing of phases. In Figure
rate of interface growth length which indicates an enhanced S3 (a−d, Supporting Information), stable contours of Mach
degree of mixing between two fluids. The recovery of residual number were obtained near the inlet part of the pore structure.
oil highly depends on the degree of interaction between the This can be correlated to the WAG 1 phase-id profile in Figure
two fluid layers. This interaction can be quantified through 12a. In this region, no further scope of additional oil recovery
vorticity magnitude as illustrated in Figure 11c,g. The from the pores was possible with the injection of sc-CO2
magnitude of vorticity is higher in the case of WAG 2 (residual oil shown in green, Figure 12a). We can notice a
compared to WAG 3 which leads to a better intermixing of oil nearly single-phase flow with no disturbance rising due to
and sc-CO2 at the dead-end pores. Similar observations were mixing interfaces from residual oil or water. However, a higher
also found by Waitz et al.,78 where they have extensively Mach number can be observed in the downstream part of the
described the mechanism behind it.78 Improved distribution of pore structure which was due to the recovery of oil and water
vorticity along the walls was observed in WAG 2 due to which in progress, as displaced by sc-CO2. Contrastingly, for WAG 2,
higher recovery rates were observed at a particular time, unlike, WAG 3, and WAG 4 (Figure S3b,d), high intensity of Mach
WAG 3 (Figure 8b). Augmentation in mixing is due to the number can be found in the inlet and further downstream parts
induced strain-rate fields that are allied with vortices. In of the pore structure. We can fairly conclude that these were
general, they contribute to enhancing the driving potential for due to the ongoing recovery of oil and water as the injection of
mixing across interfaces as well as interface areas. sc-CO2 is in progress. Thus, the interpenetration of interfaces
For low reservoir pressure conditions, the room for CO2 can still be observed. Due to high-temperature and low-
sequestration inside the pore spaces is less. sc-CO2 flooding is pressure conditions in WAG 3, the sc-CO2 injection was
more efficient at low-temperature conditions.79 This phenom- commenced at lower viscosities which led to high Mach
enon was observed in the case of WAG 1 simulating under number profiles. This can be confirmed by Figure 11h, where
low-pressure and temperature conditions (Figures 12a and 8c). the loss of the viscous finger front takes place with sharp
Contrastingly, WAG 2, WAG 3, and WAG 4 show similar discontinuity in the volume fraction of sc-CO2 compared to
trends for sc-CO2 sequestration either due to high-pressure or WAG 2 (Figure 11d).
high-temperature environments (Figures 12b,c,d and 8c). An While studying the recovery mechanism of oil being
interesting phenomenon can be noticed where higher sc-CO2 displaced by sc-CO2 (Figures 10 and 12), it was observed
sequestration does not mean higher oil recovery (Figure 8b,c). that the stripping of residual oil from the blind pores was
WAG 1 has the highest sc-CO2 sequestration where it has an produced in discrete globules as seen in Figure 13c−e. Due to
occupancy of 50.7% of its pore space, but the least oil recovery the elongated viscous front of sc-CO2 (Figure 11a,e), it
among all cases which is 73.91% (Figures 12 and 8b,c). It completely bypasses the two small pores that are placed in the
might be an effect due to the higher interaction of sc-CO2- upper section near the inlet zone (as labeled in Figure 13a).
water compared to sc-CO2-oil, where sc-CO2 primarily drives However, it was able to influence the recovery from a larger
off the water from the pore space. pore in the basal region near the inlet (Figure 13b). In porous
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Figure 14. Absolute pressure fluctuation in the flow domain and its consequent interface changes at upper blind pores for WAG 4 case. The color
contours represent oil-VOF with their values identical to Figure 12.
media, immiscible flow is determined by capillarity. Haines Figure 15a−e represents the simulation results of single-
instabilities are characterized by abrupt jumps in the fluid stage SAG over the tortuous media. Reservoir pressure and
interface, fluid redistribution, and a momentary pressure temperature conditions were kept the same as that of WAG
response.80 In porous media, Haines jumps are frequent simulations. The change in performance due to the lowered
occurrences.81 They enhance fingered invasion, amplify fluid surface tension force between oil and water was studied which
discontinuity, and produce unstable local displacement.82 captured the addition of surfactant in the aqueous phase.
Haines instabilities thus influence global displacement patterns, Overall, many stable trends were observed for all of the
boost fluid trapping, and aid in hysteretic saturation in porous examining parameters considered for the study. The water
media.83 As the sc-CO2 front tries to pass through the first breakthrough time for the cases is represented in Figure 15a. It
pore throat constriction, the injected volume upstream to the was noticed that for SAG 3, the water breakthrough at the
front experiences a back pressure owing to which, it enters the outlet was delayed compared to the other three cases. The
smaller pores (Figure 14a,b). This convection of fluid into the breakthrough gradually decreases after the injection of sc-CO2.
upper blind pores releases the pressure immediately (Figure Initially, it drops rapidly for SAG 2 and 3; while the
14c,d), which marks a decrease in flow. Consequently, the breakthrough gradually decreases for SAG 1 and 4. At the
pressure builds up and sc-CO2 invades the pores (Figure 14e). end of the flooding process, the minimum fractional flow of
With each of these oscillating flows, an amount of oil is 0.006 is shown by SAG 2. Another observation was the delayed
observed to be recovered for every period. Because of this oil recovery trend of SAG 3 in Figure 15b. A period of stable
periodic influx of sc-CO2 in the small blind pores, oil recovery
production was obtained during the transition of injecting fluid
is discrete in form of patches or globules (Figure 13).
from water to sc-CO2. Before sc-CO2 injection; SAG 1, SAG 2,
Figure S4a−e (Supporting Information) represents the
and SAG 4 showed similar courses (Figure 15b). The final
displacement of water as sc-CO2 is injected. It was observed
that certain saturation of water near the pore and throat recovery was 89.51, 88.37, 88.21, and 89.91% for SAG 1, 2, 3,
interface is left behind as the sc-CO2 moves forward (Figure and 4 respectively. The amount of sc-CO2 sequestration was
S4a,c). This is due to the existing interfacial tension between the least for SAG 3 (Figure 15c). SAG 3 also reported high
oil and water. It can also be noticed that water contributes to retention of surfactant of 16.4% inside the flow channel. SAG 4
driving away the trapped oil within the extended blind pore which resulted in the highest oil recovery, had a relatively high
downstream to the first throat (Figure S4d,e). retention of surfactant solution of about 3.3%. However, a
4.2. Single-Stage Surfactant-Alternating Gas. The diverse trend was observed for the fractional flow of sc-CO2 at
dissolution of surfactants in water reduces the interfacial the outlet (Figure 15e). Furthermore, it was observed that the
tension between water and crude oil which is a necessary residence time of the surfactant solution was less than that of
parameter to increase the value of the capillary number.84 water in WAG cases (Figures 8 and 15). However, compared
Surfactant molecules get oriented on the surface replacing to the WAG simulations, the total recovery due to surfactant
some of the water molecules and thus a reduction in the flooding was significantly higher in the case of single-stage SAG
hydrophobic regions. At the oil−water interface (immiscible (Figures 8b and 15b). Figure S5a−d (Supporting Information)
liquids interface), surfactant molecules arrange themselves in a depicts the front of the surfactant solution-oil interface at an
manner that the hydrophilic end in the water and hydrophobic instantaneous time, under different temperature and pressure
end in the oil reduce the contraction force.85 conditions. Similar to WAG cases, here, the microscopic
Energy Fuels 2023, 37, 5270−5290
Figure 15. (a) Fractional flow of surfactant solution at outlet vs time to observe for water breakthrough, (b) recovery factor of oil vs time, (c)
surface integral of sc-CO2 sequestration inside flow domain vs time, (d) surface integral of surfactant solution volume fraction inside flow domain vs
time, and (e) fractional flow of sc-CO2 at outlet vs time to observe for sc-CO2 breakthrough.
surfactant flood interface for SAG 2 had traveled more sweep Compared to Figure S2 (Supporting Information) represent-
distance compared to the other cases. ing the water injection front of WAG, the leading surfactant
The evolution of the surfactant solution-oil interface with front in the case of SAG shows a more diffused interface
time for SAG 2 and SAG 3 has been represented in Figure 16 between oil and injected fluid. Additionally, a similar
(a−d for SAG 2 and e−h for SAG 3). Similar to WAG, a phenomenon can also be observed between the interface of
change in the shape of interface curvature was observed as the residual oil and surfactant solution along the blind pores.
aqueous surfactant front passes through different geometric Figure 17 (a, b for WAG 4 and c, d for SAG 4) represents
constrictions inside the flow domain. The interaction between the strain-rate magnitude at two instantaneous time steps just
surfactant and oil in this instance was stronger for SAG 2 after the injection of sc-CO2. It can be observed that the strain
because of the advantageous mobility ratio. Consequently, the rate is higher in the case of WAG 4 compared to SAG 4 along
temperature of the reservoir is what drives the change in the the residual interfaces (Figure 17a,c). This phenomenon is due
surfactant solution’s viscosity. Compared to SAG 2, SAG 3 to the difference in the interfacial tension between the
simulates high reservoir temperature, resulting in a less viscous representative cases. A higher strain rate produces more
reservoir fluid. As a result, viscous finger contact of SAG 3 was shear stress between the viscous layers, thereby, reducing the
relatively blunt than that of the SAG 2 case. Hence, the apparent velocity. This serves as the rationale behind the faster
residence time of injection fluid for SAG 3 was significantly breakthrough of the sc-CO2 in SAG cases. Figure S6 (a−d for
more than that of SAG 2. These can be verified by examining SAG 2 and e−h for SAG 3) depicts the evolution of injected
the displacing front of SAG 2 and 3 cases, where the latter sc-CO2 front inside the tortuous domain. It was observed that
covers less distance at an instantaneous time. Also, the the net increase in production of residual oil recovery due to
emergence of late breakthrough can be confirmed in Figure sc-CO2 injection was not significantly affected due to the
15a. introduction of a surfactant solution instead of water. However,
Energy Fuels 2023, 37, 5270−5290
Figure 16. Comparison between the evolution of oil−water interface with time from 0.002 to 0.005 s for SAG 2 (a−d) and SAG 3 (e−h) cases.
Figure 17. Strain rate magnitude at the start of sc-CO2 injection for (a, b) representing WAG 4 and (c, d) representing SAG 4 for two consecutive
time steps.
the reduced strain-rate magnitude in the case of SAG other cases (Figure 18c). Also, the net sc-CO2 sequestration
simulations increased the net water recovery and sc-CO2 amount is the least for SAG 3 compared to other SAG
sequestration after sc-CO2 injection (Figures 8c and 15c). simulations (Figure 18a,b,d).
The final sc-CO2 sequestration amount for SAG simulations is Figure 19 compares the final sc-CO2 sequestration for all of
displayed in Figure 18a−d. It was observed that in the case of the simulated cases of WAG and SAG. It can be seen that SAG
SAG 3, due to high-temperature and low-pressure conditions, cases have a higher total volume of sc-CO2 sequestration
the phases co-exist in a more discrete form compared to the compared to WAG cases. However, it is interesting to know
Energy Fuels 2023, 37, 5270−5290
Figure 18. Final phase distribution of oil, water, and sc-CO2 at t = 0.032 s (end of simulation) for (a) SAG 1, (b) SAG 2, (c) SAG 3, and (d) SAG
4. Blue signifies water, green indicates trapped oil, and red represents injected sc-CO2 as indicated by phase-id contours.
Figure 19. Comparison of final sc-CO2 sequestration (%) between all WAG and SAG cases.
that in case of high temperature and pressure just above the showed that the highest recovery factor was observed for SAG
critical point (WAG 3 and SAG 3), the sequestration of sc- i.e., 87%, compared to 70%, 66%, and 59% for WAG, water
CO2 as well as oil recovery is adversely affected. On comparing flooding, and gas flooding respectively. Among different SAG
all of the parameters, it was observed that SAG 2 and SAG 4 ratios, 1:1 was found to be optimum with maximum oil
were the best cases of all. Similar observations were found by recovery factor.21
Salehi et al.,21 who compared WAG and SAG processes in a To qualitatively assess the sensitivity of oil recovery and
sand pack with flooding experiments. The experimental results sequestration, it has been observed in our study that the
Energy Fuels 2023, 37, 5270−5290
increase in reservoir pressure has a significant effect on the in temperature just above the supercritical state of CO2 yield
situ oil viscosity which decreases with an increase in more storage for both WAG and SAG cases, where 50.71% and
temperature. However, an increase in pressure does offset 86.93% of the total porous media were sequestered by CO2.
the effect of temperature. As the viscosity decreases with an However, greater sequestration does not mean an effective
increase in temperature, resident time for water or surfactant recovery of oil. It was seen that SAG performed better than
flooding increases. A stable displacing front can also be WAG in all given reservoir pressure and temperature. Recovery
observed for those cases (WAG 3, WAG 4, SAG 3, and SAG 4) of oil and retrieval from blind spaces largely depend on the
where the degree of viscous fingering is reduced. It can be vorticity magnitude that leads to a better intermixing of two
concluded that the effect of temperature is more dominant fluids. The recovery factor of oil was reported highest for SAG
than the pressure in the case of liquid−liquid interaction 1 and SAG 4 with 89.51% and 89.91%, respectively. However,
(water or surfactant displacing oil), as it influences the mobility for the same reservoir temperature and pressure, WAG cases
ratio to a greater extent. However, during the injection of sc- (1 and 4) reported recovery of 73.91% and 78.61%. It was
CO2, pressure plays a more critical role compared to the detected that pressure oscillation near blind pores due to sc-
temperature. The density and viscosity of sc-CO2 increase in CO2 injection releases trapped oil in form of globules or
case of high-pressure regimes (WAG 2, WAG 4, SAG 2, and patches. In the case of water and surfactant injection (before
SAG 4) which provide a more stable front of sc-CO2 that sc-CO2 injection) for WAG and SAG cases, the latter shows a
displaces water and oil present from the porous channel, which more diffused interface between the two immiscible fluids
consequently improves residence time. In a nutshell, oil across the advancing front. A similar phenomenon can also be
recovery during liquid−liquid displacement can be said to be observed in blind pore spaces. The faster breakthrough of sc-
more sensitive to temperature, while sequestration of CO2 CO2 in the case of SAG was due to less shear stress along fluid
majorly depends on the pressure profile of the reservoir. interfaces as quantified from strain rates. Furthermore, the
However, the effects of temperature in both cases cannot be temperature had a strong effect on flow dynamics. The high
ignored completely. temperature had a detrimental effect on sc-CO2 storage and
Carbon capture and sequestration have recently become a devours more time to fully displace the previously injected
point of interest for industries like construction, manufactur- displacement fluid. WAG 3 and SAG 3, where temperatures
ing, cement, agriculture, transport, and other allied areas. If were high (353 K), the sequestration was quite inferior
these operating plants are located close to a natural reservoir (38.71% for WAG 3 and 71.78% for SAG 3). In a nutshell, it
that bears hydrocarbon; utilizing the captured CO2 for can be concluded that SAG techniques are more effective in
enhancing oil production and simultaneously storing it in CO2 sequestration compared to the WAG technique. This
subsurface can become a viable and attractive option. study provides enough evidence that interfacial tension
However, the condition of the reservoir (in terms of pressure between oil and water plays an important role in better oil
and temperature) commands the level of efficacy of the recovery as well as faster and more effective storage of sc-CO2
process. From a microscopic perspective, this article aims to in oil reservoirs. Future work shall cover studies related to
provide meaningful insights into the interaction of oil, water, multistage WAG and SAG studies in random porous media.
and CO2. The interfacial effects and behavior thus cumulate to Investigations must also be carried out on how a recurring
the overall recovery and sequestration of oil and CO2, injection of brine, sc-CO2, and oil interact with one another to
respectively. affect flow characteristics and oil recovery. Statistical study
through sensitivity analysis would also yield various informa-
5. CONCLUSIONS tion on the effect of oil properties, reservoir conditions, CO2
This study presents a comprehensive transient numerical study properties, wettability, etc. on oil recovery and CO2 geo-
that investigates the effect of different oil reservoir pressure and sequestration.
temperature on CO2 sequestration and additional hydrocarbon
recovery at a microscopic level inside a porous media. The
works also capture the dynamic intrinsic properties of sc-CO2,
■
*
ASSOCIATED CONTENT
sı Supporting Information
which is one of the vital parameters to realize the interaction of The Supporting Information is available free of charge at
sc-CO2, water, and oil in a torturous path. Navier−Stokes was https://pubs.acs.org/doi/10.1021/acs.energyfuels.2c03982.
coupled with the EOS model for CO2 as given by Helmholtz’s Contours of molecular viscosity, Mach number dis-
free energy equation. The injection conditions were incorpo- tribution, and various interface of water, surfactant, and
rated in the supercritical state of CO2 which represented the sc-CO2 front for different considerations (PDF)
sc-CO2-EOR technique, a method widely used to recover
additional oil from oil reservoirs. The simulation studies were
conducted to specifically represent single-stage WAG and SAG
cases in which the gas used was sc-CO2. The goal of this study
■ AUTHOR INFORMATION
Corresponding Author
was to assess the variations and mechanisms of oil recoveries in Jitendra S. Sangwai − Gas Hydrate and Flow Assurance
the WAG and SAG processes under various reservoir pressure Laboratory, Petroleum Engineering Program, Department of
and temperature conditions. Given that sc-CO2-EOR is often Ocean Engineering, Indian Institute of Technology Madras,
more effective in oil gravities higher than 25° API, constant oil Chennai 600 036, India; Department of Chemical
viscosity and density of 0.091378 Pa·s and 854 kg/m3 were Engineering and Center of Excellence on Subsurface
considered, respectively, that were constant throughout all Mechanics and Geo-Energy, Indian Institute of Technology
scenarios. The microporous media shaped for this study had a Madras, Chennai 600 036, India; orcid.org/0000-0001-
series of blind pores that were connected with a tortuous 8931-0483; Phone: +91-44-2257-4825;
channel; that provided scope for the oil to be left as a residue Email: jitendrasangwai@iitm.ac.in; Fax: +91-44-2257-
after the initial injection. It was observed that pressure and 4802
Energy Fuels 2023, 37, 5270−5290
Authors Technologies in the United States. Renewable Sustainable Energy Rev.

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Funding (18) Kulkarni, M. M. M. Immiscible and Miscible Gas-Oil Displace-
This work was supported by Rajiv Gandhi Institute of ments in Porous Media; Louisiana State University, 2003.
Petroleum Technology under Research Seed Grant (Project (19) Liao, H.; He, Y.; Xu, G.; Cui, M.; Zhang, Y.; Fang, X.; Yang, S.
number: P-2136). Jitendra Sangwai acknowledges IIT Madras Field Application and Experimental Investigation of Interfacial
for providing partial financial assistance for this work as part of Characteristics of Surfactant and CO2 Alternative Injection. ACS
the Institute Research and Development Award (IRDA), Mid- Omega 2022, 7, 34222−34229.
Career, 2021 (ref: RF/21-22/0989/OE/RFIR/008450). (20) Sun, X.; Liu, J.; Dai, X.; Wang, X.; Yapanto, L. M.; Zekiy, A. O.
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Notes WAG) Injection to Improve Oil Recovery in Tight Reservoirs. Energy
The authors declare no competing financial interest. Rep. 2021, 7, 2452−2459.
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ABSTRACT: Sequestration of CO2 in geologic formations such as

1. INTRODUCTION goal of 1.5 °C. To accomplish climate goals, we need to

© 2023 American Chemical Society https://doi.org/10.1021/acs.energyfuels.2c03982

is injected first, then water, and the process is repeated in a

Figure 2. Schematic representation of sc-CO2 WAG EOR process.

Figure 7. Flowchart of VOF method used for this study.

Authors Technologies in the United States. Renewable Sustainable Energy Rev.

(71) Guo, F.; Chen, B. Numerical Study on Taylor Bubble

Minireview of Microscopic CO2 Interactions with Fluids and

Simulation of Microscopic Seepage Characteristics of

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