Impact of variation in multicomponent diffusion coefficients and salinity in CO 2 -EOR: A numerical study using molecular dynamics simulation Masoud Babaei *1 , Junju Mu 1 , Andrew Masters 1 1 School of Chemical Engineering and Analytical Science, the University of Manchester, M13 9PL, Manchester, UK Abstract CO 2 injection in depleted or partially depleted oil reservoirs entails a three phase flow system governed by physical processes such as molecular diffusion and solubility. Using numerical modelling, the aims of this paper are two-fold. (i) We investigate the impact of variations in the magnitude of diffusion of CO 2 into oil on dissolution of CO 2 in brine, and quantify the sensitivity of the simulation outputs (recovery factor and amount of CO 2 stored in water and oil phases) by use of different sets of diffusion coefficients throughout the simulation based on the variations in the compositions of the fluids. (ii) We investigate whether CO 2 dissolution in brine in a water-flooded system will be a competing or limiting factor for enhanced oil recovery by molecular diffusion of CO 2 into oil. To this end, we use molecular dynamics (MD) * Corresponding author: Telephone +44 (0)161 306 4554, email: [email protected]1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 2
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Impact of variation in multicomponent diffusion coefficients and salinity in
CO2-EOR: A numerical study using molecular dynamics simulation
Masoud Babaei*1, Junju Mu1, Andrew Masters1
1School of Chemical Engineering and Analytical Science, the University of Manchester, M13 9PL, Manchester,
UK
Abstract
CO2 injection in depleted or partially depleted oil reservoirs entails a three phase flow system
governed by physical processes such as molecular diffusion and solubility. Using numerical
modelling, the aims of this paper are two-fold. (i) We investigate the impact of variations in the
magnitude of diffusion of CO2 into oil on dissolution of CO2 in brine, and quantify the sensitivity of
the simulation outputs (recovery factor and amount of CO2 stored in water and oil phases) by use of
different sets of diffusion coefficients throughout the simulation based on the variations in the
compositions of the fluids. (ii) We investigate whether CO2 dissolution in brine in a water-flooded
system will be a competing or limiting factor for enhanced oil recovery by molecular diffusion of CO 2
into oil. To this end, we use molecular dynamics (MD) simulation to determine composition-
dependent diffusion coefficients for a multicomponent fluid system in a synthetic fractured reservoir
that undergoes CO2 injection. In total we consider 5 components interacting in the reservoir model,
namely, CO2, CH4, C4H10, C6H14 and C10H22. The fracture-matrix interaction is simplified with the
dual-porosity assumption. Our results show that (i) molecular diffusion not only enhances oil recovery
but also enhances CO2 dissolution in water. The enhancement, nevertheless, depends on the values of
the multicomponent diffusion coefficients and may exhibit an optimal condition for dissolution due to
the impact of CO2 diffusion and entrapment into matrix oil. (ii) The amount of CO2 stored in oil is
strongly affected by variation in molecular diffusion coefficients (we observe up to %13 difference).
(iii) The results show that there is 4% discrepancy between estimates of the recovery factor for
simulation cases that are run with different values of diffusion coefficients. Therefore it is important * Corresponding author: Telephone +44 (0)161 306 4554, email: [email protected]
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to account for compositions-dependent diffusion coefficients in simulation of CO2-enhanced oil
recovery processes.
1 – Background and introduction
Recent two-decade long attention to anthropogenic climatic change and greenhouse gas emissions is
rendering the CO2 injection into oil fields a “two birds one stone” operation: both to improve oil
production, i.e., CO2-enhanced oil recovery (CO2-EOR), and to sequestrate large amounts of CO2 and
offset the extra cost of storage. CO2-EOR is the second most common EOR process after thermal
methods (Espie, 2005). Holtz et al., (2001) investigated the possibilities of CO2 sequestration within
oil reservoirs in Texas, US. Screening more than 3,000 oil reservoirs, the authors found that there is
technical and economic potential in Texas for capture and sequestration of CO2 emitted from existing
fossil fuel-fired plants and using the CO2 for enhanced oil recovery. Other worldwide examples of
CO2-EOR feasibility studies include Weyburn CO2-EOR project in Canada (Whittaker et al., 2011),
North Sea (Lindeberg and Holt, 1994; Mendelevitch, 2014), China (Su et al., 2013). Ever since the
first commercial CO2 injection for enhanced oil recovery was conducted at SACROC Unit in Texas,
1972 (Brock and Bryan, 1989), understanding the mechanisms of enhanced oil recovery by CO2
injection has been the focus of continuous attention in the community of petroleum engineering.
Laboratory and field studies have established that CO2 can be an efficient agent featuring different
mechanisms by which it can displace oil from porous media, including oil swelling, interfacial tension
and viscosity reduction, increasing the injectivity index due to solubility of CO 2 in water and
subsequent reaction of carbonic acid with minerals (Alipour Tabrizy, 2014). An underlying physical
processes for these mechanisms of oil recovery is molecular diffusion. Molecular (interphase and
intraphase) diffusion is responsible for mixing of CO2 into oil at the pore level through a rate-
controlling mechanism that governs the gas-oil miscibility (Grogan et al., 1988). In secondary
recovery, the molecular diffusion is responsible for multiple contact miscibility achieved through
vaporising gas drive mechanism (where gas vaporises intermediate components from oil and becomes
oil-like) and condensing gas drive mechanism (where rich-gas intermediate components condensate
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into in-place oil and oil becomes gas like) (Stalkup, 1987). In tertiary recovery, the molecular
diffusion leads to mobilisation of waterflood residual oil by swelling of residual oil blobs when CO 2
diffuses through a blocking water phase (Grogan and Pinczewski, 1987). For a wide range of
conventional and unconventional reservoirs, e.g. heavy oil extraction in VAPEX (Yang and Gu, 2005)
or oil extraction by solution-gas-drive (Li and Yortsos, 1995), diffusion can act as an important
transport process.
In fractured reservoirs, the dispersive and segregated flux through fractures tends to accentuate
compositional differences between matrix and fracture hydrocarbons (da Silva and Belery, 1989) and
as a result the incremental oil recovery from CO2 injection processes in fractured reservoir are more
influenced by molecular diffusion. Extensive computational and experimental studies are available in
literature that evaluate the diffusion effects on hydrocarbon recovery from fractured reservoirs when
diffusion is a controlling mechanism (da Silva and Belery, 1989; Ghorayeb and Firoozabadi, 2000;
Darvish et al., 2006; Hoteit and Firoozabadi, 2009; Yanze and Clemens, 2012; Moortgat and Firoozabadi, 2013a; Wan et al., 2014; Trivedi
and Babadagli, 2009; Kazemi and Jamialahmadi, 2009; Zuloaga-Molero et al., 2016). As oil remains in matrix blocks in fractured
reservoir after primary recovery, the gravity drainage mechanism provides initial recovery of oil. The
density difference between gas in the fracture and oil in the matrix causes production of oil until
gravitational forces are equalised by capillary forces (Kazemi and Jamialahmadi, 2009). In low
permeability matrix the dominant mechanism is molecular diffusion of oil and gas (Kazemi and
Jamialahmadi, 2009). In small size matrix blocks and high capillary pressure, gravity drainage is very
low or ineffective. Injection of dry gas causes mass transfer between the gas in the fracture and the
gas/oil system saturating the matrix blocks (Kazemi and Jamialahmadi, 2009). The process leads to
horizontal movement of CO2 in addition to gravitational drainage.
When the rate of oil recovery during secondary or tertiary oil displacement by injection gas is
significantly affected by diffusion, multicomponent molecular diffusion coefficients are important
parameters to be determined. There are numerous experimental analyses in the past displaying the
range of composition-dependency of the diffusion coefficients for multicomponent systems, such as,
CO2/CH4/N2-rich gas-crude oil systems (Guo et al., 2009), crude oil-CO2 systems (Yang and Gu,
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2008)(Li and Dong, 2009), CO2/N2-water systems (Cadogan et al., 2014), C3H8–nC4H10 CO2-heavy oil
systems (Zheng and Yang, 2016), CO2 n-decane systems (Liu et al., 2016), CO2-heavy oil systems
(Zheng and Yang, 2017). Numerical examples include the work by da Silva and Berry (da Silva and
Belery, 1989) that predicted multicomponent molecular diffusion based on each component pair in a
hypothetical "average mixture" corresponded to the final equilibrium state of the two fluids in contact.
They assumed equal amounts of moles from each fluid are mixed to form the average mixture and
then they used the composition of the average mixture and binary diffusion coefficients calculated
through density-diffusivity correlation (extended Sigmund’s correlation) to calculate an effective
diffusion coefficient. As a drawback of this approach, since the diffusion inside the gas phase
(vapour-vapour diffusion) is usually tenfold faster than the liquid phase (vapour-liquid and liquid-
liquid diffusion), the effective diffusion coefficient will be unphysically closer to the gaseous phase
instead of an average mixture or liquid phase. Several researchers (e.g., Hoteit and Firoozabadi, 2009;
Moortgat and Firoozabadi, 2013a; Leahy-Dios and Firoozabadi, 2007) used composition-dependent matrix of
diffusion coefficients based on Stefan-Maxwell binary coefficients (described later)─ in which
gradients in chemical potential are the driving force for Fickian diffusion in fractured reservoirs. They
showed that unlike phase compositions-derived diffusion, chemical potentials do not require phase
identification and the gradient can be computed self-consistently across the phase boundaries. In their
work, however, they did not consider a three-phase CO2-oil-water system.
The two most important performance indicators for CO2-EOR is the oil recovery factor (Rf) and
amount or volume of CO2 stored ( , or , i.e., number of moles, volume or mass of
CO2) in the reservoir fluid by dissolution, or trapped in its own phase by capillary hysteresis or in
stratigraphic entrapments. EOR and EGR (enhanced gas recovery) operations are reported to have the
lowest capacity of all options for geological CO2 sequestration (Bachu et al., 2004). However there is
a potential to utilize at least some parts of the existing infrastructure (Kovscek, 2002). A crucial factor
to be explored for different geological structures and storage sites is the amount of CO2 that is “lost”
to water through dissolution that may not be accessible to mobilise the oil. Therefore, CO2-EOR and
CO2 storage objectives may not be aligned. This potential conflict often ends in favour of the EOR
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objective because the tangible economic benefits of EOR outweigh that of the storage (Kovscek and
Cakici, 2005; Leach et al., 2011; Ettehadtavakkol et al., 2014; Ampomah et al., 2016b). In order to determine the level of
competition between water and oil in absorbing CO2, dissolution and diffusion have to be taken into
account.
Using the capabilities of molecular dynamics simulation and numerical modelling of CO2-EOR
processes, in this work we investigate the effects of concurrent dissolution of CO2 into water and its
diffusion into remaining oil in a fractured reservoir. We account for diffusion by calculating the
multicomponent diffusion coefficients and account for dissolution using the correlations for
dissolution of CO2 into variably saline water. This is a novel application of molecular dynamics
simulation in the context of CO2-EOR. We aim to answer the following questions in this article using
three phase CO2-oil-water system:
1 – What is the susceptibility of the simulation results towards the range of variation in the
multicomponent diffusion coefficients and to their method of representation (concentration
gradient-based or chemical potential-based)?
2 – What is the interplay between diffusion of CO2 into oil and its dissolution in brine in the context
of CO2-EOR performance metrics?
Outline
In Section 2 we briefly introduce the formulation of diffusive flux, in Section 3 we define the metrics
for CO2-EOR and the methodology to extract data from the simulator to determine amount of CO 2
stored in water. In Section 4 we describe the geological model and fluid properties used in the
simulation, In Section 5 we describe our molecular dynamics simulations to obtain the molecular
diffusion coefficients. In Section 6 we describe the numerical simulation cases and the results of
simulation. We finish the article with conclusions in Section 7.
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2 – Formulation of diffusive flux
To represent diffusion flux, we can use two formulations for diffusion: (i) diffusion driven by
concentration:
Eq. 1
and (ii) diffusion driven by the chemical potential:
Eq. 2
where is the molar flux of component i per unit time, is the total molar concentration and
is the total volume of the mixture, is the normal or concentration-based diffusion coefficient
of component i, is the activity-corrected diffusion coefficient of component i, is the thermal
diffusion coefficient of component i (which is assumed zero for all components in this study), is
the mole fraction of component i, is the gradient in the direction of flow, is the molecular
weight of component i, is the acceleration due to gravity, is the height, is the reference
height, is the temperature, is the gas universal constant. The chemical potential of component i
is , where is the reference chemical potential, and is the component
fugacity. For a horizontal flow in isothermal systems, Eq. 2, can be written as:
Eq. 3
where , Comparing Eq. 1 and Eq. 2, one can find that
Eq. 4
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In the matrix form, several researchers (Moortgat and Firoozabadi, 2013a; Leahy-Dios and
Firoozabadi, 2007) formulated the diffusive flux as:
Eq. 5
where , and by using Stefan-Maxwell binary diffusion
coefficients ( ), the matrix of activity-corrected composition-dependent diffusion coefficients (
) can be written as:
Eq. 6
where is the number of components and is the mole fraction of mixture.
In this study we calculate normal diffusion coefficients ( ) of each component in liquid mixture by
molecular dynamics (MD) simulation using the GROMACS 4.6.7 package (Bekker et al., 1993;
Berendsen et al., 1995; van der Spoel et al., 2005). In order to make comparison, we use Eq. 4 and
model the CO2-EOR process with molecular diffusion driven by chemical potential gradient as well.
The term is a thermodynamic factor of the liquid mixture and is calculated
analytically by Peng-Robinson EoS extended for multicomponent mixtures from analytical
formulation derived for binary mixtures (Tuan et al., 1999). The formulation is given in Appendix A.
Using above formulation we combine molecular dynamics simulation-based normal diffusion
coefficients ( ) of liquid or gas, with EoS-based thermodynamics factor ( ). Procedurally, we need
certain mixtures of fluid at different pressures. We carry out flash calculations on these mixtures to
calculate Z-factor and phase molar compositions at equilibrium, from which the thermodynamic
factor for each component is computed. We develop a flash calculation code based on the
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combination of the successive substitution method and Powell’s method (in case of poor convergence)
to solve Rachford-Rice isothermal multicomponent flash equation based on Peng-Robinson EoS. The
procedure is fully described elsewhere (Nghiem et al., 1983).
We use Schlumberger ECLIPSE E300 (Schlumberger, 2010) as an industry-standard software tool for
modelling compositional three phase CO2-water-oil systems (with CO2SOL option enabled) in dual
porosity-dual permeability setting. The dual porosity-dual permeability model is an oversimplification
to discrete fractured and matrix (DFM) models, replacing a complex set of fractures with upscaled
orthogonal fracture media surrounding the matrix media. Unfortunately the computational expense of
simulating flow over DFM’s means that petroleum engineering modelling relies heavily on use of
dual porosity-dual permeability models. Oda method (Oda, 1985) built in Schlumberger is used for
upscaling DFM to dual grid. The Oda permeability upscaling method is based on the statistical
calculation of fracture geometry and distribution in each cell. The method is described in (Dershowitz
et al., 1998). Oda’s solution does not require flow simulations, therefore it does not take fracture size
and connectivity into account and is limited to well-connected fracture networks. More advanced
methods of upscaling DFM is presented in (Matthai and Nick, 2009; Nick and Matthäi, 2011; Correia
et al., 2015).
The software, is also unable to account for the variations in the multicomponent diffusion coefficients
due to compositional changes. Therefore we will run various cases of simulation with constant
diffusion coefficients and provide a range of variations in CO2-EOR metrics. Stored amounts of CO2
in water and oil are calculated by the following from Schlumberger ECLIPSE E300 (Schlumberger,
2010) outputs:
(a) In order to calculate CO2 stored in water we use two dynamic outputs of the simulation:
water moles per volume of gridblock j, , and aqueous component mole fraction
:
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Eq. 7
Eq. 8
where is the pore volume of the gridblock j (that can be either matrix or fracture), and the
strikethrough variables show that the water is not allowed to vaporise, and CH4, C4H10,
C6H14 and C10H22 are not dissolved into aqueous phase. Eq. 7 and 8 are used to calculate
amount of CO2 stored in aqueous phase, .
(b) To calculate the amount of CO2 dissolved/stored in oil we use:
Eq. 9
Where , and are molar fraction of CO2 in oil, oil density and oil saturation in
gridblock j, respectively. With above formulations, we can determine the contribution of
matrix and fracture continua in storing CO2.
3 – Geological model and fluid properties
In this paper we model a 3D dual porosity system with information reported in Table 1. Position of
the injection and production wells and an illustration of the dual continua are shown in Figure 2. The
injection and production schedule consists of injecting water with the rate of Qinj = 16 standard
condition m3/day (sm3/day) to the initially fully oil saturated reservoir for first 10 years and then
injection of CO2 with Qinj = 31.8 s m3/day for another 10 years. The oil production is constrained with
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Qo = 16 sm3/day on both stages of injection. For fluid Pressure-Volume-Temperature (PVT)
properties we use information reported in Table 2.
In CO2SOL, CO2 component is allowed to exist in all three phases, it uses modified Peng Robinson
EoS to describe the state of the fluid and the interaction between oil and gas. Data required for water
include CO2 solubility in water, water formation volume factor, water compressibility, and water
viscosity. They are entered as a function of pressure at the reservoir temperature (Schlumberger,
2010).
For solubility of CO2 in water as a function of salinity of water, the decreased solubility of CO 2 in
brine is accounted for empirically (Chang et al., 1996), by the following factor correlated to the
weight percent of dissolved solid:
Eq. 10
Where is CO2 solubility in standard m3 of CO2 per standard m3 of brine, is CO2 solubility in
standard m3 of CO2 per standard m3 of distilled water (itself correlated with pressure and temperature
(Chang et al., 1996)), is the salinity of brine in weight percent of solid, and is temperature (°F).
Eq. 7 matches the CO2 solubility data in NaCl solution within ≈ %18 sm3/sm3 (Chang et al., 1996).
Figure 1 shows the comparison between measured and calculated solubility curves with respect to
pressure. The error of Eq. 7 can clearly increase for high pressure systems.
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0 100 200 300 400 500 600 700 800 900 10000
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Exp. Data distilled waterExp. Data distilled waterExp. Data distilled waterExp. Data for S = 10 wt%Exp. Data for S = 26 wt%Calculated for S = 10 wt%
Pressure (bar)
Rs (s
m3/
sm3)
Figure 1 – Comparison of experimental data and calculated values for solubility of CO2. The
experimental data for distilled water is for various temperatures (313.15 K, 323.15 K and 373.15 K)
Wiebe (Wiebe, 1941). The experimental data for NaCl brine are from McRee (McRee, 1977).
For formation volume of water saturated with gas at the specified pressures, first the density of pure
water is calculated (Kell and Whalley, 1975), then Ezrokhi’s method is used to calculate the effect of
salt and CO2 (Zaytsev and Aseyev, 1992). For water compressibility and viscosity we use cw =
4.41⨯10─5 bar─1 and 0.31 cp, respectively.
Table 1 – Geometrical and geological properties of the simulation domain.
Properties Values Description
Lx, Ly, Lz1825.8 m, 30.48 m, 18.288 m Length in x, y and z directions
dx, dy, dz 30.48 m, 30.48 m, 3.048 m Block dimensions in x, y and z directionsZ 2,133.6 m Depth of top of the reservoir
0.1 Matrix porosity
0.005 Fracture porosity
, and 1 mD Matrix permeability
, and 100 mD Fracture permeability
917,465 m3 Rock volume of matrix continuum1,014,309 m3 Rock volume of fracture continuum101,904 m3 Pore volume of matrix continuum
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5,095 m3 Pore volume of fracture continuum
1 m-2 Multiplier in the construction of the matrix-fracture coupling transmissibilities
S 100,000 ppm (10 wt%) and 260,000 ppm (26 wt%) Salinity of water considered in two cases
T0 345 K Constant reservoir temperaturep0 200 bar Initial pressure at 2133.6 m
Figure 2 – The illustration of dual porosity dual permeability division of the domain (red shows
fracture while blue shows matrix). We note that the vertical direction is exaggerated 10-fold.
Table 2 – Fluid PVT properties of the reservoir and injection stream, BIC stands for binary
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