a numerical study of capillary pressure–saturation relationship for supercritical carbon dioxide...

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chemical engineering research and design x x x ( 2 0 1 4 ) xxx–xxx

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Chemical Engineering Research and Design

j ourna l h omepage: www.elsev ier .com/ locate /cherd

numerical study of capillary pressure–saturationelationship for supercritical carbon dioxide (CO2)njection in deep saline aquifer

amal Jawher Khudaida, Diganta Bhusan Das ∗

epartment of Chemical Engineering, Loughborough University, Loughborough LE11 3TU, UK

a b s t r a c t

Carbon capture and sequestration (CCS) is expected to play a major role in reducing greenhouse gas in the atmo-

sphere. It is applied using different methods including geological, oceanic and mineral sequestration. Geological

sequestration refers to storing of CO2 in underground geological formations including deep saline aquifers (DSAs).

This process induces multiphase fluid flow and solute transport behaviour besides some geochemical reactions

between the fluids and minerals in the geological formation. In this work, a series of numerical simulations are

carried out to investigate the injection and transport behaviour of supercritical CO2 in DSAs as a two-phase flow in

porous media in addition to studying the influence of different parameters such as time scale, temperature, pressure,

permeability and geochemical condition on the supercritical CO2 injection in underground domains. In contrast to

most works which are focussed on determining mass fraction of CO2, this paper focuses on determining CO2 gas sat-

uration (i.e., volume fraction) at various time scales, temperatures and pressure conditions taking into consideration

the effects of porosity/permeability, heterogeneity and capillarity for CO2–water system. A series of numerical simu-

lations is carried out to illustrate how the saturation, capillary pressure and the amount of dissolved CO2 change with

the change of injection process, hydrostatic pressure and geothermal gradient. For example, the obtained results are

used to correlate how increase in the mean permeability of the geological formation allows greater injectivity and

mobility of CO2 which should lead to increase in CO2 dissolution into the resident brine in the subsurface.

© 2014 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Two-phase flow; Capillary pressure; Porous media; Deep saline aquifer; CO2 sequestration

. Introduction

arbon sequestration is a technique for managing carbonioxide (CO2) that has been emitted into the atmosphere byarious activities, e.g., combustion of carbon-based fuels. It is

relatively new concept that had been developed to addresshe problem of global warming, which is attributed to high lev-ls of atmospheric CO2. In a more specific approach, geologicalequestration aims to inject supercritical CO2 into porous for-ations underground while attempting to prevent leakage of

O2 to the surface again. This method can be applied to declin-

Please cite this article in press as: Khudaida, K.J., Das, D.B., A numericalcarbon dioxide (CO2) injection in deep saline aquifer. Chem. Eng. Res. Des

ng oil fields, un-minable coal seams as well as deep salinequifers (DSAs). Injecting CO2 into DSAs is considered to be

∗ Corresponding author. Tel.: +44 1509222509.E-mail addresses: [email protected], [email protected] (D.B.

ttp://dx.doi.org/10.1016/j.cherd.2014.04.020263-8762/© 2014 The Institution of Chemical Engineers. Published by

one of the most feasible sequestration methods of CO2. Froma fluid mechanics point of view, injecting supercritical CO2 intogeological formations can be treated as a two-phase flow in aporous medium (Tsang et al., 2008). Supercritical CO2 is con-siderably denser than the gaseous CO2 phase but has lowerdensity and viscosity than the occupant brine in the porousspace. As a result of the differences of fluid densities, super-critical CO2 migrates buoyantly towards the upper confininglayer. The preferred depths to inject CO2 are greater than 800 m(Prevost et al., 2005) as they provide the required conditionsabove the critical points of CO2 for it to stay in supercritical

study of capillary pressure–saturation relationship for supercritical. (2014), http://dx.doi.org/10.1016/j.cherd.2014.04.020

Das).

phase. This increases the storage capacity of the site becausemore CO2 can be stored within a specific volume.

Elsevier B.V. All rights reserved.

dx.doi.org/10.1016/j.cherd.2014.04.020

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dx.doi.org/10.1016/j.cherd.2014.04.020


2 chemical engineering research and design x x x ( 2 0 1 4 ) xxx–xxx

It must be emphasized that there are particular conditions,which the geological formation must meet for CO2 storage tobe successful. According to Bachu and Bennion (2008), threebasic conditions must be met, namely, (i) capacity, i.e., the geo-logical media must have the capacity to allow the anticipatedamount of CO2 over the duration of the project operation; (ii)injectivity, i.e., the media must be able to allow the CO2 atits injection rate and, (iii) confinement, i.e., the media mustbe able to impede leakage of CO2 from the storage zone orminimize leakage to the tolerable levels. Furthermore, geolog-ical storage of CO2 is determined by four foremost trappingmechanisms as discussed below.

(a) Structural trapping, which takes place when CO2 gasbecomes immobile in the porous sedimentary layers withexisted brine by impermeable barriers (White et al., 2013).

(b) Residual trapping that takes place as a result of the hys-teresis effect when the saturation direction is reversedafter the injection process stops and, the existing brinemoves back and tries to displace CO2 in the pores (Ide et al.,2007).

(c) Solubility trapping takes place when the injected CO2 dis-solves in the resident fluid and increases the acidity anddensity of the brine creating convective currents that allowthe denser brine with high concentration of CO2 to settleat the bottom part of the aquifer trapping the CO2 moresecurely (Silin et al., 2009).

(d) Mineral trapping occurs when the dissolved CO2 reactswith the brine producing carbonic acid that reacts withthe dissolved ions within the aquifer brine and mineralsforming the host rock resulting in chemical precipitationof solid carbonate minerals (Beni et al., 2012).

Modelling of underground injection of CO2 primarily repre-sents modelling a system of two-phase flow in porous mediawhich requires one to identify the relevant parameters. Theseparameters describe various physical and chemical propertiesof the geological formation such as entry pressure (dependingon pore/particle size of the domain), hydrodynamic condi-tions (e.g., pressure difference, groundwater velocity), fluidproperties, permeability, chemical species from geochemi-cal reactions and fluid/fluid interfacial mass transfer (Ideet al., 2007). Considerable uncertainty may however exist withregards to the formation-related parameters because of thedifficulty in collecting sufficient data across the huge areasthat should be taken into account for any geologic seques-tration project. A number of studies have been conductedto determine the capillary pressure–saturation–relative per-meability relationships for subsurface injection of CO2 intoporous media (e.g., Bachu et al., 1994; Pruess et al., 2003; Kumaret al., 2005; Knauss et al., 2005; Juanes et al., 2006; Birkholzeret al., 2009; Schnaar and Digiulio, 2009). They demonstrate thatcomputational models are able to replicate complex forma-tion heterogeneities by employing statistical routines; residualCO2 trapping and hysteretic relative permeability curves, dis-solution reactions and mineral precipitation and others. Forexample, Nordbotten et al. (2004) analytically described thetime evolution of the CO2 plume dominated by viscous forceswith irrelevant effects of the CO2 buoyancy forces using asimplified form of Buckley–Leverett equation. They utilizedtheir modelling results to inspect the accuracy/implicationof assuming constant properties for the fluids in the stor-


age formation and discussed some cases where buoyancyand non-zero residual saturations have more influence on the

mobility of CO2 plume in addition to the effects of CO2 disso-lution in the existing brine.

One of the critical issues in CO2 geological sequestrationis the phase transition from liquid or supercritical to gasaccording to the temperature and pressure changes duringthe injection progression. Therefore, numerical simulation forCO2 sequestration in saline aquifers should have the ability toenvisage when the CO2 phase transition occurs. It must alsobe able to determine the buoyancy and viscous forces influ-ence on the fluid flow and, CO2 dissolution in the aqueousfluid (White and Oostrom, 2003). Though capillarity plays acrucial role in assessment of saline aquifers for CO2 seques-tration, there is not much real (field) data available about thebehaviour of CO2–brine flow system in the porous rocks. Plugand Bruining (2007) developed a laboratory scale method toinvestigate the static capillary pressure change as a functionof saturation at different pressure and temperature condi-tions. They examined the influence of CO2 dissolution in waterby comparing its behaviour to the behaviour of nitrogen (N2)under the same conditions and observed that the residualwater saturation (Swc) for CO2 is much smaller than that forN2 due to the difference in interfacial tension.

Capillary trapping, which is also called residual trapping,is closely related to the capillary forces between CO2 andresident fluid at the scale of the grains of reservoir rockwhich is controlled by interfacial forces, pore size and wett-ability (Alkan et al., 2010). Experimental studies conductedby Bennion and Bachu (2008), and Plug and Bruining (2007)reported that permeability and capillarity are influenced byinterfacial forces and wettability of CO2–brine–rock systems.Another study on CO2 sequestration has been conducted byBickle et al. (2007) who modelled CO2 flow behaviour in Sleip-ner field in the North Sea. They used a theoretical model andvalidated it with experimental results by Lyle et al. (2005)to characterize the gravity flow in porous media. To attaintheir solutions they employed a number of assumptions, e.g.,neglecting the motion of the existing fluid within the host-ing formation and ignored both capillary and viscous forces inthe fluid flow system which exhibited some limitations in theapplicability of their solutions. Bickle et al. (2007) concludedthat the radius of accumulated CO2 ponds in the subsurfaceincreases linearly with the square-root of the elapsed time.They observed an increase in CO2 input in higher layers of thedomain with a decrease in lower ones due to the leakage intothe upper structures of the modelled formation. Their solu-tions provide important predictions on CO2 behaviour withno need to carry out full simulation for any potential storagesites.

Unlike most conventional approaches for determining cap-illary pressure relationships which are based on equilibriumflow conditions (i.e., time derivative of fluid saturation is zero),dynamic capillary pressure effects have been shown to havea great influence on two-phase flow in porous media (Helmiget al., 2007; Mirzaei and Das, 2007; Hanspal and Das, 2012).A number of fundamental studies (e.g., Oung et al., 2005;Manthey et al., 2005; Bottero et al., 2006) have investigatedthe dynamic capillary pressure effects in two-phase flow sys-tems, and this gives rise to the possibility of applying theseunderstanding to determine if these effects are significant forsupercritical CO2 flow in the geological formation as well.

In addressing most of the above issues, the main goal of thisstudy is to carry out a simulation study to determine static and


dynamic capillary pressures for CO2–water system as a func-tion of saturation for different permeability and heterogeneity

dx.doi.org/10.1016/j.cherd.2014.04.020


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t various time scales, temperature and pressure conditionsn order to evaluate the implications of different CO2 injec-ion strategy and its storage capacity in briny aquifers. Forhis purpose a series of numerical simulations are to be car-ied out under various pressure, temperature, heterogeneitynd injection rate conditions. It is envisaged that this wouldelp the prediction of the right CO2 injection process and CO2

ehaviour within the aquifer formation during sequestrationife time which has a vast impact on the energy cost and stor-ge process safety. It is believed that this study will provideetter understanding of the injection and sequestration pro-esses.

. Modelling approach

.1. Main equations

n this work the injection of CO2 into saline aquifers is definedo represent the flow of two immiscible fluids, namely, waterbrine) as a wetting phase and CO2 as a non-wetting phase in aorous medium where supercritical CO2 replaces the existinguid in a process called drainage.

.1.1. Mass and momentum conservation equationsodelling CO2 injection into geological formation is governed

y the equations of mass and momentum conservation.The conservation of momentum is described by the follow-

ng form of Darcy’s law:

∂(S˛��˛)∂t

+ ∇ · (�˛v˛) − �˛q˛ = 0 (1)

here S˛ is the phase (water or CO2) saturation, � is theorosity, �˛ is the density, t refers to the elapsed time, v˛ is theverage pore velocity of the phase and q˛ refers to the phaseux.

From the generalized Darcy’s law (equation of momentum),elocity vector v˛ is b calculated as

˛ = −kr˛

�˛K(∇p˛ − �˛g) (2)

r˛ identifies the relative permeability for the phase (water orO2), � refers to the dynamic velocity, p˛ identifies the pres-ure, K is the tensor of absolute permeability (defined to besotropic) and g the vector of gravity. The phase permeabilityeffective permeability) (k˛) is related to the relative perme-bility (kr˛) as:

r˛ = k˛

K(3)

here K signifies the domain permeability for a single-phaseow (the absolute permeability).

By substituting Eq. (2) in Eq. (1) the following general form ofass conservation equation is obtained for both fluid phases:

∂(S˛��˛)∂t

− ∇ ·(

�˛kr˛

�˛K(∇p˛ − �˛g)

)− �˛q˛ = 0 (4)

.1.2. Constitutive relationshipshe two fluid flow process is dominated by capillary pressure

Pc)–saturation (Sw)–relative permeability (kr) relationshipsecause any decrease in the wetting phase saturation results


n non-wetting fluid retreatment into smaller pores whichncreases the capillary pressure. In a two phase flow the

capillary pressure is defined as the difference between theaverage phase pressures of non-wetting (nw) and wetting (w)phases,

Pc = Pnw − Pw (5)

One of the most common formulations used to determinePc–Sw–Kr relationships is Brooks–Corey function (Brooks andCorey, 1964), in which the displacement pressure of the wet-ting fluid from the largest pore (Pd) is involved while thispressure has been ignored by other authors for fully saturatedporous media. The relationship defines the effective satura-tion as:

Sew =(

Pc

Pd

)−�

for Pc > Pd (6)

Sew = 1 for Pc ≤ Pd (7)

Sew = (Sw − Swr)(1 − Swr)

for 0 ≤ Sew ≤ 1 (8)

where (Sew) denotes the effective water saturation, (Swr) is theresidual water saturation, (Pd) represents entry (displacement)pressure, (�) is the pore size distribution index.

Brooks–Corey correlations in conjunction with the Bur-dine theorem (Burdine, 1953) are used to define the relativepermeability-saturation relationships for wetting (w) and non-wetting (nw) phases.

krw = Sew(2+3�)/� (9)

krnw = (1 − Sew)2(1 − Sew(2+�)/�) (10)

The coupled equations are solved for the primary variableswhere the porous domain is assumed to be a rigid rock andboth fluids are defined as incompressible. Furthermore, thedynamic viscosities of the fluids are assumed to be constantand all source and sink terms are ignored.

2.2. Simulation approach

The scope of this research is to simulate the process ofinjecting CO2 as a supercritical fluid into DSAs. It focuseson the flow of multiphase fluid (H2O–CO2–NaCl) in a porousmedia for which STOM32 (STOMP-CO2) operational mode ofSTOMP (subsurface transport over multiple phases) simulationcode is used. In this mode water (brine) is the wetting phaseand CO2 is a non-wetting fluid which is injected at differentpressure rates into the porous domain which is fully saturatedwith water (brine). This leads to a situation where CO2 drainswater out of the domain in a process called drainage followedby an imbibition process when CO2 injection ends and waterflows back into the domain to replace CO2 in the domainpores leaving some traces of it trapped. This operationalmode is able to incorporate buoyancy and viscous forcesdriven flow, CO2 dissolution in aqueous fluid, phase transi-tion, dispersion and diffusivity of the gas and uses the finitevolume technique to numerically simulate the process. Theseare discussed in detail by White and Oostrom (2003) and arenot repeated in this paper. However it should be mentionedthat STOMP-CO2 simulator is written in FORTRAN 90 with acapability of dynamic memory allocation for faster execution.


The collection of source files is required to be compiled intoan executable file that can be used on various computing

dx.doi.org/10.1016/j.cherd.2014.04.020



Table 1 – Selected aquifer parameters for simulation.

Parameter Value/function Reference

Diameter (m) 5000 –Thickness (m) 100 –Depth (m) 2900 –Grid (nodes) 71 × 4 × 10 –Porosity Sandstone 0.25 (Wechselfolgen) 0.16 May et al. (2004)Horizontal permeability (m2) (5.625e−13) (0.5428e−13) May et al. (2004)Vertical permeability (m2) (1.688e−13) (11.15e−16) May et al. (2004)Rock density (kg/m3) 2430 2470 May et al. (2004)Specific storativity (1/m) 9.2e−4 May et al. (2004)Surface temperature (◦C) 8 May et al. (2004)Reservoir temperature (◦C) 58 Beni et al. (2012)Temperature gradient (K/m) 0.035 –Reservoir pressure (MPa) 32 Beni et al. (2012)

increased to 36 MPa in one step and maintained till the endof injection period.

Pressure gradient (KPa/m)

platforms including Linux and Windows to read the input filethat is created by the user including a number of cards thatcontain calculation instructions and required parameters tosolve the simulation problem. The code has been effectivelyoptimized for workstations (HP, IBM, Sun) in addition to main-frames. The speed and memory requirements for runningSTOMP-CO2 executable files depend on the complexity of theproblem and computational grid refinement. There is no min-imum memory or processor speed provided by the developer.However, from our experience it has been found out that thecode better functions on UNIX operating system with 2.4 GHzCPU and 1 GB memory. STOMP-CO2 is utilized to numericallysolve the coupled conservation equations (water mass, CO2

mass and NaCl mass) by converting them to algebraic equa-tions using finite volume method (FVM) and Euler-backwardtime differencing for spatial and temporal discretizations,respectively. Backword Euler method is a first order timestepping method that makes an error of �t2 for each timestep. This method offers more stability and accuracy thanforward Euler method especially for problems with large andnonlinear functions like diffusion equations. The producedalgebraic equations in the discretised equations are closedusing a number of constitutive relationships as explainedin Section 2 and solved using Newton–Raphson iteration toresolve their nonlinearities (White and Oostrom, 2003).

2.3. Initial and boundary conditions

The domain is considered to be anisotropic and almost fullysaturated with brine before injecting supercritical CO2 in thecentre. The initial condition for all simulation conditions areshown in Table 4. We generate two-phase conditions withinthe computational domain by setting the aqueous saturationvalue at 0.9999 as an initial condition for the employed equa-tions of state in the simulation code (e.g., Kelvin equation(Nitao, 1988), and the formulation by Battistelli et al. (1997))which take into account the changes in thermodynamic prop-erties of the fluid phases as the simulation conditions change.The non-wetting fluid (CO2) saturation was assumed to be 1.0at the injection source at the outer wall of the reservoir and0.00001 in the rest of the computation domain as initial con-dition for the reason above. It is injected into the lower 3 gridcells (i.e. 30 m from the bottom of the domain). Vertically zeroflux is considered for aqueous phase at the well case as innerboundary while the outer boundary was assumed to be infinite


with zero flux for gas phase. Horizontally zero flux is consid-ered at the upper and lower surfaces which force the injected

10.5 –

gas to spread laterally. For both dynamic and static conditions,fluids saturation, pressure and volume are measured at eachnode and the CO2 saturation is plotted vs. simulation time.This procedure is repeated twice: once for sandstone (coarse)and another for Wechselfolgen (fine) homogeneous domains.This procedure is repeated twice: once for sandstone (coarse)and another for Wechselfolgen (fine) homogeneous domains.

2.4. Dynamic and quasi-static simulations

In this research work, simulations are carried out by injectingCO2 into the centre of the computational domain which is ini-tially fully saturated with brine. The gas pressure is defined tobe zero all over the domain. The CO2 injection starts at 32 MPaand increased at a rate of 0.1 MPa every 0.5 year for 20 yearsfor quasi-static simulations. This increment in injection pres-sure increases the capillary pressure (Pc) in the domain untilit reaches the displacement pressure (Pd) when the injectedCO2 starts displacing the existing brine and continues till asteady state is reached when average values of aqueous sat-uration and capillary pressure are calculated to give a singlepoint for the Pc–Sw relationships. This procedure is repeatedfor each time step from which the Pc–Sw curves are produced.For dynamic simulations the imposed injection pressure is


Fig. 1 – A schematic diagram of geological CO2

sequestration process in a deep saline aquifer (DSA).

dx.doi.org/10.1016/j.cherd.2014.04.020



Table 2 – Important parameters and initial conditions.

Parameter Value Reference

Irreducible saturationswater, Slr

0.1 Beni et al. (2012)

CO2, Sgr 0.05 Beni et al. (2012)Brooks/Corey exponent, � 0.457 Beni et al. (2012)Strength coefficient, P0 19,610 Pa Beni et al. (2012)Pore compressibility, k 1 × e−9 Pa−1 Beni et al. (2012)Pore expansivity, 1 × e−6 K−1 Beni et al. (2012)Injection pressure 36 MPa –Temperature 58 ◦C Beni et al. (2012)Salinity 0.2 Beni et al. (2012)Pressure gradient 10.5 MPa/km May et al. (2004)Salinity gradient 80 g/L km May et al. (2004)CO2 injection rate 40 kg/s –Injection time 20 years –Simulation time 1000 years –

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.5. Capillary pressure and saturation averaging

rom the locally predicted values of saturation and pressuret each grid node for each time step (tn) the volume-weightedverage water saturation (Sw) and saturation-weighted aver-ge capillary pressure (Pc) values for the whole domain areetermined using the following equations.

The average saturation at any time step (tn) is calculatedy;

w|tn =∑j=1

mSwjVj|tn∑j=1m

Vj

(11)

nd the average capillary pressure is calculated by;

c|tn =[∑j=1

m(1 − Swj)Pnwj∑j=1

m(1 − Swj)

–

∑j=1m

SwjPwj∑j=1m

Swj

]|tn (12)

here Vj, is the volume of node j, and, Swj, Pwj and Pnwj denoteater saturation, water pressure and CO2 pressure at node j,

espectively.The time derivative of saturation dependency can be calcu-

ated from the average saturation values calculated from Eq.13) as follows:


∂s

∂t|swtn = Sw|tn+1 − Sw|tn−1

tn+1 − tn−1(13)

Table 3 – Simulation cases and parameters.

Conditions Case no. Domain Inject. press.(MPa)

Te

Dynamic

1 Homogeneous(fine)

36

2

Homogeneous(course)

36

3 36

4 36

5 34

6 32

7 Heterogeneousfine–coarse–fine

36

8 Heterogeneouscoarse–fine–coarse

36

Quasi static 9 Homogeneous(fine)

36

Quasi static 10 Homogeneous(coarse)

36

As shown in Eqs. (11) and (12), both calculated average val-ues are based on water saturation and, hence, they are calledsaturation-weighted averages (Mirzaei and Das, 2007; Hanspaland Das, 2012).

Conventional theories (Collins, 1961; Scheidegger, 1974;Bear and Verruijt, 1987; Helmig, 1997) define capillary pressureas a function of fluid saturation only for fluids at equilibriumconditions. However, this is not always the case as fluids mightnot flow under steady conditions especially at early stagesof flow when the change rate of saturation is thought to behigh. Therefore, it has been suggested by many authors thatan additional term ought to be added to the capillary pressureEq. (5) for dynamic fluid flow in porous media (Hassanizadehand Gray, 1993a; Beliaev and Schotting, 2002; Dahle et al., 2005;Hanyga and Seredynska, 2005; Oung et al., 2005).

In this study we will be investigating the dynamic effects ata field-scale domain. The additional term is called the dynamiccoefficient (�) which represents dynamic capillary pressureeffect on the flow behaviour and is determined from the slopeof a linear relationship between the capillary pressures atdynamic and static flow conditions and the time derivativeof saturation as shown in Eq. (14):

(Pc,dyn − Pc,stat)|s = −�∂s

∂t|s (14)

where Pc,dyn and Pc,stat represent dynamic and static capil-lary pressures calculated at a specific value of saturation(s), respectively. The dynamic coefficient has been used bymany previous workers (e.g. Tian et al., 2012; Fucík et al.,2010; Mirzaei and Das, 2007, 2013; Hanspal and Das, 2012; Dasand Mirzaei, 2013; Hanspal et al., 2013) to take into accountdynamic capillary pressure effect and, therefore, a detaileddiscussion on dynamic capillary pressure effect is avoided inthis paper.

2.6. Computational domain

Our simulation parameters are based on Bunter SandstoneAquifer in North German Basin in North-Eastern Germany.This aquifer consists of four cycles beginning with basal sand-stone which has three cycles of permeable layers (Detfurth,Hardegsen and Solling-Folge) and ending with an alternat-ing succession of silt, sand and clay stone (May et al., 2004).


In this research study we focus on Detfurth cycle which isdivided to a lower sandstone with high permeability and upper

mp. (◦C) Porosity Horiz. perm.(m2)

Vert. perm.(m2)

58 0.16 0.5428e−13 0.01115e−13

58

0.25 5.625e−13 1.6876e−137080585858 0.16–0.25–0.16 Variable Variable

58 0.25–.016–0.25 Variable Variable

58 0.16 0.5428e−13 0.01115e−13

58 0.25 5.625e−13 1.6876e−13

dx.doi.org/10.1016/j.cherd.2014.04.020



Table 4 – Initial and boundary conditions.

Case no. Domaintype/cond.

Horizontalpermeability (m2)

Domaintemp. (◦C)

CO2 injectionpressure (MPa)

Dynamic1 Homogenous

fine sand0.5428e−13 58 36

2 Homogenouscoarse sand

5.625e−13 58 36


5.625e−13 70 36


5.625e−13 80 36


5.625e−13 58 34


5.625e−13 58 32

7 Heterogeneouscoarse in finesand

0.5428e−13–5.625e−13–0.5428e−13 58 36

8 Heterogeneouscoarse in finesand

5.625e−13–0.5428e−13–5.625e−13 58 36

Quasi-static9 Homogenous

fine sand0.5428e−13 58 36

10 Homogenousfine sand

0.5428e−13 58 36

11 Homogenousfine sand

0.5428e−13 58 32

Source: illustrated in Tables 1 and 2.

Porosity; fine sand = 0.16, coarse sand = 0.25.Vertical permeability; fine sand = 0.01115e−13, coarse sand = 1.6876e−13.Hydrostatic pressure = 32 MPa, pressure gradient = 10.5 MPa/km, salinity = 0.2.

alternating succession of sand, silt and clay stones whichis called (Wechselfolgen) with low permeability because itdemonstrates heterogeneity in regards to porosity and per-meability.

The simulated three-dimensional cylindrical domainextends laterally (r-direction) from the injection point whichis represented by the well radius of 0.2–2500 m and verticallyfrom 2900 to 3000 m below land surface while at the top andbottom are impermeable layers that preserve the injected CO2

safely in the storage formation. This depth ensures that theinjected CO2 will remain in supercritical state which increasesthe storage capacity of the site. The system can be modelledas a two-dimensional radial domain, as there is no hetero-geneity in the azimuthal direction. The field is segregatedinto 71 × 4 × 10 grids cells. This grid refinement was optimizedfor less computational time and accurate outputs through aseries of experiments that showed no significant effect of thegrid refinement up to a magnitude of 10 times on the pro-duced CO2 saturation contours. It is a fact that fine block gridsproduce smoother contours, however noticeable reduction ofexecution time was observed by using coarser grids with nomomentous influence on the smoothness of CO2 profiles. Thisis consistent with studies by Gonzalez-Nicolas et al. (2011) andHanspal and Das (2012) which indicate that grid refinementhas no significant influence on Pc–Sw profiles.

Supercritical CO2 is to be injected at pressure and tem-perature above CO2 critical conditions into the centre of thecomputational domain at the lower 30 m at a constant rate


of 40 kg/s for 20 years followed by 980 years lockup period asillustrated in Fig. 1. This injection rate represents about 25%

of a medium size coal-fired power generation plant. Differenttypes of heterogeneities have been considered for the domainand various scenarios of injection process are applied to inves-tigate the effects of permeability, temperature, porosity, andinjection pressure on capillary pressure (Pc)–saturation (Sw)relationships at static and dynamic flow conditions which hasa significant influence on the fate of CO2 after the injectionprocess.

Firstly, we run our simulations on fine and coursehomogenous domains with porosity of 0.16 and 0.25, respec-tively, to determine the effect of porosity and permeabilityon Pc–Sw relationships. Unlike other works (Mirzaei andDas, 2007; Peszynska and Yi, 2008; Hsu and Hilpert, 2011),dynamic and quasi-static simulations are conducted forcomparison purposes. The simulated aquifer and simula-tion parameters are illustrated in details in Tables 1 and 2,respectively.

In spite of considering three-dimensional flow in a per-meable media, it is noted by Domenico and Schwartz (2000)that under the same hydraulic gradient, horizontal flow isof the order of six orders of magnitude faster than verticalflow. In our simulation the lateral flow dominates, there-fore we can refine our computational domain by declaringour reference nodes in the output control card in the inputfile, vertically at distances from the bottom of the forma-tion at 20, 40 and 70 m while horizontally at radial distancesof 100, 200, 500, 800, and 1000 m, from the injection wellwhile azimuthally a single reference plane is considered at


45◦ to measure our simulation variables for two-dimensionalscenarios.

dx.doi.org/10.1016/j.cherd.2014.04.020



Fig. 2 – Evolution of CO2 plume in low permeability homogenous aquifer (case 1): (A–D) CO2 distribution after 1, 5, 10 and 20years of simulation during injection process (drainage). (E–H) CO2 distribution after 50, 200, 500 and 1000 years posti

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opPtoli

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Adief

njection process (imbibition).

. Results and discussions

o evaluate the behaviour of CO2 in three-dimensional cylin-rical field-scale formation a medium-term of 1000 years ofimulations of CO2 injection into homogeneous and heteroge-eous formations were carried out in this work. The injectionrocess continued for 20 years followed by 980 years of lockup.upercritical CO2 is injected azimuthally at 4 nodes which areniformly distributed towards the lower 30 m of the domain.

As stated earlier, this study aims to examine the effectsf injection pressure, temperature, heterogeneities (layering),orosity, permeability and injection condition states on the

c–Sw relationships and the behaviour of the injected CO2 inerms of its dissolution or mobility. To show how CO2 behavesver the simulation time period, a series of numerical simu-ation models displayed in Table 3 were created for differentnitial and boundary conditions shown in Table 4.

.1. CO2 migration

s soon as the injection process starts the supercritical CO2

isplaces the existing brine and migrates away from thenjection well as illustrated in Fig. 2. For different time lev-


ls, the simulated CO2 spatial distribution profiles are shownor drainage process (Fig. 2(A–D)) during the injection period

and imbibition process (Fig. 2(E–H)) presenting the post injec-tion period for case 1 simulation conditions (Table 3). CO2

continues to migrate laterally due to the governing forces,e.g., (i) hydrostatic pressure difference between the injectionpoint and aquifer, and (ii) capillary pressure. Furthermore, asa result of densities difference between the ambient brineand injected supercritical CO2 buoyancy forces push the lat-ter upwards until it reaches the impervious confining layer(caprock) under which it is trapped or extends more laterally.Fig. 2(E–H) demonstrates that when injection process ends thedomain is invaded by brine which displaces most of the CO2

leaving part of it trapped in small pores. This leads to residualtrapping of the injected CO2. Meanwhile a volume fraction ofthe injected CO2 are dissolved in the brine after the injectionprocess to produce a rich CO2 layer that settles permanentlyat the bottom of the domain.

3.2. Effects of porosity and permeability

It has been suggested by some researches (e.g., Kumar et al.,2005; Xu et al., 2006; Kopp et al., 2009; Chasset et al., 2011)that an increase in the mean permeability results in greaterinjectivity and mobility of CO2 which increases dissolution


into the formation brine. To explore this further and, in par-ticular, determine the effects of porosity and permeability on

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Fig. 3 – CO2 plume evolution in low and high permeability homogenous aquifers at different time scales: (A–D) fine sand
domain (case 1); (E–H) coarse sand domain (case 2).
the injectivity of CO2, two sets of simulations were carriedout in this study. The first set in cases 1 and 2 explores theseeffects in fine and coarse homogeneous domains, respectively.The second set (cases 7 and 8) looks at the effects of two


heterogeneous porous layers involving fine–coarse–fine and

coarse–fine–coarse layers. In all injection cases illustrated inFig. 3, it is observed that the coarse domain produces largerCO2 plumes during the injection time at middle altitudes ofthe domain. This means that the higher the permeability the


higher the CO2 saturation is during the drainage process when

dx.doi.org/10.1016/j.cherd.2014.04.020



s: ca

tdrsaaeoc

bunusptpaesittNhw

3

Cl(oc3disvsotve

fi

is unlikely subject to any permanent trapping in short-term

Fig. 5 – (A) Capillary pressure vs. aqueous saturation at

Fig. 4 – CO2 saturation plots for homogenous domain

he hydrostatic forces dominate. Different plumes are pro-uced during the imbibition process when the aquifer brineeverses back to displace the CO2. Though the CO2 plumeize looks larger for the fine sand domain (Fig. 3(B–D)) thectual sequestration of CO2 was still higher because by then

considerable amount of injected CO2 had dissolved in thexisting brine and most of it would have settled at the topf the domain. This is clearly displayed in the coarse domainontours illustrated in Fig. 3(G, H).

CO2 distribution profiles in Fig. 4 demonstrates a differentehaviour of the injected CO2 in fine domain where CO2 resid-al saturation was never reached though some tendency wasoticed at a radial distance of 1000 m after 800 years of sim-lation compared to the coarse domain where residual CO2

aturation was reached at about 200 years. In contrast, all CO2

rofiles in the coarse domain reach the CO2 residual satura-ion levels after 200 years. This is because lower permeabilityorous media limits both lateral and vertical CO2 mobilitynd maintain more contact with the surrounding brine whichnhances the solubility trapping to keep the injected gas moreecurely within the aquifer. In addition, the small size poresn the fine domain play like meniscus tubes which allow CO2

o break through due to capillary forces to enhance residualrapping. These results are consistent with those obtained byordbotten et al. (2005) and Kumar et al. (2005). In the case ofeterogeneity these profile show completely different trendshich will be discussed in more details in Section 3.6.

.3. Effects of injectivity

apillarity plays an important role in sequestering CO2 in geo-ogical formations because it enhances the residual trappingone of the means of sequestration). To investigate the effectf injection pressure on capillarity in the domain, supercriti-al CO2 was injected into a coarse sand domain at 36, 34 and2 MPa (cases 2, 5 and 6), respectively, under dynamic flow con-itions. The results presented in Fig. 5(A) show no significant

nfluence of the injection pressure on capillary pressure at allaturation values which is most likely due to the employedalues of injection pressure being very close to the hydro-tatic pressure in the aquifer, in fact in case 6 the same valuef 32 MPa was used in addition to the high permeability ofhe domain which offers easier migration of CO2 laterally andertically. These results are qualitatively consistent with thexperimental results achieved by Plug and Bruining (2007).


The influence of injection pressure on CO2 saturation pro-les is displayed in Fig. 5(B), which shows a steep increase

se 1 – fine sand (left) and case 2 – coarse sand (right).

in CO2 saturation at 70 m altitude for all injection pressuresas a result of gravity forces which cause most of the injectedCO2 to migrate up towards the top of the aquifer. This increasereaches the highest value at 200 years when the trends sharplysteep down till they reach CO2 residual saturation. The resultsindicate that the higher the injection pressure, the larger theamount of CO2 accumulated at the top of the aquifer at timesbetween 200 and 500 years of simulation. This amount of CO2


different injection pressures. (B) CO2 saturation curves atR = 500 m and Z = 70 m in a coarse homogeneous domain.

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Fig. 6 – CO2 plume evolution in high permeability homogenous aquifer at different times and temperatures: (A) after 20 yea

Our investigations explain that in addition to the saturation,capillary pressure is strongly influenced by the flow conditions

years at 58 ◦C, (B) after 200 years at 58 ◦C (case 2), (C) after 20

periods of simulation because it is not affected by the imbibi-tion process.

3.4. Temperature effects on CO2 distribution

In this research work we inspected the effects of temperatureon CO2 distribution during drainage and imbibition processes.CO2 saturation contours in Fig. 6 demonstrate smaller plumesof supercritical CO2 after 20 years of injection (i.e. end ofdrainage process) and 200 years (during imbibition process)at a domain temperature of 80 ◦C (case 5) compared to thosefor 58 ◦C (case 3) under the same injection pressure condi-tions. This is because increasing the temperature decreasesthe density and viscosity of the injected CO2 and conse-quently increases buoyancy and gravity forces that contributein spreading CO2 laterally and vertically. The effect of tem-perature on CO2 dissolution in the hosted brine is illustratedin Fig. 7. It shows that after about 200 years of simulationhigher temperature results in more CO2 dissolved becauseit decreases CO2 density which migrates upwards to get incontact with more fresh brine which enhances the solubil-ity trapping mechanism. Moreover it is observed in Fig. 8 thatcapillary pressure increases proportionally with temperatureand this change is more prominent between saturation valuesof 0.55–0.7. The results in Fig. 8 demonstrate that about 50%increase in capillary pressure is obtained when the tempera-


ture is increased from 58 ◦C to 80 ◦C. This increase in capillarypressure permits more CO2 flow into the small pores and trap

rs at 80 ◦C, (D) after 200 years at 80 ◦C (case 4).

there as a residual solute, which is referred to as residualtrapping of CO2.

3.5. Dynamic capillary pressure effects


Fig. 7 – Temperature effects on dissolved CO2 mass (cases2, 3 and 4).

dx.doi.org/10.1016/j.cherd.2014.04.020



Fig. 8 – Capillary pressure vs. aqueous saturation atd

iceddqisltCvfir

itdttsva

Fhc

Fig. 10 – Dynamic and quasi-static capillary

ifferent temperatures (cases 2, 3 and 4).

n the system. Several simulation tests were carried out toompare the CO2 saturation change in homogeneous and het-rogeneous computational domains under quasi-static andynamic conditions. The results are illustrated in Fig. 9 whichemonstrates that higher CO2 saturation is obtained underuasi-static flow conditions at any radial distance from the

njection well at all time levels. The elapsed time to attaintatic conditions allows more CO2 into small pores by capil-ary forces and it may increase convective mixing between thewo fluids which enhances solubility trapping of the injectedO2. Additionally, it is noticed from Fig. 10 that at saturationalues above 0.55 higher capillary pressures are generated inne-grained domain which is consistent to the theories whichelate capillary pressure directly to the pore size.

To determine the dynamic or damping coefficient (�), whichndicates the extent of dynamic capillary pressure effect,wo numerical simulations (cases 2 and 10) were run underynamic and quasi-static condition, respectively. All calcula-ion results are displayed in Fig. 11. From Eq. (16) we calculatedhe dynamic coefficient for each average value of the aqueousaturation calculated by Eq. (14), the corresponding average


alues of dynamic and static capillary pressures (Pc,dyn, Pc,stat),nd the calculated values of the time derivative of saturation

ig. 9 – CO2 saturation (volume fraction) curves foromogenous fine domain under static and dynamiconditions at altitude of 40 m (cases 1 and 9).

pressure–saturation curves for homogenous domains.

(∂S/∂t). Fig. 11 shows that the value of dynamic coefficientdecreases when the rate of change of aqueous saturationincreases and this decline is very sharp at low saturation val-ues when the rate of change in aqueous saturation is slow (i.e.lower values of ∂S/∂t). The attained relationship between thedynamic coefficient and aqueous saturation can be clarifiedby the longer time required to attain the residual saturationat higher values of dynamic coefficient.

3.6. Effects of heterogeneity

Heterogeneity is closely related to the disparity in permeabil-ity which strongly rules the CO2 transport through differentparts of the domain. To investigate this influence we com-pare four study cases (1, 2, 7 and 8) in terms of CO2 saturationdistribution in homogenous and heterogeneous domains. Asexpected, and in agreement with previous studies (e.g., Ataie-Ashtiani et al., 2001; Das et al., 2006), heterogeneity has shownan important influence on the characteristics of two-phaseflow. It is shown in Fig. 12 that all trends behave similarlyat 200 m and 40 m horizontal and vertical distances, respec-tively, as they display an increase in the integrated aqueousCO2 upon injection stops and tend to plateau after about 200years except in case 8 (coarse sand embedded in fine) whichstarts to drop after 50 years of simulation. This behaviour isrelated to the injection section into which the supercriticalCO2 was injected (lower 30 m) which for this case is a finelayer bounded by a coarse one above. This scenario encour-


ages vertical migration of CO2 due to the lower entry pressure

Fig. 11 – Dynamic coefficient change with aqueoussaturation in a homogeneous coarse sand domain (cases 2and 10).

dx.doi.org/10.1016/j.cherd.2014.04.020

Please cite this article in press as: Khudaida, K.J., Das, D.B., A numerical study of capillary pressure–saturation relationship for supercriticalcarbon dioxide (CO2) injection in deep saline aquifer. Chem. Eng. Res. Des. (2014), http://dx.doi.org/10.1016/j.cherd.2014.04.020



Fig. 12 – Integrated aqueous change for homogeneous andheterogeneous domains (cases 1, 2, 7 and 8) at radialdistance of 200 m and altitude of 40 m.

Fig. 13 – Total integrated CO2 profiles for homogeneous andheterogeneous domains (cases 1, 2, 7 and 8) at radialdistance of 200 m and altitude of 40 m.

Fig. 14 – Evolution of CO2 plume (volume fraction of CO2) in heterogeneous domain for 5, 20, 100 and 500 years: (A–D)fine–coarse–fine domain (case 7); (E–H) coarse–fine–coarse domain (case 8).

dx.doi.org/10.1016/j.cherd.2014.04.020



oubCtbwodtw5efpocmimt

cigDsofdfo

iatitlpltTNfti

4

AtorttmaTotIg

f the upper strata which consequently reduces both resid-al and solubility trapping by eliminating the contact timeetween CO2 and existing brine. However, larger amount ofO2 was dissolved in the homogenous coarse domain due

o the high permeability which increases CO2 movement inoth directions maintaining more contact with fresh brine inhich it dissolves. Fig. 13 presents the total integrated amountf CO2 in aqueous and gas phases at the same grid blockescribed above. It is apparent that all curves decline andend to plateau soon after the injection stops except case 8hich shows sharp increase in total integrated CO2 till about

0 years of simulation and continuously increases until thend of 1000 years of simulation. This can be explained by theact that the injected CO2 favourably move through large sizeores which increases the hydrodynamic trapping as a resultf pressure difference forces and CO2 concentration. This isombined with the solubility trapping due to the convectiveixing of CO2 and the surrounding brine. Residual trapping

s larger in the surrounded fine layer which slows down theigration of the injected CO2 providing more chance to enter

he small pores.CO2 spatial spread is demonstrated in three-dimensional

ylindrical contours in Fig. 14, which demonstrates how thenjected supercritical CO2 spreads through different hetero-eneous domains (cases 7 and 8) at different time steps.uring a drainage process period of 20 years for case 7 (coarseand embedded in fine), higher CO2 saturation values werebtained. This increase is a result of the pressure differenceorces that control the lateral migration of CO2 and verticallyue to the buoyancy forces that transfer the supercritical fluidrom the low permeability layer up to the higher permeabilityne as evidently shown in Fig. 14(A–D).

In contrast during imbibition process (post injection) whichs presented in case 8, higher concentrations of CO2 werechieved as shown in Fig. 14(E, H) because in this case advec-ive, diffusive and gravity forces all contribute in trapping thenjected CO2 in addition to the reversed-back movement ofhe brine behind the CO2 plume to displace the CO2 againeaving traces of it as residual contaminants in small-sizedores which is referred to as residual trapping. Moreover the

ow permeability layer retains more contact time between thewo fluids which enhances the solubility trapping mechanism.he results of this work are consistent with those obtained byordbotten et al. (2005) as they found out that the buoyancy

orces places the highest mobility layer of injected CO2 at theop of the domain considering that in their case the CO2 wasnjected along the whole altitude of the domain.

. Conclusion

series of numerical simulations have been conducted inhis work to identify the possible implications of a numberf important parameters on the capillary pressure–saturationelationship for supercritical CO2 in deep saline aquifer. Fromhe results of this work it is obvious that the higher the injec-ion pressure, the higher the capillary forces are; however, the

aximum sustainable pressure has to be taken into consider-tion to avoid any geochemical fracture to the formation rock.he value of the dynamic coefficient (�) increases as the ratef change of aqueous saturation (∂S/∂t) declines because moreime is required for the residual saturation to be attained.


t has been found that capillary forces are higher in fine-rained domains and they enhance storage capacity of the

site by amplifying the residual trapping mechanism of CO2

during the imbibitions process. Solubility trapping is moreefficient in fine domains because they maintain more contactbetween the fluid phases which leads to more CO2 dissolvedin aquifer brine. Warm aquifers are more competent in CO2

sequestration because higher temperatures increase the cap-illary pressure and consequently enhance residual trappingof CO2. Fine sand embedded in coarse pattern of heterogene-ity is found to be more effective method over long periods ofstorage procedure however more research is required to clar-ify how the field distribution of heterogeneity and injectionscenarios of CO2 affect the efficiency of the sequestration.

Acknowledgments

We thank Dr Mark D. White from Pacific Northwest NationalLaboratory (PNNL), USA, for his insights and helpful commentsin employing the STOMP simulation code in this study.

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a numerical study of capillary pressure–saturation relationship for supercritical carbon dioxide...

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