# Injection, Flow, and Mixing of CO2 in Porous Media with Residual Gas

**ABSTRACT** Geologic structures associated with depleted natural gas reservoirs are desirable targets for geologic carbon sequestration

(GCS) as evidenced by numerous pilot and industrial-scale GCS projects in these environments world-wide. One feature of these

GCS targets that may affect injection is the presence of residual CH4. It is well known that CH4 drastically alters supercritical CO2 density and viscosity. Furthermore, residual gas of any kind affects the relative permeability of the liquid and gas phases,

with relative permeability of the gas phase strongly dependent on the time-history of imbibition or drainage, i.e., dependent

on hysteretic relative permeability. In this study, the effects of residual CH4 on supercritical CO2 injection were investigated by numerical simulation in an idealized one-dimensional system under three scenarios: (1) with

no residual gas; (2) with residual supercritical CO2; and (3) with residual CH4. We further compare results of simulations that use non-hysteretic and hysteretic relative permeability functions. The primary

effect of residual gas is to decrease injectivity by decreasing liquid-phase relative permeability. Secondary effects arise

from injected gas effectively incorporating residual gas and thereby extending the mobile-gas plume relative to cases with

no residual gas. Third-order effects arise from gas mixing and associated compositional effects on density that effectively

create a larger plume per unit mass. Non-hysteretic models of relative permeability can be used to approximate some parts

of the behavior of the system, but fully hysteretic formulations are needed to accurately model the entire system.

KeywordsGeologic carbon sequestration–Depleted gas reservoir–Enhanced gas recovery–Residual gas–Hysteretic relative permeability

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**ABSTRACT:**During CO2 injection into brine aquifers-containing residual and/or dissolved CH4, three distinct regions develop: (1) a single-phase, dry-out region around the well-bore filled with pure supercritical CO2; (2) a two-phase, two-component system containing CO2 and brine; and (3) a two-phase, two-component system containing CH4, and brine. This article extends an existing analytical solution, for pressure buildup during CO2 injection into brine aquifers, by incorporating dissolved and/or residual CH4. In this way, the solution additionally accounts for partial miscibility of the CO2–CH4–brine system and the relative permeability hysteresis associated with historic imbibition of brine and current drainage due to CO2 injection and CH4 bank development. Comparison of the analytical solution results with commercial simulator, CMG-GEM, shows excellent agreement among a range of different scenarios. The presence of residual CH4 in a brine aquifer summons two competing phenomena, (1) reduction in relative permeability (phase interference), which increases pressure buildup by reducing total mobility, and (2) increase in bulk compressibility which decreases pressure buildup of the system. If initial CH4 is dissolved (no free CH4), these effects are not as important as they are in the residual gas scenario. Relative permeability hysteresis increased the CH4 bank length (compared to non-hysteretic relative permeability), which led to further reduction in pressure buildup. The nature of relative permeability functions controls whether residual CH4 is beneficial or disadvantageous to CO2 storage capacity and injectivity in a candid brine aquifer.Transport in Porous Media 94(3). · 1.55 Impact Factor -
##### Article: Modeling CO2 injection at Cranfield, Mississippi: Investigation of methane and temperature effects

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**ABSTRACT:**A large-scale carbon dioxide (CO2) injection pilot is ongoing at Cranfield, Mississippi, in a saline aquifer with high dissolved methane (CH4) content, employing one injection well and two observation wells. The breakthrough of CH4 and CO2 at the observation wells provides insights to phase partitioning and the multipath nature of flow through the formation. Injected CO2 is cooler than the formation temperature, making temperature another useful observation. Simulations of the first year of CO2 injection were conducted with the numerical simulator TOUGH2 and the equation of state module EOS7C, which includes CO2, CH4, and H2O, using an axisymmetric model with layering based on well logs from the injection well. Although the simplification of an axisymmetric model precludes study of formation dip or lateral heterogeneity, its simple structure enables a focus on physical processes involving the phase partitioning of CH4 and CO2, and temperature effects. Field observations that the model reproduces include the arrival of a bank of free-phase CH4 ahead of the main CO2 plume at each observation well, and non-monotonic changes in CH4 and CO2 mole fraction as a function of time, suggesting that multiple distinct flow paths exist between the injection well and the observation wells, each with its own bank of free-phase CH4 leading the CO2. Model results are compared with temperature observations made in the field with a Distributed Temperature Sensor (DTS) system, suggesting that a well-defined thermal response reached the near observation well within the seven-month monitoring period, but not the more distant observation well. © 2013 Society of Chemical Industry and John Wiley & Sons, LtdGreenhouse Gases: Science and Technology 12/2013; 3(6). · 2.92 Impact Factor - Seyyed Abolfazl Hosseini, Hamidreza Lashgari, Jong W Choi, Jean-Philippe Nicot, Jiemin Lu, Susan D HovorkaInternational Journal of Greenhouse Gas Control 10/2013; 18:449-462. · 3.82 Impact Factor

Page 1

Transp Porous Med (2011) 90:201–218

DOI 10.1007/s11242-010-9645-1

Injection, Flow, and Mixing of CO2in Porous Media

with Residual Gas

C. M. Oldenburg · Christine Doughty

Received: 11 March 2010 / Accepted: 9 August 2010 / Published online: 2 September 2010

© The Author(s) 2010. This article is published with open access at Springerlink.com

Abstract

able targets for geologic carbon sequestration (GCS) as evidenced by numerous pilot and

industrial-scale GCS projects in these environments world-wide. One feature of these GCS

targets that may affect injection is the presence of residual CH4. It is well known that CH4

drastically alters supercritical CO2density and viscosity. Furthermore, residual gas of any

kindaffectstherelativepermeabilityoftheliquidandgasphases,withrelativepermeabilityof

thegasphasestronglydependentonthetime-historyofimbibitionordrainage,i.e.,dependent

on hysteretic relative permeability. In this study, the effects of residual CH4on supercritical

CO2injection were investigated by numerical simulation in an idealized one-dimensional

system under three scenarios: (1) with no residual gas; (2) with residual supercritical CO2;

and (3) with residual CH4. We further compare results of simulations that use non-hyster-

etic and hysteretic relative permeability functions. The primary effect of residual gas is to

decrease injectivity by decreasing liquid-phase relative permeability. Secondary effects arise

from injected gas effectively incorporating residual gas and thereby extending the mobile-

gas plume relative to cases with no residual gas. Third-order effects arise from gas mixing

and associated compositional effects on density that effectively create a larger plume per

unit mass. Non-hysteretic models of relative permeability can be used to approximate some

parts of the behavior of the system, but fully hysteretic formulations are needed to accurately

model the entire system.

Geologic structures associated with depleted natural gas reservoirs are desir-

Keywords

recovery · Residual gas · Hysteretic relative permeability

Geologic carbon sequestration · Depleted gas reservoir · Enhanced gas

C. M. Oldenburg (B ) · C. Doughty

Earth Sciences Division 90-1116, Lawrence Berkeley National Laboratory,

Berkeley, CA, USA

e-mail: cmoldenburg@lbl.gov

C. Doughty

e-mail: cadoughty@lbl.gov

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202C. M. Oldenburg, C. Doughty

1 Introduction

Severalgeologiccarbonsequestration(GCS)projectsaroundtheworldinvolveCO2injection

into depleted gas reservoirs. In some cases, injection is directly into the depleted reservoir

(e.g., K12-B, Van der Meer et al. 2004), while in others it is into the water leg of the reser-

voir (e.g., Otway Basin Pilot Project (Sharma et al. 2007); In Salah (Ringrose et al. 2009)).

Regardlessofthedetailsofindividualprojects,injectionintodepletedreservoirsmayinvolve

injection into porous media that are filled predominantly with brine and residual methane

(CH4) gas.

There are numerous potential effects of residual CH4gas on supercritical CO2injection.

First, residual gas of any kind will decrease the mobility of the brine, all other things being

equal. Second, residual CH4provides an initial gas-phase saturation that can be mobilized

andincorporatedintotheinjectedplume,therebyincreasingitssize.Third,themixingofCH4

into supercritical CO2causes a large decrease in gas mixture density and viscosity that can

affect the injectivity and mobility of the gas. In this study, the effects of residual gas on injec-

tion of supercritical CO2are investigated through modeling of an idealized one-dimensional

radial system using TOUGH2/EOS7C (Oldenburg et al. 2004a,b) enhanced with hysteretic

capillarypressureandrelativepermeabilitycurves(Doughty2007).Toevaluateandcompare

results, we refer to the concept of injectivity, defined loosely here as the pressure rise at the

well for a given mass injection rate.

2 Motivation

2.1 Prior Work

There are numerous papers on the concept and evaluation of general feasibility of CO2injec-

tionintonaturalgasreservoirsforGCSandforenhancedgasrecovery(Bloketal.1997;Koide

et al. 1992; van der Burgt et al. 1992; Oldenburg et al. 2001, 2004a,b). In addition, studies

of thermal effects of injecting high-pressure CO2into low-pressure depleted reservoirs have

been made (Oldenburg 2007; Maloney and Briceno 2009; Mathias et al. 2010). The drastic

changes in CO2properties arising from mixing with CH4are well known (e.g., Oldenburg

etal.2004a,b)andtheassociatedpotentialbeneficialuseshavebeennoted(Oldenburg2007).

None of these prior studies has investigated the effects of residual gas saturation in general,

or the compositional effects associated with mixing supercritical CO2and residual CH4

gas in particular. Furthermore, studies that compare hysteretic and non-hysteretic capillary

pressureandrelativepermeabilitycurveshavefocusedonsalineformationsandCO2trapping

(Doughty 2007) rather than on depleted gas-reservoirs and CO2injectivity.

2.2 Effect of Residual Gas on Injection

Residual gas may affect an injection process in many different ways, e.g., inhibiting the dis-

placementofbrinethroughreducedrelativepermeabilityofbrine,enhancinginjectionofgas

asresidualgasbecomesmobileattheleadingedgeoftheinjectedgasplume,orchangingthe

composition of the gas and therefore gas-phase properties as injected gas mixes with resid-

ual gas of different composition. The purpose of this study is to investigate the processes of

interactionbetweeninjectedsupercriticalCO2andresidualgastounderstandpotentialimpli-

cations for gas-reservoir injection projects in general. A simplified one-dimensional radial

geometry is used to focus on mobility and gas composition effects. The idealized system was

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas203

Fig. 1 Three alternative cases for injection of CO2. a Zero residual gas. b 20% residual gas consisting of

CO2(white stipple). c 20% residual gas consisting of CH4(dark stipple)

Fig. 2 Variation of gas density and viscosity as a function of CO2–CH4mole fraction and pressure at a 40◦C

and b 90◦C

chosen to have a constant-pressure boundary condition at a radius of approximately 1km to

model injection into the water leg of a depleted gas-reservoir system with a nearby gas cap

that would tend to moderate pressure rise due to injection.

Three different situations are shown in Fig. 1 to illustrate the question being addressed.

The base case is the injection of CO2into a system with no residual gas (Fig. 1a). Figure 1b

shows the case of injection of supercritical CO2into an aquifer with supercritical CO2at

residual saturation. Lastly, Fig. 1c shows the case of injection of supercritical CO2into a

system with CH4at residual saturation. The specific question being addressed in this study

is:whatistheeffectofresidualgasanditscompositionontheinjectionofsupercriticalCO2?

The factors that make this problem potentially interesting are illustrated in Figs. 2 and 3.

Figure2showsaplotofdensityandviscosityforgas-mixturecompositionsbetweenpureCO2

and pure CH4as a function of pressure at reservoir temperatures of 40◦C (left-hand side) and

90◦C (right-hand side). Density in the figures is calculated using WebGasEOS (Reagan and

Oldenburg 2006), a publicly available web-based tool for calculating gas-mixture properties,

whichimplementsthePeng–Robinsonequationofstatefordensity,andthemethodofChung

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204C. M. Oldenburg, C. Doughty

Fig.3 Non-hystereticvariationofacapillarypressureandbgasandliquidrelativepermeabilityasafunction

of liquid saturation using functions given in Table 1 and two different Sgrvalues. Hysteretic variation of

c capillary pressure and d gas and liquid relative permeability using functions given in Table 1, for several

possible turning points (dots). The drainage branches (red) and the imbibition branches with turning points

at Slr(blue) form an envelope in which other imbibition branches lie. Arrows identify whether drainage (Sg

increasing) or imbibition (Slincreasing) occurs on a given branch

etal.(1988)forviscosity.Asshown,thepropertiesofthemixturevarystronglywithcomposi-

tionatallpressuresandparticularlyatpressuresabovethecriticalpressureofCO2(7.4MPa).

The reason for this is that pure CO2compresses readily into its supercritical form, but this

compressibilityissignificantlydiminishedbyadmixedcomponentssuchasCH4,creatingthe

strong compositional dependence on density. One can imagine a scenario in which injected

supercriticalCO2encountersresidualCH4resultinginadrasticexpansionofthegasmixture.

Figure 3a, b shows typical non-hysteretic curves (van Genuchten 1980 for capillary pres-

sure and liquid relative permeability, and Corey 1954 for gas relative permeability; see

Table 1). As shown, gas relative permeability increases with gas saturation (liquid satura-

tion decreasing), while water relative permeability decreases with increasing gas saturation.

The presence of residual gas thus causes the liquid relative permeability to be lower, all other

thingsbeingequal.BecausetheinjectionoflargequantitiesofCO2forGCSrequiresboththe

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas205

Table 1 Properties of the idealized one-dimensional radial model reservoir

Thickness

Radius

Porosity (φ)

Pressure (Pa)

30m

1km (open right-hand side boundary, see Fig. 4)

0.2

Shallow reservoir case: 1 × 107Pa

Deep reservoir case: 2 × 107Pa

Shallow reservoir case: 40◦C

Deep reservoir case: 90◦C

5 × 10−13m2

van Genuchtena,b

λ = 0.63, Slr= 0.19,α = 1.5 × 10−3Pa−1,

Pmax= 1 × 105Pa, Sls= 1.

Non-hysteretic liquid: van Genuchtena,b;

Gas: Coreycλ = 0.63, Slr= 0.21, Sgr= 0.20 or 0.01;

Hysteretic liquid and gas relative permeabilityd

λ = 0.63, Slr= 0.21, Sgrmax= 0.20,γ = 2,λgas= 0.5

Liquid: 10−10m2s−1

Gas: 10−5m2s−1

θ= 0.0, P0=105Pa

0.25

Equal to relative permeability

Temperature (T)

Permeability (k)

Capillary pressure (Pc)

Relative permeability (kr)

Molec. diffusivity coefficients (dκ

β)1

Tortuosity (τ0)

Saturation-dependent tortuosity (τβ)

aPruess et al. (1999)

bλ is m in van Genuchten (1980)

cCorey (1954)

dDoughty (2007, 2009)

injectedCO2andthenativeaqueousfluids(brine)tomove,thepermeabilityoftheformation

to both the injected gas and the brine influences injection pressure, along with the size and

characteroftheinjectedCO2plume.Figure3c,dshowshystereticcurvesusingparametersin

Table 1, for several possible turning points (i.e., the saturation at which flow process changes

from drainage to imbibition or vice versa). As shown, drainage and imbibition branches are

distinct from one another, a feature that models the dependence of capillary pressure and

relative permeability on the flow process (drainage or imbibition) that is occurring as well

as on the saturation history (Doughty 2007). Moreover, imbibition branches with different

turning points have different values of residual gas saturation Sgr. In Fig. 3c, d, the drainage

branches (red) and the imbibition branches with turning points at Slr(blue) form an envelope

in which other imbibition branches lie. Values of Sgrrange from 0 for the drainage branch

to Sgrmax= 0.2 for the imbibition branch with turning point at Slr.

Prior to injection of CO2into depleted gas reservoirs, we envision a history of imbibi-

tion during the gas-production phase, i.e., as gas is produced, water flows into the formerly

gas-filled regions of the reservoir, entrapping residual gas. By this argument, our simulations

of CO2injection into the water leg of a depleted reservoir should begin on the imbibition

branch of the hysteretic curves with turning point Slr. However, the injection of the gas

(CO2) itself is a drainage process. In short, the part of the domain near the well experiencing

CO2injection (gas saturation increasing) has capillary pressure defined by the second-order

drainage branch of the capillary pressure curve (Fig. 3c), while the region where brine is

being displaced with unchanged gas saturation remains on the imbibition branch.

Our hysteretic formulation (Doughty 2009) for relative permeability does not distinguish

betweenfirst-orderimbibitionandsecond-orderdrainage,asindicatedbythetwo-wayarrows

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206C. M. Oldenburg, C. Doughty

on Fig. 3d. This approximation has worked well for previous problems involving CO2injec-

tion into saline formations. However, for the present problem, this approximation will not

adequatelyrepresentthesecond-orderdrainageaccompanyinginjectionofCO2intoresidual

gas. Therefore, being guided by the form of the capillary pressure curve, in which the sec-

ond-order drainage branch rapidly approaches the primary drainage branch as Sgincreases

(green dashed line in Fig. 3c), for relative permeability we approximate the second-order

drainage branch by the first-order imbibition branch with turning point at Sl= 0.6 (green

dashed line in Fig. 3d), but use a slightly increased value of Sgrmax= 0.265, which makes

Sgr= 0.2andassuresthattheinitialconditionsrepresentimmobilegas.Althoughadmittedly

ad hoc, this approach captures the essential features of the problem: it preserves the zero gas

relative permeability far from the injection well while enabling a rapidly increasing gas rel-

ative permeability near the injection well. Of course, it would be preferable to incorporate

the second-order drainage branches directly in the relative permeability functions, and such

an effort is planned as part of continuing code development.

This study is aimed at understanding the role of residual gas, from both the phase-

interference and compositional perspectives, in controlling CO2injection processes. Fluid

flow problems in which drainage and imbibition occur in different regions at different times

cannot be fully captured using non-hysteretic curves, but it is of interest to see if any relevant

features of the problem can be represented using the simpler non-hysteretic forms.

3 Methods

InjectionsimulationswerecarriedoutusingTOUGH2/EOS7C(Pruessetal.1999;Oldenburg

et al. 2004a,b) to accurately model multiphase flow and multicomponent CO2and CH4gas-

mixture properties. TOUGH2/EOS7C models five components (water, brine, CO2, a tracer,

and CH4). TOUGH2/EOS7C uses the Peng–Robinson equation of state to calculate gas-

mixture density, and the method of Chung et al. (1988) for calculating mixture viscosity.

EOS7C uses a fugacity equilibrium approach for gas-mixture solubility that is well-suited

for deep reservoir environments (Oldenburg et al. 2004a,b). Salinity effects on gas solubility

in the aqueous phase are not modeled, and we have used pure water (zero salinity) as the

aqueous phase in the results shown below. To investigate the phase interference effects of the

presence of residual gas on injection in a simplified geometry, we have used both hysteretic

and non-hysteretic models as implemented in iTOUGH2/EOS7C (Finsterle 2004; Finsterle

et al. 2008; Doughty 2007, 2009).

For this problem, a one-dimensional radial grid was used to emphasize the residual-gas

effects being investigated without the complications added by a more complicated geometry.

The discretization of the one-dimensional radial problem is shown in Fig. 4, emphasizing

the details of the fine discretization around the well. Beyond the near-well region, grid spac-

ing is uniform (2m) out to a radial distance of 300m (the maximum extent of CO2during

the 2-year simulation period), beyond which the grid gradually coarsens. Preliminary stud-

ies using a grid that gradually coarsened over all r showed that fronts can be significantly

smearedoutbynumericaldispersion.Theconstant-pressureboundaryconditionatr = 1074

m was chosen to model the presence of a gas cap somewhere in the system that would tend

to moderate pressure changes during water-leg CO2injection. The injection rate is 100t

CO2/day (1.16kg/s) into a 30-m thick layer with permeability of 500mD (5 × 10−13m2)

and porosity equal to 0.20. Two different reservoir scenarios are considered: (1) a 1km-deep

reservoir with initial pressure P = 1× 107Pa, T = 40◦C; and (2) a 2 km-deep system with

initial pressure P = 2×107Pa, T = 90◦C. All simulations are isothermal. The residual gas

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas 207

Fig. 4 Discretization of the one-dimensional radial problem showing detail around the well at r = 0m. All

boundaries are closed except the right-hand side which is held at constant pressure

saturation, Sgr, is set to 0.20 or 0.01 for the non-hysteretic case, to mimic various aspects of

the hysteretic case, in which Sgr= 0 during drainage and Sgrvaries from 0 to Sgrmax= 0.2

during imbibition. See Table 1 for specific values of parameters, and Fig. 3 for the capillary

pressure and relative permeability curves used in the simulations. Note that a small amount

of CH4is co-injected in all the simulations for an efficient numerical solution, but it does not

materially affect the results.

4 Results

Pressure (P), liquid saturation (Sl), mass fraction of CO2in the gas (XCO2

(ρg), and mass fraction of CH4in the gas (XCH4

Figs. 5, 6, and 7 for a shallow reservoir (P = 1 × 107Pa, T = 40◦C) and for a deep reser-

voir (P = 2 × 107Pa, T = 90◦C). Results from both hysteretic and non-hysteretic relative

permeability curves (with two different values of residual gas saturation) are presented for

P and Sl, the differences between which will be discussed first for each of the three cases.

In particular, for the case of no residual gas (Fig. 5) the pressure curves reveal differ-

ences for hysteretic and non-hysteretic results. Pressure rise for the case of non-hysteretic

Sgr= 0.20 is larger than for the cases of non-hysteretic Sgr= 0.01 and hysteretic relative

permeability. The reason for the difference is that non-hysteretic Sgr = 0.20 requires the

gas saturation in the injection zone to exceed 0.20 before CO2becomes mobile, hence the

pressure builds up more before flow occurs. For non-hysteretic Sgr = 0.01,CO2with gas

saturation exceeding 0.01 is mobile, thus creating less pressure build up. The hysteretic case

involves gas relative permeability following the drainage branch as CO2is injected, which

matches closely the non-hysteretic Sgr = 0.01 case. For locations beyond the gas front,

pressures are nearly equal for non-hysteretic and hysteretic cases because there is no gas

saturation to cause phase interference. Note in this first scenario the CO2plume extends to

r = 140m after 2years.

Figures 6 and 7 show results for the cases of CO2injection into the system with gas at

residual saturation. The results for pressure show large differences between hysteretic and

non-hysteretic curves and for the two different values of Sgr. The small pressure increase

obtained for non-hysteretic curves with Sgr= 0.01 arises because gas is mobile at nearly all

saturations. In contrast, for Sgr= 0.20, the gas relative permeability near the well and the

liquid relative permeability beyond the injected gas plume are lower than in the Sgr= 0.01

casecausinggreaterpressureincrease.Thehystereticpressureprofileisintermediatebetween

g

), gas density

g

) for the three cases considered are shown in

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208C. M. Oldenburg, C. Doughty

Fig. 5 Results after two years of injection of CO2into a formation saturated with brine, showing pressure,

saturation, gas density (kg m−3), and mass fractions for the shallow a and deep b reservoirs. In the upper

frames, where the dash-dot line is not visible, it coincides with the solid line

these extremes as it models drainage conditions near the well and imbibition conditions

beyond the injected plume front. The hysteretic liquid saturation profile is also intermedi-

ate between the non-hysteretic profiles over most of the plume. At low liquid saturations

(small r), the hysteretic profile follows the non-hysteretic profile with Sgr= 0.01. Starting

at Sl= 0.6 it then parallels the non-hysteretic profile with Sgr= 0.20. This behavior reflects

the gas-phase relative permeability curve shown in Fig. 3d, in which the dashed line used to

represent the second-order drainage branch coincides with the primary drainage branch for

Sl≤ 0.6, but more closely resembles the first-order imbibition branch for Sl> 0.6. Compar-

ing Fig. 3d to b indicates that the primary drainage and first-order imbibition branches are

identicaltothenon-hystereticgasrelativepermeabilitycurvesfor Sgr= 0.01and Sgr= 0.20,

respectively.

Considering now just the hysteretic results of Figs. 5 and 6, we see the first-order observa-

tion that the pressure increase at the well is larger for the case with residual CO2gas (Fig. 6)

than for the case of fully saturated conditions with zero residual gas (Fig. 5). This occurs

because of the decreased mobility of brine in the cases where residual gas is present. By this

mechanism, rather than enhancing injectivity as might be expected by the presence of gas at

the outset, residual gas inhibits injectivity by limiting the mobility of the brine that must be

displaced in order for injection to occur. The second observation from comparison of results

ofFigs.5and6isthattheplumeradiusasdefinedbytheregioninwhichgasismobileislarger

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas209

Fig. 6 Results after 2years of injection of CO2into a formation containing 20% residual gas consisting

mainly of CO2, showing pressure, saturation, gas density (kg m−3), and mass fractions for the shallow a and

deep b reservoirs

in Fig. 6 than in Fig. 5. Specifically, in the case of zero residual gas (Fig. 5), the injected CO2

plume extends approximately 140m as defined by the gas saturation. For the case with resid-

ual CO2gas (Fig. 6), the gas saturation front extends about 230m. Apparently, the injected

gas is augmented by the initial residual gas which is incorporated into the mobile gas plume.

Some of this increase in plume extent occurs because a small fraction of the injected CO2

dissolves when no CO2is initially present. Without this dissolution, simulation results (not

shown) indicate that the plume in the no-residual-gas case would extend to about 160m.

We now consider the most interesting case, that of supercritical CO2injection into a sys-

tem with residual CH4gas. Comparing only the hysteretic results, we observe the pressure

rise is slightly lower for the case of supercritical CO2injection into the system with residual

CH4(Fig. 7) than into the system with residual CO2(Fig. 6). The reason for this appears to

be the lower viscosity of CH4gas relative to supercritical CO2. Apparently, the displacement

of CH4ahead of the CO2injection front requires less pressure than does the displacement

of CO2. The drastic reduction in gas-mixture density as supercritical CO2mixes with CH4

reveals itself as a third-order effect in the liquid saturation curve which shows the larger

gas plume size (r = 260m for the shallow reservoir and r = 240m for the deep reservoir)

(Fig. 7) relative to the gas plume size (r = 230m) in Fig. 6. The effect is stronger for the

lower pressure and temperature case than for the higher pressure and temperature case. This

large decrease in density causes a volume expansion that is also reflected in the shape of

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210C. M. Oldenburg, C. Doughty

Fig. 7 Results after 2years of injection of CO2into a formation containing 20% residual gas consisting

mainly of CH4, showing pressure, saturation, gas density (kg m−3), and mass fractions for the shallow a and

deep b reservoirs

the liquid saturation curve. In contrast to the smooth increase in liquid saturation with radial

distance shown in Fig. 6, the liquid saturation curve in Fig. 7 shows two distinct regions: one

from r = 0 to r = 140m (where gas is predominantly CO2) and the other from r = 140 to

r = 260m (where gas is predominantly CH4) with a notable break in slope at the transition

from CO2to CH4. Note as an aside that the local maximum in liquid saturation (minimum

in gas saturation) near the plume front for the non-hysteretic case (Sgr= 0.01) is an artifact

of the non-hysteretic relative permeability model and does not occur for the hysteretic case.

In short, the simulations show that supercritical CO2mixes with residual CH4causing the

total volume of gas to increase, which creates a larger gas plume relative to the residual-CO2

gas case.

For the conditions considered here, the radial extent of the plume increases by almost

a factor of two when residual CH4is present (260m, Fig. 7) compared to injection into

a formation with no residual gas (140m, Fig. 5). This finding raises the question of how

much, if at all, plume extent would increase for CO2injection into a liquid-saturated for-

mation containing dissolved CH4, which is considered a likely scenario for CO2injection

into the water leg of a depleted gas reservoir or a saline formation located in the vicinity of

a petroleum resource. Figure 8 shows simulation results for a case in which the formation

initially contains dissolved CH4just below the solubility limit. Comparison of the saturation

profiles for Figs. 5 and 8 shows that they are identical right up to the leading edge, where

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas 211

Fig. 8 Results after 2years of injection of CO2into a formation containing dissolved CH4just below the

solubility limit, showing pressure, saturation, gas density (kg m−3), and mass fractions for the shallow a and

deep b reservoirs. In the upper frames, where the dash-dot line is not visible, it coincides with the solid line

the plume for the dissolved CH4case extends about 10m farther, to r = 150m. The mass

fraction profile indicates that the plume is nearly pure CO2out to r = 140, then nearly pure

CH4at the leading edge, indicating that as CO2moves out into the formation, creating a

gas phase and partially dissolving into the liquid phase, the initially dissolved CH4exsolves

immediately, and is then pushed ahead of the growing CO2plume. Because the mass of CH4

initially present for the dissolved case (Fig. 8) is much smaller than for the residual gas case

(Fig. 7), the increase in radial extent of the plume is correspondingly much smaller.

In summary, the three main effects observed in the preceding simulations are (1) the

reduction in injectivity caused by decreased brine mobility due to the presence of residual

gas regardless of composition, (2) the larger extent of the gas plume caused by incorpora-

tion of dissolved or residual gas into the injected gas plume, and (3) the expansion of the

gas plume caused by mixing of injected CO2with residual CH4. Hysteretic relative per-

meability is needed to model properly all of the variables over the whole domain, although

non-hysteretic models can be used for modeling parts of the system.

4.1 Effects of Alternative Outer Radial Boundary Conditions

Toexaminetheimpactoftheconstant-pressureboundaryapproximately1kmfromtheinjec-

tion well, several cases with an infinite-acting reservoir were also modeled. For these cases,

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Fig.9 Resultsafter2yearsofinjectionofCO2intoaninfinite-actingshallowreservoircontainingadissolved

CH4and b 20% residual gas consisting mainly of CH4, showing pressure, saturation, gas density (kg m−3),

and mass fractions. In the upper frames, where the dash-dot line is not visible, it coincides with the solid line

the grid extends 100km, farther than any of the pressure responses propagate during the

2-year injection period. Figure 9a shows results for a shallow formation containing dissolved

CH4(compare to Fig. 8a) and Fig 9b shows results for a shallow formation containing 20%

residual CH4gas (compare to Fig. 7a). The only noticeable differences are the pressure pro-

files, which are about 0.05MPa higher for the infinite-acting reservoir. The resulting density

increase is barely noticeable (as expected based on Fig. 2a), and the saturation and mass

fraction profiles are essentially unchanged. Simulation results for other initial conditions are

comparable.Thus,wecanconcludethatasfarasplumedevelopmentgoes,theopenreservoir

model is equivalent to an infinite reservoir model.

A more extreme change in the outer radial boundary condition is to consider a closed

reservoir.Thisiseasilymodeledbyreplacingtheconstant-pressuregridblockatr = 1074m

in the original grid (Fig. 4) with a normal grid block. Figure 10 shows results for a closed

shallow reservoir after 2years for the cases with dissolved CH4initially present (Fig. 10a;

compare to Figs. 8a and 9a) and 20% residual CH4initially present (Fig. 10b; compare

to Figs. 7a and 9b). For the closed right-hand side boundary condition, there is a large

pressure increase accompanying CO2injection when no gas is initially present (Fig. 10a)

because liquid compressibility is small, enabling the pressure response to propagate rapidly

to the closed boundary. The large pressure increase (about 7.6MPa, compared to less than

0.1MPa for the open and infinite-acting cases) causes CO2density to increase dramatically

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas213

Fig. 10 Results after 2years of injection of CO2into a closed shallow reservoir containing a dissolved CH4

and b 20% residual gas consisting mainly of CH4, showing pressure, saturation, gas density (kg m−3), and

mass fractions. In the upper frames, where the dash-dot line is not visible, it coincides with the solid line. Note

the two different pressure scales for a and b; initial reservoir pressure is 10MPa for both

(from 570kg/m3to 795kg/m3), resulting in a more compact CO2plume (a plume extent

of r = 120m at 2years rather than the r = 150m previously obtained). In contrast, when

residual gas is initially present, fluid compressibility is significantly larger, and the closed

boundary has only a small effect (Fig. 10b), with pressure increasing about 0.15MPa more

than for the open case and 0.10MPa more than for the infinite-acting case. This completely

closed reservoir is probably not a realistic choice for actual CO2storage, but it serves as a

limiting case for the more promising “semi-closed” reservoirs, which are bounded radially,

but allow significant pressure release through under- and overlying shale layers (Zhou et al.

2009).

4.2 Displaying Results as Transients for Observation Well Locations

Displaying simulation results as a function of radial distance for a given time provides an

excellent way to visualize the multi-phase flow and transport processes accompanying CO2

injection, but it is not necessarily the optimal approach for designing field experiments or

interpreting field data. Rather than having a complete picture of pressure, saturation, and gas

content throughout the subsurface at a given time, we typically have a transient record from

a limited number of observation wells. Figure 11 shows the simulation results for 4years of

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214C. M. Oldenburg, C. Doughty

Fig.11 Transientresponseat50m(solid),100m(longdash),and150m(shortdash)awayfromtheinjection

wellforCO2injectionintoaopenandbclosedshallowreservoirscontainingbrinewithdissolvedCH4.When

no gas phase exists (Sl= 1), gas mass fractions are shown as zero and ρgshows the density a gas phase would

have if it were present

CO2injection into open and closed shallow reservoirs for initial conditions of brine nearly

saturated with dissolved CH4, as the transient response at three observation wells located 50,

100, and 150m away from the injection well. Figure 12 shows the same results for initial

conditions of brine containing 20% residual CH4.

The open-reservoir case satisfies the conditions required for a similarity-variable r2/t to

exist: one-dimensional radial geometry, essentially infinite radial extent, spatially uniform

material properties and initial conditions, and steady flow rate at the injection well. Thus, the

transient responses at each observation well can be collapsed to a single curve by dividing

each time by the r2value of that well. Such an exercise can provide useful insight into grid

discretization errors, and in fact was used for that purpose here, to confirm that the 2-m grid

spacingwithinthedomainoftheCO2plumeisadequate.However,plottingversust/r2does

not illustrate the actual timing of CH4and CO2arrival as well as plotting versus t does. For

example, Fig. 11a illustrates clearly that as observation well distance increases, the duration

of the CH4pulse at the leading edge of the CO2plume increases.

The difference in pressure response for the open and closed reservoirs is strikingly dis-

played in the transient plots. When plotted on a scale big enough to show the entire range of

pressures reached for the closed reservoir, as is done in Fig. 11, the responses for the differ-

ent observation wells collapse to a single curve. That is, the pressure over the entire model

is roughly uniform. For the open reservoir (Fig. 11a), this uniform pressure is essentially

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Injection, Flow, and Mixing of CO2in Porous Media with Residual Gas215

Fig.12 Transientresponseat50m(solid),100m(longdash),and150m(shortdash)awayfromtheinjection

well for CO2injection into a open and b closed shallow reservoirs containing brine with 20% residual CH4

constant, so the gas density is purely a function of gas-phase composition. In contrast, for

the closed reservoir (Fig. 11b), as pressure increases, CO2density increases sharply and

CH4density increases modestly (consistent with Fig. 2a), and this variation is superposed

on the gas-phase composition dependence as CH4and CO2arrive at each observation well.

The overall density increase makes the plume much more compact, greatly lengthening the

arrival time at more distant observation wells.

When residual gas is present (Fig. 12), the difference between open and closed reservoir

cases is much smaller, as the overall pressure increase for the closed reservoir case is small.

Here the transient response highlights how long a time delay there is between the arrival

of the plume (as manifested by a liquid saturation decrease) and the arrival of CO2at an

observation well, and how this delay grows significantly as observation well distance from

the injection well increases. In contrast to the dissolved CH4initial condition, where the

CH4pulse is rather narrow (Fig. 11), when residual CH4is initially present, CO2arrival

may not occur for a considerable time after the initial decrease in Sl(Fig. 12). For example,

for the 100-m observation well, with dissolved CH4initially present, CO2begins to arrive

simultaneously with the initial Sldecline, whereas with residual CH4initially present, there

is a delay of more than 200days between initial Sldecline and CO2arrival.

Figure 13 summarizes all the effects of initial and boundary conditions on plume devel-

opment by plotting plume arrival time at each observation well for all cases modeled. For

an open or infinite-acting reservoir, the arrival time of the plume at a given observation well

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