Advances in Water Resources 33 (2010) 867–879

Contents lists available at ScienceDirect

Advances in Water Resources

j ourna l homepage: www.e lsev ie r.com/ locate /advwatres

A contribution to risk analysis for leakage through abandoned wells in geologicalCO2 storage

Andreas Kopp c, P.J. Binning a, K. Johannsen b, R. Helmig c, H. Class c,⁎a Institute of Environment and Resources, Technical University of Denmark, Bygningstorvet, 2800 Kongens Lyngby, Denmarkb Parallab, Bergen Center for Computational Science, University of Bergen, Hoeyteknologisenteret, Thormoehlensgate 55, 5008 Bergen, Norwayc Department of Hydromechanics and Modelling of Hydrosystems, Universität Stuttgart, Pfaffenwaldring 61, 70569 Stuttgart, Germany

⁎ Corresponding author.E-mail addresses: andreas.kopp@iws.uni-stuttgart.de

(P.J. Binning), klaus.johannsen@bccs.uib.no (K. Johannserainer.helmig@iws.uni-stuttgart.de (R. Helmig), holger.c(H. Class).

0309-1708/$ – see front matter © 2010 Elsevier Ltd. Aldoi:10.1016/j.advwatres.2010.05.001

a b s t r a c t

a r t i c l e i n f o

Article history:Received 16 October 2009Received in revised form 4 May 2010Accepted 4 May 2010Available online 15 May 2010

Keywords:CO2 storageMultiphase flowRisk assessmentLeakage

The selection and the subsequent design of a subsurface CO2 storage system are subject to considerableuncertainty. It is therefore important to assess the potential risks for health, safety and environment. Thisstudy contributes to the development of methods for quantitative risk assessment of CO2 leakage fromsubsurface reservoirs. The amounts of leaking CO2 are estimated by evaluating the extent of CO2 plumes afternumerically simulating a large number of reservoir realizations with a radially symmetric, homogeneousmodel. To conduct the computationally very expensive simulations, the ‘CO2 Community Grid’ was used,which allows the execution of many parallel simulations simultaneously. The individual realizations are setup by randomly choosing reservoir properties from statistical distributions. The statistical characteristics ofthese distributions have been calculated from a large reservoir database, holding data from over 1200reservoirs. An analytical risk equation is given, allowing the calculation of average risk due to multiple leakywells with varying distance in the surrounding of the injection well. The reservoir parameters most affectingrisk are identified. Using these results, the placement of an injection well can be optimized with respect torisk and uncertainty of leakage. The risk and uncertainty assessment can be used to determine whether asite, compared to others, should be considered for further investigations or rejected for CO2 storage.

(A. Kopp), pjb@env.dtu.dkn),lass@iws.uni-stuttgart.de

l rights reserved.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Carbon dioxide storage in subsurface reservoirs is a promisingtechnology for managing anthropogenic carbon dioxide fluxes intothe atmosphere. The design of a carbon dioxide storage system issubject to considerable uncertainty. For example, there is somechance that geological conditions will lead to leakage from the CO2

reservoir. But uncertainty is also involved in the engineering work, inpossible leakage through manmade pathways back into the atmo-sphere and in the abandonment of the site. In order to select suitablegeological formations for CO2 storage and design these systems it istherefore important to develop a concept of risk. The management ofrisk is an inevitable part of every CO2 storage attempt to mitigatepotential harm to the health of humans and animals, and to theenvironment. Risk management must be site specific to be successful.Nevertheless, a general framework should be adopted to serve as abasis for site specific risk management. This work addresses thedevelopment of a novel risk assessment framework for CO2 storage. As

a first step, CO2 plume evolution is investigated in a reservoir usingnumerical simulations based on a large statistical database ofpotential reservoir properties. The proposed approach to riskassessment is not specific to any site, region or basin. Rather itreflects the entire range of possible reservoir properties that can beencountered.

In this study, the entire range of reservoir properties provided bythe database is considered. Such an approach can be relevant in thevery early project phase, when very little information about the actualreservoir properties is available. The assessment might lead to theconclusion, that a specific reservoir is more suitable for CO2 storagethan another. Further investigations of a pre-selected reservoir(seismic investigations, well core analysis, detailed numerical simula-tions etc), must then be used to determine the suitability of the site orreject it. Hence, this risk assessment serves as an initial analysismethod, and is intended to determine the need for additionalreservoir investigations.

A characteristic of CO2 storage in geologic formations is theinfluence of several physical and geochemical trapping mechanismson very different time scales. On a short time scale, structural andstratigraphic trapping are the dominant trapping mechanisms. On themedium time scale, residual and solubility trapping become increas-ingly important [16,30,33,41,62], while at the long time scale mineraltrapping may become the dominant mechanism provided that

868 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

geochemical conditions are favorable [25]. Storage security increasesover time, since residual, solubility and mineral trapping represent along-term fixation of CO2.

The contribution of various trapping mechanisms onmultiple timescales adds complication to risk assessments. Similarities can be foundin radioactive waste disposal where performance assessment calcula-tions must consider the return of radionuclides to the accessibleenvironment over periods of longer than 10,000 years [46]. For CO2

storage, two time scales may be of interest, and these are directlyrelated to the environmental impacts that might occur from leakage:local environmental effects or global effects. The scope of the riskassessment and the associated time scales are defined dependent onthese impacts [31]. Themedium to long timescale (20 years or longer)considers global effects, that is the return of the CO2 back into theatmosphere. The short time scale considers local environmentalimpacts, leading to risk directly associated with exposure to leakedCO2; that is local health, safety and environmental hazards. Forexample, Ref. [59] suggests a potential for self-enhancement ofleakage rates, leading to a so-called ‘pneumatic eruption’; althoughthe author says it is unlikely. Ref. [56] states that local risks (togetherwith economic considerations) are likely to constrain allowableleakage rates more tightly than global impacts. Hence, the focus ofthe risk assessment method developed here is on the short time scale,i.e. up to 20 years. Only the injection period is simulated.

Risk is usually defined in terms of three questions [34]: How can asystem fail? What is the likelihood of failure? What are theconsequences of failure? The evaluation of these questions issometimes difficult because of the lack of data, poor knowledge ofprocesses, etc. Refs. [5] and [4] investigated natural and industrialanalogues (natural gas storage, liquid waste disposal, and nuclearwaste disposal) that could be used to guide risk mitigation insubsurface CO2 storage.

At present, geological CO2 storage risk assessments rely on expertopinions to rate individual scenarios, which then get combined toform an overall perception of risk. For example, Ref. [55] developed ascreening and ranking framework to evaluate potential storage siteson the basis of risk arising from possible CO2 leakage to health, safetyand the environment. In their spreadsheet-type analysis, theinvestigator has to rate, for example, the lithology of the storageformation by giving it a ‘weight’ (relative importance), an ‘assessmentattribute relative to risk’ and a ‘certainty factor’ (judging howwell theinformation is known). Estimates of the reliability and uncertainty aredependent on the level of knowledge of the investigator. The riskassessment outlined in the following, decreases subjectivity andtherefore may increase confidence of investigators/experts using suchcomprehensive frameworks. The rather simple method presentedhere tries to evaluate risk, associated with CO2 leakage based on theuncertainty of reservoir properties.

The first question addressed is ‘how can a storage system fail’. ACO2 reservoir can fail by leakage through fractures, wells or othergeological weaknesses located at some distance away from the CO2

injection well. We focus here on CO2 leakage through abandonedwells, although the method can be extended naturally, for example, tofractures. Leakage through an abandoned well can occur by multiplepathways [8]. Since information is limited on the state of such a well(material, condition and set-up of cement plugs, casings, etc.),uncertainty of potential leakage is large. The leakage through onewell is thenmultiplied by the number of wells encountered by the CO2

plume in the subsurface, yielding cumulative leakage out of thestorage formation. Leakage rates have been investigated by Refs. [51],[53], and [52] by a semi-analytical approach. Ref. [23] analyzed thespatial characteristics of well locations in the Alberta basin (Canada)and states that a typical CO2 plume can encounter up to severalhundreds of wells in high-density areas. Here, leakage is judged to besignificant if it occurs within a given time period. Such a failure can beevaluated by numerical simulation. The numerical simulator (see

Section 4) is used to determine the distribution of CO2 in the reservoir,and failure is defined to occur if leakage is produced. This is equivalentto stating that in reservoirs where the CO2 is spread over a greaterlateral area it is more likely that leakage occurs than in reservoirs witha compact CO2 volume.

The second part of a risk assessment is to determine the likelihoodthat such a failure will occur. This is assessed here by considering thepotential range of reservoir parameters, like porosity, geothermalgradient, depth, permeability anisotropy etc. by examining informa-tion recorded in a reservoir property database. Here the parametersare assumed to be uncorrelated. As is explained below in Section 2, acomputationally costly methodology is proposed that allows randomsampling of the parameter space and requires many simulations, foreach of which failure is assessed by examining whether CO2 hasleaked or not. For completing a total number of 50 large-scalesimulations, the ‘CO2 Community Grid’ environment [32] was used.

The final part of a risk assessment is to determine the consequenceof failure, or the damage. In this paper, damage is defined to beequivalent to the potential mass of CO2 leaking out of a reservoir. Herethe potential leakage mass is defined to be the total amount of CO2

that has passed by a leaky well at a given radial distance away fromthe injection well at a given time. This is equivalent to saying, that allCO2 that reaches a leaky well is damaging. Within the givenframework, this can be considered a conservative approach to riskestimation (see Sections 6 and 7).

For this risk analysis, only homogeneous and radially symmetriccases are studied, the proposed approach can easily be extended tomore complex scenarios. However, their interpretation would bemore difficult.

The approach to risk assessment presented in this paper is quitegeneral and can be applied using either numerical or analyticalmodels of the distribution of CO2 in repositories. Here a numericalapproach is employed, in part so that the method can be easilyextended to more complex cases in subsequent work, and in part todemonstrate how advances in computing technologies can be appliedto engineering problems.

2. Risk analysis concept

Risk can be defined in many ways. According to Ref. [34] it can bedefined in terms of three questions:

• How can a system fail?• What is the likelihood of failure?• What are the consequences of failure?

For the first question, there are many ways in which a CO2 storagesystem can fail. For example the system can fail to provide thenecessary injectivity with respect to the CO2 mass delivered by thesurface installations (power plant, pipe network, process engineeringdevices etc.). There are a number of engineering failures associatedwith the design of the installations and the injection process, forexample well corrosion, untight well plugs, and formation cloggingdue to halite precipitation in the close vicinity of the injection well.There might be failure associated with the design of the CO2

monitoring devices to measure CO2 plume evolution and possibleCO2 leakage. The system can also fail to provide the necessary capacityto store the intended CO2 production. Finally, the system can fail afterinjection due to CO2 leakage, e.g. through the injection well.

The risk study conducted here focuses on CO2 leakage out of thestorage reservoir. Ref. [31] summarized number of possible leakagepathways: (i) through the pore system in low-permeability caprockssuch as shales, if the capillary entry pressure at which CO2 may enterthe caprock is exceeded; (ii) through openings in the caprock orfractures and faults; and (iii) through anthropomorphic pathways,such as poorly completed and/or abandoned pre-existing wells. Wefocus on leakage through poorly completed and/or abandoned pre-

869A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

existing wells although the approach presented can also be applied tothe other leakage pathways. Abandoned wells have been identified asone of the most probable leakage pathways for CO2 ([4,23]). A pre-existing (leaky) well is assumed to exist at some distance from theinjection well. It has a constant diameter of 1 m and is screened overthe full reservoir thickness. The leakage pathway in the abandonedwell is not explicitly modelled, as will be explained below in theparagraph on the consequences of failure.

The likelihood of failure can be assessed by considering thepotential range of reservoir parameters like porosity, geothermalgradient, depth, and anisotropy. The statistical characteristics ofreservoir parameters were determined from a database includinginformation from over 1200 reservoirs or by a model (permeabilityanisotropy). Based on this data, probability density functions (pdf's)have been derived. The parameter space of potential reservoirproperties is then randomly sampled and simulations are conductedto assess the distribution of CO2 in the subsurface. Correlationsbetween the parameters given in the database were investigated andare very low [39]. For each simulation, failure is assessed byexamining whether CO2 has spread to a given radius within a giventime. If CO2 has spread beyond the leaky well radius, this case hasfailed. By simulation of many such cases, a likelihood of failure can bedetermined by relating the number of cases that failed nf (dependenton distance r from the injection well to the leaky well and time t) tothe total number of cases simulated (N).

To determine the consequences of failure, we define the damage tobe the amount of CO2 mass that has spread within the leaky wellsector beyond the leaky well distance (compare to Fig. 1). Theassumption is that damage (D)measures themass that can potentiallyleak through the pre-existing well out of the system. This means thatin this study the leakage process itself is not modelled.

Ref. [31] outline a framework for assessing environmental risks. Twocategories of potential environmental impacts from geological CO2

storage are defined: local environmental effects and global effects.Global effects arise from CO2 leakage to the atmosphere and relate tothe uncertainty in the effectivity of CO2 storage. Local effects arise, forexample, from the direct exposure of plant and/or life species to CO2

close to the site. This study does not distinguish between these impactcategories. The impact of leaking CO2 is not explicitly considered.Leaking CO2 could possibly (i) reach the next shallower geologicalunit where it is safely stored, (ii) pollute a fresh-water aquifer, or (iii)leak back to the atmosphere. One should be aware that for anindividual leakage scenario, the real damage may not be proportionalto the amount of CO2 that has leaked.

Fig. 1. Sketch of the radially symmetric model domain and definition of the leakage thatoccurred after time t at a leaky well in distance rleakywell from the injection well. CO2 isinjected into the center boundary and spreads laterally in the reservoir. Buoyancyforces drive the CO2 upwards where it accumulates below the caprock. Consequentlythe CO2 plume spreads faster at the top than at the bottom.

Since a simple reservoir geometry is used in this study togetherwitha random sampling of statistical parameter distributions, this riskassessment does not refer to any specific site. Rather risk, as it is definedhere, refers to a statistical leakage probability that might occur at a pre-existingwell. Risk is definedbymultiplying the likelihood of failurewiththe consequence of failure, which is expressed in Eq. (1).

Risk ½kg� = nf

N|{z}likelihood of failure

⋅ ∑N

i=1

Di

nf;|{z}

consequence of failure

ð1Þ

where nf [–] is the number of cases that failed (dependent on distancer [m] from the injection well to the leaky well and time t [d]), N [–] isthe total number of cases simulated, and Di is the damage [kg] of case iat time t.

The calculation of the damageDi is done in two steps. First, all massof CO2 that passes the distance r from the injection point isdetermined. This mass of CO2 is then multiplied with d

2πrin order to

count only that fraction of CO2 mass that swept over the leaky well ofdiameter d (m). Risk has the unit of mass (kg). For this study, thediameter of the leaky well is 1 m (as indicated in Fig. 1). Since leakageis not explicitly modeled (the leaky well is not included in thesimulations), a single model run can be used to calculate damage andrisk for many leaky wells radii r at different distances r. This allows aflexible and efficient evaluation of risk.

The concept outlined above, calculates risk as an average over theentire parameter space. This becomes apparent because nf cancels outof Eq. (1) and what is left is average risk ∑N

i = 1Di

N. The average risk,

using the statistical distribution within the parameter space, can beused tomotivate important conclusions (as given in Sections 5 and 7),but does not determine the risk of an individual case.

A procedure to calculate risk for an individual case, could be thefollowing: Assume that each simulation has four independent inputparameters, call them p1…p4, coming from the parameter distribu-tions. When fixing p2, p3, and p4, the probability of failure P1 due tovariation of parameter p1 can be determined by varying p1 and findingp1⁎ that partitions between failure and no failure. The probability P1 isthen determined from the probability distribution to be theprobability that p1Np1⁎, where p1Np1⁎ defines the range of parametersp1 leading to failure. The total failure probability P of this case can thenbe calculated by P=P1·P2·P3·P4. The risk associated with this casewould be the damage produced by this case times the failureprobability, i.e. Riski=Di·P1·P2·P3·P4. This individual risk is of coursedependent on the distance r from the injection well to the leaky welland the time t. This study does not consider the risk of an individualcase any further, but instead focuses on the average risk and theconclusions that can be drawn from it.

3. Parameters

To define parameter input sets for simulations, four independentparameter distributions are randomly sampled. These four para-meters are porosity φ, depth of the reservoir below surface D, averagegeothermal gradient at the site denoted dTdz, and the anisotropybetween vertical and horizontal absolute permeability AnIso. Theseare called primary parameters. All other parameters, called secondaryparameters, are functions of primary parameters or constants.

The primary parameters have been selected based on previoussensitivity investigations [36] where they are shown to be theparameters which are most influential on CO2 plume evolutionbehavior in a reservoir. Other parameters are not selected as primaryparameters for three reasons, (i) lack of data, (ii) correlation with theprimary parameters, and (iii) computational effort would be too high.Detailed information on statistical characteristics of primary para-meters, dependencies of secondary on primary parameters, mutual

870 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

interrelation of parameters, parameter sources, etc. is given in thefollowing and summarized in Table 2.

3.1. Primary parameters

Statistical characteristics of the primary parameters φ, D, and dTdzcan be calculated from the U.S. National Petroleum Council publicdatabase [54]. The NPC database is part of the TORIS database, whichcontains data for over 2500 crude oil reservoirs in the US. TORIS isunfortunately not available to the public. Nevertheless, the public NPCdatabase includes data from over 1200 reservoirs. Detailed informa-tion on the statistical analysis of the database is given in [37]. Table 1summarizes the resulting statistical characteristics. In Fig. 2 thehistograms of the NPC parameter distributions employed in thefollowing are shown. The hypothesis that datasets follow either anormal or log–normal distribution (shown in Fig. 2 as lines), isrejected by a Kolmogorov–Smirnov test [43]. Consequently, standardprobability distributions cannot be used.

To calculate statistical characteristics of the 4th primary parameter,the absolute permeability anisotropy (AnIso), a layered reservoir isconsidered. Layers have varying thickness and an alternating constantabsolute permeability of 3.24ot10−15 m2 and 1451.85·10−15m2.These permeabilities reflect the 5th and 95th percentiles of theabsolute permeability distribution in the NPC database. Whenestimating upscaled or effective permeability for flow in a layeredreservoir, the direction of the flow is of importance. The harmonicmean (see Eq. (2)) of the permeabilities is used to estimate effectivepermeability for flow perpendicular to the layers.

HM =∑imi

∑imi

Ki

ð2Þ

where i is the layer index, mi [m] is the thickness of the layer havingpermeability Ki [m2].

The arithmetic mean (see Eq. (3)) of the permeabilities is used toestimate effective permeability for flow parallel to the layers,

AM =∑imi⋅Ki

∑imi: ð3Þ

The anisotropy of effective flow permeability is calculated as theharmonic mean divided by the arithmetic mean. When varying thenumber and the thickness of the layers, the distribution shown inFig. 2 (bottom-right) is the result. Statistical characteristics of thedistribution are: minimum=0.0089, maximum=1.0, arithmeticmean=0.0283, median=0.0118, 5th percentile=0.00891 and 95thpercentile=0.0842.

Section 3.3 gives the procedure of sampling the primary parameterdistributions in order to define a simulation case.

Table 1Statistical characteristics for parameters in the NPC-database: porosity (φ), averagegeothermal gradient (dTdz) and depth below surface (D). Stated is the number ofdatasets used (n), minimum (Min), maximum (Max), arithmetic mean (A. Mean),median, 5th and 95th percentile of the data. Note that random sampling of the primaryparameters occurs only in the range between the 5th and 95th percentile of the data, sothat unrealistically high values of porosity and geothermal gradient are not relevanthere.

Parameter n Min Max A. Mean Median 5th Perc. 95th Perc.

φ [%] 1222 7 58 21 20 9 34dTdz [K/m] 1250 0.009 0.298 0.036 0.03 0.018 0.062D [m] 1273 17 5502 1680 1524 386 3495

3.2. Secondary parameters

Secondary parameters, for example absolute horizontal andvertical permeability, capillary pressure, residual phase saturationsand relative permeabilities, are dependent on primary parameters.Functional dependencies are given in the following.

In Fig. 3, correlation functions from the literature (Carman-Kozenytype [28,57,64]) along with NPC database values of porosity φ andabsolute horizontal permeability Kh are given. Correlation coefficientsof functions and database values are rather poor. However, theCarman-Kozeny function given in Eq. (4) with an average graindiameter of 35 μm fits the interpolated NPC database valuesreasonably well. The absolute horizontal permeability is thereforecalculated from porosity by using:

Kh =1

150d50

φ3

ð1−φÞ2 ð4Þ

where Kh is absolute horizontal permeability [m2] and d50 is averagegrain diameter [μm].

Absolute vertical permeability Kv [m2] is calculated by multiplyingthe absolute horizontal permeability Kh by the anisotropy factor AnIso(a primary parameter).

Calculation of residual water saturation Sw,r as a function ofabsolute permeability and porosity is given by Ref. [28] for a specificsite analyzed in this study. However, the permeability and porosityranges and distributions leading to the functionality given in Ref. [28]are not identical to the data considered here. This results in unrealisticvalues for residual water saturation Sw,r. Since no other correlationfunction is known to the authors, residual water saturation is definedas constant. Likewise, residual gas saturation SCO2,r is constant.

Relative water and gas permeability kr [–] is defined by aBrooks&Corey model ([7]). Since Brooks&Corey input parametersSw,r, SCO2,r together with the sorting factor λ are constant, the relationis identical in all simulations. This is a simplification which isnecessary due to lack of better knowledge (data). Only very fewmeasured relative permeability relations of CO2-brine systems areknown, e.g. [2]. But this sparse data does not allow the definition ofdependencies on e.g. primary parameters. Relative permeability has ahigh influence on plume evolution behavior, as will be discussed inSection 7.

Capillary pressure pc [Pa] is dependent on porosity, interfacialsurface tension between the water and the CO2 phase, water-rockcontact angle, and water saturation. A measured capillary pressurerelation and the Leverett J-function are used to determine a distributionof capillary pressure relations as a function of the primary parameters.The measured data is from [58] Experiment no. 12 where the sandcolumnhas a permeability of approx. 2·10−10m2 and a porosity of 0.37.The experimentwas conducted at a pressure of 8.5 MPa and at 300.15 K.The author also gives values for interfacial tension and contact angle.These data allow to use a Leverett J-function [44] to normalize thecapillary pressure relation. This relation is representative for theinvestigated rock-type. The dimensionless Leverett J-function is givenin Eq. (5):

JðSwÞ =pcðSwÞσ⋅cosΘ

ffiffiffiffiffiffiKh

Φ

r: ð5Þ

where pc is capillary pressure [Pa], σ is interfacial surface tension [Nm],

andΘ is the contact angle [°]. The assumption, underlying Eq. (5) is, thatthe porous medium can be modelled as a bundle of non-connectingcapillaries. In this model,

ffiffiffiffiffiKh

Φ

q[m] is proportional to the typical pore

Fig. 2. Histograms data show relative frequency of porosity [%] (top-left), geothermal gradient [Km] (top-right) and reservoir depth below surface [m] (bottom-left) derived from the

NPC database and relative frequency of the natural logarithm of anisotropy between vertical and horizontal intrinsic permeability [–] (bottom-right) derived from a anisotropymodel. Lines indicate normal distributions having the same statistical characteristics as the respective histogram datasets.

871A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

throat radius. The Leverett J-function is used to scale the given capillarypressure relation to other values of permeability, porosity, temperatureand pressure (since the interfacial tension σ changes with pressure and

Fig. 3. Correlation functions between porosity and absolute permeability and NPCdatabase reservoir values. Given are correlations by a Carman-Kozeny model ([64]) fordifferent average grain diameters, correlations by Ref. [57] for average sandstones andRotliegend sandstone and a correlation given by Ref. [28].

temperature). This is done by equating the J-function for two cases andsolving for the capillary pressure of interest (c.f. Eq. (6)).

pc;2ðSwÞ = pc;1ðSwÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiKh;1

Kh;2

Φ2

Φ1

sσ2cosΘ2

σ1cosΘ1: ð6Þ

Subscript ‘1’ indicates the reference capillary pressure relation androck properties (here experiment 12 in [58]), and subscript ‘2’ thecapillary pressure relation for the reservoir of interest. An equation forthe interfacial tension σ for water and CO2 systems, as a function ofpressure and temperature, is given by Ref. [42] (see Fig. 4). Examplesof resulting capillary pressure relations are shown in Fig. 5.

Salinity S [kg/kg] is defined as a constant. This is because a previoussensitivity study has shown that this parameter had little influence onplume evolution [36]. However, statistical characteristics could havebeen calculated from the NPC database.

Reservoir dip [°] is defined to be a constant at zero. Although,statistical characteristics could have been calculated from the NPCdatabase, the computational effort required to include reservoir dip asa primary parameter would have been too high. In order to includereservoir dip in simulations, full 3D simulations would have becomenecessary and the computational advantage of employing radialsymmetry would have been lost. Nevertheless, reservoir dip stronglyinfluences plume evolution behavior and results will be discussedwith respect to this simplification in Section 7.

CO2 fluid properties (density [kg/m3] and viscosity [Pa·s]) arecalculated and depend on temperature and pressure. Since in the riskanalysis, reservoir depth D is a primary parameter and its rangeincludes depths where CO2 occurs in the gaseous, liquid, andsupercritical states, the calculation of CO2 fluid properties needs tocover a broad range of possible pressures and temperatures. Adifficulty occurs when conditions change during the simulation, so

Fig. 4. Interfacial tension between CO2 and water dependent on pressure andtemperature [42]. Accuracy is reported to be greater than 95% within the experimentalrange. The experimental range includes temperatures between 278 and 335 K andpressures between 0.1 and 20 MPa. The range included in this work is expanded beyondthe experimental range; however interfacial tension does not vary significantly at highpressures and temperatures (reflecting great depth). At shallower depth, pressure andtemperature conditions are covered by the experimental range.

Table 2Definition of primary and secondary model input parameters, dependencies, andsources.

Parameter type Symbol Unit Dependency/Type

Source/Remark

Primary parametersPorosity φ [–] Statistical

Distribution[54]

G.grad dTdz [K/m] StatisticalDistribution

[54]

Depth D [m] StatisticalDistribution

[54]

Permeabilityanisotropy

AnIso [–] StatisticalDistribution

Layered reservoirmodel

Secondary parameters (variable)Horizontalpermeability

Kh [m2] f(φ) Carman-Kozenymodel ([64])

Verticalpermeability

Kv [m2] f(Kh,AnIso) Definition

Temperature TBC+ Init

[K] f(D,dTdz] Geothermal boundaryand initial condition

Pressure pBC

+ Init

[Pa] f(D,ϱb⁎) Hydrostatic boundary

and initial conditionCO2 solubilityin brine

XwCO2 [kg/kg] f(T,p) [14]

CO2 density ϱCO2 [kg/m3] f(T,p) [65]CO2 enthalpy hCO2 [J/kg] f(T,p) [65]CO2 viscosity μCO2 [Pa⋅s] f(T,p) [18]Brine density ϱb [kg/m3] f(T,p,S,Xw

CO2) [1,21][29]

Brine enthalpy hb [J/kg] f(T,p,S,XwCO2) [12,14,29,47]

Brine viscosity μb [Pa⋅s] f(T,S) [1]CO2-brineinterfacialtension

σ [N/m] f(T,p) [42]

Capillarypressure

pc [Pa] f(φ,σ,Θ,Sw⁎⁎) scaled by a LeverettJ-function based on apc relation given in [58]

Relativepermeability

kr [–] f(Sw,r,SCO2,r,λ,Sw⁎⁎)

[7]

Secondary parameters (constant) Value

Salinity S [kg/kg] 0.048 [54] median valueWatersolubility in CO2

XCO2w [kg/kg] 0.001 Negligible

Contact angle Θ [∘] 49.46 [58]Residual watersaturation

Sw,r [–] 0.3 –

872 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

that the vapor pressure curve is crossed, and gas and liquid can co-exist. In these cases CO2 properties change discontinuously by ordersof magnitude. If the conditions change from sub-critical to super-critical, or vice versa, without crossing the vapor pressure curve, CO2

properties change continuously.Other secondary parameters, like brine fluid properties, solubility

of CO2 in brine etc. are calculated by functions given in literature (ascited in Table 2) or are defined as constant values since results areinsensitive to variation of these parameters.

All parameters given in the NPC database are tested for mutualinterrelations. Apart from the considered dependencies (betweenporosity and absolute permeability and between depth and temper-ature) no significant correlations have been found.

Fig. 5. Capillary pressure dependence on water saturation and porosity. Here σ1=σ2,i.e. relations are at constant temperature and pressure.

Residual CO2

saturationSCO2,r [–] 0.05 –

Sorting factor λ [–] 5.87 [58][7]

Reservoir dip dip [∘] 0 –

Injection Value/Dependency

CO2 massinflux

qCO2 [MtCO2/yr]

1 Medium-sized coalfired power plant

Heat influx qh [J/yr] f(p,T,qCO2) Resembles injectionat actual reservoirconditions

.⁎ ϱb is constant for the calculation of initial and boundary conditions (1160 [kg/m3]).⁎⁎ Sw indicates water phase saturation [–].

3.3. Procedure of defining a simulation case

The four independent primary parameters are sampled bygenerating four random numbers between zero and one. Theserandom numbers reflect percentiles of the parameter distributions,for example if the random number is 0.5, the median of the parameterdistribution is obtained. Primary parameters are constant throughouta simulation. Following the generation of four random primaryparameters, the secondary parameters are calculated. All secondary

Table 3Details on the supercomputers used in this study.

Frontendname

Location No. ofnodes

No. ofcores

CPUtype

Theoretical totalpeak [Tflops]

ce02.titan.uio.no Univ. of Oslo 304 2432 Xeon/Opteron

21.5

norgrid.uit.no Univ. of Tromso 704 5632 Xeon 2 60hexgrid.bccs.uib.no Univ. of Bergen 1388 5552 Opteron 51

873A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

parameters, which are dependent on the unknowns in the simulation,i.e. pressure, temperature, saturation or CO2mass fraction dissolved inbrine, are continuously updated during model simulations. Thismeans, for example, that the capillary pressure relation could bedifferent in each gridblock and that it changes with time. Othersecondary parameters are fixed during the simulation.

4. Numerical simulation

In the simulations, a two-phase two-component non-isothermalmodel approach is used. Phases include a CO2-rich phase and a water-rich-phase (brine). Components are CO2 and water. Mass transferbetween the phases is considered, depending on pressure, temper-ature and salinity. An energy balance is solved (assuming localthermodynamic equilibrium), which accounts for temperaturechanges in the reservoir, e.g. due to gas expansion and resultingJoule-Thompson cooling. Salt is not treated as a component, butsalinity as a (constant) secondary parameter. An overview ofdependencies of CO2 and brine fluid properties and the solubilitymodel used to calculate CO2 dissolution in the water-rich phase isgiven in Table 2 where literature references are cited. While the fluidsare compressible, compressibility of the rock matrix is not considered,since the pressure-induced reduction of porosity and permeability isnegligible at great depth if the plume evolution is of interest (not ifresulting overpressures are of interest). The numerical simulator usedfor the study is the research code MUFTE_UG. It has been extensivelytested in code intercomparison studies and provides results in goodagreement with other commercial and non-commercial codes([9,35,60]). For a detailed review of the simulation environmentMUFTE_UG see Refs. [26] and [10]. Detailed information on thecapabilities of MUFTE_UG for simulation of CO2 storage in geologicalreservoirs is given in [6].

CO2 is injected in a radially symmetric model domain as shown inFig. 1. The reservoir has a lateral extent (radius) of 100 km and aheight of 100 m. A radially symmetric grid is used with 5750elements. The smallest radius is 1 m. Grid spacing increases towardsthe outer edge of the domain with 100 elements used for rb5000 mand an additional 15 elements between 5000 m and 100.000 m radius.A constant vertical spacing of 2 m per grid cell is used. The numericalperformance of the simulator is documented in the intercomparisonstudy of Ref. [9].

CO2 is injected at the center boundary at a constant rate of 1MtCO2

per year. This rate resembles the CO2 produced by a medium-sizedcoal-fired power plant. Since a heat balance is solved, a heat influx atthe center boundary also has to be defined. We assume that CO2 isinjected at reservoir conditions. Note that the reservoir conditionschange with time and heat influx is adapted to these changingconditions. Top, bottom and side boundaries are closed to any flux(Neumann). At the lateral boundary, hydrostatic pressure, geothermaltemperature and fully water saturated conditions are assumed. Thisresembles a laterally infinite aquifer with impermeable cap- andbaserock.

To conduct the computationally very expensive simulations, theCO2 Community Grid was used [32]. The CO2 Community Grid is avirtual research environment (VRE) for massively parallel simulationsrelated to CO2 storage in porous media. The VRE allows for the usageof a number of supercomputers located in Norway. Table 3 lists somedetails on the supercomputers used. The grid infrastructure iscontrolled by a kind of meta-computing system, based on theNordugrid [50] software ARC (Advanced resource connector [17]), amiddleware for lightweight computational grids, which provides aunified access to supercomputers. The gateway to the VRE is through aservice computer. This computer gives access to users and providesthem a simple, unified access to supercomputer platforms. The systemallows the execution of multiple parallel simulations simultaneously.During development, testing, and production of the results, statistics

on the number of CPUs used per job have been collected. Themaximum number of CPUs used for an individual job was 512 whilemost jobs used 64 CPUs.

5. Results

Typical results are shown in Fig. 6 for two cases. In both cases, theamount of injected CO2 is 20 MtCO2. Randomly sampled primaryparameters for Case 11 are φ11=0.19, dTdz11=0.020364 K/m,D11=1920.24 m, AnIso11=0.00898, and for Case 48 are φ48=0.26,dTdz48=0.053162 K/m, D48=640.08 m, AnIso11=0.02255. Thesesettings lead to CO2 density around 790 kg/m3 in Case 11 and330 kg/m3 in Case 48. In Case 11 no leakage occurs up to the timerepresented by the figure, whereas for Case 48 leakage occurs.

Given the definition of risk in Eq. (1), the two terms of the equationare evaluated separately and then combined to yield risk.

In Fig. 7 the likelihood of failure (LOF) is shown. Each point on thesurface shows the combined results of all simulations conducted. Therange of LOF is between zero (no case has failed) and one (all caseshave failed). Initially no CO2 is injected and consequently no failurehas occurred. After 7000 days all cases below rleakywell=1100 mhave failed and LOF is equal to one. For distances larger thanrleakywell=1100 m LOF reduces, since less cases fail within creasingdistances. For rleakywell=2000 m only 20% of cases fail after 7000 daysof CO2 injection. Generally LOF increases with time and decreaseswith distance rleakywell.

In Fig. 8 the consequence of failure (COF) is shown. As before, eachpoint on the surface shows the combined results of all simulationsconducted. The range of COF is between zero (no leakage occurred inany case) and 2.72·107 kg, where all cases produced considerabledamage after 7000 days at rleakywell=100 m. COF increases with timeand decreases with distance rleakywell. For any given distance rleakywell

COF increases quickly once damage has started to occur. For example,the COF is larger than zero for a leaky well at 200 m distance after91 days of injection, then increases to 106 kg at 792 days, and to107 kg after 5401 days. Another example is a leaky well in 2000 mdistance, where the COF is larger than zero after 2409 days ofinjection, increases to 104 kg at 2806 days, and to 105 kg after4819 days.

Risk is the product of the likelihood of failure and the consequenceof failure and is shown in Fig. 9. The range of risk is identical to therange of COF because LOF has a value between zero and one. Riskincreases with time and decreases with distance rleakywell, as onewould expect.

Risk contour lines (e.g., the red line in Fig. 9 identifies risk equal to0.001 kg) are fitted by the power-law

t½d� = eA⋅logðrÞ + B; ð7Þ

where r is leaky well distance in metres, and A and B are power-fittedcoefficients given in Table 4. The accuracy of fit of the power-functionis shown in the last column of the table.

Fig. 6. Slice of the radially symmetric domain showing CO2 saturation after 20 years of continuous injection for Case 11 (left) and Case 48 (right). Shown is only the center (inner)part of the domain and the vertical axis is exaggerated. No leakage can occur in Case 11, whereas for Case 48, CO2 has spread beyond the leaky well distance and the potential forleakage is high.

874 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

The time contour lines (c.f. black lines in Fig. 9) can be used tocalculate risk dependent on leaky well radii r. They are fitted by anexponential function to the risk surface given by

Risk½log kg� = ∑9

i=0Ai⋅r

i; ð8Þ

where r is leaky well distance in metres, and Ai are coefficients givenin Table 5.

In Fig. 10 risk is shown for a few selected leakywell distances and forvarious primary parameters. In general, risk for all cases increases withtimeof injection andwith smaller leakywell radii. For a leakywellwith aradius of 200 m, risk is basically identical in all cases. This result isexpected given the short time and spatial scale, because the results areindependent of the multiphase flow and transport regime in thereservoir and consequently independent of reservoir parameters. Theeffect and sensitivity of primary parameters is discussed below:

Fig. 10 (top-left) shows risk as a function of porosity. No cleartrend of risk as a function of porosity can be seen. Cases with aporosity of 0.106 produce almost the same risk as those with aporosity of 0.19, and 0.32 respectively. With increasing porosity onewould expect a retardation of the plume evolution velocity, simply

Fig. 7. Likelihood of failure [–] calculated as nf/N. nf is the number of cases that failed fordistance rleakywell [m] between injection well and leaky well at time t [d]), N [–] is thetotal number of cases simulated.

due to increased pore space, and consequently a later increase of risk,i.e. lower risk at any time. But the permeability also increases withporosity, since it is coupled by a Karman-Kozeny functionality (c.f.Section 3.2). The increased permeability leads to stronger gravitysegregation and hence to increased plume evolution velocity belowthe caprock. Note that the vertical permeability is coupled tohorizontal permeability via the Anisotropy parameter. The effects ofthe retarded plume evolution velocity due to increased porosity andstronger gravity segregation due to increased horizontal and verticalpermeability cancel each other out, i.e. risk appears to be independentof porosity. Small differences in risk are due to the other (random)primary parameters (e.g. depth).

Fig. 10 (top-right) shows risk for a given geothermal gradient. Itcan be seen that risk increases earlier with increasing geothermalgradient. This is because of the lower CO2 density for a higherreservoir temperature. Gravity segregation is stronger at highertemperatures and fast lateral plume evolution occurs below thecaprock. For rleakywell=1000 m, risk increases after 884 days for athermal gradient of 0.0532 K/m, after 2287 days for a thermalgradient of 0.0323 K/m, and after 3538 days for a thermal gradientof 0.0204 K/m. Risk is also quite different after 7000 days, i.e.4.31·105 kg, 8.96·105 kg, and 1.2·106 kg (Factor 3 in between).

Fig. 8. Consequence of failure [log kg] calculated as∑Ni = 1

Di

nfversus distance rleakywell [m]

between injectionwell and leakywell and time t [d].Di [kg] is damage in case i, nf [–] is thenumber of cases that failed (produced damage), N [–] is the total number of casessimulated.

Fig. 9. Risk [log kg] calculated as nf

N⋅∑N

i = 1Di

nfversus distance rleakywell [m] between

injection well and leaky well and time t [d]. Di [kg] is damage in case i, nf [–] is thenumber of cases that failed (produced damage), N [–] is the total number of casessimulated.

875A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

Fig. 10 (bottom-left) shows risk as a function of depth belowground surface and shows that risk increases earlier with decreasingdepth. This is also because of CO2 density: at lower density gravitysegregation is stronger, leading to fast lateral plume evolution belowthe caprock. For rleakywell=1000 m, risk increases after 884 days for adepth of 640 m, after 1433 days for a depth of 1403 m, and after2684 days for a depth of 2943 m. However, after 7000 days, risk canbe viewed as being identical for all depths.

Fig. 10 (bottom-right) shows risk as a function of permeabilityanisotropy. Risk increases earlier with increasing anisotropy factor.The gravity segregation effect is stronger for larger values of theanisotropy factor, i.e. less anisotropic permeability. Parametersensitivity is however lower, compared with the sensitivity togeothermal gradient and depth. For rleakywell=1000 m, risk increasesafter 1952 days for an anisotropy of 0.04274, after 2165 days for ananisotropy of 0.01282, and after 2318 days for an anisotropy of0.00898. This difference in time gets larger with increasing rleakywell.

Results show that the risk of leakage is primarily dependent on theplume development and the breakthrough of the formed gravitytongue. The influence of buoyant flow is well known in reservoirengineering [11,44]. In a previous study [37,38] developed estimatesfor CO2 storage capacity by dimensional analysis. There the gravita-tional number Gr and the capillary number Ca are used to describe theinfluence of buoyant forces and capillary forces on the development ofthe CO2 plume.

The gravitational number is defined as

Gr =ϱw−ϱCO2ð Þ⋅g⋅k

μCO2⋅vcr; ð9Þ

Table 4Power-fitted coefficients A and B in Eq. (7) to calculate risk contour lines. R2 indicatesgoodness of fit (that is the ratio of the sum of the squares of the regression to the totalsum of the squares) between {0,1}, where a value closer to one indicates better fit.

Risk contour line [log kg] A B R2

0.001 1.5487 −3.9691 0.99531 1.4654 −3.2771 0.99672 1.4024 −2.7152 0.99803 1.3565 −2.1370 0.99764 1.4615 −2.3706 0.98875 1.6048 −2.7717 0.99566 1.3875 −0.6535 0.99917 1.0798 2.8553 0.9981

where vcr is a characteristic velocity in the system, for example, theaverage plume velocity. High values of Gr indicate a large influence ofbuoyant forces in comparison to viscous forces, thus a tendencytowards gravity segregation. It can be shown that low Gr leads to highCO2 storage capacities, mainly because of the plume shape (lessgravity segregation). Since high storage capacities should correlatewith a low risk of leakage, risk should also be lower for smaller Gr.

The gravitational number Gr can be related to the primaryparameters considered in this risk study: porosity, depth, geothermalgradient, and an anisotropy factor kv/kh. Porosity does not appear inthe definition of Gr. However, it is coupled to the permeability k. Lowφ means low k, thus also a low Gr number. On the other hand, lowporosity requires more matrix volume for a given amount of CO2 to befilled, thus a larger extent of the plume. As outlined above, the resultsof this study showed that the porosity does not strongly influence risk.The influence of depth on Gr is rather obvious. With depth the densitydifference ϱw−ϱCO2 decreases resulting in low Gr and in a lower risk.High geothermal gradients imply more risky scenarios leading to highdensity differences and high Gr numbers. Anisotropy is not consideredin the definition of Gr but if kv is employed instead of the isotropic k inthe definition of Gr, then low Gr is achieved by low kv which is inagreement with less tendency towards gravity segregation.

Ref. [37] defined the capillary number as

Ca =k⋅pcr

μCO2⋅vcr⋅lcr; ð10Þ

where pcr and lcr represent characteristic values for the capillarypressure and a corresponding length scale in the reservoir. Low valuesof Ca indicate that viscous forces dominate over capillary effects,while high Ca numbers are favorable for good storage capacity and,presumably, also for low risk of leakage.

High geothermal gradients lead to lower capillary pressures. Ifcapillary pressure was the only parameter that depends on temper-ature, this would result in low Ca numbers. However, the viscosity andthe characteristic velocities are also temperature dependent. Thus, Ca(and Gr) are not strongly dependent on temperature. Low porosities(and thereby low permeabilities) also result in low Ca numbers. Ingeneral it has been shown that low Gr and high Ca lead to low risk, butthe results of this risk study lead to the conclusion that Gr dominatesboth the estimation of risk and storage capacity.

Summarizing this discussion of the results, it can be concluded thathigh risk is produced by small leaky well distances, long injection time,high geothermal gradients, high permeability anisotropy, and by lowdepth. Risk, as it is defined here, is almost not dependent on porosity.

6. Qualitative sensitivity analysis

The assumptions made for the secondary parameters, togetherwith other simplifications, are discussed in the following with respectto their potential to lower (−) or increase (+) leakage (lead to later(−) or earlier (+) leakage):

• Reservoir geometry +/−: An increased thickness of the reservoir, anegative dip angle towards the leaky well, and a sealing fracture inthe reservoir in between the injection and the leaky well leads tolower/later leakage at the leakywell. If assumptionswere vice versa,i.e. decreased thickness, positive dip angle and a sealing fracture onthe opposite side of the injection well, this would lead to higher/earlier leakage. Ref. [49] studied the influence of varying dippingangles and described the influence using dimensionless numbers.Ref. [27] suggests that an increasing slope of an aquifer acceleratesresidual trapping and that lateral migration of the injected CO2 trapsthe CO2 relatively quickly as residual saturation. The results were,however, obtained with simplified 2D models neglecting (amongstother simplifications) density and viscosity changes.

Table 5Coefficients Ai fitted to Eq. (8) to calculate time contour lines. R2 indicates goodness of fit (that is the ratio of the sum of the squares of the regression to the total sum of the squares)between {0,1}, where a value closer to one indicates better fit.

Timecontourline[days]

A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 R2

1000 1.0685E+00 1.4859E−01 −1.5375E−03 8.01300E−06 −2.3983E−08 4.2862E−11 −4.5849E−14 2.8163E−17 −8.8019E−21 9.8655E−25 0.99972000 5.0088E+00 4.9038E−02 −4.6774E−04 2.0879E−06 −5.2227E−09 7.7607E−12 −6.9974E−15 3.7556E−18 −1.1029E−21 1.3634E−25 0.99983000 7.4770E+00 −3.9704E−03 −7.6240E−06 7.2986E−08 −1.9675E−10 2.5317E−13 −1.7582E−16 6.6951E−20 −1.2949E−23 9.6473E−28 0.99954000 8.4316E+00 −1.9807E−02 9.8945E−05 −2.7483E−07 4.3676E−10 −4.2399E−13 2.5517E−16 −9.2601E−20 1.8511E−23 −1.5627E−27 0.99875000 8.0576E+00 −1.0807E−02 3.9636E−05 −8.7095E−08 1.1024E−10 −8.6559E−14 4.2855E−17 −1.2960E−20 2.1768E−24 −1.5516E−28 0.99736000 8.1624E+00 −1.0943E−02 3.8833E−05 −8.0753E−08 9.6220E−11 −7.0288E−14 3.1944E−17 −8.7698E−21 1.3262E−24 −8.4625E−29 0.99747000 8.3008E+00 −1.1898E−02 4.2956E−05 −8.8591E−08 1.0433E−10 −7.4669E−14 3.2931E−17 −8.7074E−21 1.2621E−24 −7.6946E−29 0.9964

876 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

• Diffuse leakage through caprock -: Diffusive leakage into shallowerreservoirs could reduce leakage at the leaky well. The effect on riskdepends of course on the judgment whether this diffusive leakage isacceptable (e.g. because leaking CO2 is trapped in the shalloweraquifer) or is not acceptable (leads also to damage/risk). However,

Fig. 10. Risk [log kg] versus time [d] for selected rleakywell distances (shown in the boxes) and(top-right), depth (bottom-left), and absolute permeability anisotropy (bottom-right).

Ref. [45] showed that if the sealing pressure of the caprock is notexceeded, leakage of CO2 by molecular diffusion is negligible duringthe short-term injection stage. If the sealing pressure is exceededthough, leakage rates can become (very) large. Ref. [24] shows thatwhen the transport of chemicals primarily occurs by molecular

various values of primary parameters including porosity (top-left), geothermal gradient

Fig. 11. Comparison of leakage rates versus time obtained by Ref. [15] and calculated bythe methodology presented in this study. The well diameter is 0.30 m. Leakage rates aregiven as a fraction of the CO2 rate injected.

877A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

diffusion in the liquid phase, CO2 leakage becomes self-limiting, i.e.pores become clogged after a very short time. In case of a fracturedcaprock, however, gaseous CO2 penetrates into the caprock andinduces some enhancement in porosity and permeability, whichreduces the sealing efficiency of the caprock.

• Permeability: +/−: A different functionality of permeability onporosity (e.g. [28,57], or a Karman-Kozeny model with modifiedparameters), could lead to reduction or increase of leakage.Considering the concept of risk developed here, leakage is lower/occurs later for lower permeabilities, i.e. the CO2 plume is morecompact [37].

• Viscous fingering: +/−: The radially symmetric and homogeneoussetup prevents viscous fingering from occurring. Since the injectedCO2 is less viscous than the displaced brine, viscousfingeringmay leadto an earlier breakthrough than predicted when radial symmetry isassumed. Leakage events can become more likely to occur throughviscous fingers. However, the resulting damage and the total amountsof leaking CO2 might be even less since capillary pressure anddissolution of CO2 into brine are acting against the protrusion offingers. Thus, a higher probability for leakage events does notnecessarily imply higher risk. In the literature [22,68] show that thedistribution of permeability dominates the fluid displacement anddevelopment of fingers rather than hydrodynamic instability.

• Heterogeneity +/−: This study neglects reservoir heterogeneityeven though it has dominant influence on potential fingerdevelopment, as explained in the previous paragraph. For example,a high permeable channel structure towards the leaky well, leads toearlier leakage. On the other hand, low permeability structures inthe reservoir, can reduce gravitational segregation, and consequent-ly leakage is retarded. Ref. [20] studied the impact of different net-sand-to-gross-shale ratios on the development of the CO2 plumeshape and on dissolved, residually trapped, and mobile CO2 massfractions. They conclude that with increasing amounts of shale inthe reservoir, vertical movement of the plume is restricted andlateral movement encouraged. An increasing amount of shale andconsequently a restricted vertical movement leads to reducedleakage. Consequently, for such cases an assumption of homogene-ity is presumably a conservative approach on risk. In general,however, reservoir heterogeneity can lead to either increased/earlier or decreased/later leakage leaving this point open to beaddressed in more detail.

• Relative Permeability +/−: Considering a different shape of therelative permeability relation, or different irreducible saturations, couldlead to either increased/earlier or decreased/later leakage. Ref. [3]measured relative permeability relations for CO2-brine systems in theAlberta basin in Canada, and these do influence the plume evolutionbehavior (as shown by Ref. [38]) in a similar way to the reservoirproperties considered here (depth, geothermal gradient, etc.).

• Capillary Pressure +/−: The approach employed to scale ameasured capillary pressure relation to actual reservoir conditionsat a given pressure, temperature, and (constant) porosity is quitesophisticated. However, such a scaling assumes the same rock-typein all reservoirs. As this is not generally the case, a different capillarypressure relation might lead to an increase or decrease of leakage.Generally, stronger capillary forces lead to less leakage, since moreCO2 is stored by capillary trapping ([30,38]). In a heterogeneousreservoir, the effect of high capillary entry pressures of lowpermeable shale structures amplifies the effects discussed in bulletHeterogeneity.

• Hysteresis -: Hysteretic behavior in either the relative permeabil-ity relation or in capillary pressure influences plume evolution,and thus influences leakage. Various authors ([19,33,66], [13],[67]) investigated hysteretic behavior by experimental setups orby numerical investigations. Incorporating hysteresis of any kindwill lead to decreased/later leakage, since additional CO2 istrapped.

• Anisotropy model +/−: A different anisotropy distribution (here aprimary parameter derived by conceptual modeling) could lead toincreased/earlier or decreased/later leakage. Generally, an increasein anisotropy leads to decreased/later leakage due to reducedgravity segregation.

• Salinity +/−: As salinity influences brine density, viscosity and thesolubility of CO2 in brine, a higher or lower salinity than assumedinfluences leakage. Generally, lower salinity leads to an increase inCO2 solubility in brine [14], hence leakage is decreased/occurs later.

• Leakage simulation -: In this study, the leakage process itselfthrough the leaky well is not modeled. It is assumed that all of themass passing by the leakage point will flow through the leaky wellout of the reservoir, which should be expected to be a worst casescenario. To justify this approach, a comparison is made with themodel of Ref. [15] who investigated CO2 leakage rates through anabandoned well. The considered reservoir has an open leaky well of0.30 m diameter at a 100 m distance to the injection well, whichconnects to a shallower aquifer. Results of the model of Ref. [15] arecompared with the leakage rates predicted using the simplifiedapproach of this study in Fig. 11 for the reservoir parameters and thesetup presented by Ref. [15]. The time when significant leakagestarts to occur is almost identical. The difference is due to slightlydifferent boundary conditions and the different reservoir geometry(single radially symmetric reservoir in this study versus a full 3Dsimulation with two reservoirs, connected by the leaky well in thecenter in the study of Ref. [15]). Leakage rates start to increase at aslower rate in the study of Ref. [15], reach a peak leakage rate, anddecrease on the long term. The gradual increase of the leakage rate isexplained by up-coning of the brine into the well [53]. The higherpeak rate and later decrease is explained by thermodynamic andhydraulic processes in the leaky well. These results show thatdespite neglecting the leakage process the predicted leakage agreessatisfactory with a model that describes the leakage process indetail. It is therefore reasonable to employ a simplified modelwithout simulating leakage to gain the benefit of faster simulationand greater flexibility in the post-simulation evaluation of risk.

• Additional assumptions on leaky well properties -: Here the leakywell is assumed to penetrate the entire formation thickness and isassumed to be completely open to the atmosphere. In practice this isnot the case. For example partial penetration of the formation, wellplugs, incorporation of detailed leakage pathways in the leaky well,

878 A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

knowledge about material behavior etc. will always reduce leakagerates.

• Injection scheme+/−: In this work a continuous injection of CO2 isassumed. By amodified injection scheme, i.e. alternating injection ofgas and fresh brine (WAG [61]), additional CO2 could be residuallytrapped [30]. Ref. [38] showed that the injection rate also has anconsiderable influence on the shape of the plume and therefore onthe potential leakage. High injection rates lead to cylindrical plumeshapes, which leads to less lateral extent of the plume.

• Injection well design -: By intelligent design of the injection well(horizontal setup, screening in lower regions, etc) leakage could bereduced (could be deferred to later times), see also Ref. [40].

• Geochemistry -: Geochemical processes can lead to mineraltrapping in the reservoir ([48,63,69]), which could lead to lower/later leakage. These processes are important in the long term, i.e.later than 10-100 years, but are not considered in this study. If thecaprock is subject to chemical processes, this can lead to very largeleakage rates as stated in the Diffuse leakage through caprock bullet.

7. Conclusions

The leakage risk concept developed utilizes a well testedsimulation code to derive risk of potential CO2 leakage through pre-existing leaky wells, subject to multiphase transport processesoccurring in a reservoir. Leakage is not explicitly modeled, butcalculated as the accumulated CO2 mass that has spread within theleaky well sector beyond the leaky well distance of interest at time t.The reservoir is assumed to have a simplified geometry and ishomogeneous. The study takes into account four independentprimary parameters randomly sampled from probability densityfunctions derived from a large reservoir properties database. Therisk surface derived is thus an average risk over the consideredprimary parameter ranges. Additional leaky wells in the surroundingof the injection well can be easily incorporated by summing up theindividual risk for each well provided that leaky wells do not interactor significantly affect the CO2 distribution. Since other than primaryreservoir properties are fixed or are dependent on primary para-meters, different assumptions made for these parameters or for thereservoir could lead to lower/higher or earlier/later leakage at theleaky well, and hence to lower/larger risk. This is discussed inSection 6.

This study adopts a conservative approach to estimating theparameters for determining the leakage of CO2 through abandonedwells. However, risk can be underestimated if reservoir geometry isvery different (large dip, small height) or if the relative permeabilityshows high CO2 permeability together with large irreducible watersaturation (significantly larger than 0.3).

The main findings and conclusions are:

• The first quantitative approach for the evaluation of risk withrespect to CO2 leakage through pre-existing wells based oncomprehensive reservoir properties statistics has been presented.

• Within the given framework, a range of possible risks is defined.This can be used to determine whether an individual site isrelatively good or not. Hence, assistance is given to experts whenrating storage sites with unknown/uncertain reservoir properties.The cumulative risk for any site with given leaky well distances canbe calculated, and sites can be compared to each other. Thus, therelative risk might assist in making decisions on where to conductfurther investigations or to help experts when utilizing morecomprehensive screening and ranking frameworks.

• The study identifies reservoir parameters of importance to riskassessment. Among the four selected independent primary para-meters, the depth of the reservoir and the geothermal gradient areshown to have the greatest influence on risk. Anisotropy isinfluential only for short distances from the injection well. In this

study, risk is independent of porosity (due to coupling ofpermeability to porosity). An ideal reservoir should thus be locatedat great depth, should have a low geothermal gradient, and shouldhave a high anisotropy.

• The placement of the injectionwell can be optimizedwith respect torisk arising from abandoned wells in the surroundings. For a giveninjection well location, the combined risk for any number of leakywells in the surroundings can be calculated analytically for the timeof interest. Thus, it is possible to compare risk for several injectionwell locations and pre-select the location yielding the lowest risk.

Acknowledgements

The authors gratefully acknowledge funding and support from theCO2SINK project (SES6-CT-2004-5025599) sponsored by the Com-mission of the European Communities and the industry (Statoil, RWE,Shell, Schlumberger, Vattenfall, and VNG), the GEOTECHNOLOGIENprogram of the German Federal Ministry of Education and Researchand the Deutsche Forschungsgemeinschaft, the Nordic Data GridFacility (NDGF) and the Norwegian national infrastructure forcomputational science (NOTUR).

References

[1] Batzle M, Wang Z. Seismic properties of pore fluids. Geophysics 1992;57:1396–408.

[2] Bennion B, Bachu S. Relative Permeability Characteristics for Supercritical CO2

Displacing Water in a Variety of Potential Sequestration Zones in the WesternCanada Sedimentary Basin. Society of Petroleum Engineers SPE 95547; 2005.

[3] Bennion B, Bachu S. Drainage and Imbibition Relative Permeability Relationshipsfor Supercritical CO2/Brine and H2S/Brine Systems in Intergranular Sandstone,Carbonate, Shale, and Anhydrite Rocks. SPE Reservoir Evaluation & Engineering2008;11(3).

[4] Benson S. Lessons learned from industrial and natural analogs for health, safetyand environmental risk assessment for geologic storage of carbon dioxide. CarbonDioxide Capture for Storage in Deep Geologic Formations - Results from the CO2Capture Project, Elsevier Publishing, UK 2; 2005.

[5] Benson S, Hepple R, Apps J, Tsang C, Lippmann M. Lessons Learned from Naturaland Industrial Analogues for Storage of Carbon Dioxide in Deep GeologicalFormations. Energy Citations Database, Report Number LBNL–51170, LawrenceBerkeley National Laboratory, Berkeley, CA, U.S; 2005.

[6] Bielinski, A., 2006. Numerical Simulation of CO2 Sequestration in GeologicalFormations. Ph.D. thesis, Universität Stuttgart, Mitteilungsheft Nr. 155, Institut fürWasserbau, Universität Stuttgart.

[7] Brooks A, Corey A. Hydraulic Properties of Porous Media. Colorado State UniversityHydrology Paper; 1964.

[8] Celia M, Bachu S, Nordbotten J, Gasda S, Dahle H. Quantitative Estimation of CO2

Leakage from Geological Storage: Analytical Models, Numerical Models, and DataNeeds. In: Rubin ES, Keith DW, Gilboy CF, editors. 7th International Conference onGreenhouse Gas Control Technologies (GHGT-7). Vancouver, Canada, Sept. 5-9;2004. p. 9.

[9] Class H, Ebigbo A, Helmig R, Dahle H, Nordbotten J, Celia M, et al. A benchmark-study on problems related to CO2 storage in geologic formations — summary anddiscussion of the results. Computers and Geosciences 2009;13(4):409–34.

[10] Class H, Helmig R, Bastian P. Numerical simulation of non-isothermal multiphasemulticomponent processes in porous media. — 1. An efficient solution technique.Advances in Water Resources 2002;25:533–50.

[11] Dake LP. Fundamentals of Reservoir Engineering. Elsevier Science B.V; 1978.[12] Daubert T, Danner R. Physical and thermodynamic properties of pure chemicals:

data compilation. Design Institute for Physical Property Data; 1989.[13] Doughty C. Modeling geologic storage of carbon dioxide: comparison of non-

hysteretic and hysteretic characteristic curves. Energy Conversion and Manage-ment 2007;48(6):1768–81.

[14] Duan Z, Sun R. An improved model calculating CO2 solubility in pure water andaqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar. ChemicalGeology 2003;193:257–71.

[15] Ebigbo A, Class H, Helmig R. CO2 leakage through an abandoned well: problem-oriented benchmarks. Computers and Geosciences 2007;11(2):103–15.

[16] Ennis-King J, Paterson L. The role of convective mixing in the long-term storage ofcarbon dioxide in deep saline formations. Society of Petroleum Engineers Journal2005;10(3):349–56.

[17] Ellert M, Gronager M, Konstantinov A, Konya B, Lindemann J, Livenson I, et al.Advanced resource connector middleware for lightweight computational grids.Future Generation Computer Systems 2007;23:2191–240.

[18] Fenghour A, Wakeham W, Vesovic V. The viscosity of carbon dioxide. Journal ofPhysical and Chemical Reference Data 1998;27(1):31–44.

[19] Flett M, Gurton R, Taggart I. The function of gas–water relative permeabilityhysteresis in the sequestration of carbon dioxide in saline formations. Society ofPetroleum Engineers SPE 88485-MS; 2005.

879A. Kopp et al. / Advances in Water Resources 33 (2010) 867–879

[20] Flett M, Gurton R, Weir G. Heterogeneous saline formations for carbon dioxidedisposal: impact of varying heterogeneity on containment and trapping. Journal ofPetroleum Science and Engineering 2007;57(1–2):106–18.

[21] Garcia J. Density of Aqueous Solutions of CO2. Tech. rep., LBNL Report 49023,Lawrence Berkeley National Laboratory, Berkeley, CA, U.S.A; 2001.

[22] Garcia J, Pruess K. Flow instabilities during injection of CO2 into saline aquifers.Proceedings TOUGH Symposium 2003, Lawrence Berkeley National Laboratory,Berkeley, CA, U.S.A; 2003.

[23] Gasda S, Bachu S, Celia M. The potential for CO2 leakage from storage sites ingeological media: analysis of well distribution in mature sedimentary basins.Environmental Geology 2004;46(67):707–20.

[24] Gherardi F, Xu T, Pruess K. Numerical modeling of self-limiting and self-enhancingcaprock alteration induced by CO2 storage in a depleted gas reservoir. ChemicalGeology 2007;244:103–29.

[25] Haszeldine RS, Quinn O, England G, Wilkinson M, Shipton ZK, Evans JP, et al.Natural geochemical analogues for carbon dioxide storage in deep geologicalporous reservoirs, a United Kingdom perspective. Oil & Gas Science andTechnology 2005;60(1):33–49.

[26] Helmig R, Class H, Huber R, Sheta H, Ewing R, Hinkelmann R, et al. Architecture ofthe Modular Program System MUFTE_UG for simulating multiphase flow andtransport processes in heterogeneous porous media. Mathematische Geologie1998;2:123–31.

[27] Hesse M, Orr JF, Tchelepi H. Gravity currents with residual trapping. Journal ofFluid Mechanics 2008;611:35–60.

[28] Holtz M. Residual Gas Saturation to Aquifer Influx: A Calculation Method for 3-DComputer Reservoir Model Construction. SPE 75503, paper presented at the SPE GasTechnology Symposium held in Calgary, Alberta, Canada, 30 April - 2 May 2002; 2002.

[29] IAPWS. Release on the International Association for the Properties of Water andSteam Industrial Formulation 1997 for the Thermodynamic Properties of Waterand Steam; 1997. (http://www.iapws.org/).

[30] Ide S, Jessen K, F.M., O. J.. Storage of CO2 in saline aquifers: effects of gravity,viscous, and capillary forces on amount and timing of trapping. InternationalJournal of Greenhouse Gas Control 2007;1:481–91.

[31] IPCC. Carbon dioxide capture and storage. Intergovernmental Panel on ClimateChange. uk: Cambridge university press; 2005. p. 431. (http://www.ipcc.ch/ipccreports/special-reports.htm).

[32] Johannsen K, Tourunen O, Kleist J. The CO2-Community Grid. http://wiki.ndgf.org/display/ndgfwiki/CO22008.

[33] Juanes R, Spiteri E, Orr F, Blunt M. Impact of relative permeability hysteresis ongeological CO2 storage. Water Resources Research 2006;42.

[34] Kaplan S. The words of risk analysis. Risk Analysis 1997;17(4):407–8.[35] Kopp, A., Bielinski, A., Class, H., Helmig, R., Hurter, S., Bech, N., 2006. Deliverable

6.1–1 Interim Progress Report- Concept for numerical modelling (Intercompar-ison Study). Progress report, not published, EU CO2SINK Project (Contract NumberSES6-CT-2004–502599).

[36] Kopp A, Class H, Helmig R. Sensitivity analysis of CO2 injection processes in brineaquifers. Proceedings European Geosciences Union (EGU) General Assembly, 18thApril 2007, Vienna, Austria; 2007.

[37] KoppA, Class H, Helmig R. Investigations on CO2 storage capacity in saline aquifers—part 1: dimensional analysis of flow processes and reservoir characteristics.International Journal of Greenhouse Gas Control 2009;3:263–76.

[38] KoppA, Class H, Helmig R. Investigations on CO2 storage capacity in saline aquifers—part 2: estimation of storage capacity coefficients. International Journal ofGreenhouse Gas Control 2009;3:277–87.

[39] Kopp, A., 2009. Evaluation of CO2 injection processes in geological formations forsite screening. Ph.D. thesis, Universität Stuttgart, Mitteilungsheft Nr. 182, Institutfür Wasserbau, Universität Stuttgart.

[40] Kovscek AR, Cakici CM. Geological storage of carbon dioxide and enhanced oilrecovery II: cooptimization of storage and recovery. Energy Conversion andManagement 2005;46:1941–56.

[41] Kumar A, Ozah RC, Noh M, Pope GA, Bryant SL, Sepehrnoori K, et al. Reservoirsimulation of CO2 storage in deep saline aquifers. Society of Petroleum EngineersJournal 2005;10(3):336–48.

[42] Kvamme B, Kuznetsova T, Hebach A, Oberhof A, Lunde E. Measurements andmodelling of interfacial tension for water+carbon dioxide systems at elevatedpressures. Journal of Computational Materials Science 2007;38:506–13.

[43] Laha IMRG, Chakravarti JR. Handbook of Methods of Applied Statistics, Volume I.John Wiley and Sons; 1967.

[44] Lake L. Enhanced Oil Recovery. Englewood Cliffs, New Jersey: Prentice-Hall, Inc.;1989.

[45] Li Z, Dong M, Li S, Huang S. CO2 sequestration in depleted oil and gas reservoirscaprock characterization and storage capacity. Energy and Conversion Manage-ment 2006;47:1372–82.

[46] Maul P, Metcalf R, Pearce J, Savage D, West J. Performance assessment for thegeologic storage of carbon dioxide: learning from the radioactive waste disposalexperience. International Journal of Greenhouse Gas Control 2007;1:444–55.

[47] Michaelides E. Thermodynamic properties of geothermal fluids. GeothermalResources Council Transactions 1981;5:361–4.

[48] Mito S, Xue Z, Ohsumi T. Case study of geochemical reactions at the Nagaoka CO2

injection site, Japan. International Journal ofGreenhouseGas Control 2008;2:309–18.[49] Mosthaf, K., 2007. CO2 Storage into Dipped Saline Aquifers Including Ambient

Water Flow. Diploma Thesis, Institute of Hydraulic Engineering, UniversityStuttgart, Germany, http://www.iws.uni-stuttgart.de/publikationen/ausgabe.php?person=1&autor[0]=1195.

[50] NDGF. Nordic Data Grid Facility. http://www.ndgf.org2008.[51] Nordbotten J, Celia M, Bachu S. Analytical solutions for leakage rates through

abandoned wells. Water Resources Research 2004;40(4):W04204.[52] Nordbotten J, Celia M, Bachu S. Injection and storage of CO2 in deep saline aquifers:

analytical solution for CO2 plume evolution during injection. Transport in PorousMedia 2005;58(3):339–60.

[53] Nordbotten J, Celia M, Bachu S, Dahle H. Semi-analytical solution for CO2 leakagethrough an abandonedwell. Environmental Science& Technology 2005;39(2):602–11.

[54] NPC. U.S. National Petroleum Council Public Database. http://www.netl.doe.gov. 1984.[55] Oldenburg C. Screening and ranking framework for geologic CO2 storage site

selection on the basis of health, safety, and environmental risk. EnvironmentalGeology 2007.

[56] Pacala S. Global constraints on reservoir leakage. In: Gale J, Kaya Y, editors.Proceedings of the Sixth International Conference on Greenhouse Gas ControlTechnologies; 2003. p. 267–72.

[57] Pape H, Clasuer C, Iffland J. Permeability prediction based on fractal pore-spacegeometry. Geophysics 1999;64(5):1447–60.

[58] Plug W-J, Bruining J. Capillary pressure for the sand–CO2–water system undervarious pressure conditions. Application to CO2 sequestration. Advances in WaterResources 2007;30(11):2339–53.

[59] Pruess K. On CO2 fluid flow and heat transfer behavior in the subsurface, followingleakage froma geologic storage reservoir. Environmental Geology2008;54:1677–86.

[60] Pruess K, Bielinski A, Ennis-King J, Fabriol R, Le Gallo Y, Garcia J, et al. Codeintercomparison builds confidence in numerical models for geologic disposal ofCO2. In: Gale J, Kaya Y, editors. GHGT-6 Conference Proceedings: Greenhouse GasControl Technologies; 2003. p. 463–70.

[61] Qi R, LaForce TC, Blunt MJ. Design of carbon dioxide storage in aquifers.International Journal of Greenhouse Gas Control 2009;3:195–205.

[62] Riaz A, Hesse M, Tchelepi H, Orr FM. Onset of convection in a graviatationallyunstable, diffusive boundary layer in porous media. Journal of Fluid Mechanics2006;548:87–111.

[63] Rosenbauer R, Koksalan T, Palandri J. Experimental investigation of CO2–brine–rockinteractions at elevated temperature and pressure: implications for CO2 sequestra-tion in deep-saline aquifers. Fuel Processing Technology 2005;86:1581–97.

[64] Scheidegger AE. The physics of flow through porous media. New York, NY:Macmillan Co.; 1960.

[65] Span R, Wagner W. A new equation of state for carbon dioxide covering the fluidregion from the triple-point temperature to 1100 K at pressures up to 800 MPa.Journal of Physical and Chemical Reference Data 1996;25(6):1509–96.

[66] Spiteri E, Juanes R, Blunt M, Orr Jr F. Relative-Permeability Hysteresis: TrappingModels and Application to Geological CO2 Sequestration. SPE Annual TechnicalConference and Exhibition, 9-12 October 2005, Dallas, U.S. SPE 96448-MS; 2005.

[67] Spiteri E, Juanes R, Blunt M, Orr Jr F. A new model of trapping and relativepermeability hysteresis for all wettability characteristics. Society of PetroleumEngineers 2008;13(3):277–88 (SPE 96448-PA).

[68] Tchelepi HA, Orr FM. Interaction of viscous fingering, permeability heterogeneity,and gravity segregation in three dimensions. SPE Reservoir Engineering 1994;SPE25235:266–71.

[69] Xu T, Apps J, Pruess K, Yamamoto H. Numerical modeling of injection and mineraltrapping of CO2 with H2S and SO2 in a sandstone formation. Chemical Geology2007;242:319–46.