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Energy 45 (2012) 512e518

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Energy

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The effect of mechanical rock properties on CO2 storage capacity

Domagoj Vulin*, Tomislav Kurevija, Iva KolenkovicFaculty of Mining, Geology and Petroleum Engineering, Pierottijeva 6, Zagreb, Croatia

a r t i c l e i n f o

Article history:Received 23 August 2011Received in revised form2 December 2011Accepted 22 January 2012Available online 24 February 2012

Keywords:CCSDeep saline aquifersPore compressibilityStorage efficiencyPressure buildup

* Corresponding author. Tel.: þ385 95 518 50 29; fE-mail addresses: dvulin@rgn.hr, dvulin@yahoo.co

0360-5442/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.energy.2012.01.059

a b s t r a c t

One of the most important issues when estimating CO2 storage capacity, especially in the case of thestorage into deep saline aquifers, is the mechanical integrity of rock, i.e. estimate of cap rock fracturepressure. In the case of storage into mature oil and gas reservoirs, reservoir pressure should not presentan issue since it was significantly decreased due to hydrocarbon production, so it is reasonable to assumethat the rock integrity would not be disturbed by injecting CO2 to the initial reservoir pressure. Becauseestimates of fracture pressure are necessary, but not convenient for regional aquifers, the analysis of porevolume changes due to pressure buildup for the chosen CO2 site in Croatia has been made. Pressurebuildup depends on reservoir fluid (brine) compressibility, CO2 compressibility at given reservoirconditions before CO2 injection and on rock compressibility i.e. pore compressibility. Implementing thesimple method for analysis of pressure buildup considering elastic properties of fluids and rock, largerCO2 storage capacity estimate was achieved than by using storage efficiency coefficient (E), as defined byU.S. DOE [1] and which was used for estimating storage capacities in regional deep saline aquifers inCroatia as the part of EU GeoCapacity project [2].

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Significant mitigation of climate change effects caused bygreenhouse gas emissions is possible by geological storage ofcarbon dioxide captured at large stationary point sources (primarilycoal and hydrocarbon power plants). The reliability of storagecapacity estimates depends on the level of research undertaken.Storage capacity estimates for depleted oil and gas reservoirs aregenerally more accurate than aquifer estimates, due to numerousdata collected during the hydrocarbon exploration and production.Aquifers are expected to be significantly larger carbon dioxidestorage objects.

According to Tek [3] minimum requirements for temporaryaquifer storage of gases (in order to preserve and monitor volumeof gas in storage) are: existence of structural trap, sufficientporosity, sufficient permeability and cap rock of adequate integrityto ensure against leak and migration. If no closure exists, or if theporosity or permeability is too low or if the cap rock strength isinsufficient to persist poro-elastic effects caused by changes in porefluid pressure, there would be no need for further evaluation ofa storage site.

After USDOE [1], in order to calculate storage capacity ina regional aquifer, simple volumetric approach can be used:

ax: þ385 1 483 60 74.m (D. Vulin).

All rights reserved.

mCO2¼ A� h� f� E � rCO2 ðp;TÞ (1)

where mCO2is the geological storage capacity in kg, A is the areal

distribution of the aquifer (m2), h is the cumulative thickness ofreservoir rocks (m), f is the effective porosity, E is storage capacitycoefficient, which is in matter of fact assumption of a volumetricsweep efficiency and rCO2

is the density (kgm�3) of pure CO2 underreservoir conditions. After USDOE [1], for saline aquifers in USA andCanada storage estimated value of capacity coefficient variesbetween 0.01 and 0.04, these values providing 15%e85% confidencerange.

Difference between real aquifer data and assumed average datainevitably burden these storage estimations with considerableerrors.

CSLF [4] defined equations for static storage of CO2. Besidesstatic trapping (in structural and stratigraphic traps), time depen-dent mechanisms were defined: residual-gas saturation trapping,dissolution, precipitation and hydrodynamic trapping.

The theoretical volume available for volumetric (static) CO2storage in structural or stratigraphic traps, VCO2t, can be calculatedusing the formula [4]:

VCO2t ¼ Vtrap � f� ð1eSwirrÞhA� h� f� ð1eSwirrÞ (2)

where A and h are the trap area and average thickness, respectively.Swirr is irreducible (immobile) water saturation, and Vtrap denotesbulk volume of the trap.

σz

σz

σxσx

σy

σxy

σxz

σyz

σyx

σzy

σzx

σyz

σyx

σxy

σxz

σzx

σzy

σy

Fig. 1. Cubic rock sample in a three dimensional stress field.

D. Vulin et al. / Energy 45 (2012) 512e518 513

The effective storage volume, VCO2e, is given by:

VCO2e ¼ Cc � VCO2t (3)

where Cc is a capacity coefficient that incorporates the cumulativeeffects of trap heterogeneity, CO2 buoyancy and sweep efficiency. Itshould be emphasized that capacity coefficient determinationrepresents very complex issue that is to be solved by numericalsimulations. So far there are no values found for this coefficient inthe literature.

The compressibility approach is generally applied for estimatesof storage capacity in depleted single-phase oil reservoirs andconfined deep saline aquifers [5]. Van der Meer and Yavuz [6]emphasize that in order to store CO2 in the underground, extraspace has to be created by the compressibility of the total system e

i.e. rock and fluids e in combination with a pressure increase. Theywarn that it is somewhat naive to expect that formation water willbe pushed out to create space for the injected CO2. Namely,

1

2

5

4

op

Fig. 2. Schematics of rock compressibility apparatus: (1) micro-volumetric pump, (2) pressuhydrostatic core holder, (4) vacuum/pore fluid line, (5) external pressure line & volumetric

volumetric approach disregards the fact that displaced water itselfneeds storage space elsewhere.

There are three kinds of compressibility that describe elasticproperties of the porous rock:

1. rock matrix compressibility (to define pressure dependentchange of solid rock material volume, without pores)

2. bulk compressibility (defines pressure dependent change ofbulk rock volume, i.e. pores and solid rock material)

3. pore compressibility (pressure dependent change in porevolume).

Internal (pore) stress variation depends on the fluid productionrate or fluid injection rate and it is equal in all directions (behaves ashydrostatic stress). External stress is the result of rock stresses andhas different values in different directions [8].

The theory of elastic deformation of porous rock has beentreated by several authors ([6e10]). Underground stress conditionsin a unit of a porous rock volume are described by a stress tensor (s)and by the pore pressure (p). Three normal stress components andsix shear stress components describe cubic model subjected toexternal forces, resulting with deformation of the model bychanging its shape and volume (Fig. 1). Following notations ofnormal stress are common: (parallel to x, y, and z coordinate) sxx,syy and szz (or sx, sy and sz). Normal stress at xy plane is szz. Thenshear stresses in z and y direction on a plane normal to the x axiswill be szx and szy. In theory, the confining stresses are different in x,y and z direction (lateral components of resulting stress are almostinsignificant), which is not possible to perfectly simulate in a lab(core sample is under hydraulic loading).

In Cartesian coordinate system (x, y ¼ horizontal, z ¼ verticalaxis), the tensor is according to Fig. 1 defined as

s ¼������sxx sxy sxzsyx syy syzszx szy szz

������ (4)

Vertical component of the stress (petrostatic stress) is due to theweight of overlaying rocks and is defined as:

szz ¼Zh

0

g ½rw4þ rrð1� 4Þ�dh (5)

2

6

3b

p

re transducers & gauges, (p ¼ pore pressure, bar; pob ¼ overburden pressure, bar); (3)pump, (6) thermostated air bath.

4.6

4.7

4.8

4.9

5.0

5.1

5.2

5.3

5.4

5.5

0 100 200 300 400 500 600 700

Vp,

cm

3

pe, bar

Fig. 3. pe�Vp plot for one sample (from Lipovljani oil field).Fig. 5. Measured pe vs. Vp data and corresponding compressibility curve.

D. Vulin et al. / Energy 45 (2012) 512e518514

Compressibility coefficients have been defined:

cr ¼ 1Vr

�vVr

vp

�ðs�pÞ

¼ � 1Vr

�vVr

vs

�ðs�pÞ

(6)

cb ¼ � 1Vb

�vVbvs

�p

(7)

cf ¼ 1Vp

�vVp

vp

�s (8)

cp ¼ � 1Vp

�vVp

vs

�p

(9)

where s is the confining stress (i.e. overburden pressure Pob) and pis the pore pressure. Subscripts r, b, f and p refer to rock, bulk,formation and pore respectively, while the difference pe ¼ pob � prepresents effective stress acting on rock (i.e. net overburdenpressure, NOB or net confining pressure, NCF or effective over-burden, EOB).

0

100

200

300

400

500

600

700

800

0 200 400 600

cp, 1

0-6ba

r-1

pe, bar

consolidated

friable

unconsolidated

Fig. 4. Formation compressibility type curves for a three different degrees of consol-idation (recalculated from Yale et al. [15]).

By applying instantaneous pore compressibility for changedpressure, new pore volume can be also calculated:

Vp ¼ Vp0�1� cppe

�or f ¼ f0

�1� cppe

�(10)

2. Laboratory pore compressibility measurement

Newman [10] described in detail pore compressibilitymeasurement apparatus. The stress cycling effect was examinedand it was determined that compressibility curve changes its shape(lower compressibility) when measured several times (stresscycles).

Measurement of pore volume changes (conducted by INA d.d.,Fig. 2) was performed by stepwise decrease of internal fluid volumeusing precision-bore piston assembly while keeping externalpressure at a constant value. Induced volumetric changes and thecorresponding pore pressure changes were recorded. Since theexternal pressure is kept constant, each volumetric brine expansionincrement is related to pore volume reduction due to the effectivepressure pe ¼ pob � p change.

Recorded Vpepe relationship was corrected for compressibilityof the brine used, applying published correlations [11,12], and forequipment compressibility (the equipment volumetric correctionwas determined by calibration run using steel plugs of a knownpore volume and under identical load conditions as those in actualtests).

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0 200 400 600

rela

tive

erro

r

pe , bar

Fig. 6. Relative errors of Vp calculated by Eqn. (10).

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

1100 1300 1500 1700 1900

cp, b

ar-1

h, m

pe=50 bar

pe=100 bar

pe=150 bar

pe=200 bar

10

12

14

16

18

20

22

24

26

28

1000 1200 1400 1600

φ, %

h, m

Fig. 7. Depth (h) vs. cp (bar�1) and depth vs. porosity (f, %).

D. Vulin et al. / Energy 45 (2012) 512e518 515

The measurement results were plotted on a pe vs. Vp diagram.Results of measurements performed on one core are given asexample in Fig. 3.

Pore compressibility was calculated according to the equation:

cp ¼ 1Vp

�dVp

dpe

�pob

(11)

where dVp is measured pore volume reduction due to a particularpe change (dpe) and Vp is pore volume corresponding to a pe on theexperimental Vpepe curve.

There are a number of similar approaches to correlate porecompressibility. Hall [13] measured both cp and cf values for a seriesof sandstone and limestone rock samples and published well-known cp vs. f correlation that has been often used in reservoirengineering calculations. Fatt [14] performed core compressibilitystudy of consolidated sandstones.

Yale et al. [15] analyzed overpressured oil and gas reservoirs andnoted that wide range of compressibility levels obtained fromlaboratory measurements depend on type of rock and level ofconsolidation. Also, they presented variability of pore compress-ibility with pressure and rock type (Fig. 4).

Further decisions in analysis of pore compressibilities of 43cores from Lipovljani field (depth range: 1100e1700 m, porosityrange: 11%e28%) used in this work were made by applying severaltypes of curves to measured data, and by considering work of Hall

Table 1Corrected estimates of storage capacity for Sava e central ([2], [19]).

Aquifer Sava e central

Net area, A, km2 517Average depth, H, m 1700Average thickness, h, m 550Porosity, f 0.18Storage capacity coefficient, E 0.03Average pressure, p, bar 198Average temperature, t, �C 87Density of CO2, rCO2

, kg/m3 545.5Storage capacity, mCO2

, Mt CO2 837.6

([13], i.e. that pore compressibility can be correlated with porosityby applying power-law function) and Hammerlindl ([16], i.e. linearapproximation of pore compressibility).

3. Measured data analysis

Pore volumes calculated by using pore compressibility couldsignificantly differ from storage volumes calculated without poro-elastic definition. Experimental data from 6 different wells (anddepths) were used in order to extend pore compressibility to thelarger area of interest. As heterogeneity plays a big role in petro-physical properties extrapolation, data from only one sample perwell were used, because a number of experiments from the samewell gave almost the same pore compressibility values.

For measured values, several functions were tested to fit peeVp

and peecp curves: power-law function ðVp ¼ apbeÞ, cubic spline and3rd degree polynomial. Despite the best fit with cubic spline, which

requires numerical solving of cp (i.e. cpi ¼ � 1Vpi

�Vp iþ1 � Vp i�1

pe iþ1 � pe i�1

�),

to describe peeVp relationship functionally, and to locate critical areaof measurement, 3rd degree polynomial has been chosen. Conse-quently, cp values that were calculated by deriving a functionVp ¼ ap3e þ bp2e þ cpe þ d were again fitted with 3rd degree poly-nomial giving almost no error (Fig. 5).

When fitted to experimental data, at higher effective pressure,(pe), the increase of pore compressibility was perceived.

It should be noted that this occurrence was noticed for allmeasurements, and even though it is not proven, it was credited todisturbed integrity of the rockmatrix. However, it is inadmissible touse that data for calculations of pore space volumetric changes andperformance bounds were narrowed to maximum pe ¼ 420 bar(average pe, at inflection point).

By analyzing relative errors (Fig. 6) of calculated Vp (Eqn. (10)),the maximum pe that could be used for further calculations ofaquifer storage will not cause misleads in storage capacity esti-mates (considering the fact that for calculated CO2 storage capac-ities E ¼ 0.03).

Fig. 6 shows that relative error in cp continuously increases withpe increase.

Fig. 8. Map of selected regional saline aquifers in Republic of Croatia (modified after [2], [17]).

D. Vulin et al. / Energy 45 (2012) 512e518516

Pore compressibility coefficient is the parameter that should beused very carefully due to heterogeneity. Data for linear part ofcompressibility curves, up to pe ¼ 200 bar were sorted in Fig. 7.

4. Storage capacity in Sava-central aquifer e the example ofestimate

Theoretical storage capacities for aquifers in Republic of Croatiawere presented in several works [2,17e19]. Variations of estimates

0

500

1000

1500

2000

2500

3000

3500

4000

0 100 200 300 40p, bar

h, m

Fig. 9. . Verification of measured pressures ([19]). It was assumed that reservoir pressure shohad density of 2900 kg/m3 and no porosity (f ¼ 0). (For interpretation of the references to

are mostly related to development in aquifer temperature andpressure assessments.

The most recent assessment for Sava-Central aquifer, obtainedby applying Eqn. (1), without accompanied pore compressibility isshown in Table 1:

Sava e central aquifer is a regional deep saline aquifer situatedin central part of Sava depression. It comprises Upper Miocenesandstones that are identified as the most prominent reservoirrocks that could be used for CO2 storage within southern part of

0 500 600

hydrostatic pressure

petrostatic presure,ro=2900kg/m3oil fields

gas fields

petrostatic pressure,ro=2200kg/m3

uld not be bellow hydrostatic pressure. Red line is petrostatic gradient, if reservoir rockcolour in this figure legend, the reader is referred to the web version of this article.)

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

22.0

22.5

23.0

23.5

24.0

24.5

25.0

25.5

0 50 100 150 200 250 300 350 400 450

cp. b

ar

-1

φ, %

pe, bar

porositycp

Fig. 10. Pore compressibility curve from Lipovljani oil field, depth ¼ 1151 m.

Table 2Aquifer pore volume vs. pressure, and resulting storage capacities.

p pe cp f Vp rCO2mCO2

mCO2(cp)

bar bar bar�1 % 106 m3 kg/m3 Mt Mt

198 286 0.000316 18.00 51,183.0 548.07 837.55 837.55199 285 0.000317 18.02 51,252.8 560.70 841.56 842.70204 280 0.000319 18.04 51,297.4 572.68 860.95 862.87209 275 0.000322 18.06 51,342.6 584.03 879.34 882.09214 270 0.000325 18.07 51,388.3 594.80 896.77 900.37219 265 0.000327 18.09 51,434.5 605.03 913.31 917.80224 260 0.000330 18.10 51,481.5 614.76 929.02 934.44229 255 0.000333 18.12 51,529.2 624.04 943.96 950.34234 250 0.000336 18.14 51,577.6 632.88 958.21 965.59239 245 0.000339 18.16 51,626.8 548.07 971.78 980.21

Densities of CO2 were calculated by using Span and Wagner [21] equation of state.

D. Vulin et al. / Energy 45 (2012) 512e518 517

Pannonian basin because they are numerous, can be reliablycorrelated and are situated in the convenient depth range. LateMiocene is characterized by post-rift thermal subsidence of thePannonian basin [20]. Lake Pannon deposits are formed inbrackish (Pannonian) to freshwater environment (Pontian). Aftersedimentation of carbonates in the littoral lake zone, deposition ofhemipelagic calcareous and clayey marls takes place [20]. Thedeepest depressions, including Sava depression, are filled bylacustrine turbidite lobes and channel fills of considerable thick-ness, thus gradually levelling initial basin floor topography [20].Turbiditic successions are overlain by shale-prone delta slope andsandy delta front to coastal plain sediments [20]. Deltaic sandbodies or turbiditic sand lobes are interlayered with silty marlsand represent “the regional petroleum reservoirs”. Since Plioceneand Quaternary sediments are deposited in the remnants of LakePannon and in the subsequent fluvial systems and are mostlyrepresented by sands and sandy gravels with some clay and silt[20], it can be assumed that no cap rock of regional extension canbe found within these deposits. Instead, valid cap rock may beidentified as one of the marl layers within Upper Miocenesandstone-marl sequence.

Regional aquifers in Croatian part of Pannonian basin (Fig. 8)were defined based on the two criteria e extension of the UpperMiocene sandstones (from the regional subsurface maps) andthickness of the overlying Pliocene and Quaternary sediments ofover 1000 m [2].

The next step is correction for pore compressibility. In order tocalculate pore volume at some increased pressure, due to injectionof CO2, it is necessary to obtain effective pressure. It is assumed thatoverburden pressure (the weight of underlying rocks) is constant atsome depth, and that it could not be greater than pressure thatwould come from the rock with no porosity (Fig. 9).

Only mechanical properties of rock were observed e withpressure increase and pore expansion. The brine compressibilitycan be taken into account (also by using pessimistic approach toobtain minimum brine compressibility) by using one of the manypublished correlations ([11,22e25]), but correlations should also beadjusted for the actual (measured) brine properties that were notavailable at the moment.

Pessimistic assumptions of parameters included in CO2 storagecapacity calculation were made (the lowest pore compressibility,and the highest pressure gradients). Data in Fig. 9 show thatreservoir (pore) pressure cannot be higher than petrostatic

pressure calculated with density of 2200 kg/m3 (average sandstonegrain density).

Although the pore compressibility curve measured on samplefrom the depth of 1700 m could be applied in order to makepessimistic estimate, the curve that gives the lowest porecompressibility was used (Fig. 10).

Measured data seem inconsistent at the end of the measure-ment (usually for the last two measured pressures, due to stresscycling during the sampling and measurement).

Petrostatic pressure for Sava-central aquifer will than bepob ¼ 484 bar, pore pressure p ¼ 198 bar and effective pressurerespectively pe ¼ pob � p ¼ 286 bar which is inside acceptableperformance bounds ðpe < 420 barÞ.

By applying Eqn. (11), i.e. cp ¼ 1Vp

ðdVp

dpeÞpob

¼ 1fð dfdpe

Þpobit

was calculatedcpð@pe ¼ 286 barÞ ¼ 0:000316352 bar�1.Then the analysis of porosity changes was made for a set of

pressures (Table 2). Changes of two capacities emCO2andmCO2

ðcpÞare compared in Table 2. Storage capacity (after USDOE [1], that wasalso used in calculations for GeoCapacity project) mCO2

increaseswith pressure increase, because of CO2 density change. Results forstorage capacities with included pore compressibility mCO2

ðcpÞshow even larger increase.

The changes expressed as percentage do not seem so dramatic,however results can be compared as capacity with pore

D. Vulin et al. / Energy 45 (2012) 512e518518

compressibility vs. capacity without pore compressibilityincluded.

5. Conclusions

The following conclusions can be derived from measured dataand the results of data analysis:

� Pore compressibility increases as the amount of injected fluidincreases, i.e. with increase of aquifer pressure: for first 10 barsincrease in Table 2, the pore volume will increase by 0.175%, fornext 10 bars, pore volume will increase by 0.179%.

� The analysis is conducted as pessimistic e petrostatic pressureis probably lower (which would result in lower effectivepressure and thus higher pore compressibility), the chosenpore compressibility curve is the one with the lowest averagecompressibility of 6 available curves.

� By 3rd order polynomial, that was selected as correlation curve,it is possible to detect above mentioned inconsistency, butcertain other correlation methods (for example, cubic spline)might give, in the range of interest, slightly more accurate porecompressibility curves.

� Higher compressibilities of pores and fluids result in largerstorage capacity at corresponding pressures. As the significantpore volume could be defined by taking into accountcompressibilities, issues concerning cap rock threshold pres-sure and cap rock integrity are reduced.

Nomenclature

A areal distribution of the aquifer, m2

cb bulk compressibility coefficient, bar�1

cf formation compressibility coefficient, bar�1

cp pore compressibility coefficient, bar�1

cr rock compressibility coefficient, bar�1

Cc CO2 storage capacity coefficient after CSLFE storage capacity coefficient after USDOEH average depth, mh average thickness of reservoir rocks, mmCO2

geological storage capacity, kgp pore pressure, barpe effective stress acting on rock or net overburden pressure,

barpob overburden pressure, barSwirr irreducible (immobile) water saturationt rock temperature, �CVCO2t theoretical volume available for volumetric CO2 storage in

structural traps, m�3

VCO2e effective storage volume for CO2, m�3

Vp pore volume, m�3

Vtrap bulk volume of the structural trap, m�3

f effective porosityrCO2

density of pure CO2, kgm�3

rw density of water, kgm�3

rr density of rock, kgm�3

s stress tensor which describes stress conditions in a unit ofa porous rock volume

s confining stress

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