International Journal of Greenhouse Gas Control 28 (2014) 2534

Contents lists available at ScienceDirect

International Journal of Greenhouse Gas Control

j ourna l h o mepage: www.elsev ier .com/ locate / i jggc

Comparison of different methods for determiningaffectin

Changlin ingXiaopenga Petroleum En ab PetroChina Re of Chinc Geological Ex CompPeoples Repub

a r t i c l

Article history:Received 9 NoReceived in reAccepted 10 June 2014Available online 28 June 2014

Keywords:Storage capacityDetermination methodsOil reservoirsStepwise regreCarbon seques

ly an onom

capacity in oil reservoirs which is very important for the implementation of CO2 storage includes theevaluation of theoretical, effective, practical and matched storage capacities. Based on the volumetricbalance theory, considering CO2 dissolved in remaining oil and water, sweep efciency and displacementefciency, this paper utilizes three methods to calculate theoretical and effective CO2 storage capacityin oil reservoirs, in which CO2 volumetric sweep efciency, oil recovery factor and sequestration factorare key parameters. This work presents a reservoir numerical simulation method, an empirical formula

1. Introdu

The undbon sequesgas emissioresources tve major gpromising tmations, un2005). Afterhave been bstorage capthan in othe

CorresponChangping, Befax: +86 010 8

E-mail add

http://dx.doi.o1750-5836/ ssiontration

method, and a stepwise regression method. The feasibility, superiority and limitations of the methodsfor calculating these three key parameters and storage capacities including theoretical and actual CO2storage capacities were analyzed through simulated applications in three reservoirs of the XinjiangOileld of China. The results indicated that the assessment results of stepwise regression has a high levelof accuracy, and that this oileld can provide a large storage capacity and is thereby worthy of furtherstudy.

2014 Elsevier Ltd. All rights reserved.

ction

erground storage of carbon dioxide (CO2), i.e., car-tration, is a promising method to reduce greenhousen. Many international institutions have been investingo evaluate geological CO2 storage potential. There areeological systems that have been identied as the mostargets for CO2 storage: oil and gas reservoirs, saline for--minable coal areas, shale, and basalt formations (IPCC,

signicant exploration and development, oil reservoirsetter characterized, which makes the estimation of CO2acity in oil reservoirs simpler and more straightforwardr geologic formations in normal situations.

ding author at: China University of Petroleum-Beijing, Mail Box 269,ijing 102249, Peoples Republic of China. Tel.: +86 010 8973 3223;973 3223.ress: liaocup@163.com (C. Liao).

Based on the volumetric balance theory, the fundamentalassumption made in storage capacity calculations is that the vol-ume previously vacated by liquid recovery is fully available for CO2storage (Stevens et al., 2001; Bachu and Shaw, 2003). The CarbonSequestration Leadership Forum (CSLF) presented a method to cal-culate theoretical storage capacity based on this assumption. Thecalculation is shown by Eq. (1) (CSLF, 2007). The volume of injectedwater, aquifer inux and produced water were considered in thisequation.

MCO2t = CO2r [Rfl A h (1 Swi) Viw + Vpw] (1)

The United States Department of Energy applied anothermethod to calculate CO2 theoretical storage capacity, based on CO2enhanced oil recovery theory and volumetric balance theory. Thegeneral form of the volumetric equation to calculate CO2 theoreti-cal storage capacity in oil reservoirs is shown by Eq. (2) (Goodmanet al., 2011). Table 1 summarizes the terms shown in Eqs. (1) and(2).

MCO2t = CO2s A h (1 Swi) Bo Eoil (2)

rg/10.1016/j.ijggc.2014.06.0102014 Elsevier Ltd. All rights reserved.g CO2 storage capacity in oil reservoirs

Liaoa,b,, Xinwei Liaoa, Xiaoliang Zhaoa, Hongna D Liuc, Yongge Liua, Jing Chena, Ning Lua

gineering Department, China University of Petroleum, Beijing, Peoples Republic of Chinsearch Institute of Petroleum Exploration and Development, Beijing, Peoples Republic ploration and Development Research Institute of CNPC, Chuanqing Drilling Engineeringlic of China

e i n f o

vember 2012vised form 9 June 2014

a b s t r a c t

Storing CO2 in oil reservoirs is not oneffects, but also a means to be more ec key parameters

a,

aany Limited, Chengdu, Sichuan,

effective method for reducing CO2 emissions and greenhouseical by enhancing oil recovery. The evaluation of CO2 storage

26 C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534

Table 1Parameters for theoretical storage capacity estimation published in references.

Parameter Units Description

MCO2 t kg Theoretical storage capacityCO2r kg/m

3 CO2 density under reservoirconditions

R m3/m3 Total oil recovery factor onreservoir volume basis

A m2 Oil reservoir areah m Oil reservoir thickness m3/m3 Oil reservoir porositySwi m3/m3 Initial water saturationViw m3 Cumulative volume of injected

water and aquifer inuxVpw m3 Cumulative volume of

produced waterCO2s kg/m

3 CO2 density under standardconditions

Bo standard m3/reservoir m3 Oil formation volume factorEoil m3-CO2/m3-OOIP Storage efciency factor that is

derived from local CO2enhanced oil recovery (EOR)experience or reservoirsimulation, as the ratio ofstandard cumulative volume ofCO2 to standard volume oforiginal oil-in-place

Others (Shaw and Bachu, 2006; Shen and Liao, 2009; Brennanet al., 2010to differentwere based

In this volumetric implementjiang oilelcapacity calcalculated wto the Xinjiprovides a Xinjiang oil

2. Calculat

The techage capacit

Fig. 1. Techno2007).

There are four types in the pyramid theoretical, effective, practi-cal and matched storage capacities, and each of them is a subset ofthe previous one except theoretical capacity. The theoretical stor-age capacity (Bachu et al., 2007) represents the physical limit thatthe geologipyramid. Thacquired bying) cutoff concentratesome introare based obubble poinpore space

The volulate storage2007). Howwater of thin the stora2002), was study, the Cby using ththe remain

2.1. Calcula

The theoree p2 disn in Fal poty. Aase ing opartsthat

calchown

the free-oirs ig ovmulaiginacurac) presented a number of various methods according reservoir development characteristics, but all of them

on the volumetric balance theory.paper, CO2 dissolved in remaining oil and water,sweep efciency and displacement efciency were

ed according to the development characteristics of Xin-d in China, while using theoretical and effective storageculations. The three key parameters Rf, Ef and SCO2 wereith three different methods, which have been applied

ang oileld for storage capacity calculations. The workreference for the feasibility study of CO2 stored in the

reservoirs.

ion of storage capacity

no-economic resource-reserve pyramid for CO2 stor-y (CSLF, 2005; Bachu et al., 2007) is shown in Fig. 1.

into thand CO(showthe totcapacifree-phremainswept water

Thewere ssum ofof the reservoodinthe cuand orthe ac-economic resourcereserve pyramid for CO2 storage capacity (CSLF,

the storageoil reservoi(4), and theand (6) areremaining oinators of rand PWIP +priate methoil and watand they arfore, it is asremaining osweep efc

MCO2t = MfMfree-phase C

MCO2 in swep

MCO2in sweptc system can accept, and it occupies the entire resourcee effective storage capacity (Bachu et al., 2007) can be

applying a range of technical (geological and engineer-limits in a storage capacity assessment. This paper will

on the theoretical and effective storage capacities withduction to their calculation methods. The calculationsn the assumption that reservoir pressure is above thet pressure of crude oil, and only oil and water in thewithout free gas.metric balance theory is commonly adopted to calcu-

capacity (Bachu and Shaw, 2003, 2005; Bachu et al.,ever, the effect of CO2 dissolved in the remaining oil ande storage capacity, which is considerable and essentialge capacity calculation (Enick and Klara, 1990; Kovscek,not been taken into consideration in their studies. In thisO2 storage capacities of oil reservoirs were calculatede volumetric balance theory, and the CO2 dissolved ining oil and water was considered.

tion of theoretical storage capacity

retical storage capacity in oil reservoirs can be dividedarts: free-phase CO2, CO2 dissolved in the remaining oil,solved in the remaining water. The rectangular sketchesig. 2-12-3) are adopted to present the components ofre volume (entire rectangle) in the theoretical storagefter CO2 ooding, the total pore volume is lled withCO2, remaining oil and water. And the volume of theil and water are composed of two parts: swept and un-. In this way, the CO2 dissolved in the remaining oil andhad been swept by CO2 was considered.ulation model is shown by Eqs. (3)(6). The terms that

in Eqs. (3)(6) are summarized in Table 2. Eq. (3) is thethree parts of the storage capacity. The storage capacityphase CO2 (Eq. (4)) is a derivation of Eq. (1). Most oiln the Xinjiang oileld have been developed by waterer a long period of time. The historical data such astive volume of injected water, produced water and oil,l oil-in-place are incomplete, which signicantly affectsy of the CO2 storage capacity calculation. Therefore,

capacity is estimated based on the present situation ofrs. Therefore, the present oil-in-place is adopted in Eq.

present water-in-place is adopted in Eq. (5). Eqs. (5) the storage capacities that CO2 dissolved in the sweptil and water respectively. The sweep efciency denom-emaining oil and remaining water are POIP (1 Rf)

Viw Vpw respectively. However, there are no appro-ods to obtain the sweep efciencies of the remaininger. The two sweep efciency may have the same values,e near to the overall volumetric sweep efciency. There-sumed that the values of the sweep efciencies of theil and water are equal to that of the overall volumetriciency.

ree-phase CO2 + MCO2 in sweptoil + MCO2 in sweptwater (3)

O2 = CO2r[Rf POIP Viw + Vpw] (4)

toil = CO2r Ef POIP (1 Rf ) mCO2 in oil (5)

water = CO2r Ef (PWIP + Viw Vpw) mCO2 in water(6)

C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534 27

Fig. 2. Rectangular sketches for showing the components of the total pore volume. Fig. 2-1 shows thecomponents of pore volume after CO2 ooding, Fig. 2-3 shows the components of the swept pore vovolume for effective storage capacity after CO2 ooding. The entire outer rectangle represents the tofree-phase CO2, remaining oil and water after CO2 ooding. Both the remaining oil and water were costorage capacity is part of the volume of the free-phase CO2, the swept remaining oil and the swept rem

mCO2 inoil is calculated by Eqs. (7)(9) (Xue et al., 2005).

mCO2 in oil =KP

1 + KP44xTMave

(7)

ln K = 773.247 1T 273.15 18.5898 (8)

= 0.00008286(T 273.15) 0.7287 (9)The mCO2 in water can be determined by the estimation model

(Duan and Sun, 2003). This model was based on a specic particle

Table 2Parameters for theoretical storage capacity estimation.

Parameter Units Description

Mfree-phase CO2 kg Mass of free-phase CO2MCO2 in sweptoil kg Mass of CO2 dissolved in the swept

remaining oilMCO2 in sweptwater kg Mass of CO2 dissolved in the swept

remaining waterRf m3/m3 Oil recovery factor from CO2

ooding, dened as the ratio ofcumulative volume of produced oilto present oil-in-place (POIP)

POIP PWIP Ef

mCO2 in oil

mCO2 in water

K P osxT

Mave

T Swp

Rw

interactionequation ofwith tempefrom 0 to 2

It was asvoir in this CO2 oodintinuous COsubstituted

Mfree-phase C

MCO2 in swep

2.2. Estima

Many pacapacity, sureduce the would mak

tical 3 andore v4, the vo

A calachu

= Cmlculaubstim3 Present oil-in-placem3 Present water-in-placem3/m3 Overall volumetric sweep

efciency, dened as the ratio ofswept pore volume to total porevolume

m3-CO2/m3-oil CO2 solubility in oil at reservoirpressure and temperature

m3-CO2/m3-H2O CO2 solubility in water at reservoirpressure and temperatureEquilibrium constant

106 Pa Oil reservoir pressure(kg/m3 Oil density at standard condition

theoreFig. 2-total pFig. 2-all threwater.CSLF (B

MCO2e

A caafter skg/kg Weight fraction of hydrocarboncomponents in oil

kg/kg The secondary dissolvingcoefcient that indicates thedissolving capacity of CO2 in themixture composed of hydrocarboncomponents and CO2

g/mol Average molecular weight ofhydrocarbon in oil

K Oil reservoir temperaturem3/m3 Present average water saturation

over entire pore volumem3-H2O/m3-PWIP Water recovery factor which is the

ratio of the volume of waterproduced after CO2 ooding tovolume of the presentwater-in-place

(12). DetailAppendix.

MCO2e = C

SCO2 = Ce

Sfree-phase CO

SCO2 in swept

SCO2 in swept components of pore volume before CO2 ooding, Fig. 2-2 shows thelume after CO2 ooding, Fig. 2-4 shows the components of the poretal pore volume, including POIP and PWIP before CO2 ooding andmposed of swept and un-swept parts. The pore volume for effectiveaining water.

theory for the liquid phase and a highly accurate state for the vapor phase, and has a broad applicationrature ranges from 0 C to 260 C and pressure ranges00 MPa.sumed that there was no aquifer beneath the oil reser-paper. The volume of injected and invaded water beforeg is not considered, and the method is limited to con-2 ooding, so Viw is zero. Thus, Eqs. (4) and (6) can be

by Eqs. (10) and (11) respectively.

O2 = CO2r POIP Rf + PWIP Rw (10)

twater = CO2r Ef (PWIP Vpw) mCO2 in water(11)

tion of effective storage capacity

rameters out of considered in the theoretical storagech as buoyancy, mobility ratio and heterogeneity, couldpore volume available for CO2 storage (IPCC, 2005). Ite the effective storage capacity inevitably less than thestorage capacity. The rectangular sketches (shown in

2-4) are adopted to illustrate the components of theolume in the effective storage capacity. As shown in

e pore volume for effective storage capacity is part oflumes: the free-phase CO2, the swept remaining oil andculation of effective storage capacity was introduced by

et al., 2007):

Cb Ch Cw Ca MCO2t = Ce MCO2t (12)tion method for effective storage capacity is generatedtuting the results of Eqs. (3), (5), (10) and (11) into Eq.

ed derived steps for Eqs. (13)(17) are shown in the

O2r A h (1 Swp) SCO2 (13)

(Sfree-phase CO2 + SCO2 in sweptoil + SCO2 in sweptwater)(14)

2= Rf +

Swp1 Swp Rw (15)

oil = Ef (1 Rf ) mCO2 inoil (16)

water = Ef Swp

1 Swp (1 Rw) mCO2 in water (17)

28 C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534

Table 3Parameters for effective storage capacity estimation.

Parameter Units Description

MCO2e kg CmCbChCwCaCe

SCO2SCO2 displaceSCO2 in oilSCO2 in wate

The storstorage capshown in Eq

2.3. Determ

Rf, Ef andof theoreticcapacities, them.

2.3.1. NumThe num

method. Thinclude setreservoir mhistory maadopted toing CO2 storeservoirs a

Numericestimation be chosen treservoir grwell trajectical dynamdata can offor the calcsituations, tpresented i

2.3.2. EmpiThe thre

empirical fotionship (Stprojects (Fiaccording tThe SCO2 cations, the w(Rice, 2007

Rw =Swp

where t is p

2.3.3. StepwMathem

sion methothe functiodent param

Fig. 3. Oil recovery empirical relationship (Stevens et al., 1999).

eters Rf, Ef and SCO2 were obtained from conceptual mod-numerical reservoirs which are established with differentndent parameters including permeability, heterogeneity,uration, uid mobility, injection and production pressures,oir pressure, and injection time. The stepwise regression wasd to establish the relationship between the dependent andndent parameters. This method will be helpful for evaluatingorage capacity in oil reservoirs.

basic conceptual model for the numerical reservoir waserted pattern, including four production wells and a centralon well. Each grid block measured 25 m 25 m 2 m, overire grid of 37 25 5 cells. Top depth and reservoir temper-ere 1980 m and 335.3 K, respectively. Relative permeability

are shown in Fig. 4. The three-parameter PengRobinsonon of state was used for ash calculation. Different concep-odels with different independent parameters of a numerical(kg-CO2-effective)/(kg-CO2-theoretical)(kg-CO2-effective)/(kg-CO2-theoretical) (kg-CO2-effective)/(kg-CO2-theoretical) (kg-CO2-effective)/(kg-CO2-theoretical) (kg-CO2-effective)/(kg-CO2-theoretical) (kg-CO2-effective)/(kg-CO2-theoretical)

m3-CO2/m3-POIPm3-CO2/m3-POIP m3-CO2/m3-POIP

r m3-CO2/m3-POIP

age factor SCO2 from Eq. (14) reects the effective CO2acity in oil reservoir. Table 3 summarizes the termss. (12)(17).

ination of key parameters

SCO2 are the three key parameters for the calculational (Eqs. (3)(6)) and effective (Eqs. (13)(17)) storageand these three methods are introduced to determine

erical reservoir simulationerical reservoir simulation is a mature and acceptede steps to establish a numerical reservoir simulationting up a geological model, establishing a numericalodel, and adjusting parameters of rock and uid throughtching. The Eclipse software (Schlumberger Ltd.) was

establish a numerical model for accurately simulat-rage conditions, and the numerical models of three oilt the Xinjiang oileld were used.al reservoir simulation is considered as a very reliablemethod for reservoir development. Certain data shouldo establish an actual numerical reservoir model, such asid, earth coordinates of production and injection wells,ory, log interpretation, well test, well measures, histor-ic and other relevant data. For some oil reservoirs, thisten be difcult to obtain, which represents a challengeulation of the three parameters. Consequently, in somewo additional methods of parameter determination aren Sections 2.3.2 and 2.3.3.

rical formulae key parameters Rf, Ef and SCO2 can be obtained byrmulae. The Rf can be obtained from an empirical rela-evens and Kuuskraa, 1999) derived from seven eld EORg. 3). At the Xinjiang oileld, Ef was assumed to be 0.58,o CO2 ooding that adopted by 2D visible experiment.n be calculated by Eqs. (14)(17). Among these equa-ater recovery factor Rw can be estimated by Eq. (18)

paramels of indepeoil satreservadopteindepeCO2 st

Thean invinjectithe entature wgraphsequatitual m).

Rf (1 Swp) 1.8149912 10144e(665492.66)/t

, (18)

roduction time, year.

ise regressionatics and statistics were used in the stepwise regres-d (Zhu, 2012). It has been widely adopted to establishnal relationship between the dependent and indepen-eters so as to analyze experimental data. Dependent

reservoir wnumerical r

The indeoil saturatireservoir pdimensionlparametersin the dimvertical andation coefof the permto characteEffective CO2 storage capacityCapacity coefcient effected by mobilityCapacity coefcient effected by buoyancyCapacity coefcient effected by heterogeneityCapacity coefcient effected by water saturationCapacity coefcient effected by aquifer strengthEffective capacity coefcient that incorporates thecumulative effects of all the other parametersStorage factorStorage factors for the free-phase CO2 in pore volumeStorage factors for CO2 dissolved in remaining oilStorage factors for CO2 dissolved in remaining waterere expressed using the basic conceptual model of aeservoir.pendent parameters, i.e., permeability, heterogeneity,on, uid mobility, injection and production pressures,ressure, and injection time were transformed to beess. The dimensionless equations of the independent

are shown in Table 4. Table 5 summarizes the termsensionless equations. The permeability ratio between

horizontal permeability (kv/h) and permeability vari-cient (Vk) were used to characterize the heterogeneityeability. The oilCO2 mobility ratio (Mog ) was adoptedrize the mobility of CO2 in the reservoir. Because the

C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534 29

Fig. 4. Curves tive p

Table 4The dimension

Equations

Kv/h = kv/khSop

Mog =korgo

korog

Vk =

PinjD = Pinj/PMPpD = Pp/PMMPrD = Pr/PMMtD = Vinj/POIP

Table 5Parameters for

Parameter

kvkhkorgkoroo

g

hi

kiPinjPMMPpPrVinj

miscibility miscible presure, injectiThe dimenscumulativedimensionl

BoxBehintroduced

Table 6The values of d

Levels

Low IntermediateHigh of wateroil and gasoil relative permeability. Fig. 4-1 is the curves of wateroil rela

less equations and denitions of the independent dimensionless parameters.Deni

Ratio Presen

Mobil

n

i=1ki(n

i=1hiki/n

i=1hi1)n

i=1hi1

2

/

(n

i=1

hiki/

ni=1

hi 1

)Perme

M DimenDimenDimen

Dimen

the dimensionless equations.

Units Description

m2 Vertical permeabilitym2 Horizontal permeabilitym2/m2 End-point relative permeability of CO2m2/m2 End-point relative permeability of oilPa s Oil viscosity at reservoir pressure and

temperaturePa s CO2 viscosity at reservoir pressure and

temperaturem Thickness of layer i, subscript i is the

layer numberm2 Permeability of layer iPa Bottom hole injection pressurePa Minimum miscible pressurePa Bottom hole production pressurePa Average reservoir pressurem3 Cumulative volume of injected CO2 at

reservoir pressure and temperature

between CO2 and crude oil is determined by minimumssure, the dimensionless parameters of reservoir pres-on pressure and production pressure were introduced.ionless injection time tD was used to characterize the

volume of injected CO2. The values of the independentess parameters are shown in Table 6.nken design (BBD) (Box and Behnken, 1960) wasto design the experiment. BoxBehnken experimental

design is an(low, intermparameter tions are at that a BBD nexperimentcontained eparameter formed by E

The stepparametric

y = C0 +n

i=

The moparametersone througshown as fo

Y =

y1

y2

...

ym

imensionless independent parameters corresponding to the three levels.

Kv/h Sop Mog Vk

0.1 0.40 27.5 0.05 0.55 0.55 51.75 0.455

1 0.70 76.0 0.86 ermeability, and Fig. 4-2 is the curves of gasoil relative permeability.

tions

of vertical permeability to horizontal permeabilityt oil saturation, (1 Swp)ity ratio of CO2 displacing oil

ability variation coefcient (Liu et al., 1993)

sionless injection pressuresionless production pressuresionless reservoir pressuresionless injection time

independent quadratic design requiring three levelsediate and high) for each independent dimensionless

so as to capture quadratic effects. Treatment combina-midpoints of the process space, which essentially meansever uses all the extreme values at the same time. Theal design included 120 groups of simulations, whichight independent dimensionless parameters with each

having three levels. All the simulation runs were per-clipse.wise regression method (Zhu, 2012) was applied in

regression to establish the estimation model shown by

1

aixi +ij

bijxixj +n

i=1cix

2i (19)

del included multinomial and random error of the. This non-linear model can be converted into a linearh parameters substitution. The converted equation isllows:

, X = (xij)mp, e =

e1

e2

...

em

, =

1

2

...

p

(20)

PinjD PpD PrD tD

1.21 0.61 0.89 0.21.305 0.705 0.985 0.71.40 0.80 1.08 1.2

30 C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534

Fig. 5. Relation graphs of predicted values and actual values. Fig. 5 1Fig. 5-3 are the relation graphs oThe straight lines in the gures represent places where predictive values are equal to actual values. Thepredicted and the actual values.

Eq. (20) can be expressed by Eqs. (21) and (22).

Y = X + e (21)

Q () =m

j=1

Table 7Parameters fo

Parameter

y C0ai , bij , cixi , xj

Y y1, y2 ,. . ., ymm X xijn p

e e1 , e2 , . . ., em 1 , 2 , . . ., pQ()

When Qthe regressregression cin Eqs. (19)

= (X Y)1

Ef anas thnt dimeter evel pwis

Rf = 0.70 kv/h

+ 0.0 0.2

1.8 228

Ef = 1.25 kv/h+ 0.3 0.3

0.3 .609SCO2 = 0. 52So

+ 0.0 + 0.

+ 0.1 82(Vordinith

5. Thted v, the[yi (1xi1 + 2xi2 + + pxip)]2 (22)

r stepwise regression.

Description

Rf, taken pendeparamicant lthe ste

66 + 0.2716PinjD 0.1468kv/h Sop + 0.001151kv/h Mog + 0.07318

4611 kv/h tD + 0.8285Sop PpD + 0.1237Sop tD 0.2110Vk PinjD

66(Sop 0.3794)2 0.7967(Vk 0.7191)2 0.00001665Mo2g 0.2

8 0.2471kv/h Sop + 0.002169kv/h Mog + 0.1172kv/h Vk 0.3054359Sop tD + 0.001323Mog PinjD 0.2372Vk PinjD 0.2563Vk tD +

416(kv/h 1.158)2 0.7520(Sop 0.3967)2 0.00003974Mo2g 06575 0.3143kv/h Sop + 0.1564kv/h tD 0.003718Sop Mog + 0.4601081 Mog Vk + 0.001024Mog tD 0.1993Vk PinjD 0.5189Vk tD410 PpD tD 0.1665(kv/h 1.057)2 1.729(Sop 0.6120)2 0.61

Accpared win Fig. predicguresDependent parametersA constantRegression coefcientsIndependent parameters, i and j are the order number ofthe parameters, and i /= jMatrix of dependent parametersDependent parametersThe number of simulationsMatrix of independent parametersIndependent parameters or their combinationsthe number of independent parameters (x), n = 8The number of independent parameters and theircombinationsMatrix of random errorsRandom errorsMatrix of multinomial coefcientsMultinomial coefcientsSum of squared errors of each parameter

matched, a0.9519, resptions obtainestimate Rfsionless paused withinvalues of sovariation teobtained ushave been awith differeence of Pinjcorrespond

Rf, Ef anobvious at f predicted values and actual values for Rf , Ef and SCO2 respectively.se lines were used as the standard to measure matching between the

() was at its minimum, the corresponding would beion coefcient. When X was a non-singular matrix, theoefcient was as follows. Table 7 summarizes the terms(23).

X Y (23)

d SCO2 obtained from the performed simulations weree dependent parameters. It is assumed that the inde-ensionless parameter would not affect the dependent

when the signicant level is very low. The least signif-of p = 0.05 was used. Rf, Ef and SCO2 were calculated bye regression method. The equations are as the follows:

Vk 0.2682kv/h PinjD606Vk tD 0.1629(kv/h 1.622)2

P2pD 0.4109(tD 1.087)2

(24)

PinjD + 0.1702kv/h tD503PinjD tD + 0.07813PrD PpD6(Vk 0.8701)2 0.5066(tD 0.4603)2

(25)

p Vk 0.3406Sop PinjD4828PinjD tD

k 0.6091)2 0.2247t2D

(26)

g to the above equations, predicted values were com-actual values to acquire their relational graphs, as showne straight lines in the gures represent places where thealues are equal to the actual values. As shown in those

predicted and actual values of Rf, Ef and SCO2 are well

nd their correlation coefcients are 0.9538, 0.9411 andectively. This demonstrates that the established equa-ed by the stepwise regression method can be used to, Ef and SCO2 . It should be pointed out that the dimen-rameters are limited in ranges. The correlations can be

the ranges. Further studies need to be conducted if theme dimensionless parameters are beyond ranges. Thendency of Rf, Ef and SCO2 with different parameters areing the three equations. As shown in Fig. 6, four graphsdded to show the variation tendency of Rf, Ef and SCO2nt Kv/h, Sop, Mog and Vk respectively. Because the inu-

D, PpD and PrD to Rf, Ef and SCO2 are insignicant, theiring graphs will not be given in this paper.d SCO2 increase with the increase of tD. The growth isthe beginning but the growth tapers off after tD = 0.8

C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534 31

Fig. 6. Rf , Ef and SCO2 change with tD with different values of the parameters. Fig. 6 1Fig. 6-4 are the variation tendency of Rf , Ef and SCO2 with different Kv/h , Sop , Mog , Vk

respectively. And Rf , Ef and SCO2 change with tD .

Fig. 7. Rf , Ef and SCO2 change with tD with different values of the parameters. Rf and SCO2 are different with that of Fig. 6. The denominators of the new Rf , Ef and SCO2 are alltotal pore volume. Fig. 7-1Fig. 7-4 are the variation tendency of Rf , Ef and SCO2 with different Kv/h , Sop , M

og , Vk respectively. And Rf , Ef and SCO2 change with tD .

32 C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534

Fig. 8. The abs on trends of the absolute differences respectively. The absolute differencesare the differe nimum values of Kv/h , Sop , Mog and Vk respectively.

because of increase of In this papeduced oil towhich makpaper is seeratio of cumand reservomiscible precan achieveare still somsuch as homand well shof swept voing. Howevother refereto the usuapresented. recovery is If it is convethe value is

In ordervalues whicare shown inew Rf andtors are all is higher thcorrelationsare shown iwhich corremum valueRf, Ef and SCences of thewith the incRf, Ef and SCences of thwith the incdecrease w

3. Exampleoilelds re

XinjiangAutonomou(Fig. 9). It ilike low perability and

water in most reservoirs is relatively simple and uid prop-are relatively favorable. The oil is of low density and lowty, and is classied as light oil. The high pressure, low poros-

permeability and strong heterogeneity make some parts ofeld ee re

valieters.20, of thlace .253educervo

106

e is ndention, umeoir fere ate par

numegreetersulate2005ptabtainolute differences of Rf , Ef and SCO2 change with tD . Fig. 8 1Fig. 8-3 show the variatint values of Rf , Ef and SCO2 respectively, which correspond to the maximum and mi

CO2 breakthrough. Rf, Ef and SCO2 increase with theSop, and decrease with the increase of Kv/h, Mog and Vk.r, oil recovery is dened as the ratio of cumulative pro-

POIP. POIP is often the oil-in-place after water ooding,es it less than OOIP. Therefore, the oil recovery in thismingly higher than the oil recovery that dened as theulative produced oil to OOIP. The injection pressureir pressure in many models are higher than minimumssure. Therefore, most oilCO2 systems in these models

miscibility which can leads to higher oil recovery. Theree other situations that can achieve higher oil recovery,ogeneous reservoir, low density and viscosity of the oil,ot wells. All these situations can easily lead to increaselume which may further result in oil recovery increas-er, the oil recovery in this paper has rarely been used innces. For comparison, the oil recovery can be convertedl oil recovery. An example of this conversion has beenPOIP is 0.7 times of OOIP after water ooding. The oil0.25 after CO2 ooding, with the denominator of POIP.rted to the oil recovery with the denominator of OOIP,

70% of the oil recovery, i.e. 0.175. to compare with Ef, Rf and SCO2 were converted to theh the denominators are total pore volume. The trendsn Fig. 7. The overall trends are the same as Fig. 6, but the

SCO2 are less than the former because their denomina-total pore volume. Ef is higher than Rf and SCO2 . And Rfan SCO2 . In order to analyze the further trends of these, the curves of the absolute differences of Rf, Ef and SCO2n Fig. 8. The absolute differences values of Rf, Ef and SCO2 ,spond to Vk, Kv/h and SCO2 respectively, are the maxi-s. It indicates that the most inuential parameters onO2 are Vk, Kv/h and Sop respectively. The absolute differ-

three key parameters, corresponding to Kv/h, increase

oil anderties viscosiity, lowthe oil

Thrsen toparam0.160cosity of in-pis 335The irrage resis 7.3 reservindepesaturafrom nreservters weof thes

Thewise rparamto simet al., be acceities obrease of tD, which indicates that the inuence of Kv/h toO2 increase with the increase of tD .The absolute differ-e three key parameters, corresponding to Vk, decreaserease of tD, showing the inuence of Vk to Rf, Ef and SCO2ith the increase of tD.

storage capacity calculation of Xinjiangservoirs

oileld is in the northern part of Xinjiang Uygurs Region in China with an area of 13.487 104 km2s a representative oileld characterized with featuresmeability, low porosity, and high pressure. Both perme-porosity show strong heterogeneity. The distribution of

Fig. 9. Locatiocolored regionThe dashed linborder line of difcult to develop via water ooding.servoirs in Xinjiang oileld (CN, XS and BQ) were cho-date the three methods for estimating the three key. Their locations are shown in Fig. 9. The porosity isand permeability is 4.7 101559.74 1015 m2. Vis-e oil is 1.1 1034.4 103 Pa s. The specic gravityoil is 0.7240.814. The original reservoir temperature51.45 K and its pressure is 20.6 10629.5 106 Pa.ible water saturation ranges from 30.4% to 47%. Aver-ir depth is 22252597.5 m, and the development area39.7 106 m2. Reservoir thickness is 6.910.8 m. Oil7.54 10928.83 109 m3. The average values of thet parameters including permeability, heterogeneity, oiluid mobility and reservoir pressure were obtainedrical reservoir simulations and were used to depict theatures. Then, the independent dimensionless parame-tained through the dimensionless formulae. The valuesameters for the three oil reservoirs are shown in Table 8.erical reservoir simulation, empirical formula and step-ssion methods were used to estimate the three key. The numerical simulation has been adopted widely

CO2 storage in formations (Kumar et al., 2004; Ozah; Jahangiri and Zhang, 2012), and has been proven tole. Therefore, it is assumed that the CO2 storage capac-ed through the numerical reservoir simulation are then of the three reservoirs (BQ, XS and CN) in Xinjiang oileld. The light- is the uplift belt, and the dark-colored region is the depression belt.e depicts the boundaries of the regions, and the solid line means thethe oileld.

C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534 33

Table 8The values of independent dimensionless parameters of example reservoirs in Xinjiang oileld.

Reservoir kv/h Sop Mog Vk PinjD PpD PrD tD

BQ 0.1 0.47 41.9 0.28 1.42 0.79 1.01 0.47CN 0.13 0.45 37.4 0.35 XS 0.11 0.56 44.8 0.24

Table 9Calculated values of the key parameters and their corresponding storage capacitiesusing three different methods for three reservoirs in Xinjiang oileld.

Reservoir Numericalsimulation

Empiricalformula

Stepwiseregression

Rf , m3/m3 BQ 0.46 0.54 0.49CN 0.52 0.59 0.47XS 0.43 0.49 0.40

Ef , m3/m3 BQ 0.56 0.58 0.54CN 0.65 0.58 0.70XS 0.59 0.58 0.53

SCO2 , kg/kg BQ 0.32 0.38 0.35CN 0.41 0.46 0.43XS 0.37 0.42 0.35

POIP, 109 m3 BQ 28.83 28.83 28.83CN 22.46 22.46 22.46

MCO2 t , 109 kg

MCO2e , 109 k

standard vacapacities olation modeIt shows thacloser to themula. SCO2 imakes CN rcal and effePOIP in genregression mthe numeriative errorseffective stomethod is 3is 4.1218.76.02% and 1method is hthat the stethe CO2 sto

Fig. 10. Relatiical formula an

limited. Thethat it has a

4. Discussi

Most oilwater oodwater produCO2 in remthe heterogwhich is caciency musmethods ofreservoirs i

obtacuratparamlabletual

caperimin. T

conethoe uti

the

clus

ed otion aininere XS 7.54 7.54 7.54BQ 13.96 15.22 14.59CN 12.99 13.53 12.54XS 3.77 4.03 3.53

g BQ 5.71 6.78 6.24CN 5.55 6.22 5.91XS 1.70 1.93 1.61

lues in this paper. The theoretical and effective storagef the reservoirs were estimated according to the calcu-l of CO2 storage capacity. The result is shown in Table 9.t Rf, Ef and SCO2 obtained by the stepwise regression are

numerical simulation as compared to the empirical for-n CN reservoir is higher than in other reservoirs whicheservoir more suitable for storing CO2. The theoreti-ctive storage capacities of the reservoirs increase witheral. CO2 storage capacities obtained by the stepwiseethod are very close to the results obtained through

cal simulation. As shown in Fig. 10, most of the rel- of theoretical storage capacity are less than that of

can beand acthose is avaiconcepstorageon expto obtastrictlysion mit can blacking

5. Con

Bascalculain remSCO wrage capacity. The relative error of stepwise regression.089.12%, and that of the empirical formula method5%. The average relative errors of the two methods are0.73%. Therefore, the accuracy of stepwise regressionigher than the empirical formula method. This suggestspwise regression method is more suitable to evaluaterage capacity of Xinjiang oileld when needed data is

ve errors of the storage capacities of the three reservoirs in the empir-d stepwise regression methods.

2lation, empused to detison of the numerical rever, it requdata. A reducision of theon experimso, some arbe strictly poor. The sreservoir sitive blocks after whichdoes not reresults are

Acknowled

This wogram of ChiNational M006 and 2involved ineditor and t1.32 0.61 0.89 0.611.39 0.72 1.12 0.52

calculated CO2 storage capacity of the oileld shows very large storage potential.

on

reservoirs in Xinjiang oileld have been developed viaing, and most of them are experiencing a stage of highction. To store CO2 in such reservoirs, the dissolution of

aining oil and water should be considered. Consideringeneity of permeability as well as the gravity separation,used by the density variation of oil and CO2, sweep ef-t be contemplated. In the present work, the calculation

CO2 storage capacity were based on Rf, Ef and SCO2 of then the Xinjiang oileld. The three key parameters aboveined in different ways. For oil reservoirs with abundante data, the numerical simulation method can determineeters with relatively high precision. When less data

, the stepwise regression method based on numerical reservoir simulation can be utilized to estimate CO2acity. The empirical formula method is mainly basedental and empirical data, which are sometimes difcultherefore, applicable conditions of this method must besidered before application. Because the stepwise regres-d requires less data and has a wide range of application,lized to predict storage capacity for oil reservoirs when

required data.

ions

n the volumetric balance theory, this work presentedmodels for CO2 storage capacity with the CO2 dissolvedg oil and water considered. In these models, Rf, Ef andthe three key parameters. Numerical reservoir simu-irical formula, and stepwise regression methods wereermine these parameters in the models. After compar-results obtained from the three different methods, theeservoir simulation method is the most reliable. How-ires substantial geological, reservoir and experimentalced amount of data would impact the accuracy and pre-

results. The empirical formula method is mainly basedental and empirical data. Less data is required, but evene still difcult to acquire. Its applicable condition mustconsidered. And the estimation accuracy is relativelytepwise regression method is based on the numericalmulation method, and only requires small representa-of the oil reservoir to build the numerical simulation

many parameter values can then be obtained easily. Itquire a substantial amount of data, but the calculationaccurate.

gements

rk was supported by the National Basic Research Pro-na (973 program, grant no. 2011CB707302), and Chinese

ajor Science and Technology Projects (2011ZX05016-011ZX05009-004-001).We are grateful to all staff

these projects, and also thank the journal associatehe reviewers.

34 C. Liao et al. / International Journal of Greenhouse Gas Control 28 (2014) 2534

Appendix A

Detailed derived steps for Eqs. (13)(17)Eqs. (3), (5), (10), (11), (12) are shown as follows:

MCO2e = Ce MCO2t (12)

MCO2t = Mfree-phase CO2 + MCO2 in sweptoil + MCO2 in sweptwater (3)

MCO2 in sweptoil = CO2r Ef POIP (1 Rf ) mCO2 in oil (5)

Mfree-phase C

MCO2 in swept

When Eqequation is

MCO2t = C+ Ef PO+Ef (P

where, POIP

PWIP = A

PWIP Vpw(The secondCO2 oodin

The twoEq. (3-1-1)

MCO2 t = CO2r

+ Ef A

+ Ef (A

= CO2r A

+ Ef (1

= CO2r A

where,

Sfree-phase CO

SCO2 in swept

SCO2 in swept

The SCO2

SCO2 = Ce

Then, Eq. (3-1-1) can be simplied as follows

MCO2t = CO2r A h (1 Swp) SCO2Ce

After substituting the last equation into Eq. (12), Eq. (13) isobtained.

MCO2e = Ce MCO2t = CO2r A h (1 Swp) SCO2 (13)

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1 Swp (1 Rw) mCO2in water

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Swp1 Swp Rw (15)

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Comparison of different methods for determining key parameters affecting CO2 storage capacity in oil reservoirs1 Introduction2 Calculation of storage capacity2.1 Calculation of theoretical storage capacity2.2 Estimation of effective storage capacity2.3 Determination of key parameters2.3.1 Numerical reservoir simulation2.3.2 Empirical formula2.3.3 Stepwise regression

3 Example storage capacity calculation of Xinjiang oilfield's reservoirs4 Discussion5 ConclusionsAcknowledgementsAppendix AReferences