Journal of Petroleum Science and Engineering 108 (2013) 40–51

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Journal of Petroleum Science and Engineering

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n CorrChina UPR Chin

E-m

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Estimation of water saturation from nuclear magnetic resonance(NMR) and conventional logs in low permeability sandstone reservoirs

Xiao Lianga,b,n, Zou Chang-chuna,b, Mao Zhi-qiangc, Shi Yu-jiangd, Liu xiao-penge, Jin Yanf,Guo Hao-pengd, Hu Xiao-xine

a Key Laboratory of Geo-detection, China University of Geosciences, Ministry of Education, Beijing, PR Chinab School of Geophysics and Information Technology, China University of Geosciences, Beijing, PR Chinac State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, PR Chinad Research Institute of Exploration & Development, Changqing Oilfield Comapny, PetroChina, Shaanxi, PR Chinae Geological Exploration and Development Research Institute in Sichuan-Changqing Drilling and Exploration Engineering Corporation,CNPC, Sichuan, PR Chinaf Southwest Oil and Gas Field Branch Company, PetroChina, Sichuan, PR China

a r t i c l e i n f o

Article history:Received 22 March 2012Accepted 19 May 2013Available online 15 June 2013

Keywords:low permeability sandstone reservoirscementation exponentsaturation exponentnuclear magnetic resonance (NMR) logsirreducible water saturationT2 lm

pore structure

05/$ - see front matter & 2013 Elsevier B.V. Ax.doi.org/10.1016/j.petrol.2013.05.009

esponding author at: School of Geophysicsniversity of Geosciences, No. 29, Xueyuan Roaa. Tel.: +86 10 8232 0692 (office); +86 152 10ail address: xiaoliang@cugb.edu.cn (L. Xiao).

a b s t r a c t

It is difficult to obtain rock resistivity parameters by using the cross plots of porosity vs. formation factorand water saturation vs. resistivity index to calculate reservoir water saturation in low permeabilitysandstones. The cementation and saturation exponents (m and n separately) are divergent, and no fixedvalues can be obtained due to the complicated pore structure. This leads to a problem in water saturationcalculation. To investigate the main factors that heavily affect the cementation and saturation exponents,36 core samples, which were drilled from low permeability sands of Xujiahe Formation, Sichuan basin,southwest China, are chosen for laboratory resistivity and nuclear magnetic resonance (NMR) measure-ments, 20 of them for mercury injection capillary pressure (MICP) measurements and 10 of them forcasting thin-section analysis. The results show that these two parameters are associated with rock porestructure. For rocks with good pore structure, the proportion of macropore components is dominant,high cementation exponents and low saturation exponents can be obtained, and on the contrary, rockswith poor pore structure will be dominated by the proportion of small pore components, and they willcontain low cementation exponents and high saturation exponents. To quantitatively acquire reliablecementation and saturation exponents for water saturation estimation, a logarithmic function isestablished to calculate cementation exponent from porosity. Irreducible water saturation (Swi), whichis estimated from NMR logs by using the optimal T2cutoff, is presented to characterize the proportion ofsmall pore components. A technique of calculating saturation exponent by combining with Swi, (1−Swi)and the logarithmic mean of NMR T2 spectrum (T2 lm) is proposed, and the corresponding model isestablished. The credibility of these techniques is confirmed by comparing the predicted cementationand saturation exponents with the core analyzed results. The absolute errors between the predictedcementation exponents and the experimental results are lower than 0.08, and the absolute errorsbetween the predicted saturation exponents and the experimental results are lower than 0.2. Thesetechniques proposed in this study are extended to several low permeability sands for field applications;the field examples illustrate that cementation and saturation exponents can be accurately estimated inthe intervals with which NMR logs were acquired. By using the variable rock resistivity parameters,precisely water saturation can be calculated for low permeability sandstones evaluation.

& 2013 Elsevier B.V. All rights reserved.

1. Introduction

Hydrocarbon saturation is an important input parameter information evaluation, fluid identification and reserves estimation,and it also plays a very important role in reservoir simulation and

ll rights reserved.

and Information Technology,d, Haidian, Beijing 100083,87 9138 (mobile).

development program formulation. Hydrocarbon saturation isalways predicted after water saturation is first estimated. Hence,obtaining water saturation as accurate as possible is of greatimportance in reservoir evaluation, especially in low permeabilitysandstones with complicated pore structure. Generally, watersaturation can be accurately calculated from conventional logsonce the reliable equation is used. Archie's equation was firstproposed by Archie (1942) to calculate water saturation fromconventional logs, and it had been widely used in conventionalreservoir for a long time. With the discovery of more and more

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–51 41

complicated reservoirs (such as low resistivity contrast reservoirand low permeability sandstones), Archie's equation had beenfound not to be always effective. Since the 1960s, many derivedmodels had been proposed to estimate water saturation fromconventional logs in different types of reservoirs. Waxman andSmits (1968) and Waxman (1974) proposed Waxman–Smits' equa-tion, Clavier et al. (1977) proposed the dual-water model, andGivens (1986, 1987) and Givens and Schmidt (1988) proposed theconductive rock matrix model (CRMM) to predict water saturationin low resistivity contrast reservoirs. Rasmus and Kenyon (1985)and Rasmus (1987) proposed the appropriate model (known asRasmus's model) to calculate water saturation in reservoirs withporous media of fracture and cavern. However, in low permeabilitysandstones with complicated pore structure, no relevant modelhad been proposed to estimate water saturation at present, andArchie's equation is still being used. Archie's equation can beexpressed as

F ¼ R0

Rw¼ a

φm ð1Þ

Ir ¼Rt

R0¼ 1

Snwð2Þ

where R0 is the rock resistivity with fully saturated water, Rw is theformation water resistivity, Rt is the rock resistivity with saturatedhydrocarbon; their units are Ωm; F is the formation factor, Ir is theresistivity index; they are all zero dimension; φ is the rock porosityin fraction, Sw is the water saturation in fraction, a is the tortuosityfactor; its value always ranges from 0.6 to 1.6; m is the cementa-tion exponent and its value is always ranges from 1.0 to 2.0 for

y = 1.8389x-1.2473

R2 = 0.9312

1

10

100

0.01 0.1 1

Porosity, fraction

Form

atio

n fa

ctor

Form

atio

n fa

ctor

y = 2.8892x-1.1602

R2 = 0.8986

1

10

100

1000

0.01

Porosit

Form

atio

n fa

ctor

Fig. 1. (a) The cross plot of porosity vs. formation factor for core samples drilled from low(b) The cross plot of porosity vs. formation factor for core samples drilled from low permcross plot of porosity vs. formation factor for core samples drilled from low permeabili

sandstones; n is the saturation exponent, and its value is affectedby many factors, such as pore structure and/or wettability; a, mand n are referred to as the rock resistivity parameters.

Transforming Eq. (1) and substituting it into Eq. (2), a derivativeformula could be written as

Sw ¼ffiffiffiffiffiffiffiffiffiffiffiaRw

φmRt

n

sð3Þ

This formula illustrates that the values of a, m, n, Rw, φ andRt must be first acquired for water saturation calculation.Generally, φ can be calculated from conventional or NMR logs(Wyllie et al., 1956; Coates et al., 2000), and the deep lateralresistivity (RLLD) or deep induction resistivity (RILD) can bedirectly used as Rt; Rw can be checked from the formation watersalinity by using Schlumberger's log interpretation charts(Schlumberger Well Services, 1986).

The determination of a, m and n is of great importance inestimating water saturation by using Eq. (3). Generally, the valuesof a, m and n are obtained from laboratory resistivity measure-ments of the target core samples by using the statistical regressionmethod of power function. To obtain the values of a, m and n,several needed procedures should be covered as follows: (1) dril-ling the representative core samples from the interested intervals,porosities and permeabilities of the selective plug samples shouldcover all the target formations; (2) saturating core samples withthe same salinity as actual formation water, and all the saturatedcore samples are taken for laboratory resistivity measurements byusing the porous plate method. In our studied Xujiahe Formation,the salinity of water that was used to saturate core samples

y = 1.7819x-1.6083

R2 = 0.9253

1

10

100

1000

0.01 0.1 1

Porosity, fraction

0.1 1

y, fraction

permeability sandstones of Xujiahe Formation in Sichuan basin, southwest China.eability sandstones of Chang 8 Formation in Ordos basin, northwest China. (c) The

ty sandstones of the third basin.

1

10

0.1 1Water saturation, fraction

Res

istiv

ity in

dex

no.1 no.2no.3 no.4no.5 no.6no.7 no.8no.9 no.10no.11 no.12no.13 no.14no.15 no.16no.17 no.18no.19 no.20no.21 no.22no.23 no.24no.25 no.26no.27 no.28no.29 no.30no.31 no.32no.33 no.34no.35 no.36

1

10

0.1 1

Water saturation, fraction

Res

istiv

ity in

dex

no.x1 no.x2no.x3 no.x4no.x5 no.x6no.x7 no.x8no.x9 no.x10no.x11 no.x12no.x13 no.x14no.x15 no.x16no.x17 no.x18no.x19 no.x20no.x21 no.x22no.x23 no.x24no.x25 no.x26no.x27 no.x28no.x29 no.x30

1

10

0.1 1

Water saturation, fraction

Res

istiv

ity in

dex

no.s1 no.s2

no.s3 no.s4

no.s5 no.s6

no.s7 no.s8

no.s9 no.s10

no.s11

Fig. 2. (a) The cross plot of water saturation vs. resistivity index for core samples drilled from low permeability sandstones of Xujiahe Formation in Sichuan basin, southwestChina. (b) The cross plot of water saturation vs. resistivity index for core samples drilled from low permeability sandstones of Chang 8 Formation in Ordos basin, northwestChina. (c) The cross plot of water saturation vs. resistivity index for core samples drilled from low permeability sandstones of the third basin.

Table 1The laboratory resistivity experimental data sets for 36 core samples drilled from low permeability sands of Xujiahe Formation in Sichuan basin, southwest China.

Wells Samplenumber

Depth Brineconcentration

Temperature Rw Porosity Permeability R0 Formationfactor (F)

Saturationexponent (n)

T2cutoff T2 lm

(m) (g/l) (1C) (Ω m) (%) (mD) (Ω m) (ms) (ms)

Well A 1 xx12.56 130.00 25.00 0.07 15.73 5.87 1.31 20.03 1.93 22.85 29.09Well A 2 xx13.47 130.00 25.00 0.07 17.36 5.24 1.10 16.76 2.34 19.59 39.74Well A 3 xx24.58 130.00 25.00 0.07 16.17 1.08 1.34 20.44 2.57 13.34 28.56Well A 4 xx92.22 130.00 25.00 0.07 13.88 0.58 1.63 25.00 2.55 10.86 17.56Well A 5 xx14.70 130.00 25.00 0.07 4.60 0.08 4.63 70.82 2.79 7.19 13.13Well A 6 xx10.50 130.00 25.00 0.07 5.86 0.16 3.52 53.89 2.59 22.77 17.90Well A 7 xx09.20 130.00 25.00 0.07 6.70 0.20 3.19 48.84 2.45 12.46 18.89Well A 8 xx07.20 130.00 25.00 0.07 7.28 0.28 2.82 43.19 2.34 11.62 17.92Well A 9 xx00.00 130.00 25.00 0.07 5.57 0.15 3.16 48.33 2.62 4.74 8.26Well B 10 xx22.80 130.00 25.00 0.07 14.68 3.06 1.31 20.02 2.04 14.41 39.50Well B 11 xx07.70 130.00 25.00 0.07 12.91 12.30 1.46 22.34 1.85 13.73 63.73Well C 12 xx31.00 130.00 25.00 0.07 5.92 0.13 2.85 43.53 2.87 9.58 8.64Well C 13 xx19.30 130.00 25.00 0.07 11.71 0.23 1.92 29.37 1.69 41.81 26.93Well C 14 xx02.00 130.00 25.00 0.07 17.44 0.23 1.39 21.21 2.23 28.83 26.73Well C 15 xx95.80 130.00 25.00 0.07 12.31 0.20 1.96 29.96 2.17 22.54 44.70Well C 16 xx87.85 130.00 25.00 0.07 21.27 90.60 0.77 11.72 1.66 55.76 123.96Well C 17 xx85.90 130.00 25.00 0.07 15.89 1.05 1.31 20.00 1.89 34.58 75.18Well C 18 xx81.50 130.00 25.00 0.07 17.14 0.58 1.24 18.99 2.14 25.52 49.93Well C 19 xx71.30 130.00 25.00 0.07 15.62 0.17 1.45 22.20 1.94 27.14 25.01Well D 20 xx61.50 130.00 25.00 0.07 16.43 0.27 1.41 21.54 1.80 30.60 43.67Well D 21 xx46.20 130.00 25.00 0.07 13.13 0.21 1.82 27.85 1.78 21.81 35.60Well D 22 xx40.50 130.00 25.00 0.07 10.13 0.21 2.31 35.27 2.01 21.19 35.33Well D 23 xx35.15 130.00 25.00 0.07 9.62 0.16 2.40 36.71 2.39 21.39 33.36Well D 24 xx90.60 130.00 25.00 0.07 10.58 0.62 1.75 26.75 3.48 19.13 20.41Well D 25 xx83.80 130.00 25.00 0.07 8.54 0.33 2.71 41.49 3.02 19.03 10.12Well D 26 xx81.00 130.00 25.00 0.07 12.20 0.89 1.66 25.35 2.56 20.49 29.11Well D 27 xx78.45 130.00 25.00 0.07 11.38 0.91 1.74 26.61 3.00 23.48 30.53Well D 28 xx66.20 130.00 25.00 0.07 13.34 0.57 1.59 24.35 2.45 13.36 19.98Well D 29 xx54.35 130.00 25.00 0.07 9.04 0.62 2.34 35.84 3.31 18.59 29.09Well D 30 xx40.40 130.00 25.00 0.07 8.20 0.27 2.84 43.41 2.23 14.70 28.18Well D 31 xx22.30 130.00 25.00 0.07 7.80 0.50 2.54 38.88 2.72 21.10 34.05Well D 32 xx95.50 130.00 25.00 0.07 10.59 1.03 2.00 30.62 2.21 25.84 47.14Well D 33 xx86.65 130.00 25.00 0.07 14.00 0.49 1.65 25.20 1.63 17.90 30.62Well D 34 xx45.80 130.00 25.00 0.07 9.33 0.24 2.73 41.67 2.86 14.67 25.21Well D 35 xx98.40 130.00 25.00 0.07 9.41 0.86 2.15 32.91 2.21 22.55 43.19Well D 36 xx90.30 130.00 25.00 0.07 8.36 0.50 2.64 40.42 1.63 22.01 35.02

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–5142

Table 2The pore type information obtained from 10 core samples with casting thin-section.

Wells Sample number Depth The relative content The averagepore-throat ratio

The averagecoordinationnumber

Primaryintergranularpore

Residualintergranularpore

Intragranulardissolved pore

(m) (%)

Well A 2 xx13.47 40.00 55.00 5.00 17.05 0.40Well A 3 xx24.58 20.00 75.00 5.00 13.13 0.57Well A 7 xx09.20 5.00 95.00 0.00 0.00 0.00Well B 10 xx22.80 25.00 70.00 5.00 16.69 0.88Well C 16 xx87.85 70.00 30.00 0.00 17.30 1.22Well C 18 xx81.50 65.00 35.00 0.00 13.80 0.73Well D 20 xx61.50 65.00 35.00 0.00 13.64 0.85Well D 21 xx46.20 65.00 35.00 0.00 19.10 0.80Well D 22 xx40.50 15.00 85.00 0.00 18.63 0.46Well D 32 xx95.50 0.00 15.00 85.00 0.00 0.00

y = 2.0255x-1.1412

R2 = 0.9934

y = 2.5177x-1.129

R2 = 0.91

1

10

100

0.01 0.1 1

Porosity, fraction

Form

atio

n fa

ctor

no.36: por.=8.4%; perm.=0.5 mD

no.31: por.=7.8%; perm.=0.5 mD

Fig. 3. Comparison of relationship between porosity and formation factor for twocore samples with similar physical parameters.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–51 43

is 130.0 g/l. The data sets of core porosity, formation factor, watersaturation and the corresponding resistivity index under differentwater saturation are collected; (3) mapping the cross plots ofporosity vs. formation factor, and water saturation vs. resistivityindex for all experimental core samples in log–log coordinates;(4) using the statistical regression method of the power functionto acquire the fixed values of a and m from the cross plot ofporosity vs. formation factor, and the constant value of n from thecross plot of water saturation vs. resistivity index.

For conventional reservoirs, with the above mentioned proce-dures, the fixed a, m and n can be regressed, separately. However,for low permeability sands, the relationships of porosity andformation factor, and water saturation and resistivity index cannotbe rigidly expressed by the power function due to the complicatedpore structure and strong heterogeneity (Mao et al., 1995; Shiet al., 2008). Fig. 1a–c shows the cross plots of porosity andformation factor for three different types of low permeabilityreservoirs in China, and Fig. 2a–c displays the corresponding crossplots of water saturation and resistivity index for the same rocks.From Figs. 1 and 2, it can be observed that for low permeabilitysandstones, the relationships between porosity and formationfactors are not rigid power function; the tendency of core sampleswith porosity lower than 8.0% is not coincident with those withporosity higher than 8.0%; if the statistical regression method ofpower function is still used to obtain a and m for all core samples,the deviated values should be obtained. Moreover, the cross plot ofwater saturation and resistivity index is divergent and the powerfunction cannot be used to describe the characterization of all coresamples; a fixed saturation exponent is difficult to acquire.

In this study, 36 core samples drilled from low permeability sandsof the Xujiahe Formation in Sichuan basin, southwest China, arechosen for laboratory resistivity experiments based on the abovementioned procedures; the experimental data sets are listed in Table 1.

To investigate the correlation of pore structure and rock resistivityparameters of a,m and n, all 36 core samples are tested for laboratoryNMR measurements; 20 of them are chosen for mercury injectioncapillary pressure (MICP) measurements and 10 of them for theexperiments of core casting thin-section. From these experimentalmeasurements, the NMR spectra, MICP data and the pore typeinformation for the core samples are obtained. The experimentalparameters of laboratory NMR measurement are listed as follows:polarization time (TW): 6.0 s; inter-echo spacing (TE): 0.2 ms; thenumber of echoes per echo train (NE): 4096; and scanning number:128. The laboratory NMR measurements for all 36 core samples andpore type information for 10 core samples are listed in Tables 1 and 2,respectively.

2. Effects of pore structure on rock resistivity parametersof a, m and n in low permeability sands

2.1. Effects of pore structure on the parameters of a and m

To illustrate the effects of pore structure on a and m, the datasets listed in Table 1 are reused, and the cross plot of porosity andformation factor is shown in Fig. 3. Two core samples, which arenumbered as no. 31 and no. 36 and have the same permeabilityand similar porosity, are highlighted. Fig. 3 shows that theregularity of no. 31 and no. 36 is completely different. Core sampleno. 31 follows the regularity established by core samples withrelative low porosity and low permeability, while the relationshipbetween porosity and formation factor for core sample no. 36 issimilar with those core samples with high porosity and highpermeability.

Fig. 4(a) shows the NMR spectra of core sample no. 31 and no.36, and (b) is the comparison of MICP curves for the same two coresamples. These comparisons illustrate that the difference of therelationship between porosity and formation factor for coresamples no. 31 and no. 36 is caused by the completely disparatepore structure. Although they have the same permeability andsimilar porosity, their pore structure is quite different. The NMRT2 distribution illustrates that the proportion of macropore compo-nents of core sample no. 36 is dominant while core sample no. 31 is

0

0.04

0.08

0.12

0.16

0.2

0.24

0.1 1 10 100 1000 10000

T2, ms

Am

plitu

de, v

/v

no.31

no.36

0.001

0.01

0.1

1

10

100

020406080100

Mercury injection saturation, %

Mer

cury

inje

ctio

n pr

essu

re, M

Pa

no.36no.31

Fig. 4. (a) The NMR T2 spectra of core sample no. 31 and no. 36. (b) Comparison of MICP curves for core samples no. 31 and no. 36.

no.16y = 0.9772x-1.6628

R2 = 0.9968

no.12y = 0.9437x-2.8656

R2 = 0.9704

no.3y = 0.9991x-2.5703

R2 = 0.9953

no.10

y = 0.9974x-2.0358

R2 = 0.9975

1

10

0.1 1

Water saturation, fraction

Res

istiv

ity in

dex

no.16no.10no.3no.12

0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 1 10 100 1000 10000

T2, ms

Am

plitu

de, v

/v

no.16: n=1.66; T2lm=123.96msno.10: n=2.04; T2lm=39.50msno.3: n=2.57; T2lm=28.56msno.12: n=2.87; T2lm=8.64ms

0.001

0.01

0.1

1

10

100

020406080100

Mercury injection saturation, %

Mer

cury

inje

ctio

n pr

essu

re, M

Pa

no.16no.10no.3no.12

Fig. 5. (a) The cross plot of water saturation vs. resistivity index for four representative core samples in low permeability sands. (b) The NMR T2 distribution for the same fourcore samples. (c) The MICP curves for the same four core samples.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–5144

dominated by the proportion of small pore components, thethreshold pressure of core sample no. 36 is lower. These twocomparisons illustrate that in low permeability sands, the valuesof a and m (especially m) should be variable in rocks withcomplicated pore structure; if fixed values of a and m are definedin the whole intervals, inaccurate water saturation will becalculated.

2.2. Effects of pore structure on saturation exponent

Generally, rock saturation exponent is affected by two mainfactors: wettability and pore structure (Sweeney and Jennings,1960; Suman and Knight, 1997; Xiao et al., 2013). Based on thelaboratory measurements of sandstones, Sweeney and Jennings(1960) and Suman and Knight (1997) found that the saturationexponent can reach to 8.0 for rock with wetting oil phase. Xiaoet al. (2013) pointed out that rocks with poor pore structure willhave a high saturation exponent. Rock wettability determination

experiments in the target Xujiahe Formation showed that forma-tions are water wetted. Hence, the effect of wettability on theelectrical resistivity can be ignored.

To illustrate the relationship between rock pore structure andsaturation exponent in low permeability sands, laboratory resis-tivity and NMR experimental results for 36 core samples, mercuryinjection measurements for 20 core samples and casting thin-section experiments for 10 core samples have been studied.

Four representative core samples (which were numbered as no.16, no. 10, no. 3 and no. 12 separately) with saturation exponentincreasing from 1.6628 to 2.827 are compared and displayed inFig. 5a. To illustrate the difference of pore structure among them,the corresponding NMR T2 distributions for these four coresamples are displayed in Fig. 5b, the MICP curves are shown inFig. 5c, and the casting thin-sections for core samples no. 16, no. 10and no. 3 are displayed in Fig. 6. From these casting thin-sections,the information of pore type can be obtained, and the averagecoordination number, which was defined as the average number

150 μm

75 μm

50 μm

Fig. 6. The casting thin-section for 3 representative core samples of (a) no. 16, (b) no. 10 and (c) no. 3.

0

20

40

60

80

Primary intergranular pore Residual intergranular pore Intragranular dissolvedpore

Pore type

Rel

ativ

e co

nten

t, %

no.16no.10no.3

Fig. 7. The pore type of three representative core samples of no. 16, no. 10 and no. 3.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–51 45

of pore throats connected to a pore body and used to characterizethe connectivity (Wang and Sharma, 1988), was also acquired.The average coordination number and pore type for core samplesno. 16, no. 10 and no. 3 are showed in Figs. 6 and 7, respectively.

Based on the experimental results shown in Figs. 5–7, therelationship of saturation exponent and rock pore structure isanalyzed as follows: (1) core sample no. 16 contains the lowestsaturation exponent of 1.6628; the corresponding laboratory NMRmeasurement shows that the T2 distribution is wide; the longestT2 transverse relaxation time reaches to 2000.0 ms, T2 lm is123.96 ms; the T2 spectrum is bimodal, and the proportion ofmacropore components is dominating; the MICP curve shows thatthe pore structure of core sample no. 16 is the best; the thresholdpressure is lower than 0.05 MPa; the average coordination numberis 1.22, and the relative content of primary intergranular pore andresidual intergraular pore is 75.0% and 25.0%, separately. (2) Thesaturation exponent of core sample no. 10 is higher than no. 16;

the laboratory NMR T2 spectrum illustrates that the longest T2transverse relaxation time of core sample no. 10 is 570.0 ms; T2 lm

is 39.50 ms; it is bimodal; and the proportion of macroporecomponents is dominating; the threshold pressure is close to0.1 MPa; the average coordination number is 0.88, and the poretype is dominant with residual intergraular pore; the relativecontent of primary intergranular pore is lower than that of thecore sample no. 16. These show that the pore structure of coresample no. 10 is poorer than no. 16. (3) The saturation exponent ofcore sample no. 3 is lower than core samples no. 16 and no. 10; thecorresponding NMR T2 distribution illustrates that the T2 spectrumis narrower than those of core samples no. 16 and no. 10; T2 lm is28.56 ms. The T2 distribution is bimodal, but the proportion ofsmall pore components is dominating. The threshold pressure ishigher than 1.5 MPa, and the average coordination number is 0.57;the relative content of primary intergranular pore is furtherreduced and the relative content of residual intergraular pore isincremental. (4) The saturation exponent of core sample no. 12 isthe highest; the corresponding laboratory NMR measurement andMICP curve show that the pore structure is the poorest; the NMRspectrum is unimodal, and the main T2 transverse relaxation timeis lower than 100 ms; T2 lm is 8.64 ms, and the MICP curve lies onthe top.

To describe the universality of the analyzed relationship ofsaturation exponent and rock pore structure above, the data setslisted in Tables 1 and 2 are reused, and the cross plots of T2 lm vs.saturation exponent for 36 core samples, the average coordinationnumber vs. saturation exponent for 10 core samples are drawn,and they are shown in Fig. 8a and b, separately. These two figuresillustrate that the negative correlations between T2 lm and satura-tion exponent, the average coordination number and saturationexponent are ubiquitous. This means that the pore structure isreally the main factor that affects the saturation exponent in theXujiahe Formation.

From the displayed experimental results in Figs. 5–8, someconclusions can be observed: (1) saturation exponent is mainlyrelated with the rock pore structure. For core samples with lowsaturation exponents, they will contain good pore structure, wideT2 distribution and high T2 lm. The proportion of macropore

0

1

2

3

4

1 10 100 1000

T2lm, ms

Satu

ratio

n ex

pone

nt

0

1

2

3

4

0 0.5 1 1.5

The average coordination number

Satu

ratio

n ex

pone

nt

Fig.8. (a) The cross plot of T2 lm vs. saturation exponent for 36 core samples. (b) The cross plot of the average coordination number vs. saturation exponent for 10 coresamples.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–5146

components is dominated, and the corresponding MICP curve liesin the bottom; the threshold pressure is the lowest; the averagecoordination number is high, and thus depicts good connectivity;the main pore space is the primary intergranular pore. (2) For rockdominated by microporosity, the proportion of small pore compo-nents is large; the value of T2 lm is low; the threshold pressure ofMICP curve is high; the average coordination number is low andthe connectivity is poor; the corresponding relative content ofprimary intergranular pore is reduced and the relative content ofresidual intergraular pore is incremental; the saturation exponentwill increase.

With the above conclusions, it can be observed that the rockpore structure must be first characterized to estimate accuratelythe saturation exponent for water saturation calculation in lowpermeability sandstones.

Saturation exponent is related to the proportion of small porecomponents, MICP curve and parameters extracted from corecasting thin-section. However, the data sets cannot be acquiredconsecutively in the whole target intervals except for NMR logs infield applications. Hence, the best method is to estimate variablesaturation exponent from NMR logs. Xiao et al. (2013) proposed anempirical statistical formula to estimate saturation exponent fromNMR logs after the values of Swirr_30, Swirr_40 and Swirr_50 (irredu-cible water saturations calculated from NMR logs by defining 30.0,40.0 and 50.0 ms as T2 cutoffs). However, field applicationsillustrated that this empirical method was not always effective.For example, in low permeability sandstones, the T2 cutoff isalways lower than 30.0 ms (Mao et al. 2013). If all formations areclassified by using fixed 30.0, 40.0 and 50.0 ms as T2 cutoffs, manyeffective pore spaces are considered as useless. In the next section,an alternative technique and a general equation of estimatingsaturation exponent from NMR logs is proposed.

3. Estimation of rock resistivity parameters from NMR logs

3.1. Estimation of variable cementation exponent in lowpermeability sands

Taking logarithm on both sides in Eq. (1), a derived formula canbe expressed as follows:

logðFÞ ¼ logðaÞ−m logðφÞ ð4ÞEq. (4) illustrates that formation factor and porosity are linear

in log–log coordinate once the value of cementation exponent isfixed. For low permeability sandstones, the cementation exponentis variable. Hence, the relationship between formation factor andporosity in log–log coordinate is nonlinear.

Plenty of experimental results have illustrated that the rela-tionship between formation factor and porosity in log–log coordi-nate can be expressed by using quadratic function (Mao et al.,1997; Liu et al., 2012); this means that the formation factor can beestimated from porosity by using

logðFÞ ¼ x log2ðφÞ þ y logðφÞ þ z ð5Þwhere x, y and z are the undetermined coefficients.

Comparing Eq. (4) with (5), the coefficient z can be defined as

z¼ logðaÞ ð6ÞBased on the analysis of rock resistivity experimental data sets

acquired from different basins, Mao et al. (1997) and Liu et al.(2012) pointed out that the constant mentioned in Eq. (5) wasclose to 0.0 by using the quadratic function to express therelationship of formation factor and porosity. Hence, the value ofa approximates to 1.0. This viewpoint was also verified by ourlisted data sets in Table 1. Thereby, Eq. (5) can be rewritten as

logðFÞ ¼ x log2ðφÞ þ y logðφÞ ¼ ðx logðφÞ þ yÞlogðφÞ ð7ÞComparing Eqs. (4) and (7), we can observe that the expression

of cementation exponent can be written as

m¼ x logðφÞ þ y ð8ÞSubmitting Eq. (8) into (1), the relationship between porosity

and formation factor can be expressed as

F ¼ 1φx logðφÞþy

ð9Þ

Formation porosity φ can be directly obtained from field NMRlogs in oil bearing reservoir or water saturated layers, and it can beaccurately calculated from NMR and conventional logs in gasbearing formation (Xiao et al., 2012). In the meanwhile, φ can alsobe calculated from conventional logs while enough core sampleswere drilled for routine analysis and the core scale logging methodwas applied. Once the values of x and y are calibrated, the variablem can be precisely estimated from porosity.

Using the data sets listed in Table 1, the values of x and y arecalibrated, and Eq. (9) is expressed as

F ¼ 1φ0:48 logðφÞþ2:00

; Correlationcoefficient : 0:99 ð10Þ

Fig. 9 illustrates the principle of acquiring the optimal cemen-tation exponent from porosity. It can be observed that the trendline passes by the vast majority of core samples; this means theregressed equation can be used to express the relationship ofporosity and formation factor, and this also ensures the responsibilityof the obtained cementation exponent. The variable cementation

y =1/φ 0.48×log(φ)+2.00

Correlation coefficient: 0.99

1

10

100

0.01 0.1 1

Porosity, fraction

Form

atio

n fa

ctor

Fig. 9. The principle of acquiring the optimal cementation exponent from porosityby using the proposed technique.

0

3

6

9

12

15

18

3~10 10~17 17~24 24~31 31~38 >38

T2 cutoff, ms

Freq

uenc

y

Fig. 10. The statistical histogram of T2 cutoff for all 36 core samples drilled from theXujiahe Formation in Sichuan basin.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–51 47

exponent can be obtained consecutively in the intervals with whichprecise porosity was acquired from field NMR or conventional logsonce the proposed technique is extended to field applications.

3.2. Estimation of saturation exponent from NMR logs

Through Figs. 5–8, we have concluded that saturation exponentis proportional to the proportion of small pore components.Hence, the proportion of small pore components must be firstcharacterized to precisely estimate saturation exponent. In thisaspect, NMR logs have unique advantages. It is known thatirreducible water saturation (Swi) is an effective parameter incharacterizing the proportion of small pore components (Coateset al., 2000), and rocks with poor pore structure will contain highproportion of small pore components, and thus high irreduciblewater saturations; on the contrary, for rocks with low proportionof small pore components, the corresponding irreducible watersaturations are low. In this study, irreducible water saturationunder a defined T2 cutoff is introduced to characterize rock porestructure and the proportion of small pore components.

To compare pore structure of all core samples, the unifiedoptimal T2 cutoff is used to calculate irreducible water saturationfrom NMR logs to characterize the proportion of small porecomponents. To determine the optimal T2 cutoff, T2 cutoffsacquired from laboratory NMR measurements for all core samplesare showed in a histogram, and the T2 cutoff with the maximumfrequency is defined as the optimal T2 cutoff. By using the optimalT2 cutoff, Swi can be estimated by using (Straley et al., 1994)

Swi ¼R T2cutoffT2 min

SðTÞdtR T2maxT2 min

SðTÞdtð11Þ

where Swi is the estimated irreducible water saturation from NMRlogs by using the optimal T2 cutoff in fraction, T2min is theminimum horizontal relaxation time, T2max is the maximumhorizontal relaxation time, T2cutoff is the defined optimal T2 cutoff,and their unit is microsecond. S(T) is the porosity distributionfunction, which is associated with the T2 relaxation time.

Fig. 10 shows the statistical histogram of T2cutoff for all 36 coresamples listed in Table 1; it can be observed that the maindistribution of T2 cutoffs is 17.0–24.0 ms, and T2 cutoff with the

maximum frequency is 20.75 ms. Hence, 20.75 ms is chosen as theoptimal T2 cutoff in the Xujiahe Formation.

T2 lm is the overall signature of NMR T2 distribution, and it isassociated with the rock pore structure. For rock with good porestructure, the value of T2 lm is high, and on the contrary, low T2 lm

corresponds to poor pore structure. Hence, T2 lm is inverselyproportional to saturation exponent; in the proposed saturationexponent estimation model, T2 lm is chosen as another inputparameter besides irreducible water saturation.

Considering Swi can be used to characterize the proportion ofsmall pore components, then, (1−Swi) can be used to characterizethe proportion of macropore components; it is inversely propor-tional to saturation exponent. Hence, in the novel saturationexponent estimation model, the parameters of Swi, (1−Swi) andT2 lm are used, and the corresponding model is established as

n¼ C1−Swi

Swi

� �p

Tq2 lm ð12Þ

where C, p and q are the statistical model parameters, and theirvalues can be calibrated by using the laboratory NMR andresistivity experimental results. Considering the relationshipbetween saturation exponent and rock pore structure, the valuesof p and q should be negative.

In this study, the data sets of laboratory resistivity experimentsand NMR measurements listed in Table 1 are reused; the para-meters of C, p and q involved in Eq. (12) are calibrated, and theformula of estimating saturation exponent from NMR logs in theXujiahe low permeability sands of Sichuan basin is expressed as

n¼ 2:5481−Swi

Swi

� �−0:156

T−0:02152 lm ;

Correlation coefficient : 0:79 ð13Þ

Once this technique is extended to field applications, precisesaturation exponent can be consecutively calculated by usingEq. (13) in the intervals with which field NMR logs were acquired.

4. Reliability verification

To verify the credibility of the proposed model in calculatingcementation and saturation exponents in low permeability sands,comparisons of cementation exponents obtained from core sam-ples and calculated by using Eq. (9), and of saturation exponents

0

3

6

9

12

15

-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12

Absolute for calculated cementation exponent

Freq

uenc

y

0

2

4

6

8

10

12

14

-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60

Absolute error for calculated saturation exponent

Freq

uenc

y

Fig. 11. (a) Comparison of cementation exponents obtained from the core samples and estimated from NMR logs by using the proposed technique. (b) Comparison ofsaturation exponents obtained from core samples and estimated from NMR logs by using the proposed technique.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–5148

obtained from core samples and calculated by using Eq. (13) areplotted in Fig. 11a and b, separately. From these two comparisons,it can be observed that the predicted cementation and saturationexponents from NMR logs by using the proposed technique areclose to the laboratory measured results; the absolute error of theestimated cementation exponents is low than 0.08, and theabsolute error of the calculated saturation exponents is lowerthan 0.2. From Fig. 11a and b, it can be concluded that theproposed techniques of estimating cementation and saturationexponents are reliable.

5. Case studies

The technique for estimating cementation and saturationexponents proposed in this study is based on the laboratoryNMR measurements, and if it is extended to field low permeabilitysandstone reservoirs, consecutive cementation and saturationexponents can be obtained in the intervals with which fieldNMR logs were acquired, and precise water saturation can beestimated. Some field examples of estimating water saturation areshowed in the following section.

5.1. Estimation of water saturation in low permeability sandstonereservoirs of Sichuan basin

With the calibrated Eqs. (9) and (13) by using 36 core samplesdrilled from the Xujiahe Formation of Sichuan basin, southwestChina, several wells in Sichuan basin are processed and watersaturations are estimated. Fig. 12 shows a field example of well Afrom Sichuan basin. In the first track, the displayed curves aregamma ray (GR), spontaneous potential (SP) and borehole dia-meter (CAL), and their contribution is effective formation indica-tion. The second track is depth and its unit is meter. RLLDdisplayed in the third track is deep lateral resistivity, and RLLS isshallow lateral resistivity. In the fourth track, we show density log(RHOB), compensated neutron log (NPHI) and interval transit timelog (DT). They are used for porosity estimation. T2_distributiondisplayed in the fifth track is field NMR spectrum which wasacquired from Halliburton's MRIL-C tool, and T2cutoff is theoptimal T2 cutoff that is obtained from the statistical histogramof core derived results for 36 core samples, and its value is20.75 ms; T2 lm is the logarithmic mean of the NMR T2 spectrum.The sixth track of Fig. 12 indicates a reasonable match betweencore analyzed porosity (CPOR) and NMR derived porosity (PHIT).In the Xujiahe Formation, there are collapsed boreholes, and theconventional logs (especially density log) are heavily affected,whereas, the effects of collapsed boreholes to NMR porosityacquired from MRIL-C tool can be ignored due to the centralized

measurement pattern. It suggests that PHIT is reliable and littleerror will be introduced when it is applied in water saturationestimation. Calc_m displayed in the seventh track and Calc_nshowed in the eighth track are estimated cementation andsaturation exponents from field NMR logs by using the proposedtechnique, separately. Core_m is the cementation exponent, andCore_n is the saturation exponent, and they are all obtained fromlaboratory resistivity measurements. These comparisons illustratethat cementation and saturation exponents estimated from fieldNMR logs are close to the core analyzed results. In the meanwhile,from the displayed NMR T2 spectrum in the interval of xx24–xx60 m, it can be observed that the proportion of macroporecomponents decrease; this means reservoir pore structure ispoorer than that obtained in the above interval of xx20–xx80 m,while their NMR total porosities are proximate. Hence, theestimated cementation exponents from NMR total porosityin these two layers are similar, while the calculated saturationexponents in these two intervals are quite different. The estimatedsaturation exponents are high in the intervals with poor porestructure, and they all match with the core analyzed resultsvery well. The ninth track displays the comparisons of watersaturations obtained from three different methods. Sw is thewater saturation estimated from conventional logs by usingvariable cementation and saturation exponents, Sw_cal is calcu-lated by using fixed cementation and saturation exponents,while Core_Sw is the analyzed water saturation by using thesealed coring method. From these comparisons, it can be observedthat water saturation estimated by using variable cementationand saturation exponents matches with the core analyzed resultsvery well in the whole interval, while water saturation estimatedby using fixed cementation and saturation exponents is under-estimated. This means that the proposed technique of estimatingcementation and saturation exponents from field NMR logs inthis study is practicable in the low permeability reservoirs ofXujiahe Formation in Sichuan basin. Additionally, if we observethe value of Sw_cal, the whole interval is considered as gas bearingformation besides a thin barrier bed of xx80–xx81 m, whilefrom Sw, we can observe that the upper 100 m interval ofxx22–xx24 m is gas bearing formation, and the lower interval ofxx24–xx56 m is not effective gas bearing formation, and consider-ing the relatively high resistivity and poor pore structure, it isidentified as a dry layer. This identification is confirmed by drillstem testing data.

5.2. Estimation of water saturation in low permeability sandstonereservoirs of Ordos basin

To verify the wide applicability of the proposed technique inthis study, we applied it to Chang 8 Formation of Ordos basin,northwest China, which is another typical low permeability

Fig. 12. Comparison of water saturations estimated by using variables m and n, fixed m and n, and obtained from the core samples in the Xujiahe Formation of Sichuan basin,southwest China.

Fig. 13. Comparison of water saturation estimated by using the proposed technique and obtained from the core samples in the Chang 8 Formation of Ordos basin,northwest China.

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–51 49

sandstone reservoir in China. To calibrate the used parameters inthe formulae of estimating cementation and saturation exponentsfrom NMR logs, 20 core samples, which were drilled from Chang8 Formation, are applied for laboratory resistivity and NMR

measurements. From the laboratory NMR measurements, theoptimal T2 cutoff is determined as 18.05 ms, and the correspond-ing irreducible water saturation (Swi) is predicted. Combining theexperimental results and the predicted Swi, formulae of estimating

L. Xiao et al. / Journal of Petroleum Science and Engineering 108 (2013) 40–5150

cementation and saturation exponents are calibrated, and they areexpressed respectively as

F ¼ 1φ0:78 logðφÞþ2:69

; Correlationcoefficient : 0:99 ð14Þ

n¼ 2:3611−Swi

Swi

� �−0:0605

T−0:1112 lm ;

Correlation coefficient : 0:81 ð15Þ

A field example of well B from Ordos basin is processed byusing Eqs. (14) and (15), and water saturation is calculated, asshown in Fig. 13. In well B, no core samples are drilled forlaboratory resistivity experiments. Comparisons of water satura-tion calculated by using the obtained variable cementation andsaturation exponents, fixed cementation and saturation exponentsand derived from core samples are showed in the last track. It canbe observed that the estimated water saturation by using variablecementation and saturation exponents is consistent with the corederived result very well, and this ensures that the estimatedcementation and saturation exponents from field NMR logs aredependable, and the proposed technique and models are valuable,while the calculated water saturation by using fixed cementationand saturation exponents is overestimated.

These two field examples from different basins illustrate thatwater saturation cannot be precisely calculated from conventionallogs by defining fixed cementation and saturation exponents.However, once the proposed technique in this study is introduced,credible cementation and saturation exponents can be effectivelyestimated from field NMR logs, and accurate water saturation canbe calculated in low permeability sandstones with complicatedpore structure.

6. Conclusions

In low permeability sandstone reservoirs, the relationshipbetween porosity and formation factor, water saturation andresistivity index cannot be expressed by power functions due tothe complicated pore structure. Fixed rock resistivity parameterscannot be obtained from laboratory resistivity experiments forprecise water saturation estimation. To calculate water saturationby using Archie's equation as accurate as possible, variablecementation and saturation exponents should be first estimated.

Based on the analysis of the laboratory resistivity experiments,the relationship of quadratic function between porosity andformation factor is established, and a technique of estimatingvariable cementation exponent from porosity is proposed.

Saturation exponent is proportional to the proportion of smallpore components and inversely proportional to T2 lm. Irreduciblewater saturation (Swi) calculated by using the optimal T2 cutoff canbe used to characterize the proportion of small pore components.A novel technique, which connects saturation exponent, Swi,(1−Swi) and T2 lm, is proposed to estimate saturation exponentfrom NMR logs, and the corresponding model is established.Parameters mentioned in this model need to be calibrated byusing the laboratory resistivity experiments and NMR measure-ments that are obtained from the target core samples in differentreservoirs.

The predicted cementation and saturation exponents from fieldNMR logs by using the proposed model in this study are credible,and they are all close to the core derived results. The absoluteerrors of these two kinds of cementation exponents are lower than0.08, and the absolute errors of these two kinds of saturationexponents are lower than 0.2. These ensure the proposed techni-ques and models are reliable.

Field examples from two different low permeability sandstonereservoirs in China show that the proposed technique of estimat-ing cementation and saturation exponents from field NMR logs isapplicable widespread, and after they are used for water satura-tion calculation, precise results can be obtained. This will be ofgreat importance in improving the level of exploration andreducing the risk of development in low permeability sandstonesreservoirs.

Acknowledgments

We sincerely acknowledge the anonymous reviewers whosecorrelations and comments have greatly improved the manuscript.This research work was supported by the China PostdoctoralScience Foundation funded project (No. 2012M520347,2013T60147), National Science and Technology Major Project(No. 2011ZX05044), the Fundamental Research Funds for theCentral Universities, China (2652013036) and Open Fund of KeyLaboratory of Geo-detection (China University of Geosciences,Beijing), Ministry of Education (No. GDL1204).

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