tight gas sandstone reservoirs evaluation from nuclear ... · established, and the accuracy of...
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Arab J Sci EngDOI 10.1007/s13369-015-1608-y
RESEARCH ARTICLE - PETROLEUM ENGINEERING
Tight Gas Sandstone Reservoirs Evaluation from NuclearMagnetic Resonance (NMR) Logs: Case Studies
Xiao Liang · Mao Zhi-qiang · Jin Yan
Received: 21 October 2014 / Accepted: 4 February 2015© King Fahd University of Petroleum and Minerals 2015
Abstract Tight gas sandstone reservoirs parameters, suchas porosity, permeability and initial water saturation, are diffi-cult to be precisely estimated from conventional logs. What’smore, the effective gas-bearing formations cannot be directlyidentified either due to the characteristics of complicated porestructure, strong heterogeneity and high irreducible water sat-uration. Nuclear magnetic resonance (NMR) logs, which areusually used to evaluate reservoir pore structure, are foundto be effective in evaluating tight gas sandstone reservoirs.In this study, typical tight gas sandstone reservoirs of south-west China are used as examples; techniques of estimatingporosity, permeability, initial water saturation and construct-ing pseudo-capillary pressure curve to quantitative evaluatetight sandstone reservoirs pore structure are studied. Theacoustic and NMR logs are combined to calculate porosity.The technique proposed by Volokitin et al. (1999) is used toconstruct pseudo-capillary pressure curves from NMR logs.
X. Liang (B)Key Laboratory of Geo-detection, China Universityof Geosciences, Ministry of Education, Beijing,People’s Republic of Chinae-mail: [email protected]
X. LiangSchool of Geophysics and Information Technology, ChinaUniversity of Geosciences, Beijing, People’s Republic of China
M. Zhi-qiangState Key Laboratory of Petroleum Resource and Prospecting,China University of Petroleum, Beijing, People’s Republic of China
M. Zhi-qiangKey Laboratory of Earth Prospecting and Information Technology,Beijing, People’s Republic of China
J. YanSouthwest Oil and Gas Field Branch Company, PetroChina,Sichuan, People’s Republic of China
The saturation-height-function method is used to estimateinitial water saturation, and the Swanson parameter basedmodel is established to calculate permeability from con-structed pseudo-capillary pressure curves. Comparisons ofestimating porosity, permeability and water saturation withcore-derived results illustrate that these techniques are effec-tive in tight gas sands evaluation. Finally, the effective tightgas sands can be identified through combined use of the esti-mated reservoir parameters and constructed pseudo-capillarypressure curves from NMR logs, which is verified by the drillstem test data.
Keywords Tight gas sandstone reservoirs · Pore structure ·Nuclear magnetic resonance (NMR) logs · Conventionallogs · Reservoir evaluation
1 Introduction
With the fast development of oil and gas exploration, tight oiland gas sandstone reservoirs have played an important rolein stabilizing and increasing production. The proportion ofproduction from tight oil and gas sands is much high in China[1]. The Changqing oil field, which is the typical ultra-lowpermeability to tight sandstones, locates in the Ordos basinand has been the biggest oil field, and in the Sichuan basin,the biggest tight gas sandstone reservoirs have been foundrecently. Comparing with conventional reservoirs, tight sand-stone reservoirs evaluation is much more challenging due tomany factors, e.g., extreme low porosity, permeability, highirreducible water saturation, complicated pore structure andstrong heterogeneity [2]. To improve the accuracy of tightsandstone reservoirs study, the pore structure should be firstevaluated [2]. The nuclear magnetic resonance (NMR) logscan be used to provide useful evaluation for many reservoirs
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0
100
200
300
400
500
0~2 2~4 4~6 6~8 8~10 10~12 12~14
Freq
uenc
y
CPOR, %
X4
X6
Fig. 1 The distribution of core-derived porosities for the tight gas sandsin central Sichuan basin
parameters, such as total porosity, effective porosity and irre-ducible water saturation. The NMR logs are also effective inreservoirs pore structure evaluation. Hence, NMR logs havebecome a very important logging suite in tight sandstonereservoirs [3,4]. In this study, the typical tight gas sands ofcentral Sichuan basin are used as examples; the methodsand techniques of estimating reservoir parameters (poros-ity, permeability and initial water saturation) and evaluatingpore structure are studied. The effective models have beenestablished, and the accuracy of tight gas sandstone reser-voirs evaluation is much improved by using the proposedmethod.
2 Characteristics of Tight Gas Sandstone Reservoirs
Sichuan basin, located in southwestern China, is the biggesttight gas sandstone reservoir. The mainly gas-bearing sandsare the fourth and sixth sections of Xujiahe Formation (X4and X6, respectively) of upper Triassic in central Sichuanbasin. The distributions of routine core-derived porosities andpermeabilities for more than 1600 core samples drilled fromthese two Formations illustrate that these two formations aretypical tight gas sands (Figs. 1, 2). The porosities are mainlyranging from 2.0 to 12.0 %; the average porosity of X4 is5.87 %. The average value of X6 is 5.76 %. Permeabilitiesof these two formations are mainly distributed from 0.01 to1.0 mD. The average permeability for X4 and X6 is 0.45 and0.4 mD, respectively.
In the X4 and X6 Formations, 20 core samples were drilledfor laboratory NMR measurements. The experimental para-meters of NMR measurement are listed as following: polar-
0
200
400
600
800
Freq
uenc
y
CPERM, mD
X4
X6
Fig. 2 The distribution of core-derived permeabilities for the tight gassands in central Sichuan basin
0
0.2
0.4
0.6
0.1 10 1000 100000
Am
plitu
de, v
/v
T2, ms
Fig. 3 The NMR T2 distribution for core samples drilled from tightgas sands
ization time (TW) is 6.0 s; inter-echo spacing (TE) is 0.2 ms;the number of echoes per echo train (NE) is 4096; and scan-ning number is 128. The CPMG echo strings are acquired,after effective inversion methods are used, many parameters,including the NMR T2 spectra, irreducible water saturation,T2cutoff and effective porosity, are acquired. Figure 3 displaysthe NMR T2 distributions for all 20 core samples. This figureillustrates that for the vast majority of core samples drilledfrom tight gas sands, the NMR spectra are unimodal, andsmall-size pores (with short T2 transverse relaxation time)are dominant. This denotes that they contain high irreduciblewater saturation.
Figure 4 shows that in the X4 and X6 Formations,the irreducible water saturations (Swi) range from 37.06
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0
2
4
6
8
<35 35~40 40~45 45~50 50~55 55~60 >60
Freq
uenc
y
Irreducible water saturation (Swi), %
Fig. 4 The distribution of irreducible water saturation (Swi) for coresamples with laboratory NMR experiment
0
2
4
6
8
<8 8~12 12~16 16~20 20~24 >24
Freq
uenc
y
T2cutoff, ms
Fig. 5 The distribution of T2cutoff for core samples with laboratoryNMR experiments
to 67.84 %, and the average value is 45.28 %. This illus-trates that nearly half of the pore space is occupied bythe irreducible water. The high irreducible water saturationalways leads to relative low resistivity contrast in gas-bearingformations.
Figure 5 presents the statistical results of experimentalT2cutoff for all core samples. From this figure, we can observethat in the Xujiahe Formation, the T2cutoff s are lower than thetypical value of 33.0 ms for conventional reservoirs, and theT2cutoff s are scattered. They range from 4.74 to 25.84 ms, andthe average T2cutoff is 16.93 ms. However, no obvious fixedT2cutoff can be observed.
3 Problems of Tight Gas Sandstone ReservoirsEvaluation in the Central Sichuan Basin
In reservoir evaluation and reserves calculation, estimationof reservoir parameters, such as porosity, permeability andoil saturation (thus water saturation), is of great importance.Identification of gas-bearing formations is also indispens-able. For conventional reservoir, these parameters can berelatively easy to be estimated using conventional methods.However, estimation for reservoir parameters and effectivegas-bearing formation identification face great challenge intight gas sands. In this study, based on the analyzed resultsfrom more than 1600 core samples, the laboratory NMR mea-surements for 20 core samples, mercury injection capillarypressure (MICP) measurements for 20 core samples and thecorresponding drill stem test data are used for tight gas sand-stone reservoirs evaluation in the central Sichuan basin.
3.1 Problem of Porosity Estimation in Tight Gas Sands
Generally, reservoir porosity is estimated from conventionallogs (such as density, compensated neutron or acoustic logs),when the relationship of conventional logs with core-derivedporosity is established by using the core calibration loggingmethod [5,6]. In the target tight gas sands of central Sichuanbasin, such a traditional method was used to establish therelationships among core-derived porosity and other para-meters, including density, compensated neutron and intervaltransit, which are showed in Fig. 6. From these three curves,we can observe that the correlations of conventional densityand compensated neutron logs with core-derived porosityare weak. Hence, they cannot be used to calculate reser-voir porosity. Although the relationship of interval transittime with core-derived porosity is relatively strong, it is alsonot effective in tight gas sands porosity estimation. This isbecause the expected relative error is only 8.0 % in the reserveevaluation [7]. Table 1 lists the absolute errors with sim-ulative porosity increasing from 2.0 to 14.0 %. Simulatedporosities are coincided with the porosity distributions of X4and X6 Formations (Fig. 1). From Table 1, we can observethat porosity needed to be calculated much more accuratelyfor reserves evaluation of tight gas sands. For example, forreservoirs with porosity of 10.0 %, the discrepancy of esti-mated porosity and the true value is only 0.8 %. By using thedisplayed relationship in Fig. 6c, such accuracy cannot besatisfied.
3.2 Problem of Permeability Estimation in Tight Gas Sands
Permeability estimation is another critical element in tightgas sandstone reservoirs evaluation due to the complicatedpore structure and strong heterogeneity [6,8]. Generally, per-meability can be directly estimated from porosity in nor-
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0
4
8
12
16
20
2 2.2 2.4 2.6 2.8 3
CPO
R, %
DEN, g/cm3
X4
X6
0
4
8
12
16
20
0 5 10 15 20 25 30 35
CPO
R, %
CNL, %
X4
X6
0
4
8
12
16
20
50 60 70 80 90
CPO
R, %
AC, μs/ft
X4
X6
a
b
c
Fig. 6 Relationships between conventional logs and core-derivedporosity in the X4 and X6 Formations. a Relationship between den-sity log and core-derived porosity, b relationship between compensatedneutron log and core-derived porosity, c relationship between acousticlog and core-derived porosity
mal reservoirs, because a strong correlation between poros-ity and permeability can often be established in these typesof reservoirs [9–11]. However, in tight gas sandstone reser-
Table 1 The absolute errors for simulative porosity increasing from2.0 to 14.0 % [7]
Simulativeporosity, %
Relativeerror of+8 %
Absoluteerror, %
Relativeerror of−8 %
Absoluteerror, %
2.00 2.16 0.16 1.84 −0.16
3.00 3.24 0.24 2.76 −0.24
4.00 4.32 0.32 3.68 −0.32
5.00 5.40 0.40 4.60 −0.40
6.00 6.48 0.48 5.52 −0.48
7.00 7.56 0.56 6.44 −0.56
8.00 8.64 0.64 7.36 −0.64
9.00 9.72 0.72 8.28 −0.72
10.00 10.80 0.80 9.20 −0.80
11.00 11.88 0.88 10.12 −0.88
12.00 12.96 0.96 11.04 −0.96
13.00 14.04 1.04 11.96 −1.04
14.00 15.12 1.12 12.88 −1.12
0.00001
0.0001
0.001
0.01
0.1
1
10
100
1000
0 5 10 15 20
CPE
RM
, mD
CPOR, %
X4_Well A
X4_Well B
X4_Well C
X6_Well A
X6_Well C
X6_Well D
Fig. 7 The scatter plot of core-derived porosity and permeability inthe target tight gas sandstone reservoirs
voirs, poor correlations exist between porosity and perme-ability due to heterogeneous formations. Figure 7 displaysthe scatter plot of porosity and permeability of core samples,which were drilled from our target tight gas sands of sev-eral adjacent wells. From Fig. 7, it can be concluded thatthe relationship between porosity and permeability is poor.In all wells, the relationships between core-derived poros-ity and permeability are entirely different. No single formulacan be established to express the relationship between thesetwo attributes. Hence, conventional methods seem not to beeffective in permeability estimation for tight gas sandstonereservoirs.
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3.3 Problem of Water Saturation Estimation in Tight GasSands
For conventional reservoirs, the Archie’s equations are themost suitable for water saturation evaluation from con-ventional logs. Since the necessary input parameters werefirst determined from rock resistivity experimental measure-ments, this method has been widely used in the past 70 years.The Archie’s equations are expressed in Eqs. 1 and 2 [12].
F = R0
Rw= a
ϕm(1)
Ir = Rt
Ro= 1
Snw
(2)
where R0 is the rock resistivity with fully water saturated,Rw is the formation water resistivity, Rt is the rock resistivitywith hydrocarbon saturated. The unit for all these parame-ters is ohm m. F is the formation factor and Ir is the resis-tivity index, both of which are dimensionless; ϕ is the rockporosity in fraction; Sw is the water saturation in fraction;a is the tortuosity factor; m is the cementation exponent; nis the saturation exponent, and its value is affected by rockpore structure; a, m and n are referred to as rock resistivityparameters.
Combining Eqs. 1 and 2, a derivative formula could bewritten in Eq. 3.
Sw = n
√a × Rw
ϕm × Rt(3)
This formula illustrates that the values of a, m, n, Rw, ϕ andRt must be first determined for water saturation calculation.
Generally, the deep lateral resistivity (RLLD) or deepinduction resistivity (RILD) can be directly used as Rt , whileRw can be checked from the formation water salinity by usingthe Schlumberger’s log interpretation charts [13], and ϕ canbe accurately calculated once effective models have beenestablished.
Determination of rock resistivity parameters is the mostimportant in estimating water saturation by using Eq. 3. Gen-erally, the values of a, m and n are determined by using thestatistical regression method based on laboratory resistivitymeasurements of the target core samples. Determination ofa and m is relying on the scatter plot of porosity and forma-tion factor. The value of n can be obtained from the scatterplot of water saturation and resistivity index. For conven-tional reservoirs, the values of rock resistivity parametersare easily acquired by using the rock resistivity experimen-tal measurements, and the Archie’s equations can be usedto calculate water saturation. However, in tight gas sands,the values of rock resistivity parameters are difficult to beobtained, because the relationships between porosity and for-mation factor, water saturation and resistivity index, cannot
y = 1.8389x-1.247
R² = 0.9312
1
10
100
0.01 0.1 1
Form
atio
n fa
ctor
Porosity, fraction
1
10
0.1 1
Res
istiv
ity in
dex
Water saturation, fraction
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
a
b
Fig. 8 a The cross-plot of porosity versus formation factor for coresamples drilled from tight gas sandstones of X4 and X6 Formations inSichuan basin, southwest China [14]. b The cross-plot of water satu-ration versus resistivity index for core samples drilled from tight gassandstones of X4 and X6 Formations in Sichuan basin, southwest China[14]
by expressed by using the typical power function (Fig. 8).This is particularly challenging for the determination of n. Inthis case, Archie’s equations are invalid in water saturationestimation.
3.4 Problem of Effective Formation Identification in TightGas Sands
Based on Figs. 1, 2, 3 and 4, it can be concluded that thesetight gas sands displayed such characteristics of ultra-lowporosity, permeability and high irreducible water saturationin the X4 and X6 Formations. These characteristics posechallenges for effective gas-bearing formation identification.The resistivity contrast of gas-bearing formations and water-saturated layers is lower than that of the conventional reser-voirs. Figure 9a, b shows the conventional log responses of
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Fig. 9 a Conventional log response of gas-bearing formation [2]. b Conventional log response of water-saturated layer [2]
two adjacent wells. From the drill stem test data, it can be seenthat for the interval of xx39–xx51 m in Fig. 9a, gas productionwas estimated as 10.578×104 m3/day. While the interval ofxx70–xx07 m displayed in Fig. 9b, it is pure water-saturatedlayers. With detailed analysis of these two tested intervals,it can be further observed that these two intervals almostpresent the same bulk density of 2.4 g/cm3, which denotessimilar porosity. For the resistivity response, the gas-bearingformation shows that the resistivity is about 9 � m, and theresistivity of the water-saturated layer is about 5 � m. Theresistivity difference between these two intervals is lowerthan that of the conventional gas-bearing and water reser-voirs. This poses a challenge for effective identification oftight gas-bearing formations from conventional methods [2].
4 Novel Methods of Estimating Tight Gas SandstoneReservoir Parameters
Based on the discussion in the previous paragraphs, we canconclude that tight gas sandstone reservoirs evaluation usingconventional methods faces great challenge in the XujiaheFormation. The challenge is primarily caused by the com-plicated pore structure and strong heterogeneity of tight gassandstone reservoirs. To improve tight gas sands evaluation,
the pore structure should be first evaluated [2]. The NMRlogs have significant advantage in reservoir characterization,especially in tight sandstone reservoirs with ultra-low poros-ity, permeability and complicated pore structure [3,4]. In oilbearing or water-saturated formations, reservoir porosity canbe determined from NMR logs, whereas in tight gas sands,the extracted porosity is often underestimated due to the lowhydrogen index of natural gas [15]. Based on the analysis ofthe NMR T2 spectrum, pore structure of the formation can bequalitatively estimated. However, it still remains a challengein quantitatively estimating the pore throat radius and porestructure parameters from NMR logs. To effectively evaluatetight gas sands using the log data, a method that combinesconventional and NMR logs should be proposed. In the nextsection, we will introduce an effective method for tight gassands evaluation.
4.1 Estimation of Porosity from NMR and Acoustic Logs
4.1.1 Principle of Calculating Porosity from NMRand Acoustic Logs
In gas-bearing formations, to correct the effect of low hydro-gen index of natural gas on NMR porosity, Coates et al. [3]
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and Dunn [4] proposed the NMR porosity correction methodin Eq. 4:
CMRP = φ × Sg × HIg × Pg + φ × HI f × (1 − Sg) (4)
where
Pg = 1 − e− Tw
T1,g
where CMRP is the NMR porosity in % and can be directlyobtained from NMR logs; φ is the formation porosity in %; Sg
is the gas saturation in fraction; HIg is the gas hydrogen index,HIf is the pore fluid hydrogen index and the units of them arefraction; Pg is the polarization factor; Tw is the polarizationtime in microseconds; and T1,g is the longitudinal relaxationtime for natural gas in microseconds.
For fully water-saturated rocks where HIf is designed as1.0, Eq. 4 can be rewritten in Eq. 5:
CMRP
φ= 1 − Sg × (1 − HIg × Pg) (5)
Equation 5 illustrates that the values of Sg, HIg and Pg shouldbe first determined to obtain porosity from NMR logs for gas-bearing reservoirs. Actually, these parameters are difficult tobe obtained from conventional logs at present, bringing thedifficulty of porosity estimation from NMR logs.
Based on the general form of the Wyllie’s average timeequation, the response equation of interval transit time logcan be expressed as follows [16]:
�t = �tma×(1−φ)+�tw×φ×(1−Sg)+�tg×φ×Sg (6)
where �t is the log measured interval transit time; �tma isthe interval transit time of rock matrix for sandstone, and itsvalue is 55.5µs/ft; �tw is the interval transit time of water,and its value is 189; �tg is the interval transit time of gas.All parameters in the unit of them are microsecond per feet.
For clean sandstone, the porosity can be calculated fromEq. 7:
PHIS = �t − �tma
�t f − �tma(7)
where PHIS is porosity from acoustic log in fraction; �tf isthe interval transit time of pore fluid.
Substituting Eq. 6 into Eq. 7, a derivative expression couldbe obtained as follows:
PHIS
φ=
[1 + Sg ×
(�t − �tma
�t f − �tma
)](8)
Equation 8 illustrates that Sg and �tf are the two importantinput parameters in calculating porosity using interval transittime log. However, the determination of Sg and �tf is relied
on porosity. It is difficult in calculating porosity only fromconventional interval transit time log [5].
If we define two parameters of α and β,where
α = �t − �tma
�t f − �tma
β = 1 − HIg × Pg
Substituting these two parameters into Eqs. 4 and 8, respec-tively, Eq. 9 can be derived,
φ =(
β
α + β
)× PHIS +
(α
α + β
)× CMRP (9)
If we further define the following two parameters m and n:
m = β
α + β
n = α
α + β
Equation 9 can be simplified as follows:
φ = m × PHIS + n × CMRP (10)
where
m + n = β
α + β+ α
α + β= 1
The effects of natural gas to conventional and NMR logs canbe calibrated by using Eq. 10, and formation porosity can beestimated by integrating interval transit time and NMR logsonce the values of m and n are determined.
4.1.2 Calibration of m and n in the Target Tight Gas Sands
From Eq. 10, it can be observed that parameters m and nshould be first calibrated before the equation can be appliedto calculate tight gas sandstone porosity. To calibrate m andn, more than seven hundreds of core samples are used forcalibration and the rest are used for validation.
The core-derived porosity can be considered as the trueformation porosity. After both sides of Eq. 10 are divided byCMRP, Eq. 10 can be rewritten as:
CPOR
CMRP= m × PHIS
CMRP+ n (11)
Parameters m and n are calibrated using the core samples.Equation 11 is expressed in Fig. 10 and Eq. 12.
φ = 0.809 × PHIS + 0.191 × CMRP, R2 = 0.8939 (12)
From Fig. 10, we find strong correlation among CPOR,CMRP and PHIS. The correlation coefficient is high enough.
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y = 0.809x + 0.191R² = 0.8939
0
1
2
3
4
0 1 2 3 4
CPO
R/C
MR
P
PHIS/CMRP
Fig. 10 Calibration of m and n from core samples in the target tightgas sands
If Eq. 12 is applied in tight gas sands evaluation in the XujiaheFormation, the gas effect should be corrected and accurateporosity could be calculated.
4.2 Model of Estimating Permeability from MercuryInjection Capillary Pressure (MICP) Data
Figure 7 illustrates that permeability cannot be precisely pre-dicted from porosity due to the poor correlation betweencore-derived porosity and permeability. To effectively esti-mate reservoir permeability, the pore structure should befirst evaluated [2]. Mercury injection capillary pressure(MICP) data are the most effective in reservoir pore struc-ture evaluation [17]. Hence, the MICP data are expectedto be strongly correlated with permeability. Guo et al.[17] and Swanson [18] pointed out that the MICP curve
would be hyperbolic curve if it is displayed in log–logplots, and the inflexion point of MICP curve, the mer-cury injection saturation threshold in the main pore sys-tem which primarily controls the fluid flow, is related withpermeability. If mercury injection saturation (SHg) is dis-played along the X -axis, and the ratio of SHg and Pc
(mercury injection pressure) is displayed along the Y -axis,the inflection point is located at the apex. It is calledas the Swanson parameter and expressed as (SHg/Pc)max.Xiao et al. [19] verified that the Swanson parameter ishighly correlated with permeability in conventional andlow permeability sandstones, and permeability estimationmodels based on the Swanson parameter can be estab-lished, whereas in tight gas sands, the relationship betweenthe Swanson parameter and permeability is not alwaysexist because the MICP curve is not always a hyperboliccurve.
In the X4 and X6 Formations, 20 core samples weredrilled for laboratory MICP measurements, the results illus-trate that MICP curves for all 20 core samples can bedisplayed as hyperbolic curves in log–log plots. Hence,the Swanson-based permeability estimation model can beapplied in our target tight gas sands. Figure 11 displaysa typical MICP curve of the X4 Formation, where themethod of determining the Swanson parameter is also dis-played. Based on this method, the Swanson parametersfor all 20 core samples are obtained. We try to establishthe relationship between the Swanson parameter and per-meability; a good model is established and displayed inFig. 12.
From Fig. 12, we can observe that strong relationshipexists between the Swanson parameter and core-derived per-meability. Such relationship can be used to improve perme-ability estimation. However, one should notice that this rela-tionship is established from laboratory experimental mea-surements where a limited number of core samples are used.If we want to extend this model to field application for con-secutive permeability estimation, the MICP curves should beobtained in the whole intervals.
Fig. 11 Determination of theSwanson parameter for thetypical MICP curve
0.1
1
10
100
1 10 100
P c, M
Pa
SHg, %
0
10
20
30
0 20 40 60 80 100
S Hg/P
c
SHg, %
The Swanson parameter
The inflexion point
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y = 0.0079x1.428
R² = 0.9068
0.1
1
10
100
1000
1 10 100 1000
CPE
RM
, mD
The Swanson parameter
Fig. 12 Tight gas sands permeability estimation model based on theSwanson parameter
4.3 Method of Constructing Pseudo-Capillary PressureCurves from NMR Logs
NMR logs are the most effective in reservoir pore structureevaluation, which can be used to construct capillary pressurecurve once reliable models are applied [2,20–23]. In thisstudy, we attempt to test different methods in our target tightgas sands for constructing capillary pressure curves fromNMR logs. We found that the method presented in Volokitinet al. [21] is the most effective. Hence, we use the Volokitin’smethod to construct capillary pressure curve from NMR logs.
4.3.1 Principle of Constructing Pseudo-CapillaryPressure from NMR Logs
Based on the theory of NMR logs, the NMR transverse relax-ation time T2 for water wetting rock is dominated by the sur-face relaxation under fully water saturated, while the bulkrelaxation and diffuse relaxation can be ignored. Hence, T2
can be expressed in the following equation [3,4]:
1
T2≈ 1
T2s= ρ2
(S
V
)por
(13)
where T2 is the NMR transverse relaxation time, T2s is thesurface relaxation time, both of which are in the unit of ms;ρ2 is the proportionality constant between 1/T2 and surfaceto volume ratio of the pore; S/V is the surface relaxivity.
If the shape of rock pore is assumed as regular, such as bul-bous or cylindrical, the ration of S/V can then be expressedas follows:
S
V= ρ2
Fs
rpor(14)
where rpor is the pore radius in micrometer; Fs is the geo-metric factor of pore shape. For rock with spherical pore, thevalue of Fs is 3, and for columnar pore, Fs is 2.
Combining Eqs. 13 and 14, Eq. 15 can be obtained:
1
T2= ρ2
(S
V
)pore
= Fsρ2
rpor(15)
From Eq. 15, we can observe that the transverse relaxationtime T2 is correlative with rock pore size and shape. For rockwith low porosity and narrow pore throat, T2 is short, andvice versa.
Based on the theory of capillary pressure, the relation-ship between capillary pressure and pore throat radius canbe expressed in Eq. 16 [24]:
Pc = 2σ cos θ
rc(16)
where Pc is the capillary pressure in MPa; σ is the surfacetension between the two phases fluid in dyn/cm; θ is thecontact angle in (◦); and rc is the pore throat radius in µm.
For two phases fluid of mercury and air that used in themercury injection experiment, σ is equal to 480 dyn/cm, andθ is 140◦. Substituting these two values in Eq. 16, Eq. 17 canbe obtained:
Pc = 0.735
rc(17)
Assuming that the relationship between pore size and porethroat, radius exists and can be expressed as follows:
rpor = nrc (18)
where n is the proportionality coefficient of pore size andthroat radius.
Substituting Eq. 18 into Eq. 15, a derivative expressioncould be written as follows:
n0.735
Pc≈ ρ2 × T2 × Fs (19)
The relationship between Pc and T2 can then be described asfollows:
Pc = C × 1
T2(20)
where C is the conversion coefficient of NMR T2 relaxationtime and capillary pressure. If the value of C can be cali-brated by using core samples, the distribution of NMR T2
can be used to construct a capillary pressure curve to evalu-ate formation pore structure and predict permeability, usingthe models displayed in Fig. 12.
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00.20.40.60.810.1
1
10
100
1000
10000
1000000.0001
0.001
0.01
0.1
1
10
020406080100
Amplitude, v/v
T 2re
laxa
tion
time,
ms
1/T 2
,ms- 1
Reverse cumulative saturation, %
NMR reverse cumulative curveNMR T2 distribution
Fig. 13 Principle of acquiring NMR reversed cumulative curve fromNMR T2 distribution
To obtain the value of C , a pseudo-curve from NMR T2
spectrum that is similar MICP curve should be first obtained.To obtain this pseudo-curve, the NMR T2 amplitude is
reversely cumulated and normalized to obtain the reversedcumulative saturation. Based on the scatter plot of reverselycumulated saturation versus 1/T2, a NMR reversed cumu-lative curve can be obtained. The principle of obtaining theNMR reversed cumulative curve is displayed in Fig. 13.
Once the NMR reversed cumulative curve is acquired,the next step is to determine the optimal value of C , whichmakes the NMR reversed cumulative curve similar to theMICP curve as much as possible.
A number of methods in the literature have been proposedto determine the value of C [2,20–23,25,26], among whichthe method proposed by Volokitin et al. [20] is the mostpopular.
Volokitin et al. [20] pointed out that the conversion func-tion of NMR reversed cumulative curve and MICP curve canbe expressed as follows:
Pc =[(
1 +(
A
B × T2 + 1
)c)× D
K
]× 1
T2(21)
where A, B, C, D and K are the mentioned input parametersin the conversion function, all of which needed to be firstcalibrated.
Volokitin’s model had been applied to many areas of Chinaand had been verified to be effective [27–29]. It is also appliedin our study. Results illustrate that it is an effective methodfor our case study. Hence, in this study, the model expressedin Eq. 21 is used to construct pseudo-capillary pressure curvefrom NMR logs.
4.3.2 Calibration of the Mentioned Input Parametersin the Volokitin’s Model
To use Eq. 21 to construct capillary pressure curve fromNMR logs, the values of the parameters A, B, C, D and Kneed to be first determined. To calibrate these parametersin the Volokitin’s model, 20 core samples drilled from ourtarget tight gas sands were simultaneously applied for bothlaboratory MICP and NMR experimental measurements.The MICP and NMR measurements were obtained. To cal-ibrate these parameters, the MICP and corresponding NMRreversed cumulative curves for 20 core samples were used,which are displayed in Fig. 14a, b, separately.
By using these MICP and corresponding NMR reversedcumulative curves for 20 core samples, input parametersin Eq. 21 are calibrated. The values of A, B, C, D, and Kare 5, 1, 1, 2000, and 2, respectively. Using these calibratedparameters, the NMR logs can be constructed as pseudo-capillary pressure curves, which can be used to evaluate tightgas sandstone reservoir pore structure.
4.3.3 Reliability Verification
To verify the credibility of the calibrated Eq. 21, it is used tocore samples with NMR experimental measurements to con-
Fig. 14 a The MICP curves for20 core samples drilled fromtight gas sands. b The NMRreversed cumulative curves for20 core samples drilled fromtight gas sands
0.001
0.01
0.1
1
10
100
020406080100
P c, M
Pa
SHg, %
0.00001
0.0001
0.001
0.01
0.1
1
10
020406080100
1/T 2
, ms-1
So, %
a b
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Fig. 15 Comparisons ofcapillary pressure curvesacquired from two differentmethods
0.001
0.01
0.1
1
10
100
1000
020406080100
P c, M
Pa
SHg, %
MICP curve
Pseudo capillary pressurecurve
Por=10.6%Perm=1.05mD
0.001
0.01
0.1
1
10
100
1000
10000
020406080100
P c, M
Pa
SHg, %
MICP curve
Pseudo capillary pressurecurve
Por=7.9%Perm=0.323mD
0.001
0.01
0.1
1
10
100
1000
020406080100
P c, M
Pa
SHg, %
MICP curve
Pseudo capillary pressurecurve
Por=7.5%Perm=0.851mD
0.001
0.01
0.1
1
10
100
1000
020406080100
P c, M
Pa
SHg, %
MICP curve
Pseudo capillary pressurecurve
Por=14.7%Perm=5.06mD
a b
dc
struct pseudo-capillary pressure curves. We then compare theshapes of the constructed pseudo-capillary pressure curveswith the MICP curves. Figure 15 displays the comparisons offour representative core samples. From these comparisons,we can observe that all the constructed capillary pressurecurves match with the laboratory MICP curves very well,illustrating that Eq. 21 is effective in our target tight gassands in constructing capillary pressure curves from NMRlogs.
If this technique is extended to field application, thepseudo-capillary pressure curve, the corresponding porethroat radius distribution and the pore structure evaluationparameters, including the average pore throat radius, thethreshold pressure and median pore throat radius, can alsobe estimated from the pseudo-capillary pressure curves inthe interval with which NMR logs had been acquired.
4.4 Calculation of Irreducible Water Saturation from NMRLogs
Irreducible water saturation (Swi) is a very important para-meter in tight gas sandstone reservoirs evaluation. This isbecause in tight gas sands, the pore space is mainly occu-pied by water that cannot flow into the borehole, which is
called irreducible water. Figure 4 displays that in our targettight gas sands, the average Swi is close to 45 %, leading tolow resistivity contrast. It is therefore difficult in identifyingeffective gas-bearing formation from water-saturated layers.Estimated Swi could be used to overlap with initial watersaturation; gas-bearing formation could then be effectivelyidentified.
The NMR logs have unique advantages in estimating Swi.However, Fig. 5 illustrates that in our target tight gas sands,unified T2cutoff cannot be obtained from laboratory NMRexperimental measurements. Hence, the T2cutoff techniquecannot be used to extract Swi from NMR logs in the X4 andX6 sections.
Based on the theoretical analysis of the classical Timurand the SDR model [30–32], Xiao et al. [33] derived a modelthat combines porosity and T2 logarithmic mean of the NMRT2 spectrum (T2lm) to estimate Swi. This model is effective inSwi estimation in the Xujiahe Formation. Hence, it is directlyapplied in our target tight gas sands. This model is expressedas follows:
Swi = 118.91 × ϕ−0.08326 × T −0.245182lm (22)
where ϕ is the porosity in %, which can be estimated byusing Eq. 12; T2lm is the T2 logarithmic mean of the NMR
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T2 spectrum in ms, which can be directly obtained from theNMR logs.
By using Eq. 22, Swi can be calculated from NMR logs.
4.5 Calculation of Water Saturation by Using theSaturation-Height-Function (SHF) Method
Based on the theory of hydrocarbon migration and accu-mulation, the forming process of oil and gas reservoir canbe described as the initial water occupied pore space wasreplaced by hydrocarbon. Hence, the non-wetting hydrocar-bon will be saturated in the pore space once the capillarypressure caused by the pore throat was broken through. Thedynamic condition of saturating hydrocarbon is the buoyancyproduced from density difference of these two phases of flu-ids of hydrocarbon and water and the hydrocarbon columnheight. If the buoyancy and capillary pressure are balanced,saturating hydrocarbon is then stopped. Hence, if the freewater level (FWL) is obtained, the buoyancy that caused bythe density contrast of oil (gas)-water can be calculated asfollows:
F = �h × �ρ × g = �h × (ρw − ρh) × g (23)
where F is the buoyancy that caused by the density contrast ofhydrocarbon and water and the hydrocarbon column height;�h is the hydrocarbon column height in meter; �ρ is thedensity contrast of hydrocarbon and water in g/cm3; ρw isthe water density in g/cm3; ρh is the hydrocarbon densityin g/cm3, in our tight gas sands, ρh is the gas density andrewritten as ρg. g is the gravitational acceleration, which is9.8 m/s2.
The equilibrium state of buoyancy and capillary pressurecan be described in the following equation.
Pg−w = F = �h × �ρ × g (24)
where Pg−w is the capillary pressure of reservoir condition inMPa, which can be estimated from laboratory MICP experi-mental measurements using Eq. 25.
Pg−w = σg−w × cos θg−w
σHg−air × cos θHg−air× PHg−air (25)
where PHg−air is the mercury injection pressure; σg−w is thesurface tension of gas and water;σHg−air is the surface tensionof mercury and air; θg−w is the contact angle of natural gasand water; θHg−air is the contact angle of mercury and air.
Combining with Eqs. 23 to 25, the relationship betweengas column height (thus FWL) and water saturation in-suitsituation can be described as the saturation-height-function(SHF). In our target tight gas sands, the saturation-height-function can be obtained once input parameters are deter-
0
10
20
30
40
50
0 20 40 60 80 100
Gas
col
umn
heig
ht, m
Water saturation, %
Fig. 16 The saturation-height-function of two phase fluids of gas andwater in our target tight gas sands
mined. Figure 16 displays the acquisition of saturation-height-function for three typical core samples.
If this technique is applied in the whole intervals withpseudo-pressure curves were constructed from NMR logs,the saturation-height-function can be obtained. The initialwater saturation can then be estimated from the saturation-height-function.
5 Case Study
Using the proposed method, the target tight gas sands of X4and X6 are analyzed. Figure 17 shows a field example ofevaluating tight gas sands from NMR logs. In the first trackof Fig. 17, the displayed curves are gamma ray (GR), spon-taneous potential (SP) and borehole diameter (CAL). Theircontribution is effective formation indication. In the secondtrack, we show density log (DEN), compensated neutron log(CNL) and interval transit time log (AC), all of which are usedfor porosity estimation. RT displayed in the third track is deeplateral resistivity, and RXO is shallow lateral resistivity. Thefourth track is depth, and its unit is meter. T2_DIST displayedin the fifth track is field NMR spectrum, which was acquiredfrom Schlumberger’s CMR-plus tool. PC_DIST displayedin the sixth track is the constructed pseudo-capillary pres-sure curve from field NMR logs by using Eq. 21, and itis displayed by the variable density method. In the seventhtrack, we compare the calculated porosity (AMRP) usingthe AMR technique with core-derived porosity. From thiscomparison, it can be observed that the estimated porosi-ties from NMR and acoustic logs match with the true for-mation porosities very well. This confirms that the AMRtechnique is effective in our target tight gas sands. SWCAL
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Fig. 17 A field example of evaluating tight gas sandstone reservoir by using NMR logs
displayed in the eighth track is estimated initial water satura-tion from the pseudo-capillary pressure curves using the SHFmethod. SWICAL is the estimated irreducible water satura-tion using Eq. 21, and SWICORE is the irreducible watersaturation obtained from the core samples with laboratoryNMR experimental measurements. From the comparison ofthe values of several kinds of the water saturation, it can beconcluded that the SWCAL and SWICAL are coincided witheach other very well. Additionally, they are closed to the core-derived results. This illustrates that the estimated SWCALand SWICAL are accurate, and the proposed method is reli-able. PERM displayed in the ninth track is the estimatedpermeability from pseudo-capillary pressure curves by usingthe Swanson-based permeability model displayed in Fig. 12.A good consistency of estimated permeability with core-derived permeability (CPERM) illustrates that the Swanson-based permeability model is valuable in tight gas sands per-meability estimation. From the tenth to twelve tracks, wecompare the estimated average pore throat radius (RM),maximum pore throat radius (RMAX) and threshold pres-sure (PD) from the pseudo-capillary pressure curves withthe core-derived average pore throat radius (CRM), maxi-mum pore throat radius (CRMAX) and threshold pressure(CPD), separately. In the last track, we compare the Swan-son parameter acquired from two different kinds of methods.Swanson is the estimated Swanson parameters from con-structed pseudo-capillary pressure curve using the methodillustrated in Fig. 11, and Cswanson is the extracted Swan-son parameters from experimental MICP data. Comparisonshows that the pore structure evaluation parameters and theSwanson parameter acquired from the constructed pseudo-
capillary pressure are coincided with the core-derived results.This demonstrates the effectiveness of the technique of con-structing pseudo-capillary pressure curves from field NMRlogs.
From the estimated results, it can be found that in theinterval of xx88–xx00m, although the estimated initial watersaturation reaches to 40–50 %, it is coincided with the irre-ducible water saturation. This denotes that no free watercan be produced. After analyzing the constructed pseudo-capillary pressure, estimated porosity, permeability and porestructure evaluation parameters, it can be concluded that thepore structure of this interval is good. If necessary fracturetreatments are applied, this interval is worth of developing.Such conclusion is confirmed by the drill stem testing data.The drill stem testing data illustrate that this interval is puregas-bearing formation, where no water is produced. This fieldexample illustrates that the proposed method in this study isvaluable in tight gas reservoirs evaluation, and they can befurther extended to be applied to other types of tight sand-stone reservoirs.
6 Discussion
Detailed observing Eq. 21, we can find that in the process ofconstructing pseudo-capillary pressure curves in our targettight gas sands, the unitary input parameters in the Volok-itin’s model are calibrated and used. This is because in ourtarget tight gas sandstone reservoirs of X4 and X6 Forma-tions, the heterogeneity is not strong enough, and this canbe verified by the displayed MICP curves in Fig. 14a. From
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Fig. 14a, it can be observed that the shapes of all 20 coresamples are relative regular, and they are not divergent. Inthis case, the unified model can be used. However, if forma-tions are inhomogeneous, the unified function cannot be usedto construct pseudo Pc curve [25]. In this case, formationsshould be classified into several types by other methods, andin every type of formation, individual mentioned input para-meters in the Volokitin’s model should be calibrated. Mean-while, it need to be noticed that the SHF method is applicativeonly in the structural hydrocarbon reservoir. This is becausein this type of reservoirs, the unified oil (gas)/water inter-face can be determined, and the hydrocarbon column heightcan be calculated. However, in the lithologic hydrocarbonreservoir, there is not unified FWL, and the SHF method willbe invalid. In this case, the Rccutoff (pore throat radius cut-off) may be determined by combining with the laboratoryNMR measurements, and then, the water saturation is pre-dicted from the extracted pore throat radius distribution frompseudo Pc curve by using the determined Rccutoff [2].
7 Conclusions
Tight gas sandstone reservoirs evaluation faces great chal-lenges. The conventional methods, which are effective innormal reservoirs, are not often effective. The NMR logs,however, play an important role in tight gas reservoirs eval-uation as they provide the information of pore structure.
The AMR technique is effective in porosity calculationin tight gas sands, and it can be used to accurately estimatereservoir porosity. Comparing with conventional density andcompensated neutron log, the AMR technique can avoid theaffection of low hydrogen index to porosity estimation.
The relationship of core-derived porosity and permeabilityis divergent, making the conventional permeability estima-tion method invalid. The Swanson-based permeability esti-mation model adequately involve the pore structure informa-tion, which can be used to precisely estimate tight gas sandspermeability.
After calibrating input parameters of the Volokitin’s modelby using sufficient number of samples, the NMR logs canbe used to construct pseudo-capillary pressure curves toevaluate the pore structure of tight gas sandstone reser-voirs. Meanwhile, if the Swanson-based permeability modelis applied, permeability can be estimated. The saturation-height-function can be further used to predict initial water sat-uration, which is beyond the capacity of the typical Archie’sequation.
By combining estimated porosity, permeability, irre-ducible water saturation, initial water saturation and the infor-mation of pore structure evaluation, effective tight gas sandswith low resistivity contrast can be effectively identified frompure water-saturated layers.
Acknowledgments This research work was supported by NationalNatural Science Foundation of China (No. 41302106), China Post-doctoral Science Foundation funded project (Nos. 2012M520347,2013T60147), National Science and Technology Major Project (No.2011ZX05044), the Fundamental Research Funds for the CentralUniversities and Open Fund of Key Laboratory of Geo-detection(China University of Geosciences, Beijing), Ministry of Education (No.GDL1204).
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