Tight Gas Sandstone Reservoirs Evaluation from Nuclear Magnetic Resonance (NMR) Logs: Case Studies

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1 DOI.7/s y RESEARCH ARTICLE - PETROLEUM ENGINEERING Tight Gas Sandstone Reservoirs Evaluation from Nuclear Magnetic Resonance (NMR) Logs: Case Studies Xiao Liang Mao Zhi-qiang Jin Yan Received: 2 October 24 / Accepted: 4 February 25 King Fahd University of Petroleum and Minerals 25 Abstract Tight gas sandstone reservoirs parameters, such as porosity, permeability and initial water saturation, are difficult to be precisely estimated from conventional logs. What s more, the effective gas-bearing formations cannot be directly identified either due to the characteristics of complicated pore structure, strong heterogeneity and high irreducible water saturation. Nuclear magnetic resonance (NMR) logs, which are usually used to evaluate reservoir pore structure, are found to be effective in evaluating tight gas sandstone reservoirs. In this study, typical tight gas sandstone reservoirs of southwest China are used as examples; techniques of estimating porosity, permeability, initial water saturation and constructing pseudo-capillary pressure curve to quantitative evaluate tight sandstone reservoirs pore structure are studied. The acoustic and NMR logs are combined to calculate porosity. The technique proposed by Volokitin et al. (999)isusedto construct pseudo-capillary pressure curves from NMR logs. X. Liang (B) Key Laboratory of Geo-detection, China University of Geosciences, Ministry of Education, Beijing, People s Republic of China xiaoliang@cugb.edu.cn X. Liang School of Geophysics and Information Technology, China University of Geosciences, Beijing, People s Republic of China M. Zhi-qiang State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, People s Republic of China M. Zhi-qiang Key Laboratory of Earth Prospecting and Information Technology, Beijing, People s Republic of China J. Yan Southwest Oil and Gas Field Branch Company, PetroChina, Sichuan, People s Republic of China The saturation-height-function method is used to estimate initial water saturation, and the Swanson parameter based model is established to calculate permeability from constructed pseudo-capillary pressure curves. Comparisons of estimating porosity, permeability and water saturation with core-derived results illustrate that these techniques are effective in tight gas sands evaluation. Finally, the effective tight gas sands can be identified through combined use of the estimated reservoir parameters and constructed pseudo-capillary pressure curves from NMR logs, which is verified by the drill stem test data. Keywords Tight gas sandstone reservoirs Pore structure Nuclear magnetic resonance (NMR) logs Conventional logs Reservoir evaluation Introduction With the fast development of oil and gas exploration, tight oil and gas sandstone reservoirs have played an important role in stabilizing and increasing production. The proportion of production from tight oil and gas sands is much high in China []. The Changqing oil field, which is the typical ultra-low permeability to tight sandstones, locates in the Ordos basin and has been the biggest oil field, and in the Sichuan basin, the biggest tight gas sandstone reservoirs have been found recently. Comparing with conventional reservoirs, tight sandstone reservoirs evaluation is much more challenging due to many factors, e.g., extreme low porosity, permeability, high irreducible water saturation, complicated pore structure and strong heterogeneity [2]. To improve the accuracy of tight sandstone reservoirs study, the pore structure should be first evaluated [2]. The nuclear magnetic resonance (NMR) logs can be used to provide useful evaluation for many reservoirs 23

2 5 8 X4 X4 4 X6 6 X6 Frequency 3 2 Frequency 4 2 ~2 2~4 4~6 6~8 8~ ~2 2~4 CPOR, % Fig. The distribution of core-derived porosities for the tight gas sands in central Sichuan basin parameters, such as total porosity, effective porosity and irreducible water saturation. The NMR logs are also effective in reservoirs pore structure evaluation. Hence, NMR logs have become a very important logging suite in tight sandstone reservoirs [3,4]. In this study, the typical tight gas sands of central Sichuan basin are used as examples; the methods and techniques of estimating reservoir parameters (porosity, permeability and initial water saturation) and evaluating pore structure are studied. The effective models have been established, and the accuracy of tight gas sandstone reservoirs evaluation is much improved by using the proposed method. 2 Characteristics of Tight Gas Sandstone Reservoirs Sichuan basin, located in southwestern China, is the biggest tight gas sandstone reservoir. The mainly gas-bearing sands are the fourth and sixth sections of Xujiahe Formation (X4 and X6, respectively) of upper Triassic in central Sichuan basin. The distributions of routine core-derived porosities and permeabilities for more than 6 core samples drilled from these two Formations illustrate that these two formations are typical tight gas sands (Figs., 2). The porosities are mainly ranging from 2. to 2. %; the average porosity of X4 is 5.87 %. The average value of X6 is 5.76 %. Permeabilities of these two formations are mainly distributed from. to. md. The average permeability for X4 and X6 is.45 and.4 md, respectively. In the X4 and X6 Formations, 2 core samples were drilled for laboratory NMR measurements. The experimental parameters of NMR measurement are listed as following: polar- CPERM, md Fig. 2 The distribution of core-derived permeabilities for the tight gas sands in central Sichuan basin Amplitude, v/v T 2, ms Fig. 3 The NMR T 2 distribution for core samples drilled from tight gas sands ization time (TW) is 6. s; inter-echo spacing (TE) is.2 ms; the number of echoes per echo train (NE) is 496; and scanning number is 28. The CPMG echo strings are acquired, after effective inversion methods are used, many parameters, including the NMR T 2 spectra, irreducible water saturation, T 2cutoff and effective porosity, are acquired. Figure 3 displays the NMR T 2 distributions for all 2 core samples. This figure illustrates that for the vast majority of core samples drilled from tight gas sands, the NMR spectra are unimodal, and small-size pores (with short T 2 transverse relaxation time) are dominant. This denotes that they contain high irreducible water saturation. Figure 4 shows that in the X4 and X6 Formations, the irreducible water saturations (S wi ) range from

3 8 3 Problems of Tight Gas Sandstone Reservoirs Evaluation in the Central Sichuan Basin Frequency <35 35~4 4~45 45~5 5~55 55~6 >6 Irreducible water saturation (S wi ), % In reservoir evaluation and reserves calculation, estimation of reservoir parameters, such as porosity, permeability and oil saturation (thus water saturation), is of great importance. Identification of gas-bearing formations is also indispensable. For conventional reservoir, these parameters can be relatively easy to be estimated using conventional methods. However, estimation for reservoir parameters and effective gas-bearing formation identification face great challenge in tight gas sands. In this study, based on the analyzed results from more than 6 core samples, the laboratory NMR measurements for 2 core samples, mercury injection capillary pressure (MICP) measurements for 2 core samples and the corresponding drill stem test data are used for tight gas sandstone reservoirs evaluation in the central Sichuan basin. Fig. 4 The distribution of irreducible water saturation (S wi )forcore samples with laboratory NMR experiment Frequency <8 8~2 2~6 6~2 2~24 >24 T 2cutoff, ms Fig. 5 The distribution of T 2cutoff for core samples with laboratory NMR experiments to %, and the average value is %. This illustrates that nearly half of the pore space is occupied by the irreducible water. The high irreducible water saturation always leads to relative low resistivity contrast in gas-bearing formations. Figure 5 presents the statistical results of experimental T 2cutoff for all core samples. From this figure, we can observe that in the Xujiahe Formation, the T 2cutoff s are lower than the typical value of 33. ms for conventional reservoirs, and the T 2cutoff s are scattered. They range from 4.74 to ms, and the average T 2cutoff is 6.93 ms. However, no obvious fixed T 2cutoff can be observed. 3. Problem of Porosity Estimation in Tight Gas Sands Generally, reservoir porosity is estimated from conventional logs (such as density, compensated neutron or acoustic logs), when the relationship of conventional logs with core-derived porosity is established by using the core calibration logging method [5,6]. In the target tight gas sands of central Sichuan basin, such a traditional method was used to establish the relationships among core-derived porosity and other parameters, including density, compensated neutron and interval transit, which are showed in Fig. 6. From these three curves, we can observe that the correlations of conventional density and compensated neutron logs with core-derived porosity are weak. Hence, they cannot be used to calculate reservoir porosity. Although the relationship of interval transit time with core-derived porosity is relatively strong, it is also not effective in tight gas sands porosity estimation. This is because the expected relative error is only 8. % in the reserve evaluation [7]. Table lists the absolute errors with simulative porosity increasing from 2. to 4. %. Simulated porosities are coincided with the porosity distributions of X4 and X6 Formations (Fig. ). From Table, we can observe that porosity needed to be calculated much more accurately for reserves evaluation of tight gas sands. For example, for reservoirs with porosity of. %, the discrepancy of estimated porosity and the true value is only.8 %. By using the displayed relationship in Fig. 6c, such accuracy cannot be satisfied. 3.2 Problem of Permeability Estimation in Tight Gas Sands Permeability estimation is another critical element in tight gas sandstone reservoirs evaluation due to the complicated pore structure and strong heterogeneity [6,8]. Generally, permeability can be directly estimated from porosity in nor- 23

4 a CPOR, % b 2 X4 6 X DEN, g/cm 3 2 X4 6 X6 Table The absolute errors for simulative porosity increasing from 2. to 4. % [7] Simulative porosity, % Relative error of +8% Absolute error, % Relative error of 8% Absolute error, % CPOR, % c CPOR, % CNL, % 2 X4 6 X6 2 8 CPERM, md.... X6_Well D CPOR, % X4_Well A X4_Well B X4_Well C X6_Well A X6_Well C Fig. 7 The scatter plot of core-derived porosity and permeability in the target tight gas sandstone reservoirs AC, μs/ft Fig. 6 Relationships between conventional logs and core-derived porosity in the X4 and X6 Formations. a Relationship between density log and core-derived porosity, b relationship between compensated neutron log and core-derived porosity, c relationship between acoustic log and core-derived porosity mal reservoirs, because a strong correlation between porosity and permeability can often be established in these types of reservoirs [9 ]. However, in tight gas sandstone reser- voirs, poor correlations exist between porosity and permeability due to heterogeneous formations. Figure 7 displays the scatter plot of porosity and permeability of core samples, which were drilled from our target tight gas sands of several adjacent wells. From Fig. 7, it can be concluded that the relationship between porosity and permeability is poor. In all wells, the relationships between core-derived porosity and permeability are entirely different. No single formula can be established to express the relationship between these two attributes. Hence, conventional methods seem not to be effective in permeability estimation for tight gas sandstone reservoirs. 23

5 3.3 Problem of Water Saturation Estimation in Tight Gas Sands a For conventional reservoirs, the Archie s equations are the most suitable for water saturation evaluation from conventional logs. Since the necessary input parameters were first determined from rock resistivity experimental measurements, this method has been widely used in the past 7 years. The Archie s equations are expressed in Eqs. and 2 [2]. Formation factor y =.8389x R² =.932 F = R = a R w ϕ m () I r = R t = R o Sw n (2) where R is the rock resistivity with fully water saturated, R w is the formation water resistivity, R t is the rock resistivity with hydrocarbon saturated. The unit for all these parameters is ohm m. F is the formation factor and I r is the resistivity index, both of which are dimensionless; ϕ is the rock porosity in fraction; S w is the water saturation in fraction; a is the tortuosity factor; m is the cementation exponent; n is the saturation exponent, and its value is affected by rock pore structure; a, m and n are referred to as rock resistivity parameters. Combining Eqs. and 2, a derivative formula could be written in Eq. 3. a R S w = n w ϕ m (3) R t This formula illustrates that the values of a, m, n, R w,ϕand R t must be first determined for water saturation calculation. Generally, the deep lateral resistivity (RLLD) or deep induction resistivity (RILD) can be directly used as R t, while R w can be checked from the formation water salinity by using the Schlumberger s log interpretation charts [3], and ϕ can be accurately calculated once effective models have been established. Determination of rock resistivity parameters is the most important in estimating water saturation by using Eq. 3. Generally, the values of a, m and n are determined by using the statistical regression method based on laboratory resistivity measurements of the target core samples. Determination of a and m is relying on the scatter plot of porosity and formation factor. The value of n can be obtained from the scatter plot of water saturation and resistivity index. For conventional reservoirs, the values of rock resistivity parameters are easily acquired by using the rock resistivity experimental measurements, and the Archie s equations can be used to calculate water saturation. However, in tight gas sands, the values of rock resistivity parameters are difficult to be obtained, because the relationships between porosity and formation factor, water saturation and resistivity index, cannot b Resistivity index.. Porosity, fraction no. no.2 no.3 no.4 no.5 no.6 no.7 no.8 no.9 no. no. no.2 no.3 no.4 no.5 no.6 no.7 no.8 no.9 no.2 no.2 no.22 no.23 no.24 no.25 no.26 no.27 no.28 no.29 no.3 no.3 no.32 no.33 no.34 no.35 no.36. Water saturation, fraction Fig. 8 a The cross-plot of porosity versus formation factor for core samples drilled from tight gas sandstones of X4 and X6 Formations in Sichuan basin, southwest China [4]. b The cross-plot of water saturation versus resistivity index for core samples drilled from tight gas sandstones of X4 and X6 Formations in Sichuan basin, southwest China [4] by expressed by using the typical power function (Fig. 8). This is particularly challenging for the determination of n.in this case, Archie s equations are invalid in water saturation estimation. 3.4 Problem of Effective Formation Identification in Tight Gas Sands BasedonFigs., 2, 3 and 4, it can be concluded that these tight gas sands displayed such characteristics of ultra-low porosity, permeability and high irreducible water saturation in the X4 and X6 Formations. These characteristics pose challenges for effective gas-bearing formation identification. The resistivity contrast of gas-bearing formations and watersaturated layers is lower than that of the conventional reservoirs. Figure 9a, b shows the conventional log responses of 23

6 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 seen that for the interval of xx39 xx5 m in Fig. 9a, gas production was estimated as m 3 /day. While the interval of xx7 xx7 m displayed in Fig. 9b, it is pure water-saturated layers. With detailed analysis of these two tested intervals, it can be further observed that these two intervals almost present the same bulk density of 2.4g/cm 3, which denotes similar porosity. For the resistivity response, the gas-bearing formation shows that the resistivity is about 9 m, and the resistivity of the water-saturated layer is about 5 m. The resistivity difference between these two intervals is lower than that of the conventional gas-bearing and water reservoirs. This poses a challenge for effective identification of tight gas-bearing formations from conventional methods [2]. 4 Novel Methods of Estimating Tight Gas Sandstone Reservoir Parameters Based on the discussion in the previous paragraphs, we can conclude that tight gas sandstone reservoirs evaluation using conventional methods faces great challenge in the Xujiahe Formation. The challenge is primarily caused by the complicated pore structure and strong heterogeneity of tight gas sandstone reservoirs. To improve tight gas sands evaluation, the pore structure should be first evaluated [2]. The NMR logs have significant advantage in reservoir characterization, especially in tight sandstone reservoirs with ultra-low porosity, permeability and complicated pore structure [3,4]. Inoil bearing or water-saturated formations, reservoir porosity can be determined from NMR logs, whereas in tight gas sands, the extracted porosity is often underestimated due to the low hydrogen index of natural gas [5]. Based on the analysis of the NMR T 2 spectrum, pore structure of the formation can be qualitatively estimated. However, it still remains a challenge in quantitatively estimating the pore throat radius and pore structure parameters from NMR logs. To effectively evaluate tight gas sands using the log data, a method that combines conventional and NMR logs should be proposed. In the next section, we will introduce an effective method for tight gas sands evaluation. 4. Estimation of Porosity from NMR and Acoustic Logs 4.. Principle of Calculating Porosity from NMR and Acoustic Logs In gas-bearing formations, to correct the effect of low hydrogen index of natural gas on NMR porosity, Coates et al. [3] 23

7 and Dunn [4] proposed the NMR porosity correction method in Eq. 4: CMRP = φ S g HI g P g + φ HI f ( S g ) (4) where P g = e Tw T,g where CMRP is the NMR porosity in % and can be directly obtained from NMR logs; φ is the formation porosity in %; S g is the gas saturation in fraction; HI g is the gas hydrogen index, HI f is the pore fluid hydrogen index and the units of them are fraction; P g is the polarization factor; T w is the polarization time in microseconds; and T,g is the longitudinal relaxation time for natural gas in microseconds. For fully water-saturated rocks where HI f is designed as., Eq. 4 can be rewritten in Eq. 5: CMRP φ = S g ( HI g P g ) (5) Equation 5 illustrates that the values of S g, HI g and P g should be first determined to obtain porosity from NMR logs for gasbearing reservoirs. Actually, these parameters are difficult to be obtained from conventional logs at present, bringing the difficulty of porosity estimation from NMR logs. Based on the general form of the Wyllie s average time equation, the response equation of interval transit time log can be expressed as follows [6]: t = t ma ( φ)+ t w φ ( S g )+ t g φ S g (6) where t is the log measured interval transit time; t ma is the interval transit time of rock matrix for sandstone, and its value is 55.5 µs/ft; t w is the interval transit time of water, and its value is 89; t g 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 from Eq. 7: PHIS = t t ma t f t ma (7) where PHIS is porosity from acoustic log in fraction; t f is the interval transit time of pore fluid. Substituting Eq. 6 into Eq. 7, a derivative expression could be obtained as follows: PHIS φ = [ + S g ( )] t tma t f t ma Equation 8 illustrates that S g and t f are the two important input parameters in calculating porosity using interval transit time log. However, the determination of S g and t f is relied (8) on porosity. It is difficult in calculating porosity only from conventional interval transit time log [5]. If we define two parameters of α and β, where α = t t ma t f t ma β = HI g P g Substituting these two parameters into Eqs. 4 and 8, respectively, Eq. 9 can be derived, φ = ( ) ( ) β α PHIS + CMRP (9) α + β α + β 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 () where m + n = β α + β + α α + β = The effects of natural gas to conventional and NMR logs can be calibrated by using Eq., and formation porosity can be estimated by integrating interval transit time and NMR logs once the values of m and n are determined Calibration of m and n in the Target Tight Gas Sands From Eq., it can be observed that parameters m and n should be first calibrated before the equation can be applied to calculate tight gas sandstone porosity. To calibrate m and n, more than seven hundreds of core samples are used for calibration and the rest are used for validation. The core-derived porosity can be considered as the true formation porosity. After both sides of Eq. are divided by CMRP, Eq. can be rewritten as: CPOR CMRP = m PHIS CMRP + n () Parameters m and n are calibrated using the core samples. Equation is expressed in Fig. and Eq. 2. φ =.89 PHIS +.9 CMRP, R 2 =.8939 (2) From Fig., we find strong correlation among CPOR, CMRP and PHIS. The correlation coefficient is high enough. 23

8 CPOR/CMRP y =.89x +.9 R² = PHIS/CMRP Fig. Calibration of m and n from core samples in the target tight gas sands If Eq. 2 is applied in tight gas sands evaluation in the Xujiahe Formation, the gas effect should be corrected and accurate porosity could be calculated. 4.2 Model of Estimating Permeability from Mercury Injection Capillary Pressure (MICP) Data Figure 7 illustrates that permeability cannot be precisely predicted from porosity due to the poor correlation between core-derived porosity and permeability. To effectively estimate reservoir permeability, the pore structure should be first evaluated [2]. Mercury injection capillary pressure (MICP) data are the most effective in reservoir pore structure evaluation [7]. Hence, the MICP data are expected to be strongly correlated with permeability. Guo et al. [7] and Swanson [8] pointed out that the MICP curve would be hyperbolic curve if it is displayed in log log plots, and the inflexion point of MICP curve, the mercury injection saturation threshold in the main pore system which primarily controls the fluid flow, is related with permeability. If mercury injection saturation (S Hg ) is displayed along the X-axis, and the ratio of S Hg and P c (mercury injection pressure) is displayed along the Y -axis, the inflection point is located at the apex. It is called as the Swanson parameter and expressed as (S Hg /P c ) max. Xiao et al. [9] verified that the Swanson parameter is highly correlated with permeability in conventional and low permeability sandstones, and permeability estimation models based on the Swanson parameter can be established, whereas in tight gas sands, the relationship between the Swanson parameter and permeability is not always exist because the MICP curve is not always a hyperbolic curve. In the X4 and X6 Formations, 2 core samples were drilled for laboratory MICP measurements, the results illustrate that MICP curves for all 2 core samples can be displayed as hyperbolic curves in log log plots. Hence, the Swanson-based permeability estimation model can be applied in our target tight gas sands. Figure displays a typical MICP curve of the X4 Formation, where the method of determining the Swanson parameter is also displayed. Based on this method, the Swanson parameters for all 2 core samples are obtained. We try to establish the relationship between the Swanson parameter and permeability; a good model is established and displayed in Fig. 2. From Fig. 2, we can observe that strong relationship exists between the Swanson parameter and core-derived permeability. Such relationship can be used to improve permeability estimation. However, one should notice that this relationship is established from laboratory experimental measurements where a limited number of core samples are used. If we want to extend this model to field application for consecutive permeability estimation, the MICP curves should be obtained in the whole intervals. Fig. Determination of the Swanson parameter for the typical MICP curve 3 The Swanson parameter P c, MPa The inflexion point S Hg /P c 2. S Hg, % S Hg, % 23

9 CPERM, md y =.79x.428 R² =.968. The Swanson parameter Fig. 2 Tight gas sands permeability estimation model based on the Swanson parameter 4.3 Method of Constructing Pseudo-Capillary Pressure Curves from NMR Logs NMR logs are the most effective in reservoir pore structure evaluation, which can be used to construct capillary pressure curve once reliable models are applied [2,2 23]. In this study, we attempt to test different methods in our target tight gas sands for constructing capillary pressure curves from NMR logs. We found that the method presented in Volokitin et al. [2] is the most effective. Hence, we use the Volokitin s method to construct capillary pressure curve from NMR logs Principle of Constructing Pseudo-Capillary Pressure from NMR Logs Based on the theory of NMR logs, the NMR transverse relaxation time T 2 for water wetting rock is dominated by the surface relaxation under fully water saturated, while the bulk relaxation and diffuse relaxation can be ignored. Hence, T 2 can be expressed in the following equation [3,4]: ( ) S = ρ 2 (3) T 2 T 2s V por where T 2 is the NMR transverse relaxation time, T 2s is the surface relaxation time, both of which are in the unit of ms; ρ 2 is the proportionality constant between /T 2 and surface to volume ratio of the pore; S/V is the surface relaxivity. If the shape of rock pore is assumed as regular, such as bulbous or cylindrical, the ration of S/ V can then be expressed as follows: F s S V = ρ 2 (4) r por where r por is the pore radius in micrometer; F s is the geometric factor of pore shape. For rock with spherical pore, the value of F s is 3, and for columnar pore, F s is 2. Combining Eqs. 3 and 4, Eq.5 can be obtained: ( ) S ρ 2 = ρ 2 = F s (5) T 2 V pore r por From Eq. 5, we can observe that the transverse relaxation time T 2 is correlative with rock pore size and shape. For rock with low porosity and narrow pore throat, T 2 is short, and vice versa. Based on the theory of capillary pressure, the relationship between capillary pressure and pore throat radius can be expressed in Eq. 6 [24]: P c = 2σ cos θ r c (6) where P c is the capillary pressure in MPa; σ is the surface tension between the two phases fluid in dyn/cm; θ is the contact angle in ( ); and r c is the pore throat radius in µm. For two phases fluid of mercury and air that used in the mercury injection experiment, σ is equal to 48 dyn/cm, and θ is 4. Substituting these two values in Eq. 6,Eq.7 can be obtained: P c =.735 r c (7) Assuming that the relationship between pore size and pore throat, radius exists and can be expressed as follows: r por = nr c (8) where n is the proportionality coefficient of pore size and throat radius. Substituting Eq. 8 into Eq. 5, a derivative expression could be written as follows: n.735 P c ρ 2 T 2 F s (9) The relationship between P c and T 2 can then be described as follows: P c = C T 2 (2) where C is the conversion coefficient of NMR T 2 relaxation time and capillary pressure. If the value of C can be calibrated by using core samples, the distribution of NMR T 2 can be used to construct a capillary pressure curve to evaluate formation pore structure and predict permeability, using the models displayed in Fig

10 /T2, ms -... Amplitude, v/v NMR reverse cumulative curve NMR T2 distribution. T2 relaxation time, ms P c = [( ( + A B T 2 + ) c ) D ] (2) K T 2 where A, B, C, D and K are the mentioned input parameters in the conversion function, all of which needed to be first calibrated. Volokitin s model had been applied to many areas of China and had been verified to be effective [27 29]. It is also applied in our study. Results illustrate that it is an effective method for our case study. Hence, in this study, the model expressed in Eq. 2 is used to construct pseudo-capillary pressure curve from NMR logs Reverse cumulative saturation, % Fig. 3 Principle of acquiring NMR reversed cumulative curve from NMR T 2 distribution To obtain the value of C, a pseudo-curve from NMR T 2 spectrum that is similar MICP curve should be first obtained. To obtain this pseudo-curve, the NMR T 2 amplitude is reversely cumulated and normalized to obtain the reversed cumulative saturation. Based on the scatter plot of reversely cumulated saturation versus /T 2, a NMR reversed cumulative curve can be obtained. The principle of obtaining the NMR reversed cumulative curve is displayed in Fig. 3. Once the NMR reversed cumulative curve is acquired, the next step is to determine the optimal value of C, which makes the NMR reversed cumulative curve similar to the MICP curve as much as possible. A number of methods in the literature have been proposed to determine the value of C [2,2 23,25,26], among which the method proposed by Volokitin et al. [2] is the most popular. Volokitin et al. [2] pointed out that the conversion function of NMR reversed cumulative curve and MICP curve can be expressed as follows: Calibration of the Mentioned Input Parameters in the Volokitin s Model To use Eq. 2 to construct capillary pressure curve from NMR logs, the values of the parameters A, B, C, D and K need to be first determined. To calibrate these parameters in the Volokitin s model, 2 core samples drilled from our target tight gas sands were simultaneously applied for both laboratory MICP and NMR experimental measurements. The MICP and NMR measurements were obtained. To calibrate these parameters, the MICP and corresponding NMR reversed cumulative curves for 2 core samples were used, which are displayed in Fig. 4a, b, separately. By using these MICP and corresponding NMR reversed cumulative curves for 2 core samples, input parameters in Eq. 2 are calibrated. The values of A, B, C, D, and K are 5,,, 2, and 2, respectively. Using these calibrated parameters, the NMR logs can be constructed as pseudocapillary pressure curves, which can be used to evaluate tight gas sandstone reservoir pore structure Reliability Verification To verify the credibility of the calibrated Eq. 2, it is used to core samples with NMR experimental measurements to con- Fig. 4 a The MICP curves for 2 core samples drilled from tight gas sands. b The NMR reversed cumulative curves for 2 core samples drilled from tight gas sands a P c, MPa. b /T 2, ms S Hg, % So, % 2 23

11 Fig. 5 Comparisons of capillary pressure curves acquired from two different methods a Por=.6% Perm=.5mD b Por=7.9% Perm=.323mD P c, MPa. MICP curve P c, MPa. MICP curve.. Pseudo capillary pressure curve S Hg, % 2.. Pseudo capillary pressure curve S Hg, % 2 c Por=7.5% Perm=.85mD d Por=4.7% Perm=5.6mD P c, MPa P c, MPa. MICP curve. MICP curve.. Pseudo capillary pressure curve Pseudo capillary pressure curve S Hg, % S Hg, % struct pseudo-capillary pressure curves. We then compare the shapes of the constructed pseudo-capillary pressure curves with the MICP curves. Figure 5 displays the comparisons of four representative core samples. From these comparisons, we can observe that all the constructed capillary pressure curves match with the laboratory MICP curves very well, illustrating that Eq. 2 is effective in our target tight gas sands in constructing capillary pressure curves from NMR logs. If this technique is extended to field application, the pseudo-capillary pressure curve, the corresponding pore throat radius distribution and the pore structure evaluation parameters, including the average pore throat radius, the threshold pressure and median pore throat radius, can also be estimated from the pseudo-capillary pressure curves in the interval with which NMR logs had been acquired. 4.4 Calculation of Irreducible Water Saturation from NMR Logs Irreducible water saturation (S wi ) is a very important parameter in tight gas sandstone reservoirs evaluation. This is because in tight gas sands, the pore space is mainly occupied by water that cannot flow into the borehole, which is called irreducible water. Figure 4 displays that in our target tight gas sands, the average S wi is close to 45 %, leading to low resistivity contrast. It is therefore difficult in identifying effective gas-bearing formation from water-saturated layers. Estimated S wi could be used to overlap with initial water saturation; gas-bearing formation could then be effectively identified. The NMR logs have unique advantages in estimating S wi. However, Fig. 5 illustrates that in our target tight gas sands, unified T 2cutoff cannot be obtained from laboratory NMR experimental measurements. Hence, the T 2cutoff technique cannot be used to extract S wi from NMR logs in the X4 and X6 sections. Based on the theoretical analysis of the classical Timur and the SDR model [3 32], Xiao et al. [33] derived a model that combines porosity and T 2 logarithmic mean of the NMR T 2 spectrum (T 2lm ) to estimate S wi. This model is effective in S wi estimation in the Xujiahe Formation. Hence, it is directly applied in our target tight gas sands. This model is expressed as follows: S wi = 8.9 ϕ.8326 T lm (22) where ϕ is the porosity in %, which can be estimated by using Eq. 2; T 2lm is the T 2 logarithmic mean of the NMR 23

12 T 2 spectrum in ms, which can be directly obtained from the NMR logs. By using Eq. 22, S wi can be calculated from NMR logs. 4.5 Calculation of Water Saturation by Using the Saturation-Height-Function (SHF) Method Based on the theory of hydrocarbon migration and accumulation, the forming process of oil and gas reservoir can be described as the initial water occupied pore space was replaced by hydrocarbon. Hence, the non-wetting hydrocarbon will be saturated in the pore space once the capillary pressure caused by the pore throat was broken through. The dynamic condition of saturating hydrocarbon is the buoyancy produced from density difference of these two phases of fluids of hydrocarbon and water and the hydrocarbon column height. If the buoyancy and capillary pressure are balanced, saturating hydrocarbon is then stopped. Hence, if the free water level (FWL) is obtained, the buoyancy that caused by the density contrast of oil (gas)-water can be calculated as follows: F = h ρ g = h (ρ w ρ h ) g (23) where F is the buoyancy that caused by the density contrast of hydrocarbon and water and the hydrocarbon column height; h is the hydrocarbon column height in meter; ρ is the density contrast of hydrocarbon and water in g/cm 3 ; ρ w is the water density in g/cm 3 ; ρ h is the hydrocarbon density in g/cm 3, in our tight gas sands, ρ h is the gas density and rewritten as ρ g. g is the gravitational acceleration, which is 9.8m/s 2. The equilibrium state of buoyancy and capillary pressure can be described in the following equation. P g w = F = h ρ g (24) where P g w is the capillary pressure of reservoir condition in MPa, which can be estimated from laboratory MICP experimental measurements using Eq. 25. P g w = σ g w cos θ g w σ Hg air cos θ Hg air P Hg air (25) where P Hg air is the mercury injection pressure; σ g w is the surface tension of gas and water; σ Hg air is the surface tension of mercury and air; θ g w is the contact angle of natural gas and water; θ Hg air is the contact angle of mercury and air. Combining with Eqs. 23 to 25, the relationship between gas column height (thus FWL) and water saturation in-suit situation can be described as the saturation-height-function (SHF). In our target tight gas sands, the saturation-heightfunction can be obtained once input parameters are deter- Gas column height, m Water saturation, % Fig. 6 The saturation-height-function of two phase fluids of gas and water in our target tight gas sands mined. Figure 6 displays the acquisition of saturationheight-function for three typical core samples. If this technique is applied in the whole intervals with pseudo-pressure curves were constructed from NMR logs, the saturation-height-function can be obtained. The initial water saturation can then be estimated from the saturationheight-function. 5 Case Study Using the proposed method, the target tight gas sands of X4 and X6 are analyzed. Figure 7 shows a field example of evaluating tight gas sands from NMR logs. In the first track of Fig. 7, the displayed curves are gamma ray (GR), spontaneous potential (SP) and borehole diameter (CAL). Their contribution is effective formation indication. In the second track, we show density log (DEN), compensated neutron log (CNL) and interval transit time log (AC), all of which are used for porosity estimation. RT displayed in the third track is deep lateral resistivity, and RXO is shallow lateral resistivity. The fourth track is depth, and its unit is meter. T2_DIST displayed in the fifth track is field NMR spectrum, which was acquired from Schlumberger s CMR-plus tool. PC_DIST displayed in the sixth track is the constructed pseudo-capillary pressure curve from field NMR logs by using Eq. 2, and it is displayed by the variable density method. In the seventh track, we compare the calculated porosity (AMRP) using the AMR technique with core-derived porosity. From this comparison, it can be observed that the estimated porosities from NMR and acoustic logs match with the true formation porosities very well. This confirms that the AMR technique is effective in our target tight gas sands. SWCAL 23

13 Fig. 7 A field example of evaluating tight gas sandstone reservoir by using NMR logs displayed in the eighth track is estimated initial water saturation from the pseudo-capillary pressure curves using the SHF method. SWICAL is the estimated irreducible water saturation using Eq. 2, and SWICORE is the irreducible water saturation obtained from the core samples with laboratory NMR experimental measurements. From the comparison of the values of several kinds of the water saturation, it can be concluded that the SWCAL and SWICAL are coincided with each other very well. Additionally, they are closed to the corederived results. This illustrates that the estimated SWCAL and SWICAL are accurate, and the proposed method is reliable. PERM displayed in the ninth track is the estimated permeability from pseudo-capillary pressure curves by using the Swanson-based permeability model displayed in Fig. 2. A good consistency of estimated permeability with corederived permeability (CPERM) illustrates that the Swansonbased permeability model is valuable in tight gas sands permeability estimation. From the tenth to twelve tracks, we compare the estimated average pore throat radius (RM), maximum pore throat radius (RMAX) and threshold pressure (PD) from the pseudo-capillary pressure curves with the core-derived average pore throat radius (CRM), maximum pore throat radius (CRMAX) and threshold pressure (CPD), separately. In the last track, we compare the Swanson parameter acquired from two different kinds of methods. Swanson is the estimated Swanson parameters from constructed pseudo-capillary pressure curve using the method illustrated in Fig., and Cswanson is the extracted Swanson parameters from experimental MICP data. Comparison shows that the pore structure evaluation parameters and the Swanson parameter acquired from the constructed pseudocapillary pressure are coincided with the core-derived results. This demonstrates the effectiveness of the technique of constructing pseudo-capillary pressure curves from field NMR logs. From the estimated results, it can be found that in the interval of xx88 xxm, although the estimated initial water saturation reaches to 4 5 %, it is coincided with the irreducible water saturation. This denotes that no free water can be produced. After analyzing the constructed pseudocapillary pressure, estimated porosity, permeability and pore structure evaluation parameters, it can be concluded that the pore structure of this interval is good. If necessary fracture treatments 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 pure gas-bearing formation, where no water is produced. This field example illustrates that the proposed method in this study is valuable in tight gas reservoirs evaluation, and they can be further extended to be applied to other types of tight sandstone reservoirs. 6 Discussion Detailed observing Eq. 2, we can find that in the process of constructing pseudo-capillary pressure curves in our target tight gas sands, the unitary input parameters in the Volokitin s model are calibrated and used. This is because in our target tight gas sandstone reservoirs of X4 and X6 Formations, the heterogeneity is not strong enough, and this can be verified by the displayed MICP curves in Fig. 4a. From 23

14 Fig. 4a, it can be observed that the shapes of all 2 core samples are relative regular, and they are not divergent. In this case, the unified model can be used. However, if formations are inhomogeneous, the unified function cannot be used to construct pseudo P c curve [25]. In this case, formations should be classified into several types by other methods, and in every type of formation, individual mentioned input parameters in the Volokitin s model should be calibrated. Meanwhile, it need to be noticed that the SHF method is applicative only in the structural hydrocarbon reservoir. This is because in this type of reservoirs, the unified oil (gas)/water interface can be determined, and the hydrocarbon column height can be calculated. However, in the lithologic hydrocarbon reservoir, there is not unified FWL, and the SHF method will be invalid. In this case, the R ccutoff (pore throat radius cutoff) may be determined by combining with the laboratory NMR measurements, and then, the water saturation is predicted from the extracted pore throat radius distribution from pseudo P c curve by using the determined R ccutoff [2]. 7 Conclusions Tight gas sandstone reservoirs evaluation faces great challenges. The conventional methods, which are effective in normal reservoirs, are not often effective. The NMR logs, however, play an important role in tight gas reservoirs evaluation as they provide the information of pore structure. The AMR technique is effective in porosity calculation in tight gas sands, and it can be used to accurately estimate reservoir porosity. Comparing with conventional density and compensated neutron log, the AMR technique can avoid the affection of low hydrogen index to porosity estimation. The relationship of core-derived porosity and permeability is divergent, making the conventional permeability estimation method invalid. The Swanson-based permeability estimation model adequately involve the pore structure information, which can be used to precisely estimate tight gas sands permeability. After calibrating input parameters of the Volokitin s model by using sufficient number of samples, the NMR logs can be used to construct pseudo-capillary pressure curves to evaluate the pore structure of tight gas sandstone reservoirs. Meanwhile, if the Swanson-based permeability model is applied, permeability can be estimated. The saturationheight-function can be further used to predict initial water saturation, which is beyond the capacity of the typical Archie s equation. 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