Calculation of Irreducible Water Saturation (S wirr ) from NMR Logs in Tight Gas Sands

Appl Magn Reson (2012) 42:113 125 DOI 10.7/s00723-011-0273-x Applied Magnetic Resonance Calculation of Irreducible Water Saturation (S wirr ) from NMR Logs in Tight Gas Sands Liang Xiao Zhi-Qiang Mao Yan Jin Received: 24 May 2011 / Published online: 3 November 2011 Ó Springer-Verlag 2011 Abstract It is difficult to calculate irreducible water saturation (S wirr ) from nuclear magnetic resonance (NMR) logs in tight gas sands due to the effect of diffusion relaxation on the NMR T 2 spectrum at present. By combining with classical Timur and Schlumberger Doll Research (SDR) models, a novel model of calculating S wirr is derived. The advantage of this novel model is that S wirr can be calculated without a T 2 cutoff, and all input information can be acquired from NMR logs accurately. With the calibration of 36 core samples, which were drilled from Xujiahe Formation in Bao-jie region of Triassic, Sichuan basin, southwest China, the values of these statistic model parameters are defined. Field examples of tight gas sands show that the proposed model is reliable. The S wirr calculated with the proposed model match well with core analyzed results both in tight gas formations and water-saturated layers, the absolute error is in the range of ±4%. The calculated results by using 20.75 ms as the T 2 cutoff are accurate in water-saturated layers but are overestimated in gas-bearing intervals. Defining 33 ms as the T 2 cutoff is unusable both in gas-bearing and water layers. L. Xiao Z.-Q. Mao State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing, People s Republic of China L. Xiao Z.-Q. Mao Key Laboratory of Earth Prospecting and Information Technology, Beijing, People s Republic of China Y. Jin Southwest Oil and Gas Field Branch Company, PetroChina, Sichuan, People s Republic of China L. Xiao (&) Well logging Department, College of Geophysics and Information Engineering, China University of Petroleum, No. 18, Fuxue Road, Changping, Beijing 102249, People s Republic of China e-mail: nmrlogging@21cn.com

114 L. Xiao et al. 1 Introduction Tight gas reservoirs always display characteristics of micropore body, small pore throat radius and poor pore connectivity. The proportion of micropore space is large, which leads to irreducible water saturation (S wirr ) being higher than that of conventional formations, thus resulting in low resistivity contrast between gasbearing formations and water-saturated intervals. It is difficult to distinguish tight gas formations from water-saturated layers [1]. To improve the reliability of tight gas reservoirs evaluation, it is necessary to obtain information on S wirr and nuclear magnetic resonance (NMR) logs have an unique advantage in this aspect. Although S wirr can be calculated from NMR T 2 distribution after a T 2 cutoff is defined in conventional reservoirs, it is of great difficulty to calculate S wirr from NMR logs even if the T 2 cutoff has been obtained in low-permeability oil-bearing formations and tight gas sands. NMR T 2 spectrum is distorted due to the contribution of bulk relaxation of light oil and diffuse relaxation of natural gas. In gas-bearing intervals, the T 2 spectrum of natural gas is overlapped with that of irreducible water. Parts of the T 2 spectrum of natural gas are considered to be that of irreducible water and the calculated S wirr from NMR logs will be overestimated. To remove the effect of bulk relaxation of light oil and diffuse relaxation of natural gas on the NMR T 2 distribution, the best way is to estimate S wirr from NMR logs without a T 2 cutoff [2]. In this study, by means of transforming Timur and Schlumberger Doll Research (SDR) models, a novel model of calculating S wirr from NMR logs is derived. 2 Problems of S wirr Calculation from NMR Logs in Tight Gas Sands The common method of calculating S wirr from NMR logs is to define a T 2 cutoff, which segregates NMR T 2 distribution into two volumes [3, 4]. S wirr is defined as the ratio of the accumulation of T 2 distribution for T 2 relaxation time being lower than T 2 cutoff to the sum area of T 2 distribution. 2.1 Problems of Calculating S wirr from NMR Logs by Using a Defined T 2 Cutoff In practical applications, there are two problems of calculating S wirr by using a T 2 cutoff: 1. An appropriate T 2 cutoff determination is difficult, and there is not an optimum method to acquire T 2 cutoff from NMR T 2 distribution at present. A default T 2 cutoff of 33 ms has been proposed for clastic reservoirs and 92 ms for carbonate reservoirs [3 7]. However, in practical applications, defining 33 ms as a T 2 cutoff is not always accurate in clastic reservoirs, especially, in tight gas sands. Figure 1 shows the statistical graph of the T 2 cutoff from 36 core plugs, which were drilled from tight gas sands in Xujiahe formation in Bao-jie region of Triassic, Sichuan basin, southwest China. It illustrates that the statistic T 2 cutoff for NMR experimental data set is not 33 ms or other fixed value but is lower than 33 ms, the main distribution ranges from 17 to 24 ms, the weighted average is 20.75 ms.

Calculation of Irreducible Water Saturation (S wirr ) 115 50% Relative frequency (%) 40% 30% 20% 10% 0% 3~10 10~17 17~24 24~31 31~38 38~45 45~52 >52 T 2 cutoff (ms) Fig. 1 Statistical graph of the T 2 cutoff for 36 core samples in tight sandstones 2. S wirr cannot be estimated in field formation evaluation even if the value of T 2 cutoff has be obtained accurately from core samples because the core data set is obtained from laboratory NMR measurements with fully water saturation. For tight hydrocarbon sands, if the pore space is occupied by light oil or natural gas, the shape of the T 2 spectrum will be distorted due to the contribution of bulk relaxation of light oil and diffusion relaxation of natural gas. 2.2 Effects of Hydrocarbon on the NMR T 2 Spectrum To illustrate the effect of bulk relaxation of hydrocarbon on the NMR T 2 spectrum, kerosene and transformer oil were selected to simulate different viscosity oil, 11 sandstone plug samples were chosen for NMR experimental measurement under four saturated conditions: fully saturated with water, irreducible water saturation (the pore volume contains irreducible water and air through centrifuge), hydrocarbon-bearing condition (the pore space consists of irreducible water and hydrocarbon by kerosene or transformer oil drainage) and residual oil saturation from the drainage of the samples at hydrocarbon-bearing conditions with brine. Residual oil condition was used to simulate the flushed zone of hydrocarbon formation in field NMR logs [8]. The comparison of NMR T 2 distribution for two core samples is displayed in Fig. 2. Figure 2a shows the comparison of T 2 distribution under four conditions for conventional core samples, with the transformer oil used. Figure 2bis for low-permeability sandstone core samples with the same condition as in Fig. 2a, with kerosene used as the oil. The black dotted lines in these two figures are the trough of bimodal NMR T 2 distribution with residual oil saturation, which is always considered to be T 2 cutoff in field NMR logs, and the black solid lines mean T 2 cutoff acquired from laboratory NMR measurements under fully water-saturated condition.

116 L. Xiao et al. (a) 0.15 Por.=14.1% Perm.=12.3 10-3 µm 2 (b) 0.15 Por.=14.1% Perm.=4.1 10-3 µm 2 0.12 0.12 Relative Population 0.09 0.06 Relative Population 0.09 0.06 0.03 0.03 0 0.1 1 10 0 00 Relaxation Time T 2, ms 0 0.1 1 10 0 00 Relaxation Time T 2, ms Fig. 2 Comparison of the shape of the T 2 spectrum for four different conditions [8]: À irreducible water saturation; ` fully brine-saturated; residual oil saturation; ˆ oil-bearing condition; bulk relaxation of transformer oil; Þ bulk relaxation of kerosene As shown in Fig. 2, two core samples have the same porosity, whereas permeability of the core sample shown in Fig. 2a is higher. Figure 2a illustrates that for core plug with conventional porosity and permeability, when the pore space is occupied by transformer oil, the NMR T 2 spectrum under residual oil-saturated condition will be distorted only a little, because for rocks with good pore structure, the T 2 distribution with fully water saturation is wide, and the T 2 spectrum reflecting the bulk relaxation of transformer oil overlaps with that of movable water. The T 2 cutoff acquired from above two different conditions is almost the same. It can be concluded that the T 2 cutoff acquired from laboratory NMR measurements with fully water-saturated condition can be used in field reservoir evaluation directly for conventional rocks or formations. However, for a low-permeability sandstone core sample (Fig. 2b), the T 2 spectrum is narrow, when the pore space is occupied by non-wetting phase kerosene, the T 2 distribution with residual oil saturation will be wider than that with fully water saturation, and the NMR spectrum with long T 2 relaxation time reflects the bulk relaxation of kerosene. T 2 cutoffs obtained from these two different saturated conditions are discrepant. If the T 2 cutoff obtained from fully water-saturated laboratory NMR measurements is used for formation evaluation directly, the S wirr calculated from field NMR logs will deviate. 2.3 Effects of Natural Gas on the Field NMR T 2 Spectrum Figure 2b has demonstrated that calculating S wirr from field NMR logs by using a T 2 cutoff, which is acquired from NMR experimental measurement, is improper in low-permeability sands. The T 2 cutoff is also usable in tight gas sands because of the effect of diffusion relaxation of natural gas. At present, core NMR experimental

Calculation of Irreducible Water Saturation (S wirr ) 117 Fig. 3 Comparison of the T 2 spectra in gas-bearing formations. The indication by À and ` is the same as in Fig. 2. þ Field NMR T 2 spectrum in gas-bearing intervals corresponding to the same depth of the core sample Relative Population 0.9 0.6 0.3 0 0.1 1 10 0 00 Relaxation Time T 2, ms measurements under the gas-bearing condition cannot be carried out due to the limitation of experimental apparatus. To illustrate the effect of natural gas on the NMR T 2 spectrum, the comparison of NMR T 2 distribution obtained from experimental measurement and from field NMR logs is displayed in Fig. 3. Figure 3 illustrates that when the pore space is occupied by natural gas, the morphology of the T 2 spectrum is distorted. The T 2 spectrum moves to the left, and the signal of natural gas overlays with that of irreducible water, which makes the amplitude of the left peak increase and that of the right peak decrease. If the T 2 cutoff acquired from the NMR experimental data set is used for S wirr calculation directly, the S wirr will be overestimated. To estimate S wirr in tight gas sands accurately, the best way is to propose a novel model to calculate S wirr from NMR logs without T 2 cutoff. In the next sections, based on the transformation of Timur and SDR models, a novel model of calculating S wirr from NMR logs without T 2 cutoff is derived. 3 Novel Model of Estimating S wirr from NMR Logs 3.1 Timur Model Based on the analysis of 155 core samples originated from three different types of fields in North America, Timur [9] found that rock permeability is proportional to porosity, and inversely proportional to S wirr, that is to say, for rocks with high porosity and low S wirr, which will contain high permeability, vice versa. Based on the regression statistics, Timur established a relationship of connecting permeability with porosity and S wirr [9]. It was named as Timur model and expressed as follows:

118 L. Xiao et al. K ¼ 0:136 u4:4 S 2:0 ; ð1þ wirr where K is the rock permeability in units of 10-3 lm 2, u is the rock porosity, and S wirr is the irreducible water saturation, their units being fractions. In Timur model, the rock permeability can be estimated once the values of u and S wirr have been defined. On the contrary, S wirr can be derived with the values of K and u. Meanwhile, in the view of the difference of geologic settings in fields or regions, Timur thought the relationship among rock porosity, permeability and S wirr should be different. The differences among them could be displayed by different values of parameters in Timur model. A common formula was written as K ¼ a ub S c ; ð2þ wirr where a, b and c are statistic model parameters. For different kinds of fields or formations, different values will be defined to acquire permeability from porosity and S wirr, their values should be calibrated by core samples. Equation (2) displays the relationship among rock porosity, permeability and S wirr. After the values of a, b and c have been calibrated, S wirr can be calculated once the input parameters of porosity and permeability are acquired. Porosity can be estimated by integrating NMR with conventional logs [10, 11]. The calculation of permeability is a challenge in tight gas sands due to the generally poor correlation between porosity and permeability (Fig. 4). To obtain accurate S wirr, Eq. (2) should be transformed to avoid requiring permeability but to obtain information from NMR logs. 0 Core permeability, (10-3 µm 2 ) 10 1 0.1 0.01 X2_well A X2_well B X2_well C X2_well D X4_well B X4_well C X4_well D X6_well B X6_well D 0.001 0 5 10 15 20 Core porosity, % Fig. 4 Relationship between the core porosity and the permeability in tight reservoirs in four wells

Calculation of Irreducible Water Saturation (S wirr ) 119 3.2 SDR Model An SDR model has been proposed by Schlumberger Doll Research Center to estimate permeability from NMR logs directly [12, 13] and is written as K ¼ C 1 u m 1 T n 1 2lm ; ð3þ where T 2lm is the logarithmic mean of the NMR T 2 spectrum in ms, C 1, m 1 and n 1 are the statistical model parameters that can be acquired from core samples experimental results. Carrying out some algebraic transformations in Eq. (3) and substituting it into Eq. (2), a derivative expression can be written as following: S wirr ¼ a C 1 1 cu b m 1 c T n 1 c 2lm ; ð4þ where all the variables are the same meaning as in Eqs. (2) and (3). Once the parameters are defined as following: C 2 ¼ a 1 c; b m 1 m ¼ ; n ¼ n 1 C 1 c c ; Eq. (4) can be rewritten as S wirr ¼ C 2 u m T2lm n : ð5þ Equation (5) shows that once the values of C 2, m and n have been calibrated by NMR experimental data set, S wirr can be estimated from NMR logs. 4 Case studies With the model proposed above, the gas-bearing interval and water-saturated layer in a well with field NMR logs in Xujiahe formation are processed. 36 core samples were drilled for NMR experimental measurement in this region, the NMR experiment data set being listed in Table 1. With the data set listed in Table 1, the values of C 2, m and n in Eq. (5) are calibrated and S wirr calculation equation can be expressed as Eq. (6): S wirr ¼ 118:91 u 0:08326 T2lm 0:24518 ; R ¼ 0:834: ð6þ In Eq. (6), the value of m is -0.08326, and n is calibrated as 0.24518. Equation (6) demonstrates that there is a good correlation between S wirr, porosity and T 2lm. By using this relationship, accurate S wirr can be obtained from field NMR logs once the input parameters of u and T 2lm are obtained precisely. In practical applications, porosity can be estimated precisely in tight gas sands by integrating NMR with conventional logs [10 12], whereas T 2lm could be decreased in gas-bearing formations because of the effect of diffusion relaxation. Equation (6) is calibrated by using fully water-saturated core experimental measurements. In order to extend this model to field applications, T 2lm should be corrected. To obtain accurate T 2lm in Eq. (6), a relationship is established to correct field NMR T 2lm to laboratory simulation condition, as is shown in Fig. 5.

120 L. Xiao et al. Table 1 Data set of NMR experimental measurement from 36 plug samples in tight gas sands in Xujiahe formation in Bao-jie region of Triassic, Sichuan basin, southwest China Well name Depth (m) Horizon Sample number Porosity (%) Permeability (md) T2 logarithmic mean (ms) Irreducible water saturation (%) T2 cutoff (ms) Well name Depth (m) Horizon Sample number Porosity (%) Permeability (md) T2 logarithmic mean (ms) Irreducible water saturation (%) T2 cutoff (ms) well A T3X4 X3 15.20 5.87 29.09 40.42 22.85 well D 1,754.35 T3X4 R19 7.40 0.62 29.09 42.35 18.59 well A T3X4 X5 16.00 5.24 39.74 37.94 19.59 well D 1,766.20 T3X4 R18 11.00 0.57 19.98 45.89 13.36 well A T3X4 X6 14.00 1.08 28.56 37.06 13.34 well D 1,778.45 T3X4 R17 8.80 0.91 30.53 50.38 23.48 well A T3X4 X7 13.10 0.58 17.56 41.57 10.86 well D 1,781.00 T3X4 R16 11.60 0.89 29.11 47.12 20.49 well B 1,400.00 T3X6 J21 5.00 0.15 8.26 42.29 4.74 well D 1,783.80 T3X4 R15 6.30 0.33 10.12 67.84 19.03 well B 1,407.20 T3X6 J19 6.40 0.28 17.92 45.24 11.62 well D 1,790.60 T3X4 R14 8.80 0.62 20.41 58.57 19.13 well B 1,409.20 T3X6 J18 5.90 0.20 18.89 49.94 12.46 well D 1,835.15 T3X2 R13 9.20 0.16 33.36 41.19 21.39 well B 1,410.50 T3X6 J17 5.10 0.16 17.90 61.85 22.77 well D 1,840.50 T3X2 R12 9.50 0.21 35.33 42.20 21.19 well B 1,414.70 T3X6 J16 3.90 0.08 13.13 48.90 7.19 well D 1,846.20 T3X2 R11 11.70 0.21 35.60 43.77 21.81 well C 1,707.70 T3X4 B13 12.10 12.29 63.73 23.83 13.73 well D 1,861.50 T3X2 R10 15.30 0.27 43.67 44.67 30.60 well C 1,722.80 T3X4 B11 13.30 3.06 39.50 32.50 14.41 well D 1,871.30 T3X2 R9 14.50 0.17 25.01 56.07 27.14 well D 1,490.30 T3X6 R27-1 7.80 0.50 35.02 40.10 22.01 well D 1,881.50 T3X2 R8 16.30 0.58 49.93 35.84 25.52 well D 1,498.40 T3X6 R26 8.80 0.85 43.19 37.18 22.55 well D 1,885.90 T3X2 R7 14.80 1.05 75.18 33.66 34.58 well D 1,545.80 T3X6 R24 8.80 0.24 25.21 42.16 14.67 well D 1,887.85 T3X2 R6 19.90 90.65.96 31.22 55.76 well D 1,586.65 T3X6 R23 13.10 0.49 30.62 39.43 17.90 well D 1,895.80 T3X2 R5 11.60 0.20 44.70 34.91 22.54 well D 1,595.50 T3X6 R22 9.30 1.03 47.14 37.69 25.84 well D 1,902.00 T3X2 R4 15.30 0.23 26.73 55.99 28.83 well D 1,722.30 T3X4 R21 7.20 0.50 34.05 43.41 21.10 well D 1,919.30 T3X2 R3 11.40 0.23 26.93 60.68 41.81 well D 1,740.40 T3X4 R20 6.70 0.27 28.18 38.88 14.70 well D 1,931.00 T3X2 R2 4.80 0.13 8.64 63.19 9.58

Calculation of Irreducible Water Saturation (S wirr ) 121 T 2lm obtained from NMR experimental measurement, ms 0 10 1 1 y = 6.8033x 0.5652 R = 0.913 10 T 2lm obtained from field NMR logs, ms Fig. 5 Relationship between T 2lm measurement calculated from field NMR logs and from NMR experimental Figure 5 displays a good relationship of T 2lm under two conditions. This correlation is caused by the internal relations of three types of relaxation mechanisms, which are bulk relaxation, surface relaxation and diffusion relaxation. The experimental results of 11 core samples mentioned above can be used to verify this correlation further (Fig. 6). T 2lm obtained from laboratory NMR measurement with full water saturation, ms 10 1 1 y = 0.726x 1.0019 R = 0.996 10 T 2lm obtained from laboratory NMR measurement with residual oil saturation, ms Fig. 6 Relationship of T 2lm obtained from laboratory NMR experimental measurements under two different conditions

122 L. Xiao et al. Fig. 7 Calculation of irreducible water saturation from field NMR logs in tight gas sands and watersaturated layers and the comparison with the core analysis results Figure 7 shows a field example of calculating S wirr from field NMR logs by using the model proposed in this study. Track (e) in Fig. 7 is the comparison of T 2lm calibrated from field NMR logs by using the relationship displayed in Fig. 5 (T 2lm ) and analyzed from core samples (core_t 2lm ). Track (f) in Fig. 7 displays the comparison of the reservoir porosity calculated by integrating the interval transit time with NMR logs (total_porosity) [10] and acquired from core plugs (core_porosity). Preferable consistency in these two tracks demonstrates the accuracy of the used input parameters in Eq. (6). Track (g) in Fig. 7 displays the comparison of S wirr derived by three different methods, with S wirr calculated by using the proposed model in this study, S wi _20.75 ms calculated by using 20.75 as a T 2 cutoff and Core S wirr analyzing irreducible water saturation from core samples. The drill stem testing data displayed in the right of Fig. 7 illustrates that S wirr matches very well with that of core samples (core_s wirr ) in gas-bearing formation, whereas the irreducible water saturation calculated by using 20.75 ms as a T 2 cutoff is higher. Track (h) in Fig. 7 compares S wirr estimated from the proposed model with that calculated by using 33 ms as a T 2 cutoff (S wi _33 ms), and the result demonstrates that the latter is not reliable. These two comparisons mean that the T 2 cutoff obtained from laboratory NMR measurements with full water saturation is inapplicable in gas-bearing formations. In water-saturated

Calculation of Irreducible Water Saturation (S wirr ) (a) 80-4% +4% Core_Swirr, % 60 40 20 (b) 0 0 20 40 60 80 S wirr, % 80 Core_Swirr, % 60 40 20 (c) 0 0 20 40 60 80 Swi_20.75 ms, % 80 Core_Swirr, % 60 40 20 0 0 20 40 60 80 Swi_33 ms, % Fig. 8 Comparison cross plots of S wirr, S wi _20.75 ms, S wi _33 ms and core analyzed results (core_s wirr ) for 36 core samples

124 L. Xiao et al. layers, S wirr calculated from the proposed model and by using 20.75 ms as a T 2 cutoff almost overlap with each other. They all match well with the core analyzed results, whereas S wirr calculated by using 33 ms as a T 2 cutoff is still overestimated. This is because the formation condition is similar to the experimental simulation condition and T 2 cutoff can be used in water-bearing formations directly. The derived method is applicative not only in gas-bearing formations but also in water-saturated layers. Figure 8 displays the comparison cross plots of S wirr, S wi _20.75 ms, S wi _33 ms and core analyzed irreducible water saturation. Figure 8a illustrates that the majority of calculated S wirr is close to core_s wi, and the absolute errors between them are lower than 4%, which meets the requirements of tight gas sands evaluation. However, the calculated irreducible water saturations by using 20.75 and 33 ms as the T 2 cutoff are all overestimated (Fig. 8b, c). 5 Conclusions In tight gas formation evaluation, S wirr is a very important parameter. The S wirr calculated from field NMR logs by using a T 2 cutoff is overestimated and the effect of diffusion relaxation cannot be removed at present. By integrating Timur and SDR models, a derived model is proposed to calculate S wirr from NMR logs. The advantage of this model is that S wirr can be estimated without T 2 cutoff and the used input parameters can be obtained from field NMR logs accurately. Field examples show that the derived model is usable both in tight gas sands and water-saturated layers, and the calculated S wirr matches very well with that of core samples, the absolute errors being lower than 4%. The result calculated by using 20.75 ms as a T 2 cutoff is effective in water-saturated layers, but is overestimated in tight gas sands. Using 33 ms as a T 2 cutoff is unusable both in water-saturated and gas-bearing layers. References 1. J. Ouyang, Z.Q. Mao, L.J. Xiu, Y.J. Shi, C.X. Li (Petroleum Industry Press, Beijing, 2009), pp. 1 300 2. S.H. Chen, J.S. Chen, M. Gillen, D. Georgi, in The 49th SPWLA Annual Logging Symposium, paper DD (2008) 3. G.R. Coates, L.Z. Xiao, M.G. Primmer (Gulf Publishing Company, Houston, 200), pp. 1 200 4. L. Xiao, Z.X. Xiao, Prog. Geophys. 23, 167 172 (2008) 5. C. Staley, Appl. Phys. Lett. 51, 1146 1148 (1987) 6. C. Straley, C.E. Morriss, W.E. Kenyon, in The 32nd SPWLA Annual Logging Symposium, Paper CC (1991) 7. C.E. Morriss, J. Maclnnis, R. Freedman, in The 34th SPWLA Annual Logging Symposium, Paper GGG (1993) 8. Z.Q. Mao, L.C. Kuang, Z.C. Sun, X.P. Luo, L. Xiao, in The 48th SPWLA Annual Logging Symposium, Paper W (2007) 9. A. Timur, in The 9th SPWLA Annual Logging Symposium, Paper J (1968) 10. Z.Q. Mao, C. Zhang, L. Xiao, Oil Geophys. Prospect. 45, 105 109 (2010)

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