Estimation of Saturation Exponent from Nuclear Magnetic Resonance (NMR) Logs in Low Permeability Reservoirs

Transcription

1 Appl Magn Reson (2013) 44: DOI.07/s Applied Magnetic Resonance Estimation of Saturation Exponent from Nuclear Magnetic Resonance (NMR) Logs in Low Permeability Reservoirs Liang Xiao Zhi-qiang Mao Gao-ren Li Yan Jin Received: 26 November 2011 / Revised: 3 May 2012 / Published online: 3 June 2012 Ó Springer-Verlag 2012 Abstract The resistivity experimental measurements of 36 core samples, which were drilled from low permeability reservoirs of southwest China, illustrate that the saturation exponents are not agminate, but vary from to 3.48; this leads to a challenge for water saturation estimation in low permeability formations. Based on the analysis of resistivity experiments, laboratory nuclear magnetic resonance (NMR) measurements for all 36 core samples, and mercury injection measurements for 20 of them, it was observed that the saturation exponent is proportional to the proportion of small pore components and inversely proportional to the logarithmic mean of NMR T 2 spectrum (T 2lm ). For rocks with high proportion of small pore components and low T 2lm, there will be high saturation exponents, and vice versa. The proportion of small pore components is characterized by three different kinds of irreducible water saturations, which are estimated by defining 30, 40 and 50 ms as T 2 cutoffs separately. By integrating these three different kinds of irreducible water saturations and using T 2lm,a technique of calculating the saturation exponent from NMR logs is proposed and the corresponding model is established. The credibility of this technique is confirmed by L. Xiao (&) Key Laboratory of Geo-detection, China University of Geosciences, Beijing, Ministry of Education, No. 29, Xueyuan Road, Haidian, Beijing 0083, People s Republic of China nmrlogging@21cn.com Z. Mao College of Geophysics and Information Engineering, China University of Petroleum, Beijing, People s Republic of China G. Li Research Institute of Exploration and Development, Changqing Oilfield Company, PetroChina, Shaanxi, People s Republic of China Y. Jin Southwest Oil and Gas Field Branch Company, PetroChina, Sichuan, People s Republic of China

2 334 L. Xiao et al. comparing the predicted saturation exponents with the results from the core analysis. For more than 85 % of core samples, the absolute errors between the predicted saturation exponents from NMR logs and the experimental results are lower than Once this technique is extended to field application, the accuracy of water saturation estimation in low permeability reservoirs will be improved significantly. 1 Introduction Water saturation (thus related to hydrocarbon saturation) is an indispensable input parameter in formation evaluation, and it also plays a very important role in reservoir development program formulation. Generally, water saturation is calculated using Archie s equations after the necessary parameters have been obtained [1]. Archie s equations can be expressed as Eqs. (1) and (2): F ¼ R 0 ¼ a R w / m ð1þ I r ¼ R t ¼ b R o S n ð2þ w where R 0 is the rock resistivity at full water saturation, R t the true formation resistivity, R w the formation water resistivity, the units of which are X m, F the formation factor, I r the resistivity index, / the porosity in fraction, a and b the lithology factors, m the cementation exponent, S w the water saturation in fraction, and n is the saturation exponent. Combining with Eqs. (1) and (2), a derivative expression can be written as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n a b R w S w ¼ / m : ð3þ R t From Eq. (3), it can be observed that the values of a, b, m, n, R w, / and R t must be obtained first for the water saturation calculation, / and R t can be acquired from conventional logs [2 4], and R w can be checked from the formation water salinity using Schlumberger s log interpretation charts [5]. 2 Determination of the Values of a, b, m and n To calculate water saturation from conventional logs using Archie s equation, the determinations of the values of a, b, m and n are crucial. Generally, the determinations of a, b, m and n rely on the resistivity experimental measurements of the target core samples. To obtain the necessary resistivity experimental data, the needed procedures should be applied as follows: (1) every waterless core sample is saturated using the used saline water, and the rock resistivity R 0 at full water saturation is measured; in this study, the salinity of the used saline water is mg/l. (2) The oil is used as the displacing medium, and the centrifugal method is used to vary the water saturation (S w ) of core samples, and the corresponding rock

3 Estimation of Saturation Exponent from NMR Logs 335 resistivity R t of every core sample under different water saturations are measured. (3) R 0, R t and S w are collected as a data set to obtained the value a, b, m and n. For conventional reservoirs, after the representative core samples were drilled from the intended intervals for the resistivity experiment, the fixed values of a, b, m and n can separately be obtained from the cross plots of the porosity with the formation factor, and the water saturation with the resistivity index using the power function. However, for low permeability sands, not rigorous power function exists between the porosity and the formation factor, the water saturation and the resistivity index due to the complicated pore structure and the strong heterogeneity [6]. Wang and Sharma [7] and Mao et al. [8, 9] had proposed that the tendency of porosity and formation factor would be changed when the porosities of core samples are lower than 9.0 %, and they had demonstrated that this change is caused by the poor pore structure of low permeability plug samples. Mao et al. [8] had developed a novel method to obtain the accurate values of a and m from the porosity using binary regression. This method has been confirmed to be effective and is used widely [6]. In the low permeability formations mentioned in this study, a and m can be determined using Mao s method precisely. Thus, the technique of determining a and m from the porosity that has been proposed by Mao et al. [8] is not introduced in this paper. It is really a challenge to determine the saturation exponent in low permeability reservoirs, as the cross plot of the water saturation with the resistivity index is divergent and a fixed saturation exponent is difficult to acquire. Figure 1 shows the cross plot of the water saturation with the resistivity index of 36 core samples, which were drilled from low permeability reservoirs of southwest China. It can be observed that the relationship between the water saturation and the resistivity index for all core samples is not consistent. The saturation exponent for single core sample varies from to In this case, water saturation calculated using the regressed fixed saturation exponent from all 36 core samples would be inaccurate. Resistivity exponent, I r y = x R 2 = Water saturation, fraction Fig. 1 Relationship of water saturation and resistivity index for 36 core samples in low permeability sands of southwest China

4 336 L. Xiao et al. The best method is to estimate the water saturation using various saturation exponents along with the target intervals. 3 Influencing Factors of Saturation Exponent in Low Permeability Sandstones To acquire accurate saturation exponents for water saturation estimation at low permeability, it is necessary to understand the influencing factors and the variation of the saturation exponent. Based on the qualitative analysis of the core thin section and mercury injection capillary pressure experimental data, Mao et al. [8] had point out that the saturation exponents were related to rock pore structure. However, the quantitative relationship between them was not established, and an applicable technique was not proposed. Nuclear magnetic resonance (NMR) logs have a unique advantage in indicating reservoir pore structure. From the measured NMR T 2 distribution, the information of pore size and distribution can be obtained [ 14]. Rocks with macropore and good pore structure will display long transversal relaxation time, and wide T 2 distribution due to the contribution of surface relaxation. On the contrary, short transversal relaxation time and narrow NMR T 2 distribution mean poor pore structure for rocks (Fig. 2). Mercury injection capillary pressure curves can be used to obtain the pore throat radius distribution, which is useful in evaluating the pore throat size and the connectivity [15, 16]. To quantitatively display the relationship between the saturation exponents with the pore structure, all 36 core samples, shown in Fig. 1, have been chosen for rock resistivity and laboratory NMR experimental measurements; 20 of them were studied in mercury injection experiments. The experimental parameters of NMR measurements are designed as follows: polarization time (TW): 6.0 s; inter-echo spacing (TE): 0.2 ms; the number of echoes per echo train (NE): 4096; scanning number: 128. To illustrate the factors that heavily affect the saturation exponent, the resistivity and laboratory NMR experimental results for 36 core samples and mercury injection measurements for 20 core samples have been analyzed. Four representative core samples with saturation exponent increasing from to 3.48 are compared and displayed through Figs. 3, 4, 5 and 6. In these figures, the correlation of the water saturation and the resistivity index, the corresponding laboratory NMR T 2 distribution and the pore throat radius distribution that acquired from mercury injection capillary pressure curve are displayed in (a), (b) and (c), respectively. For the core sample no. 2, no mercury injection data have been obtained. From a comparison of the data displayed in Figs. 3, 4, 5 and 6, several regularities can be observed: 1. The saturation exponent is heavily affected by the rock pore structure. For core samples with good pore structure (with wide NMR T 2 distribution), the proportion of large pore components is dominated and the corresponding saturation exponent is low, like for the core samples 1 and 2 shown in Figs. 3 and 4. On the other hand, when the rocks are dominated by micro porosity, the proportion of small pore components is high, and the corresponding saturation exponent increase, like for the core samples 3 and 4 shown in Figs. 5 and 6.

5 Estimation of Saturation Exponent from NMR Logs 337 H 1 nuclei Equivalent rock pore space Spin-echo train NMR T 2 distribution Decay time, ms Relative amplitude inversion Multi-exponential Relative amplitude Decay time, ms Relaxation time T 2, ms Relaxation time T 2, ms Fig. 2 Relationship of rock pore size with the corresponding NMR T 2 distribution 2. The saturation exponent is hardly affected by the pore throat radius, as for the core samples 1, 3, and 4. Their saturation exponents vary strongly, but their distributions of pore throat radii are not different, especially for the core samples 1 and 3. Their saturation exponents and NMR T 2 distributions are significantly different, while the morphologies of the pore throat radius distributions are almost the same. 3. The saturation exponent is not relevant to rock porosity and permeability, but it is inversely proportional to T 2lm. This is because high T 2lm means wide NMR T 2 distributions and thus leads to low saturation exponents. 4 A Novel Model for Estimating the Saturation Exponent from NMR Logs 4.1 Estimating the Saturation Exponent Parameters from NMR Logs From Figs. 3, 4, 5 and 6, we can conclude that the saturation exponent is proportional to the proportion of small pore components and inversely proportional

6 338 L. Xiao et al. Fig. 3 Experimental results of core sample no. 1 (a) Resistivity index Core No. 1 por.=14.0% perm.=0.49 md y = x R 2 = Water saturation, fraction (b) Core No. 1 T 2lm =30.6 ms T 2, ms (c) Core No R c, um to the T 2lm. These parameters must be obtained first to estimate the saturation exponent precisely. In this aspect, NMR logs have unique advantages [17 21]. T 2lm can be obtained from the NMR logs directly, but the proportion of small pore components needs to be characterized. In this study, different kinds of irreducible water saturations, which are calculated by defining, 20, 30, 40, 50, 60, 70 and 0 ms as T 2 cutoffs separately, are

7 Estimation of Saturation Exponent from NMR Logs 339 Fig. 4 Experimental results of core sample no. 2 (a) Resistivity index Core No. 2 por.=15.9% perm.=1.05 md y = x R 2 = Water saturation, fraction (b) Core No. 2 T 2lm = ms T 2, ms chosen to characterize the proportion of small pore components. The irreducible water saturation can be estimated using Eq. (4), R T2cutoff T S wirr ¼ 2 min SðTÞdt R T2 max ð4þ SðTÞdt T 2 min where S wirr is the estimated irreducible water saturation from NMR logs using the defined T 2 cutoff, T 2min the minimum transverse relaxation time, T 2max the maximum transverse relaxation time, T 2cutoff the defined T 2 cutoff, which is used to estimate the irreducible water saturation; the units of them are ms and S(T) is the porosity distribution function, which is associated with the T 2 relaxation time. To illustrate the correlation of all the experimental parameters obtained from laboratory NMR and mercury injection measurements with the saturation exponent, the correlations of them are analyzed and listed in Table 1. Table 1 illustrates that the saturation exponents are strongly correlated with S wirr_30, S wirr_40, S wirr_50, but the correlation with S wirr_, S wirr_20, S wirr_60, S wirr_70 and S wirr_0 was reduced. This is because that for majority of core samples, the

8 340 L. Xiao et al. Fig. 5 Experimental results of core sample no. 3 (a) Core No. 3 Resistivity index por.=8.2% perm.=0.27 md y = x R 2 = Water saturation, fraction (b) Core No. 3 T 2lm =28.2 ms T 2, ms (c) 20 Core No R c, um NMR T 2 distribution mainly ranges from 20 to 60 ms. When the T 2 relaxation time is lower than 30 ms and higher than 60 ms, nearly no T 2 spectrum exists. T 2lm is the overall signature of NMR T 2. Hence, it is associated with the pore structure.

9 Estimation of Saturation Exponent from NMR Logs 341 Fig. 6 Experimental results of core sample no. 4 (a) Resistivity index Core No. 4 por.=.58% perm.=0.62 md y = x R 2 = (b) Water saturation, fraction Core No. 4 T 2lm =20.41 ms T 2, ms (c) 20 Core No R c, um Core porosity, permeability, T 2 cutoff and parameters obtained from the mercury injection measurements are weakly correlated with the saturation exponent.

10 342 L. Xiao et al. Table 1 Correlations of the saturation exponent and the experimental parameters obtained from laboratory NMR and mercury injection measurements Saturation exponent Porosity Permeability T2cutoff log(t2lm) Swirr_ Swirr_20 Swirr_30 Swirr_40 Swirr_50 Saturation exponent 1.00 Porosity Permeability T 2cutoff log(t 2lm ) Swirr_ Swirr_ Swirr_ Swirr_ S wirr_ S wirr_ S wirr_ Swirr_ Sorting coefficient Variation coefficient P R P d R max Rm

11 Estimation of Saturation Exponent from NMR Logs 343 Table 1 continued Swirr_60 Swirr_70 Swirr_0 Sorting coefficient Variation coefficient P50 R50 Pd Rmax Rm Saturation exponent Porosity Permeability T 2cutoff log(t 2lm ) Swirr_ Swirr_20 Swirr_30 Swirr_40 S wirr_50 S wirr_ S wirr_ Swirr_ Sorting coefficient Variation coefficient P R P d R max Rm In this table, Swirr_, Swirr_20, Swirr_30, Swirr_40, Swirr_50, Swirr_60, Swirr_70 and Swirr_0 are the irreducible water saturations calculated from the NMR T2 distribution using, 20, 30, 40, 50, 60, 70 and 0 ms as T 2 cutoffs P50 is the mercury injection pressure corresponding to 50.0 % mercury injection saturation, R50 is the pore throat radius corresponding to 50.0 % mercury injection saturation, P d is the threshold pressure, R max is the maximum pore throat radius, R m is the average pore throat radius

12 344 L. Xiao et al. 4.2 A Novel Model of Estimating Saturation Exponent from NMR Logs Based on the analysis described above, S wirr_30, S wirr_40, S wirr_50 and T 2lm are chosen as the input parameters to establish a model to estimate the saturation exponent. With the 36 studied core samples, multivariate regression is used. The regression model is established and expressed as Eq. (5). n ¼ 0:546 þ 0:292 logðt 2lm Þþ0:009 S wirr 30 þ 0:061 S wirr 40 ð5þ 0:044 S wirr 50 ; correlation coefficient: 0:776 Equation (5) illustrates that the precision of the saturation exponent estimation model is improved when the parameters S wirr_30, S wirr_40, S wirr_50 and T 2lm are introduced. If these three fixed T 2 cutoffs of 30, 40 and 50 ms are determined, the proportions of small pore components could be characterized and the consecutive saturation exponents can be estimated from the NMR field logs after this technique is extended to field application. Fig. 7 Comparison of saturation exponents acquired from experimental resistivity measurements of core samples and calculated from NMR field logs Saturation exponent Measured n Predicted n

13 Estimation of Saturation Exponent from NMR Logs Predicted saturation exponents from NMR field logs Experimental saturation exponents from core samples Fig. 8 Cross plot of the predicted saturation exponents and the core results 5 Case Studies To confirm the reliability of the mentioned technique in this study, saturation exponents acquired from the experimental resistivity measurements of core samples and calculated from NMR field logs are compared in Fig. 7. This comparison shows that for the vast majority of core samples, the predicted saturation exponents are close to the experimental results. To quantitatively evaluate the absolute errors of the predicted saturation exponents and the core results, the cross plot of these two kinds of saturation exponents is made and shown in Fig. 8. These two figures illustrate that the estimated saturation exponents from NMR field logs using the proposed technique are credible and the absolute errors for more than 85 % of core samples are lower than In reservoirs with consecutive NMR field logs, this technique can be applied for saturation exponent estimation and this will be valuable for water saturation calculation in low permeability sands. 6 Conclusions In low permeability reservoirs, the saturation exponents are divergent and a fixed value cannot be regressed from the cross plot of the water saturation with the resistivity index to estimate water saturation accurately.

14 346 L. Xiao et al. The rock resistivity, laboratory NMR and mercury injection measurements of core samples illustrate that the saturation exponent is heavily affected by the rock pore structure. Thus, it is proportional to the proportion of small pore components and inversely proportional to T 2lm. The saturation exponent is not relevant to rock porosity, permeability and the rock pore throat radius distribution. The proportion of small pore components can be characterized by the irreducible water saturations predicted from the NMR T 2 distribution after defining 30, 40 and 50 ms as the fixed T 2 cutoffs. An estimation model for the saturation exponent can be established based on the corresponding irreducible water saturations and T 2lm. The saturation exponents predicted from NMR field logs using the proposed model in this paper are credible, and they are close to the measured core results. For more than 85 % of the core samples, the absolute errors of these two kinds of saturation exponents are lower than This ensures that the proposed technique and model are reliable and can be extended to field application to estimate the saturation exponents from NMR field logs. This is valuable for water saturation calculation in low permeability sandstones. Acknowledgments The authors thanks for the supporting of the Fundamental Research Funds for the Central Universities, China (No. 2011YXL009) to this research work. References 1. G.E. Archie, The electrical resistivity log as an aid in determining some reservoir characteristics. TAME 146, (1942) 2. M.R.J. Wyllie, A.R. Gregory, L.W. Gardner, Elastic waves velocities in heterogeneous and porous media. Geophysics 21(1), (1956) 3. Z.H. Chu, J. Gao, L.J. Huang, L.Z. Xiao, Principles and methods of geophysical logging (Part II) (Petroleum Industry Pressure, Beijing, 2007), pp H.M. Karter, H.K. Mostafa, An approach for minimizing errors in computing effective porosity in reservoir of shaly nature in view of Wyllie Raymer Raiga relationship. J. Petrol. Sci. Eng. 77, (2011) 5. Schlumberger Well Services, Log interpretation charts. (Schlumberger Well Services, 1986), pp Y.J. Shi, G.R. Li, J.Y. Zhou, Study on litho-electric character and saturation model of argillaceous low-permeability sandstone reservoir. Well Logging Technol 32(3), (2008) 7. Y.M. Wang, M. M. Sharma, A network model for the resistivity behavior of partially saturated rocks. Paper G presented at the 29th SPWLA Annual Logging Symposium (1988) 8. Z.Q. Mao, C.G. Zhang, C.Z. Lin, J. Ouyang, Q. Wang, C.J. Yan, The effects of pore structure on electrical properties of core samples from various sandstone reservoirs in Tarim basin. Paper LL presented at the 36th SPWLA Annual Logging Symposium (1995) 9. Z.Q. Mao, T.D. Tan, C.Z. Lin, Q. Wang, The laboratory studies on pore structure and electrical properties of core samples fully-saturated with brine water. Acta Petrolei Sinica 18(3), (1997). G.R. Coates, L.Z. Xiao, M.G. Primmer, NMR logging principles and applications (Gulf Publishing Company, USA, Houston, 2000), pp S. Anferova, V. Anferov, D.G. Rata, B. Blümich, J. Arnold, C. Clauser, P. Blümler, H. Raich, A mobile NMR device for measurements of porosity and pore size distributions of drilled core samples. Concepts in Magnetic Resonance, Part B. Magn. Reson. Eng. 23B(1), (2004) 12. X.P. Liu, X.X. Hu, L. Xiao, Effects of pore structure to electrical properties in tight gas reservoirs: an experimental study, SPE (2012) 13. R. Ausbrooks, N.F. Hurley, A. May, D.G. Neese, Pore-size distributions in vuggy carbonates from core images, NMR, and capillary pressure, SPE (1999)

15 Estimation of Saturation Exponent from NMR Logs S.A. Shedid, A novel technique for the determination of microscopic pore size distribution of heterogeneous reservoir rock, SPE 7705 (2007) 15. N.C. Wardlaw, Y. Li, Pore-throat size correlation from capillary pressure curves. Transp. Porous Media 2(1987), (1994) 16. R. Askarinezhad, A new statistical approach to pore/throat size distribution of porous media using capillary pressure distribution concept. J. Petrol. Sci. Eng. 75(1 2), 0 4 (20) 17. S.H. Chen, G. Ostroff, D.T. Georgi, Improving estimation of NMR log T 2cutoff value with core NMR and capillary pressure measurements, SCA-9822, pp (1998) 18. L. Xiao, Z.Q. Mao, Y. Jin, Calculation of irreducible water saturation (S wirr ) from NMR logs in tight gas sands. Appl. Magn. Reson. 42(1), (2012) 19. C. Staley, Magnetic resonance digital image analysis and permeability of porous media. Appl. Phys. Lett. 51(15), (1987) 20. C. Straley, C.E. Morriss, W.E. Kenyon, NMR in partially saturated rocks: laboratory insights on free fluid index and comparison with borehole logs. Paper CC presented at the 32nd SPWLA Annual Logging Symposium (1991) 21. C.E. Morriss, J. Maclnnis, R. Freedman, Field test of an experimental pulsed nuclear magnetism tool. Paper GGG presented at the 34th SPWLA Annual Logging Symposium (1993)