Available online at www.sciencedirect.com ScienceDirect IERI Procedia 5 (2013 ) 271 276 2013 International Conference on Agricultural and Natural Resources Engineering Application of Classification Scale Method (CSM) in Tight Sandstone Permeability Calculation Xiao-peng Liu a,b *, Xiao-xin Hu a, Jiang-ming Deng b a Geological Exploration and Development Research Institute in Sichuan-Changqing Drilling and Exploration Engineering Corporation, CNPC, Sichuan, PR China b School of Graduate Student, Southwest Petroleum University, Chengdu, Sichuan, PR China Abstract It is difficult in directly predicting permeability from porosity in tight sandstones due to the poor relationship between core derived porosity and permeability that caused by the extreme heterogeneity. The classical SDR (Schlumberger Doll Research) and Timur-Coates models are all unusable because not enough core samples were drilled for lab NMR experimental measurements to calibrate the involved model parameters. Based on the classification scale method (CSM), after the target tight sandstones are classified into two types, the relationship between core porosity and permeability is established for every type of formations, and the corresponding permeability estimation models are established. Field examples show that the classification scale method is effective in estimating tight sandstone permeability. 2013 The Published Authors. Published by Elsevier by Elsevier B.V. B.V. Open access under CC BY-NC-ND license. Selection and and peer peer review review under responsibility under responsibility of Information of Engineering Information Research Engineering Institute Research Institute Keywords: Tight sandstone reservoirs; Permeability; Classification scale method (CSM); SDR (Schlumberger Doll Research) model; Timur-Coates model 1. Introduction Tight sandstone reservoirs always express extreme heterogeneity, this leads to a difficulty of permeability prediction. The conventional method of predicting permeability from porosity by using the model that connects porosity and permeability is out of work, because the relationships between core derived porosity * Xiao-peng Liu. Tel.: +86-10-8232-0692. E-mail address: 13101103@qq.com. 2212-6678 2013 The Authors. Published by Elsevier B.V. Open access under CC BY-NC-ND license. Selection and peer review under responsibility of Information Engineering Research Institute doi:10.1016/j.ieri.2013.11.103
272 Xiao-peng Liu et al. / IERI Procedia 5 ( 2013 ) 271 276 and permeability cannot be established (Fahad et al. 2000Vivian et al. 2011). Fig. 1 shows a cross plot of core derived porosity vs. permeability of a typical Chinese tight sandstones. It can be observed that the relationship between core derived porosity and permeability cannot be expressed by a single function, two tendencies exist between these two parameters. 10 1 CPERM, md 0.1 0.01 0.001 0 4 8 12 16 CPOR, % Fig.1 The cross plot of core derived porosity and permeability in a Chinese tight sandstone reservoir. 2. Classical Models of Estimating Permeability from NMR Logs NMR logs have the advantage in permeability estimation (Coates et al., 2000; Xiao et al., 2009). Two classical models, which were used to estimated permeability from NMR logs, were proposed separately, and they are known as SDR (Schlumberger Doll Research Center) and Tim-Coates models(kenyon et al. 1988, 1997). The SDR and Tim-Coates models are expressed as follows: m1 n1 KSDR C1 T (1) 2lm KTIM ( ) C 2 FFI BVI m2 n2 ( ) (2) Where, KSDR is permeability estimated from the SDR model and KTIM is permeability estimated from the Timur-Coates model, their units are md; is total porosity in %; T 2lm is logarithmic mean of NMR T 2 spectra in ms; FFI is free fluid bulk in %; BVI is bulk volume irreducible in %, the value of them are predicted from NMR logs by defining an appropriate T 2cutoff, which divides the NMR T 2 spectrum into two parts( Chen et al., 2007; Xiao et al., 2012); m 1, n 1, C 1, m 2 n 2 and C 2 are statistical model parameters, their values can be derived from lab NMR experimental data sets of core samples. When not enough core samples are usable, m 1, n 1, C 1, m 2 n 2 and C 2 are assigned to empirical values of 4, 2, 10, 4, 2, and 10 respectively.
Xiao-peng Liu et al. / IERI Procedia 5 ( 2013 ) 271 276 273 In our target tight sandstones, not enough core samples were drilled for lab NMR experimental measurements. Hence, the empirical values of 4, 2, 10, 4, 2, and 10 are defined to m 1, n 1, C 1, m 2 n 2 and C 2, separately, and eqs. 1 and 2 are calibrated as follows: KSDR (3) 4 2 10 T2lm 4 2 KTIM ( ) ( ) (4) 10 FFI BVI By using the calibrated eqs. 3 and 4, a typical Chinese tight sandstone reservoir is processed, the KTIM and KSDR are predicted, and they are compared with core derived permeability, as is showed in Fig. 2. In this study, FFI and BVI are calculated from field NMR logs by using 33.0 ms as the T 2cutoff. Fig. 2 A field example of estimating permeability by using classical SDR and Tiumr-Coates models in a typical Chinese tight sandstone reservoirs. In the first track of Fig. 2, the displayed curve is gamma ray (GR), it contribution is formation indication. The second track is depth and its unit is meter. In the third track, we show the interval transit time log (DT), it is used for porosity estimation. RLLD displayed in the fourth track is deep lateral resistivity. T2_DIST displayed in the fifth track is the field NMR spectrum, which was acquired from the MRIL-C tool; KSDR and KTIM displayed in the seventh track are formation permeabilities that estimated from field NMR logs by using the SDR and Timur-Coates models, separately, and CPERM is the core analyzed permeability. From this example, it can be observed that permeability cannot be predicted from classical SDR and Timur-Coates
274 Xiao-peng Liu et al. / IERI Procedia 5 ( 2013 ) 271 276 models, and formation permeabilities are all overestimated from these two models. This may be caused by the uncorrected model parameters. In our studied, the empirical model parameters are used. However, these initial model parameters were calibrated by using experimental data that obtained from normal core samples with high porosity and high permeability, if they were directly used in tight sandstones, many more errors should be introduced. 3. Permeability Estimation by Using Classification Scale Method (CSM) Mao et al. (2013) pointed out that permeability can be well estimated by using classification scale method (CSM) in inhomogeneous low permeability reservoirs [8]. The principle of classification scale method is that core samples are first classified into several types by using some classification standards; second, the relationship between core derived porosity and permeability is established for every type of core samples; finally, formations are classified by using the same classification standards, the corresponding relationships are used, and the consecutive formation permeability should be estimated. In Mao s study, formations were classified into three types of X2, X4 and X6 sections by using the depth difference, and good permeability estimated models were established for every type of formations. Following the classification scale method proposed by Mao et al. (2013), our studied tight sandstone reservoirs were classified into wto types by using the depth difference, they are J1 and J2 sections. For every section, the data set showed in Fig. 1 are reused, the relationship of core derived porosity and permeability are established, and they are displayed in Figs. 3 and 4. Log(K ) 0-1 -2 y = 0.0024x 3-0.0475x 2 + 0.3797x - 2.804 R 2 = 0.7082 Log(K ) 2 1 0-1 -2 y = 0.0031x 3-0.0526x 2 + 0.3752x - 2.729 R 2 = 0.8332-3 0 3 6 9 12 15 CPOR, % -3 0 4 8 12 16 CPOR, % Fig. 3 Relationship between core analyzed porosity and permeability in the J1 section. Fig. 4 Relationship between core analyzed porosity and permeability in the J2 section. From the displayed relationships in Figs. 3and 4, it can be observed that after formations are classified into two types, good relationships between core derived porosity and permeability can be obtained, the correlation coefficients are all high enough, once formations are classified and the corresponding models are used, accurate permeability should be predicted.
Xiao-peng Liu et al. / IERI Procedia 5 ( 2013 ) 271 276 275 4. Case study Following the proposed classification standard, our target tight sandstone reservoirs are classified, the corresponding permeability estimation models are used, and accurate permeabilities are estimated. Fig. 5 shows a field example of permeability estimation by using the proposed models showed in Figs. 3 and 4. The physical significance of these curves, shown in the first five tracks, is the same as that of the curves in Fig. 2. POR displayed in the sixth track is predicted porosity by using DT, and CPOR is the core analyzed porosity, this track illustrates that the predicted porosity from conventional logs is accurate, there will be little error when it is applied in permeability estimation. It can be observed that by introducing the classification scale method, permeabilities are well estimated, the predicted permeabilitied (PERM in the sixth track) are coincided with the core analyzed results very well. Fig. 5 A field example of estimating tight sandstone permeability by using the classification scale method. 5. Conclusions (1) Tight sandstone permeability cannot be effectively estimated by using the single relationship for all formations due to the extreme heterogeneity. The classical SDR and Timur-Coated models are also unused in
276 Xiao-peng Liu et al. / IERI Procedia 5 ( 2013 ) 271 276 our target tight sandstone reservoirs because not enough core samples were drilled for lab NMR measurements to calibrate the involved model parameters. (2) Once formations are classified into two types by using the depth difference, good relationships of core derived porosity and permeability can be established. After these relationships are used into field applications, accurate permeabilities can be estimated. Acknowledgements We sincerely acknowledge the anonymous reviewers whose correlations and comments have greatly improved the manuscript. We also thanks for the supports of Southwest Petroleum University. References [1] Coates, G.R., Xiao, L.Z., Primmer, M.G., NMR logging principles and applications. Gulf Publishing Company, Houston, 2000: 45-132. USA. [2] Chen, S.H., Chen, J.S., Gillen, M., Georgi, D., A new approach for obtaining Swir from NMR log without requiring T2cutoff. 2008, Paper DD presented at the 49th SPWLA Annual Logging Symposium. [3] Fahad, A.A.A., Stephen, A.H., Permeability estimation using hydraulic flow units in a central Arabia reservoir, 2000, SPE63254. [4] Kenyon, W.E., Day, P.I., Straley,C., Willemsen, J.F., A three-part study of NMR longitudinal relaxation properties of water-saturated sandstones. SPE Formation Evaluation, 1988, 3(3): 622-636. [5] Kenyon, W.E., Petrophysical principles of applications of NMR logging. The Log Analysis, 1997, 38(3): 21-43. [6] Mao, Z.Q., Xiao, L., Wang, Z.N., Jin, Y., Liu, X.G., Xie, B., Estimation of permeability by integrating nuclear magnetic resonance (NMR) logs with mercury injection capillary pressure (MICP) data in tight gas sands. 2013, 44(4): 449-468. [7] Straley, C., Morriss, C.E., Kenyon, W.E., NMR in partially saturated rocks: laboratory insights on free fluid index and comparison with borehole logs. 1991, Paper CC presented at SPWLA 32nd Annual Logging Symposium. [8] Timur, A., An investigation of permeability, porosity, and residual water saturation relationships. 1968, Paper Jpresented at the 9th SPWLA Annual Logging Symposium. [9] Vivian, K.B., Joshua, U.O., Paul, F.W., The challenges for carbonate petrophysics in petroleum resource estimation. SPE Reservoir Evaluation & Engineering, 2011, 14(1): 25-34. [10] Xiao, L., Mao, Z.Q., Wang, Z.N., Jin, Y., Liu, X.G., Xie, B., Comparison Study of Models for Calculating Absolute Permeability Using Nuclear Magnetic Resonance Imaging Log Technology in Tight Sandstone Gas Zones, 2009, SPE126408. [11] Xiao, L., Mao, Z.Q., Jin, Y., Estimation of saturation exponent from nuclear magnetic resonance (NMR) logs in low permeability reservoirs. Applied Magnetic Resonance, 2012, 42(1): 113-125.