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Corrections for downhole NMR logging

Corrections for downhole NMR logging resistivity, formation resistivity and sodium ions influence its radio frequency (RF) field strength and NMR logging signals. Research on these effects can provide an important basis for NMR logging data acquisition and interpretation. Three models, water-based drilling mud—water bearing formation, water- based drilling mud—oil bearing formation, oil-based drilling mud—water bearing formation, were studied by finite element method numerical simulation. The influences of drilling mud resistivity and formation resistivity on the NMR logging tool RF ¿ eld and the inÀ uences of sodium ions on the NMR logging signals were simulated numerically. On the basis of analysis, RF ¿eld correction and sodium ion correction formulae were proposed and their application range was also discussed. The results indicate that when drilling mud resistivity and formation resistivity are 0.02 ȍÂm and 0.2 ȍÂm respectively, the attenuation index of centric NMR logging tool is 8.9% and 9.47% respectively. The RF ¿ eld of an eccentric NMR logging tool is affected mainly by formation resistivity. When formation resistivity is 0.1 m, the attenuation index is 17.5%. For centric NMR logging tools, the signals coming from sodium ions can be up to 31.8% of total signal. Suggestions are proposed for further research into NMR logging tool correction method and response characteristics. NMR logging, ¿nite element method, RF ¿eld, NMR signal, formation resistivity, sodium Key words: ions also produce an NMR signal (Headley, 1973; Ferris et al, 1 Introduction 1993). On the one hand, sodium NMR signals decrease the Nuclear magnetic resonance (NMR) logging (Coates et al, NMR logging signal to noise ratio (SNR); while on the other 1999) is an open hole logging technique, which can provide hand, sodium NMR signals add to the hydrogen NMR signals, effective porosity (Xie et al, 200 ; 2008; Wang et al, 200 ), which can result in an overestimate of the porosity calculated free À uid porosity, bound water porosity, pore size distribution from NMR logging data (Xiao, 2007). For the MRIL-C NMR and permeability. It contains no contribution from the matrix logging tool, the research results showed that a high salinity materials and does not need to be calibrated for formation borehole had little effect on the electromagnetic waves and lithology. The first step of making an NMR measurement more influences on antenna Q. Sodium ions had influences is to polarize magnetic nuclei in the formation with a static on fast-decay components in T distribution, and these effects magnetic ¿ eld B and then these magnetic nuclei are excited could be eliminated with software or À uid excluder, but the by radio frequency (RF) ¿eld B generated by antenna which latter reduced the performance of the tool (Mardon et al, is also used to receive the NMR signal. These NMR data can 1995). So for the new centric and eccentric NMR logging be used for evaluating oil and gas resources. However, the tools, researching the inÀuence of borehole Àuid resistivity on resistivity of drilling mud in the borehole and formation Àuid the NMR logging RF ¿eld, analyzing the in Àuence of sodium has an inÀuence that cannot be ignored on the NMR logging ions on NMR logging signals, and developing corresponding RF field when NMR logging tool is being used downhole. correction methods have great significance to increase the This is because low resistivity drilling mud and formation SNR (Xie et al, 2010) of NMR logging data, heighten the Àuid have good electrical conductivity, which has signi ¿cant effect of NMR logging application in the oil industry, and attenuation effects on the NMR logging tool RF field and develop new techniques (Sun and Dunn, 2005; Xie and Xiao, leads to low antenna ef¿ciency, low gain and low antenna Q 2009) and data inversion of NMR logging (Xiao et al, 2009; (Chen and Hursan, 2010). In general, low resistivity drilling Sun et al, 2009; 2010). mud and formation À uid are due to the high salinity of drilling In this paper, corresponding models were established mud and formation Àuid which contain sodium ions that will for researching the influence of drilling mud resistivity and formation resistivity on centric and eccentric NMR logging tools, and corresponding correction equation was developed, Corresponding author. email xiaolizhi #cup.edu.cn the application range was also discussed. In addition, the Received April 2, 2011 influence mechanism of sodium ions on NMR logging ȍ Pet.Sci.(2012)94-52 47 signals was analyzed, and the relevant correction method was The FEM is used to discretize computational domain ȍ , developed based on numerical simulation. and the global equation is ¿nally obtained 2 Establishing models and analysis of factors KA R > @ ^ ` (3) ^ ` affecting NMR logging response where [K@ is coef¿ cient matrix; ^ } is the solution matrix; ^ R} is the known matrix. The vector potential can be 2.1 Numerical simulation theory and model A obtained by solving Eq. (3), and the magnetic Àux density establishment is obtained from Eq. (1). In this paper, the inÀuences of drilling mud resistivity and As shown in Fig. 1, NMR logging tools can be classi¿ed formation resistivity on NMR logging tools were analyzed by as centric (Prammer et al, 2001) and eccentric (Reiderman electromagnetic ¿eld ¿nite element method (FEM) numerical and Beard, 2003) according to their working mode. When the simulation. According to Maxwell equations vector is centric NMR logging tool is down the borehole, the NMR de¿ned as sensor is situated in the center of borehole and NMR sensor ww A A shell does not contact the borehole wall, so drilling mud is zz B ’u Ai  j (1) present between the NMR sensor shell and the borehole wall. ww yx Drilling mud conductivity has great inÀuence on the detection where B is the magnetic flux density; is the vector performance of NMR logging tool sensors. This is because the potential. Assuming computational domain is ȍ , and NMR logging tool RF ¿eld is an alternating electromagnetic boundary is ī , the problem satisfies known boundary ¿ eld. Low resistivity drilling mud will directly attenuate the A | A conditions and vector potential A satisfies z * z 0 1 RF ¿eld, and then RF ¿eld strength in sensitive volume may w A not reach the required level for tipping magnetization. As a | P H . The following functional can be obtained by * t result, drilling mud resistivity R >0.02 ȍÂm is required for w n variational principle centric NMR logging tools. The active part of the sensor of the eccentric NMR logging tool is held in contact with the &) borehole wall by pressure against the opposite side of the ­½ ªº &) §· §· 1 ww AA °° borehole. There is no or a little drilling mud between them, so «» :3  ( A)   J A dd xy ¨¸ ¨¸ ®¾ ¨¸ ¨¸ 2P ww xy « » the eccentric NMR logging tool is almost immune to drilling ©¹ ©¹ °° ¬ ¼ ¯¿ (2) mud resistivity. However, if the formation is water bearing, H Al d min t the measurements of NMR logging will still be affected. Because oil and gas have high resistivity, their inÀ uence *  AA on the NMR RF field can be ignored. Here, three models, water-based drilling mud—water bearing formation, water- where H is a tangential component of magnetic field based drilling mud—oil bearing formation, oil-based drilling intensity; ȝ is magnetic permeability; J is electric current mud—water bearing formation, were analyzed. density vector. As an open hole logging technique, the distance of Centric NMR Eccentric NMR logging sensor Formation Formation logging sensor Borehole Drilling mud Borehole Drilling mud Antenna 6 in 5 in 7.875 in 7.875 in (a) (b) Fig. 1 The working mode of NMR logging tools (a) Centric NMR logging tool; (b) Eccentric NMR logging tool )& )& ³³ )& )& )& )& )& )& )& )& )& )& )& )& 48 Pet.Sci.(2012)94-52 investigation (DOI) of NMR logging tools does not exceed where Ȗ is the gyromagnetic ratio, which is a measure of 12 cm. After formation invasion, the DOI is contained in the the strength of the nuclear magnetism. For hydrogen, Ȗ /2ʌ = flush zone. The distance and extent of formation invasion 42.58 MHz/T; for sodium, Ȗ/2 ʌ = 11.22 MHz/T. increases with the passage of time, so models analyzed in The centric NMR static field is a gradient field, which this paper are established at formation invasion start and reduces with distance from the tool. When DOI is 8 cm, the -2 formation invasion end. The models established at formation static ¿eld strength is 1.8×10 T, and the operation frequency invasion start are applied to NMR logging while drilling, and is 7 kHz. According to Eq. (4), the static ¿ eld strength of -2 the models established at formation invasion end are applied sodium ions on resonance is about  .8×10 T. So, if drilling to NMR logging when the formation invasion extent exceeds mud and formation À uid rich in sodium exist near the NMR the DOI of NMR logging tools. logging tool shell, the sodium ions will produce NMR signals which are added to the hydrogen NMR signals. This not only 2.2 The influence of drilling mud resistivity and decreases the NMR logging signal-to-noise ratio (SNR) but formation resistivity on the NMR logging tool RF also leads to the porosity calculated from NMR logging data ¿eld being an overestimate. So, proper correction is required to eliminate the influence and improve the accuracy of NMR 2.2.1 Water-based drilling mud—water bearing formation logging porosity. Water-based drilling mud is widely used, both onshore and offshore. Especially for offshore drilling, water-based 3 Numerical simulation and correction drilling mud is drilling engineers’ favorite choice. However, because it has low resistivity, the measurements of some method of NMR logging response logging tools will be affected, for example, electric logging, electromagnetic logging, and NMR logging, and these 3.1 Centric NMR logging tools inÀuences should not be ignored. The centric NMR logging tool is called MRIL-P by the (a) For centric NMR logging tools, because drilling mud Halliburton Company. This tool has a gradient magnetic and formation are present within the sensitive volume, the field produced by a cylindrical permanent magnet and this water-based drilling mud—water bearing formation model is static ¿ eld is distributed symmetrically around the borehole. analyzed. The sensitive volume of MRIL-P is a thin cylinder which (b) When eccentric NMR logging tools are used, there is contains omnidirectional information from a 3 0° view little or no drilling mud existing between the NMR sensor around the borehole (Hu and Xiao, 2010). Its DOI is about shell and borehole wall, so the influence of drilling mud 8-12 cm. The magnetic ¿ eld distribution can be obtained by resistivity on RF ¿eld is less. However, because the eccentric FEM numerical simulation (Hu et al, 2011). Fig. 2 shows the NMR logging tool antenna has a wide angle and the size of simulation results of RF field distribution as a function of borehole is bigger than NMR sensor size, as shown in Fig. distance without the inÀuence of drilling mud and formation. 1(b), a part of the RF ¿ eld has to penetrate drilling mud and to -4 When DOI is 8 cm, the RF field strength is 5.2 ×10 T. get to the formation, so drilling mud still has some inÀuence NMR logging uses the Carr-Purcell-Meiboom-Gill (CPMG) on the eccentric NMR RF ¿eld. sequence to measure the formation Àuid. The RF pulse should 2.2.2 Water-based drilling mud—oil bearing formation rotate the net magnetization vector 90° or 180°. The angle For this model, the main factor is water-based drilling through which the magnetization is tipped is given by mud. Because of the high resistivity of oil bearing formation, it has little influence on the RF field, and the oil bearing TJ B t (5) 0 1p formation can be treated as air in numerical simulation. The water drilling mud inÀuences centric NMR logging tools, and where B is RF field strength; t is time over which the 1 p according to above-mentioned analysis, this model still has oscillating ¿eld is applied. some inÀuence on the eccentric NMR logging tool. Formation resistivity (R ) is set to 0.1, 0.2, 1, 10, 100 xo 2.2.3 Oil-based drilling mud—water bearing formation and 500 ȍÂm respectively; drilling mud resistivity ( R ) is For a centric NMR logging tool, low resistivity water- set to 0.001, 0.005, 0.01, 0.02, 0.05, 0.1, 1, 10 and 100 ȍÂm bearing formation has inÀuence on its RF ¿eld. For eccentric respectively. The model shown in Fig. 1(a) is analyzed by NMR logging tool, this model has inÀuence on it too because FEM numerical simulation. The corresponding simulation the eccentric NMR logging tool RF ¿eld still has to penetrate results of the NMR logging tool RF ¿eld in these conditions formation within the sensitive volume. are shown in Fig. 3, and the RF ¿eld strength is chosen at the point which is 8 cm away from the sensor shell surface. Here, 2.3 The inÀuence of sodium ions in drilling mud and the RF ¿eld strength attenuation index F is de¿ned as formation Àuid on NMR logging porosity B  B During the measurement of NMR logging, when B 0 1,0 1,R () is imposed on magnetic nuclei, the nuclei will precess 1,0 around B . The precession frequency (f), called the Larmor frequency, is given by where B is the RF field strength without influence of 1,0 J B drilling mud and formation; B is the RF ¿eld strength with 1,R (4) inÀuence of drilling mud and formation. 2ʌ Pet.Sci.(2012)94-52 49 in Fig. 4. The RF ¿eld strength decreases with an increase of DOI. When R =0.001 ȍÂm - 0.02 ȍÂm, F increased with the decrease of R ; when R =0.05 ȍÂm - 100 ȍÂm, the RF ¿ eld m m strength is constant, and the inÀuence of drilling mud on RF ¿eld strength can be ignored. 0.001 0.05-100 0.005 0.01 0.02 0.02 0.05 0.01 0.1 0.005 0.001 0 6 R , ·m xo 0 2 4 6 8 10 12 14 DOI, cm Fig. 2 RF ¿eld distribution of a centric NMR logging tool 0 2 4 6 8 10 12 14 DOI, cm Fig. 4 The inÀuence of water-based drilling mud—oil bearing formation on the centric NMR logging tool RF ¿eld Because the NMR logging tool sensitive volume extends out to 8 cm away from borehole wall, the RF has to penetrate 0.1 the formation within the sensitive volume. As shown in Fig. 0.2 5, the influence of oil-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld is plotted 2 as a function of R . The RF field strength decreases with xo a decrease of formation resistivity. When R =1 ȍÂm - 100 xo ȍÂm, RF ¿eld strength is constant; when R 1 ȍÂm, RF ¿eld xo 500 strength decreases with the decrease of formation resistivity, and F is up to 9.47% when R =0.2 ȍÂm. xo R , ·m xo 0.001 0.01 0.1 1 10 100 R , ·m Fig. 3 The inÀ uence of water-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld The variation of RF ¿eld strength is plotted in Fig. 3 as a function of R . When formation resistivity R =1 ȍÂm - 500 m xo ȍ m, RF field strength of centric NMR logging tool keeps almost constant. When the formation resistivity R =0.2 xo ȍÂm, the RF field strength attenuation index F =9.5%. The centric NMR logging tool RF field strength decreases with a decrease of drilling mud resistivity. When the drilling mud resistivity R =0.1 ȍÂm -100 ȍ m, the RF field strength is almost constant. When R =0.02 ȍ m, the RF field strength attenuation index F=8.9%, which is the lowest resistivity of drilling mud allowed for centric NMR logging. When R =0.01 ȍÂm, F=28.3%, which affects the NMR logging 0.1 1 10 100 signal strength and SNR seriously, so correction of the RF is R , ·m xo needed. The influence of water-based drilling mud—oil bearing Fig. 5 The inÀuence of oil-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld formation on the centric NMR logging tool RF ¿eld is shown -4 -4 B , 10 T B , 10 T -4 -4 B , 10 T B , 10 T 1 50 Pet.Sci.(2012)94-52 3.2 Eccentric NMR logging tools mud—oil bearing formation, and R =0.01 ȍÂm, the RF ¿ eld strength is constant; when the model is oil-based drilling The inÀuence of water-based drilling mud—water bearing mud—water bearing formation, and R =0.1 ȍ m, RF field xo formation on the eccentric NMR RF field is plotted in Fig. strength decreased obviously, and F=17.5%. as a function of R . Because eccentric NMR logging tool antenna has a wide angle, and the size of borehole is bigger 3.3 Drilling mud and formation resistivity inÀ uence than the NMR sensor size, a part of the RF ¿ eld still has to correction method penetrate drilling mud to get to the formation. The results According to the simulation results and analysis above, show that when R =0.01 ȍÂm, F=4.7% which is much lower drilling mud and formation resistivity have significant than that of centric NMR logging tool (F=27.95%) at the attenuation effects on the NMR logging tool RF field and same condition. these effects can be indicated by the attenuation index F. The NMR logging tool RF ¿ eld is calibrated on the ground in order to get B which is the standard value of correction 1,0 before correcting the NMR logging tool RF ¿eld for different drilling mud and formation resistivity. Then attenuation index F is used to correct the RF field. The correction method of 4 drilling mud and formation resistivity inÀuence on the NMR logging tool RF ¿eld is proposed as B BF / (1 ) (7) 0.1 1,C 1,0 where B is the RF ¿eld after correction; B is the RF ¿eld 1,C 1,0 without inÀuence; F is the attenuation index (see Table 1 and Table 2). R , ·m xo Table 1 The attenuation index of the centric NMR logging tool RF ¿eld R , ȍÂm xo R , ȍÂm 0.001 0.01 0.1 1 10 100 0.1 0.2 1 10 100 500 R , ·m 0.001 0.90 0.91 0.932 0.937 0.937 0.937 Fig. 6 The inÀuence of water-based drilling mud—water bearing formation 0.005 0.871 0.770 0.59 0.33 0.30 0.30 on the eccentric NMR logging tool RF ¿eld 0.01 0.34 0.49 0.314 0.282 0.279 0.279 The RF field strength of the eccentric NMR tool is 0.02 0.455 0.23 0.113 0.089 0.087 0.087 affected mainly by formation resistivity. Fig. 7 shows the 0.05 0.344 0.151 0.030 0.01 0.015 0.015 inÀuence of formation resistivity and drilling mud resistivity 0.1 0.309 0.120 0.014 0.005 0.004 0.004 on the RF field. When the model is water-based drilling 1 0.280 0.097 0.005 0.000 0.000 0.000 10 0.278 0.095 0.005 0.000 0.000 0.000 100 0.277 0.095 0.004 0.000 0.000 0.000 500 0.277 0.095 0.004 0.000 0.000 0.000 Table 2 The attenuation index of the eccentric NMR logging tool RF ¿eld R , ȍÂm xo R , ȍÂm 3 m 0.1 1 10 100 500 R (oil based xo drilling mud- 0.001 0.753 0.31 0.19 0.18 0.18 water bearing formation) 0.005 0.359 0.157 0.141 0.140 0.140 0.01 0.23 0.01 0.048 0.047 0.047 R (water based drilling mud- 0.02 0.214 0.022 0.014 0.013 0.013 oil bearing formation) 0.05 0.18 0.008 0.003 0.002 0.002 0.1 0.177 0.004 0.000 0.000 0.000 0.001 0.01 0.1 1 10 100 1 0.19 0.002 0.000 0.000 0.000 R, ·m 10 0.18 0.002 0.000 0.000 0.000 Fig. 7 The inÀuence of formation resistivity and drilling 100 0.18 0.002 0.000 0.000 0.000 mud resistivity on the eccentric NMR RF ¿eld -4 B , 10 T -4 B , 10 T 1 52 Pet.Sci.(2012)94-52 media containing NaCl solution. Journal of Applied Physics. 1973. to enhance the continuity of multi-dimensional NMR logs. SPWLA 44(7) 3118-3121 51th Annual Logging Symposium, 19-23 June 2010, Perth, Australia Hou lt D I and Richards R E. The signal to noise ratio of the nuclear (SPWLA YY) magnetic resonance experiment. Journal of Magnetic Resonance. Sun B Q, Skalinski M and Dunn K J. NMR T inversion along the depth 197. 24(1) 71-85 dimension. AIP Conference Proceedings. 2009. 1081 87-90 Hu H T and Xiao L Z. Investigation characteristics of NMR wireline Wan g X W, Xiao L Z, Xie R H, et al. Study of NMR porosity for logging tools. Chinese Journal of Magnetic Resonance. 2010. 27(4) terrestrial formation in China. Science in China Series G. 200 . 572-583 (in Chinese) 49(3) 313-320 Hu H T, Xiao L Z and Wu X L. A method for evaluating the performance Xia o L Z. Some important issues for NMR logging applications in of NMR logging device. Chinese Journal of Magnetic Resonance. China. Well Logging Technology. 2007. 31(5) 401-407 (in Chinese) 2011. 28(1) 7-83 (in Chinese) Xia o L Z, Liao G Z, Xie R H, et al. Inversion of NMR relaxation Hür limann M D and Griffin D D. Spin dynamics of Carr-Purcell- measurements in well logging. In Magnetic Resonance Microscopy. Meiboom-Gill-like sequences in grossly inhomogeneous B and B Weinheim WILEY-VCH Verlag GmbH & Co. KGaA. 2009. 501- 0 1 fields and application to NMR well logging. Journal of Magnetic 517 Resonance. 2000. 143(1) 120-135 Xie Q M, Xiao L Z and Liao G Z. Application of SURE algorithm to Mar don D, Prammer M G, Taicher Z, et al. Improved environmental echo train de-noising in low ¿eld NMR logging. Chinese Journal of corrections for MRIL pulsed NMR logs run in high-salinity Geophysics. 2010. 53(11) 277-2783 (in Chinese) boreholes. SPWLA 3 th Annual Logging Symposium, 2 -29 June Xie R H and Xiao L Z. The (T , D) NMR logging method for fluids 1995, Paris, France (SPWLA DD) characterization. Chinese Journal of Geophysics. 2009. 52(9) 2410- Pra mmer M G, Bouton J, Drack E D, et al. A new multiband generation 2418 (in Chinese) of NMR logging tools. SPE Reservoir Evaluation & Engineering. Xie R H, Xiao L Z and Dunn K J. NMR logging porosity activation and 2001. 4(1) 59-3 (SPE 970-PA) data processing method. Chinese Journal of Geophysics. 200 . 49(5) Rei derman A and Beard D. Side-looking NMR probe for oil well 157-1572 (in Chinese) logging. U.S.patent 580273. 2003 Xie R H, Xiao L Z, Wang Z D, et al. The influence factors of NMR Sun B Q and Dunn K J. Two-dimensional nuclear magnetic resonance logging porosity in complex Àuid reservoir. Science in China Series petrophysics. Magnetic Resonance Imaging. 2005. 23(2) 259-22 D Earth Sciences. 2008. 51(Supp.II) 212-217 Sun B Q, Dunn K J and Clinch S. Inversion along the depth dimension (Edited by Hao Jie) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Petroleum Science Springer Journals

Corrections for downhole NMR logging

Hu, Haitao; Xiao, Lizhi; Wu, Xiling
Petroleum Science , Volume 9 (1) – Jan 29, 2012
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Publisher
Springer Journals
Copyright
Copyright © 2012 by China University of Petroleum (Beijing) and Springer-Verlag Berlin Heidelberg
Subject
Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
ISSN
1672-5107
eISSN
1995-8226
DOI
10.1007/s12182-012-0181-1
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Abstract

resistivity, formation resistivity and sodium ions influence its radio frequency (RF) field strength and NMR logging signals. Research on these effects can provide an important basis for NMR logging data acquisition and interpretation. Three models, water-based drilling mud—water bearing formation, water- based drilling mud—oil bearing formation, oil-based drilling mud—water bearing formation, were studied by finite element method numerical simulation. The influences of drilling mud resistivity and formation resistivity on the NMR logging tool RF ¿ eld and the inÀ uences of sodium ions on the NMR logging signals were simulated numerically. On the basis of analysis, RF ¿eld correction and sodium ion correction formulae were proposed and their application range was also discussed. The results indicate that when drilling mud resistivity and formation resistivity are 0.02 ȍÂm and 0.2 ȍÂm respectively, the attenuation index of centric NMR logging tool is 8.9% and 9.47% respectively. The RF ¿ eld of an eccentric NMR logging tool is affected mainly by formation resistivity. When formation resistivity is 0.1 m, the attenuation index is 17.5%. For centric NMR logging tools, the signals coming from sodium ions can be up to 31.8% of total signal. Suggestions are proposed for further research into NMR logging tool correction method and response characteristics. NMR logging, ¿nite element method, RF ¿eld, NMR signal, formation resistivity, sodium Key words: ions also produce an NMR signal (Headley, 1973; Ferris et al, 1 Introduction 1993). On the one hand, sodium NMR signals decrease the Nuclear magnetic resonance (NMR) logging (Coates et al, NMR logging signal to noise ratio (SNR); while on the other 1999) is an open hole logging technique, which can provide hand, sodium NMR signals add to the hydrogen NMR signals, effective porosity (Xie et al, 200 ; 2008; Wang et al, 200 ), which can result in an overestimate of the porosity calculated free À uid porosity, bound water porosity, pore size distribution from NMR logging data (Xiao, 2007). For the MRIL-C NMR and permeability. It contains no contribution from the matrix logging tool, the research results showed that a high salinity materials and does not need to be calibrated for formation borehole had little effect on the electromagnetic waves and lithology. The first step of making an NMR measurement more influences on antenna Q. Sodium ions had influences is to polarize magnetic nuclei in the formation with a static on fast-decay components in T distribution, and these effects magnetic ¿ eld B and then these magnetic nuclei are excited could be eliminated with software or À uid excluder, but the by radio frequency (RF) ¿eld B generated by antenna which latter reduced the performance of the tool (Mardon et al, is also used to receive the NMR signal. These NMR data can 1995). So for the new centric and eccentric NMR logging be used for evaluating oil and gas resources. However, the tools, researching the inÀuence of borehole Àuid resistivity on resistivity of drilling mud in the borehole and formation Àuid the NMR logging RF ¿eld, analyzing the in Àuence of sodium has an inÀuence that cannot be ignored on the NMR logging ions on NMR logging signals, and developing corresponding RF field when NMR logging tool is being used downhole. correction methods have great significance to increase the This is because low resistivity drilling mud and formation SNR (Xie et al, 2010) of NMR logging data, heighten the Àuid have good electrical conductivity, which has signi ¿cant effect of NMR logging application in the oil industry, and attenuation effects on the NMR logging tool RF field and develop new techniques (Sun and Dunn, 2005; Xie and Xiao, leads to low antenna ef¿ciency, low gain and low antenna Q 2009) and data inversion of NMR logging (Xiao et al, 2009; (Chen and Hursan, 2010). In general, low resistivity drilling Sun et al, 2009; 2010). mud and formation À uid are due to the high salinity of drilling In this paper, corresponding models were established mud and formation Àuid which contain sodium ions that will for researching the influence of drilling mud resistivity and formation resistivity on centric and eccentric NMR logging tools, and corresponding correction equation was developed, Corresponding author. email xiaolizhi #cup.edu.cn the application range was also discussed. In addition, the Received April 2, 2011 influence mechanism of sodium ions on NMR logging ȍ Pet.Sci.(2012)94-52 47 signals was analyzed, and the relevant correction method was The FEM is used to discretize computational domain ȍ , developed based on numerical simulation. and the global equation is ¿nally obtained 2 Establishing models and analysis of factors KA R > @ ^ ` (3) ^ ` affecting NMR logging response where [K@ is coef¿ cient matrix; ^ } is the solution matrix; ^ R} is the known matrix. The vector potential can be 2.1 Numerical simulation theory and model A obtained by solving Eq. (3), and the magnetic Àux density establishment is obtained from Eq. (1). In this paper, the inÀuences of drilling mud resistivity and As shown in Fig. 1, NMR logging tools can be classi¿ed formation resistivity on NMR logging tools were analyzed by as centric (Prammer et al, 2001) and eccentric (Reiderman electromagnetic ¿eld ¿nite element method (FEM) numerical and Beard, 2003) according to their working mode. When the simulation. According to Maxwell equations vector is centric NMR logging tool is down the borehole, the NMR de¿ned as sensor is situated in the center of borehole and NMR sensor ww A A shell does not contact the borehole wall, so drilling mud is zz B ’u Ai  j (1) present between the NMR sensor shell and the borehole wall. ww yx Drilling mud conductivity has great inÀuence on the detection where B is the magnetic flux density; is the vector performance of NMR logging tool sensors. This is because the potential. Assuming computational domain is ȍ , and NMR logging tool RF ¿eld is an alternating electromagnetic boundary is ī , the problem satisfies known boundary ¿ eld. Low resistivity drilling mud will directly attenuate the A | A conditions and vector potential A satisfies z * z 0 1 RF ¿eld, and then RF ¿eld strength in sensitive volume may w A not reach the required level for tipping magnetization. As a | P H . The following functional can be obtained by * t result, drilling mud resistivity R >0.02 ȍÂm is required for w n variational principle centric NMR logging tools. The active part of the sensor of the eccentric NMR logging tool is held in contact with the &) borehole wall by pressure against the opposite side of the ­½ ªº &) §· §· 1 ww AA °° borehole. There is no or a little drilling mud between them, so «» :3  ( A)   J A dd xy ¨¸ ¨¸ ®¾ ¨¸ ¨¸ 2P ww xy « » the eccentric NMR logging tool is almost immune to drilling ©¹ ©¹ °° ¬ ¼ ¯¿ (2) mud resistivity. However, if the formation is water bearing, H Al d min t the measurements of NMR logging will still be affected. Because oil and gas have high resistivity, their inÀ uence *  AA on the NMR RF field can be ignored. Here, three models, water-based drilling mud—water bearing formation, water- where H is a tangential component of magnetic field based drilling mud—oil bearing formation, oil-based drilling intensity; ȝ is magnetic permeability; J is electric current mud—water bearing formation, were analyzed. density vector. As an open hole logging technique, the distance of Centric NMR Eccentric NMR logging sensor Formation Formation logging sensor Borehole Drilling mud Borehole Drilling mud Antenna 6 in 5 in 7.875 in 7.875 in (a) (b) Fig. 1 The working mode of NMR logging tools (a) Centric NMR logging tool; (b) Eccentric NMR logging tool )& )& ³³ )& )& )& )& )& )& )& )& )& )& )& )& 48 Pet.Sci.(2012)94-52 investigation (DOI) of NMR logging tools does not exceed where Ȗ is the gyromagnetic ratio, which is a measure of 12 cm. After formation invasion, the DOI is contained in the the strength of the nuclear magnetism. For hydrogen, Ȗ /2ʌ = flush zone. The distance and extent of formation invasion 42.58 MHz/T; for sodium, Ȗ/2 ʌ = 11.22 MHz/T. increases with the passage of time, so models analyzed in The centric NMR static field is a gradient field, which this paper are established at formation invasion start and reduces with distance from the tool. When DOI is 8 cm, the -2 formation invasion end. The models established at formation static ¿eld strength is 1.8×10 T, and the operation frequency invasion start are applied to NMR logging while drilling, and is 7 kHz. According to Eq. (4), the static ¿ eld strength of -2 the models established at formation invasion end are applied sodium ions on resonance is about  .8×10 T. So, if drilling to NMR logging when the formation invasion extent exceeds mud and formation À uid rich in sodium exist near the NMR the DOI of NMR logging tools. logging tool shell, the sodium ions will produce NMR signals which are added to the hydrogen NMR signals. This not only 2.2 The influence of drilling mud resistivity and decreases the NMR logging signal-to-noise ratio (SNR) but formation resistivity on the NMR logging tool RF also leads to the porosity calculated from NMR logging data ¿eld being an overestimate. So, proper correction is required to eliminate the influence and improve the accuracy of NMR 2.2.1 Water-based drilling mud—water bearing formation logging porosity. Water-based drilling mud is widely used, both onshore and offshore. Especially for offshore drilling, water-based 3 Numerical simulation and correction drilling mud is drilling engineers’ favorite choice. However, because it has low resistivity, the measurements of some method of NMR logging response logging tools will be affected, for example, electric logging, electromagnetic logging, and NMR logging, and these 3.1 Centric NMR logging tools inÀuences should not be ignored. The centric NMR logging tool is called MRIL-P by the (a) For centric NMR logging tools, because drilling mud Halliburton Company. This tool has a gradient magnetic and formation are present within the sensitive volume, the field produced by a cylindrical permanent magnet and this water-based drilling mud—water bearing formation model is static ¿ eld is distributed symmetrically around the borehole. analyzed. The sensitive volume of MRIL-P is a thin cylinder which (b) When eccentric NMR logging tools are used, there is contains omnidirectional information from a 3 0° view little or no drilling mud existing between the NMR sensor around the borehole (Hu and Xiao, 2010). Its DOI is about shell and borehole wall, so the influence of drilling mud 8-12 cm. The magnetic ¿ eld distribution can be obtained by resistivity on RF ¿eld is less. However, because the eccentric FEM numerical simulation (Hu et al, 2011). Fig. 2 shows the NMR logging tool antenna has a wide angle and the size of simulation results of RF field distribution as a function of borehole is bigger than NMR sensor size, as shown in Fig. distance without the inÀuence of drilling mud and formation. 1(b), a part of the RF ¿ eld has to penetrate drilling mud and to -4 When DOI is 8 cm, the RF field strength is 5.2 ×10 T. get to the formation, so drilling mud still has some inÀuence NMR logging uses the Carr-Purcell-Meiboom-Gill (CPMG) on the eccentric NMR RF ¿eld. sequence to measure the formation Àuid. The RF pulse should 2.2.2 Water-based drilling mud—oil bearing formation rotate the net magnetization vector 90° or 180°. The angle For this model, the main factor is water-based drilling through which the magnetization is tipped is given by mud. Because of the high resistivity of oil bearing formation, it has little influence on the RF field, and the oil bearing TJ B t (5) 0 1p formation can be treated as air in numerical simulation. The water drilling mud inÀuences centric NMR logging tools, and where B is RF field strength; t is time over which the 1 p according to above-mentioned analysis, this model still has oscillating ¿eld is applied. some inÀuence on the eccentric NMR logging tool. Formation resistivity (R ) is set to 0.1, 0.2, 1, 10, 100 xo 2.2.3 Oil-based drilling mud—water bearing formation and 500 ȍÂm respectively; drilling mud resistivity ( R ) is For a centric NMR logging tool, low resistivity water- set to 0.001, 0.005, 0.01, 0.02, 0.05, 0.1, 1, 10 and 100 ȍÂm bearing formation has inÀuence on its RF ¿eld. For eccentric respectively. The model shown in Fig. 1(a) is analyzed by NMR logging tool, this model has inÀuence on it too because FEM numerical simulation. The corresponding simulation the eccentric NMR logging tool RF ¿eld still has to penetrate results of the NMR logging tool RF ¿eld in these conditions formation within the sensitive volume. are shown in Fig. 3, and the RF ¿eld strength is chosen at the point which is 8 cm away from the sensor shell surface. Here, 2.3 The inÀuence of sodium ions in drilling mud and the RF ¿eld strength attenuation index F is de¿ned as formation Àuid on NMR logging porosity B  B During the measurement of NMR logging, when B 0 1,0 1,R () is imposed on magnetic nuclei, the nuclei will precess 1,0 around B . The precession frequency (f), called the Larmor frequency, is given by where B is the RF field strength without influence of 1,0 J B drilling mud and formation; B is the RF ¿eld strength with 1,R (4) inÀuence of drilling mud and formation. 2ʌ Pet.Sci.(2012)94-52 49 in Fig. 4. The RF ¿eld strength decreases with an increase of DOI. When R =0.001 ȍÂm - 0.02 ȍÂm, F increased with the decrease of R ; when R =0.05 ȍÂm - 100 ȍÂm, the RF ¿ eld m m strength is constant, and the inÀuence of drilling mud on RF ¿eld strength can be ignored. 0.001 0.05-100 0.005 0.01 0.02 0.02 0.05 0.01 0.1 0.005 0.001 0 6 R , ·m xo 0 2 4 6 8 10 12 14 DOI, cm Fig. 2 RF ¿eld distribution of a centric NMR logging tool 0 2 4 6 8 10 12 14 DOI, cm Fig. 4 The inÀuence of water-based drilling mud—oil bearing formation on the centric NMR logging tool RF ¿eld Because the NMR logging tool sensitive volume extends out to 8 cm away from borehole wall, the RF has to penetrate 0.1 the formation within the sensitive volume. As shown in Fig. 0.2 5, the influence of oil-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld is plotted 2 as a function of R . The RF field strength decreases with xo a decrease of formation resistivity. When R =1 ȍÂm - 100 xo ȍÂm, RF ¿eld strength is constant; when R 1 ȍÂm, RF ¿eld xo 500 strength decreases with the decrease of formation resistivity, and F is up to 9.47% when R =0.2 ȍÂm. xo R , ·m xo 0.001 0.01 0.1 1 10 100 R , ·m Fig. 3 The inÀ uence of water-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld The variation of RF ¿eld strength is plotted in Fig. 3 as a function of R . When formation resistivity R =1 ȍÂm - 500 m xo ȍ m, RF field strength of centric NMR logging tool keeps almost constant. When the formation resistivity R =0.2 xo ȍÂm, the RF field strength attenuation index F =9.5%. The centric NMR logging tool RF field strength decreases with a decrease of drilling mud resistivity. When the drilling mud resistivity R =0.1 ȍÂm -100 ȍ m, the RF field strength is almost constant. When R =0.02 ȍ m, the RF field strength attenuation index F=8.9%, which is the lowest resistivity of drilling mud allowed for centric NMR logging. When R =0.01 ȍÂm, F=28.3%, which affects the NMR logging 0.1 1 10 100 signal strength and SNR seriously, so correction of the RF is R , ·m xo needed. The influence of water-based drilling mud—oil bearing Fig. 5 The inÀuence of oil-based drilling mud—water bearing formation on the centric NMR logging tool RF ¿eld formation on the centric NMR logging tool RF ¿eld is shown -4 -4 B , 10 T B , 10 T -4 -4 B , 10 T B , 10 T 1 50 Pet.Sci.(2012)94-52 3.2 Eccentric NMR logging tools mud—oil bearing formation, and R =0.01 ȍÂm, the RF ¿ eld strength is constant; when the model is oil-based drilling The inÀuence of water-based drilling mud—water bearing mud—water bearing formation, and R =0.1 ȍ m, RF field xo formation on the eccentric NMR RF field is plotted in Fig. strength decreased obviously, and F=17.5%. as a function of R . Because eccentric NMR logging tool antenna has a wide angle, and the size of borehole is bigger 3.3 Drilling mud and formation resistivity inÀ uence than the NMR sensor size, a part of the RF ¿ eld still has to correction method penetrate drilling mud to get to the formation. The results According to the simulation results and analysis above, show that when R =0.01 ȍÂm, F=4.7% which is much lower drilling mud and formation resistivity have significant than that of centric NMR logging tool (F=27.95%) at the attenuation effects on the NMR logging tool RF field and same condition. these effects can be indicated by the attenuation index F. The NMR logging tool RF ¿ eld is calibrated on the ground in order to get B which is the standard value of correction 1,0 before correcting the NMR logging tool RF ¿eld for different drilling mud and formation resistivity. Then attenuation index F is used to correct the RF field. The correction method of 4 drilling mud and formation resistivity inÀuence on the NMR logging tool RF ¿eld is proposed as B BF / (1 ) (7) 0.1 1,C 1,0 where B is the RF ¿eld after correction; B is the RF ¿eld 1,C 1,0 without inÀuence; F is the attenuation index (see Table 1 and Table 2). R , ·m xo Table 1 The attenuation index of the centric NMR logging tool RF ¿eld R , ȍÂm xo R , ȍÂm 0.001 0.01 0.1 1 10 100 0.1 0.2 1 10 100 500 R , ·m 0.001 0.90 0.91 0.932 0.937 0.937 0.937 Fig. 6 The inÀuence of water-based drilling mud—water bearing formation 0.005 0.871 0.770 0.59 0.33 0.30 0.30 on the eccentric NMR logging tool RF ¿eld 0.01 0.34 0.49 0.314 0.282 0.279 0.279 The RF field strength of the eccentric NMR tool is 0.02 0.455 0.23 0.113 0.089 0.087 0.087 affected mainly by formation resistivity. Fig. 7 shows the 0.05 0.344 0.151 0.030 0.01 0.015 0.015 inÀuence of formation resistivity and drilling mud resistivity 0.1 0.309 0.120 0.014 0.005 0.004 0.004 on the RF field. When the model is water-based drilling 1 0.280 0.097 0.005 0.000 0.000 0.000 10 0.278 0.095 0.005 0.000 0.000 0.000 100 0.277 0.095 0.004 0.000 0.000 0.000 500 0.277 0.095 0.004 0.000 0.000 0.000 Table 2 The attenuation index of the eccentric NMR logging tool RF ¿eld R , ȍÂm xo R , ȍÂm 3 m 0.1 1 10 100 500 R (oil based xo drilling mud- 0.001 0.753 0.31 0.19 0.18 0.18 water bearing formation) 0.005 0.359 0.157 0.141 0.140 0.140 0.01 0.23 0.01 0.048 0.047 0.047 R (water based drilling mud- 0.02 0.214 0.022 0.014 0.013 0.013 oil bearing formation) 0.05 0.18 0.008 0.003 0.002 0.002 0.1 0.177 0.004 0.000 0.000 0.000 0.001 0.01 0.1 1 10 100 1 0.19 0.002 0.000 0.000 0.000 R, ·m 10 0.18 0.002 0.000 0.000 0.000 Fig. 7 The inÀuence of formation resistivity and drilling 100 0.18 0.002 0.000 0.000 0.000 mud resistivity on the eccentric NMR RF ¿eld -4 B , 10 T -4 B , 10 T 1 52 Pet.Sci.(2012)94-52 media containing NaCl solution. 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Published: Jan 29, 2012

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