Deformation and failure of rock samples probed by T1 and T2 relaxation C.H. van der Zwaag*, E. Veliyulin, T. Skjetne, A.E. Lothe, R.M. Holt, O.M. Nes SINTEF, N-7465 Trondheim, Norway Abstract The objective of the study was to pinpoint the effect of stress induced rock matrix alterations on NMR-wireline-log measurements by means of laboratory T1 and T2 relaxation time measurements. The research activities were subdivided into two major parts: [1] NMR relaxation measurements on a brine saturated outcrop sandstone (Red Wildmoor Sandstone) during uniaxial compressional tests and [2] NMR relaxation measurements on artificial sandstone samples prepared with defined crack patterns. T1-measurements performed on Red Wildmoor samples during compaction showed a decrease in the mean relaxation rate 1/exp�ln (T1) up to a point assumed to characterize the yield strength of the rock. The rate decreased most probably as a result of the compaction of micropores. This trend was reversed when the rock failed. The relaxation rate increased again, most probably through the generation of fresh mineral surfaces at broken cementations or grain contacts. T2-relaxation was measured on artificial sandstone samples using CPMG pulse sequences with echo times between 175 �s and 1400 �s. Samples with larger crack volumes and crack orientation orthogonal to the B0-field showed consistently smaller exp�ln (T2) than the samples without any cracks. Further calculations indicate that internal magnetic field gradients were largest for samples having a larger number of cracks and crack orientations orthogonal to the B0-field. © 2003 Elsevier Inc. All rights reserved. Keywords: T1 and T2 relaxation; Rock mechanics; Matrix anisotropies; Sandstones 1. Introduction NMR well-logging measurements probe the wellbore envi- ronment at a short distance from the wellbore wall in order to isolate productive zones and to assess reservoir volume and flow capacity. However, the rock properties in the near well- bore zone may be altered by the mechanical impact of the drilling process or through the redistribution of stresses. Stresses exceeding the strength of the rock initiate the deformation of the rock matrix and may cause subsequent failure. The generation of fissures, cracks or fractures due to failure may affect petrophysical parameters as the rock porosity, pore size distributions and rock permeability. So far, little attention has been given to the effect of stress-induced anisotropies in a rock matrix on NMR signal response. The objective of this study was to gain a general perception of stress induced matrix alterations and their effect on NMR-log measurements. To approach the objective two separate studies were performed: NMR relaxation time measurements on sand- stone samples under stress and NMR relaxation time mea- surements on artificial sandstone samples prepared with defined crack patterns 2. Method A: measurements on sandstone samples under stress 2.1. Method To observe the effect of compression and failure on NMR relaxation measurements, a NMR-spectrometer was integrated into rock mechanical test equipment. The draw- ing in Fig. 1 illustrates the measurement set-up. Rock me- chanical measurements were performed as drained, uniaxial compression tests. The cylindrical sandstone sample, a Red Wildmoor sandstone with sample dimensions D � 38 mm, L � 76 mm, was loaded to distinct stress levels. These were increased until rock failure at a load of 5 MPa. 1H-NMR- measurements at 2 MHz proton resonance fre- quency were performed on brine saturated Red Wildmoor sandstone samples under increasing axial load at otherwise ambient conditions. The longitudinal relaxation time T1 was * Corresponding author. Tel.: �45-51876770. E-mail address:
[email protected] (C. van der Zwaag). Magnetic Resonance Imaging 21 (2003) 405–407 0730-725X/03/$ – see front matter © 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0730-725X(03)00151-6 measured using an inversion recovery pulse sequence. T1 re- laxation time distributions were calculated using a multi-expo- nential fitting routine (Sezginger, 1991-1994) and an average T1-value exp�ln (T1) was calculated from the distribution. Comparing two successive T1 measurements on the rock sam- ple under different axial load but otherwise constant conditions allowed to reduce data according to Eqn. 1. � 1 T1 � 1 T1,n � 1 T1,0 � �1,n� SnVn� � �1,0� S0V0� (1) where: �1 is surface relaxivity and S/V is surface to volume ratio. The index o denotes a reference point measurement and the index n a subsequent measurement. The reference point is here the measurement on the rock at zero load. 3. Results and discussion Fig. 2 shows the relaxation rate difference �(1/T1) plot- ted versus increasing stress levels. The rate difference is decreasing up to 4 MPa axial load, while values beyond 4 MPa are increasing again. As the Red Wildmoor sandstone is a rather weakly consol- idated sandstone, it can be expected that grains redistribute and an increasing number of pores are closed with increasing load. Pore closing starts with the smallest pores. As their contribu- tions disappear in loaded state, relaxation rates for the entire rock shift to overall smaller values. When the axial stress exceeds strength, grain bonds ultimately break and the rock starts failing. Fresh mineral surfaces at broken cementations or grain contacts are generated and surface relaxivity is assumed to increase. This process introduces rock components contrib- uting with faster relaxation. The overall relaxation rate in- creases after failure, as seen in Fig. 2 at axial stresses of 5 MPa. 4. Method B: measurements on artificial sandstone samples with defined crack patterns 4.1. Method To isolate the effect of cracks on NMR-measurements, synthetic sandstone plugs with sample dimension 25.4 mm diameter and 40.0 mm lengths were prepared with different crack patterns and saturated with deionized water using a Fig. 1. Principal set-up of NMR-measurements during rock-mechanical measurements. Fig. 2. Difference in the mean relaxation rates, �1/T1, of measurements at increasing axial stress levels compared to the unstressed rock sample. Example Red Wildmoor sandstone. Table 1 Identification and properties of artificial sandstone samples with defined crack patterns ID Cracks (Num.) Crack Width (�m) Orientation Diameter (mm) Length (mm) � (%) PV (cm3) V of cracks (cm3) crack vol. % of PV A 0 0 no cracks 25.07 39.57 40.5 7.90 – – C 19 18 orthogonal to B0 25.21 40.11 39.4 7.88 0.049 0.62 D 19 100 orthogonal to B0 25.02 40.16 38.3 7.57 0.271 3.58 E 19 18 irregular 25.15 40.02 39.4 7.84 0.049 0.62 F 19 100 irregular 25.04 40.06 40.6 8.02 0.271 3.38 G 1 100 d�15 mm, orth to B0* 25.00 39.30 40.7 7.85 0.018 0.23 H 5 100 orthogonal to B0 25.15 39.90 40.2 7.97 0.011 0.14 I 1 18 d�15 mm, orth to B0* 25.00 40.00 40.3 7.91 0.003 0.04 * Samples prepared with one Al-disk with 15 mm diameter. All other samples were prepared with Al-disks with 2.55 mm diameter. 406 C.H. van der Zwaag et al. / Magnetic Resonance Imaging 21 (2003) 405–407 technique suggested by Rathore et al. (1995). Cleaned quartz sand with an average grain diameter dg � 50 �m was used. The main features that distinguished the samples were number of cracks, crack thickness and crack orientation. Table 1 describes the set of samples used in the study. Samples were centered in the RF-coil with their length axis parallel to the B0 field. T2-relaxation measurements were performed on the samples at 10 MHz using a CPMG pulse sequence with echo times of � � 175, 350, 700, 1050 and 1400 �s, respectively. T2 relaxation time distributions and an average exp�ln (T2) was calculated as described earlier. In a fully saturated rock the water in the sample will decay with a T2 equal to: 1 T2 � 1 T2B � �2� SV� � D���� 2G2�2 3 (2) The relaxation rate of the bulk fluid, 1/T2B, and the surface relaxivity, �2, as well as the surface to volume ratio, S/V, are assumed to be constant for measurements at two different echo times. The difference between two measure- ments yields the rate difference: � 1 T2 � 1 T2,n � 1 T2,0 � D0�2 3 � fnGn 2�n 2 � f0G02�02� (3) with � as the gyromagnetic ratio, self-diffusion coefficient D0, f a fraction characterizing the effect of restricted diffu- sion on the spins at a given echo time �, and G the effective (internal) magnetic field gradient. Assuming two measure- ments, index 0 and n, at short echo time and resolving Eqn. 3 for the field gradient G yields Eqn. 4. G � �3 �T2,n�1 � T2,0�1��2D0� fn�n2 � f0�02� (4) 4.2. Results and discussion Fig. 3 shows that T2 values at echo time � � 175 �s decrease with increasing crack volume. This is valid for observations of measurements at all echo times �. To ex- plain this result, Eqn. 4 is applied under given assumptions and an internal gradient is derived that is characteristic for the sample, and thus also for the chosen crack patterns. Fig. 4 shows that the internal field gradient is different for samples with different crack sizes and orientation. It is largest for samples with cracks vertical to the B0 field and appears also to increase with crack number and crack width. 5. Summary and conclusions T1-relaxation measurements on Red Wildmoore Sandstone during loading showed decreasing relaxation rates with stress level. Loading beyond yield stress caused relaxation rates to increase again. Decreasing rates are explained with compaction and closure of micropores. The increase in rate is most probably related to the generation of fresh rock surfaces due to failure. T2 relaxation measurements on artificial sandstone sam- ples prepared with pre-defined crack patterns showed that under given assumptions cracks may affect internal field gradients. It was found that gradients were largest for sam- ples having a larger number of cracks with crack orientation orthogonal to the B0-field. Acknowledgments The work and results presented are part of the strategic institute program “Formation Evaluation” at SINTEF, which was financially supported by the Norwegian Research Council (NFR). We are grateful for the support. We also would like to thank Dr. Frank Stallmach at the University of Leipzig for fruitful discussions and his suggestions. References [1] Rathore JS, Fjær E, Holt RM, Renlie L. “P- and S-wave anisotropy of a synthetic sandstone with controlled crack geometry.” Geophysical Prospecting 1995;43:711–728. [2] Sezginger A. t1heel and t2heel software, 1991–1994�. Schlumberger- Doll Research. Fig. 3. exp ln(T2) � at echo time � � 175 �s for artificial sandstone samples with different crack patterns. Fig. 4. Internal gradient calculated from T2-relaxation measurements at two echo times �� 175 �s and �� 350 �s for artificial sandstone samples with different crack patterns. 407C.H. van der Zwaag et al. / Magnetic Resonance Imaging 21 (2003) 405–407 Deformation and failure of rock samples probed by T1 and T2 relaxation Introduction Method A: measurements on sandstone samples under stress Method Results and discussion Method B: measurements on artificial sandstone samples with defined crack patterns Method Results and discussion Summary and conclusions Acknowledgments References