THE UNIVERSITY OF CALGARY FACULTY OF GRADUATE STUDIES. The undersigned certify that they have read, and recommend to the Faculty of Graduate

Transcription

1

2 THE UNIVERSITY OF CALGARY FACULTY OF GRADUATE STUDIES The undersigned certify that they have read, and recommend to the Faculty of Graduate Studies for acceptance, a thesis entitled "Are P and Swave velocities and attenuations related to permeability?: Ultrasonic seismic data for sandstone samples from the WritingonStone Provincial Park in Alberta" submitted by Nicolas Williams Martin in partial fulfilment of the requirements for the degree of Master of Science. Supervisor, Dr. J.R. Brown Department of Geology and Geophysics Dr.

3 ABSTRACT Some experimental results measuring

4 same permeability range

5 ACKNOWLEDGMENTS FOOTPRINTS One night a man had a dream. He dreamed he was walking along the beach with the Lord. Across the sky flashed scenes from his life. For each scene,

6 TABLE OF CONTENTS Approval Page...ii Abstract... iii Acknowledgments...'...

7 porosity...: Permeabilityporosity relationship Porosityclay content relationship Permeabilityclay content relationship Description of the experimental methodology for estimating phase velocity and attenuation Identification ofp and S waves Phase velocity estimation Seismic attenuation estimation Time truncation

8 LIST

9 List

10 Fig. 2.2.

11 Fig Permeabilityporosity data and regression models from the Permian Rotliegend. sandstone (after Diederix, 1982)...34 Fig Linear

12 Fig The effect of pressure on seismic velocity and attenuation for P waves considering different lithologies (after Best, 1994)...49 Fig Influence of effective pressure on microcracked rocks using ultrasonic measurements (edited by Brulin and Hsieh, 1981) Fig Effect

13 factor. The error bars for permeability are indicated. All the measurements under watersaturated conditions Fig. 4.1 (c)) Permeabilityporosity relationship for LU and UU sandstones along Y direction (paralell to the layering). A linaer leastsquares fit of the permeabilityporosity values

14 Fig. 4.9 Example of transmitted signal obtained by placing facetoface the source and receiver transducers. The picked zerocrossover travel time is about

15 along

16 indicates that Swave phase velocity increases with permeability, as opposite

17 indicates sandstone samples with low Pwave attenuation anisotropy and with

18 CHAPTER

19 K z <K x (ork Y ) (a) Ky<K Z RllS^SIlSi^f^ (b) (C) Fig.

20 Fig. 1.2 Horizontalwell drainage pattern.

21 deciding where to place isolation packers or which sections of a cased hole to perforate (EhligEconomides

22 (b) 1000 o qsv \ Frequency (khz) 1(X Frequency (khz) (a) Fig. 1.3

23 at ultrasonic frequencies

24 to Lethbridge MILK RIVER ^ALGAR LETHBRIDGE

25 attenuation is also considered. The confining pressure ranges are between O and 2700 psi with

26 Fig. 1.5 Methods of wave velocity determination: (a) firstbreak method; (b) firstzerocrossover method. In both cases a) First break Transmitted 8 a I tt tr b) First zero crossover Transmitted Received

27 51 Crq' Os o Ef Normalized Relative Amplitude o p in en <f C 3 CD Q Q "I "t CD Q "Tl 5 JQ (D O O Ol 3 Q ar CD CA N H O cj 1 CD O Cl Ln A1/A2 «. ro c*j ^ tn Ln A1/A2 4 IS) Q * ^ O O ' N 3 CU

28 Hardware and software used Sandstone velocity

29 CHAPTER 12

30 Depth (ft) 8 a S Q = IOO (a) Q = IO Time o> o I 0.5 CL _._ Initial signal Q = IOO

31 14 This can be accounted for by introducing an attenuation coefficient, a = a(co\ which depends

32 15 2 (2o)Q a + I a = O v \ '

33 40 l/q O

34 Several mathematical models have been used 17

35 Fig. 2.3 Typical velocity dispersion curve (after Liu et at, 1976). OO Phase velocity ICT 4 1 Frequency (Hz)

36 propagate fastest 19

37 TRANSVERSELY ISOTROPIC MEDIUM VERTICAL SYMMETRY AXIS (a) NONVERTICAL SYMMETRY AXIS DIPPING BEDS VERTICAL FRACTURES AZIMUTHALLY ANISOTROPIC MEDIA (c) Fig.

38 P(v) SV(v) SH(v) P(V) SV(v) SH(v) LINE DIRECTION LINE DIRECTION Vp(h)

39 22 waves sample identical bulk elastic properties in TI media, and thus V V where SH Sl r the superscript indicates the propagation direction. In contrast, a horizontally propagating SHwave is faster than a horizontally propagating SVwave, i.e. V > V. A similar situation like that observed h v h v

40 23 there are only 21 independent stiffnesses, C secondorder (6x6) symmetric matrix ijkl. This tensor can be also written as a C ijkl»c mn (2.13) where m = i if m = 9(i

41 24 C = / / 44 (2.18) In the case of a transversely isotropic medium (the only case that will be considered here) we have five nonzero elastic constants because there exists a twodimensional isotropy in the plane where all axes are equivalent (rotational symmetry around the zaxis), but the direction perpendicular to this plane is not equivalent to any of

42 Phase and group velocities for weak anisotropy In an anisotropic media the waves emanating from a point source are not, in general, spherical (Thomsen, 1986; Vestrum, 1994). Figure

43 26 B Fig. 2.6 Definitions of group and phase velocities. The phase velocity, v, is the velocity of the wave

44 27

45 28 = CC v (K 12)a a (2.29) Y = C C C 44 5/ (2.30) = 4 v (TT/A)/a

46 <0.01 < % Homogeneous

47 Definition of permeability: Tensorial and directional 1979). The permeability is a second rank tensor connecting fluxes and gradients (Dullien,

48 ANISOTROPIC PERMEABILITY Pressure Gradient direction VP Fig.

49 PERMEABILITY ELLIPSOID (b) Fig.

50 34 10, » * / CQ o> e / _y Porosity, Fig Permeabilityporosity data

51 Klimentos 35

52 36 p = C A^U* * O 1.2 a 1.0 d PN 0.6

53 37 with 2

54 H NNU i O PERMEABILITY (md) (a)

55 Fig 2.13 Attenuation, porosity and clay content relationships, (a) Attenuation coefficient versus porosity for sandstone samples. The solid lines separate samples of given percent clay content. The regions correspond to O to 5 %, 5 to 20 %, and 20 to 30 %, respectively, (b) Attenuation coefficient versus clay content for the same samples. A confining pressure of 40 MPa and a frequency of IMHz were considered in all the measurements (after Klimentos and McCann, 1990). (b) O O Porosity (%) O Clay content (%) (a)

56 T I I I Confining pressure 40 MPa Frequency 1 MHz 100 JJ L*.

57 41 Q p = (2.40) where there

58 DC O 4 5

59 md) have relative high quality factors as shown in Figure 2.17b (Best et a/., 1994). Figure 2.18 shows

60 uwv /*> 1 i 5000 v**/

61 Pwave quality factor

62 v Sl' B O r, ', V 2 / (0) Sl' 46 (2.44) v SH p O Ci (2.45) On the other hand, the corresponding expressions for their seismic attenuations are given by: a P 2a CO Y a I sin O + cos O KJ CO CO a SV 1 2 co cl \ CO cos 9 + sin 9 co 4 J a SH

63 critical frequencies a> 47

64 measured 48

65 ' «I > a i

66 50 Westerly granite O

67 O Il Foliation 51

68 Navajo sandstone Dry o Confining pressure (MPa) 10 Fig Influence of confining pressure on quality factor,

69 a 90 S? O 3«" * * o G 1 =O SW khz ^ 1W I "* 120, C^l"* "QfS? IHT""* *T 60 ^*** Ir A

70 54

71 I Massillon sandstone Fully sat. V, Fully O

72 M assillon sandstone Partially saturated O 10

73 57 CHAPTER 3 Regional Geologic Framework 3.1 Location of the study area The study area is located in the WritingonStone Provincial Park (WOSPP), southern Alberta, about

74 sandstones collected 58

75 EPOCH AGE FORMATION/GROUP LATE CRETACEOUS CAMPANIAN BEARPAW SANTONIAN

76 60 (1) the basal Telegraph Creek Member, consisting of interbedded buffer grey shale and sandstone in transitional contact with the underlying dark grey shale of the Colorado Group; (2) the Virgelle Member, described as a lightcoloured, fine to mediumgrained sandstone, conformably overlying the Telegraph Creek Member and, equivalent to and in mappable continuity with the Virgelle Member at the base of the Eagle (sandstone) Formation of the Montana Group in Montana (Bowen, 1915);

77 Eastern limit of nonmarine strata

78 commonly containing siderite pebbles 62

79

80 sandstones with occasionally slightly asymmetric, hummocky (HCS) 64

81 IJTHOFACIES fv*i "i?* & :.:. ' ; :!" >*:«jvft '. v.^;.^. 3D crossbedded sandstone (troughs); 3CBS

82 66 CHAPTER 4 Experimental Methodology and Measurement of phase velocity and attenuation

83 Figures

84 TABLE

85 69 285HPA 285HPE 286V 286HPA 286HPE 297V 297HPA 297HPE W9201V W9136HPE W92HPA W9A112V W9A22HPA W9A64HPE W9A114V W9A29HPA W9A67HPE 1206V 1206HPA 1206HPE W789V W7174HPA W7173HPE W9294V W9177HPE W9104HPA 35X12 36Y12 37Z13 38X13 39Y13 40Z14 41X14 42Y14 43Z15 44 Yl 5 45X15 46Z16 47X17 48Yl 7 49Z18 50X18 51Y18 52Z19 53X19 54Y19 55Z20 56X20 57Y20 58Z21 59Y21 60X ±59 980±

86 70 10* Z direction Q 10 log

87 71 10* I 103 >> 9 io 2 10

88 72 evident that higher clay content values are associated with higher porosity values. The experimental results obtained by Yin and Nur (1994) on unconsolidated synthetic sediments show that

89 73 Sand Critical Clay Content Shale O Clay content (% by weight) (a) iqo i c i i i i i X OMPi 1ONfPa OMPa 5OMPa :> 5OMPa O O i. i. t

90 O ^~80 TOO Clay content (%

91 with increasing clay content, 75

92 76 ^UUU ^ 1400 Q & 1200 O\ Permeabilil hk

93 77 transducers as source and receiver. A comparison between the recorded trace generated using both Pwave source and receiver transducers and the recorded trace generate using both Swave source and receiver transducers will help to identify those signals which are enhanced

94 Ȯ Time (ms) (a) 1500 Fig Time (ms) 1500 (b)

95 P wave Watersaturated Core 6 o> 2000 V PP data 6000 O (a) 500 Time (ms) Watersaturated Core (b) " Time (ms) Fig.

96 their approach 80

97 mm 81

98 82 Transmitted signal 'O 10

99 83 band transducers have a diameter of 1.51 cm and generate an energy spectra in the range 0.1 to 1.0 MHz. In the tables 2 and 3 the P and Swave phase velocities are indicated for the sixty sandstone samples used

100 84 TABLE 2 P and Swave phase velocities measured under dry conditions SAMPLE W713V W725HPE W726HPA W74V W79HPE W78HPE W763V W7125HPE W7124HPA W791V W7178HPA W7179HPE W768V W7134HPA W7135HPE W722V W751HPE W750HPA W728V W762HPA W763HPE W77V W715HPE W716HPA W787V W7172HPA W7171HPE 263V 263HPA 263HPE 275V 275HPA 275HPE 285V No V* (mis) f V*" (ml s] t.c V* (mis) V** (mis) St I* 9 (ms) ft i* M St

101 85 285HPA 285HPE 286V 286HPA 286HPE 297V 297HPA 297HPE W9201V W9136HPE W92HPA W9A112V W9A22HPA W9A64HPE W9A114V W9A29HPA W9A67HPE 1206V 1206HPA 1206HPE W789V W7174HPA W7173HPE W9294V W9177HPE W9104HPA NOMENCLATURE dry

102 TABLE 86

103 87 286HPE 297V 297HPA 297HPE W9201V W9136HPE W92HPA W9A112V W9A22HPA W9A64HPE W9A114V W9A29HPA W9A67HPE 1206V 1206HPA 1206HPE W789V W7174HPA W7173HPE W9294V W9177HPE W9104HPA NOMENCLATURE sot sot V and V represent P and Swave phase velocities under watersaturated conditions, p s respectively.

104 88 SAMPLE PROTRACTOR Fig Schematic diagram of apparatus used for phasevelocity and attenuation measurements

105 89 experiment, to a PerkinElmer 3240 seismic processing system for storage and subsequent data processing. The signal was sampled at 100 ns for reducing the aliasing effect, which represents an equivalent sampling rate in the field of 1.0 ms Seismic attenuation estimation There

106 where/is 90

107 91 The above spectral ratio technique was applied on the sixty sandstone samples for measuring their corresponding attenuation coefficients and quality factors under dry and watersaturated conditions. But,

108 92 TABLE 4 P

109 93 286HPA 286HPE 297V 297HPA 297HPE W9201V W9136HPE W92HPA W9A112V W9A22HPA W9A64HPE W9A114V W9A29HPA W9A67HPE 1206V 1206HPA 1206HPE W789V W7174HPA W7173HPE W9294V W9177HPE W9104HPA NOMENCLATURE Ay dry

110 TABLE 94

111 95 286HPA 286HPE 297V 297HPA 297HPE W9201V W9136HPE W92HPA W9 A1 12V W9A22HPA W9A64HPE W9 A1 14V W9A29HPA W9A67HPE 1206V 1206HPA 1206HPE W789V W7174HPA W7173HPE W9294V W9177HPE W9104HPA NOMENCLATURE sal sat Ci

112 Facetoface spectra 4» Sample W78HPA f2.0 QN ^ O (a) v O.O Sandstone sample spectra Frequency (MHz) x10^ R 2 = ' 40 i 20 O a p = db/cm (b)

113 decreases monotonously with 97

114 98 signal instantaneous phase 3Jisignal with arrival interference Jl 1 phase skips

115 Instantaneous frequency Amplitude

116 Fig Geometry 100

117 This phase increment represents 101

118 102 z=16 S=0.74 Z=J 8 S=0.84 z=20 S=0.93 z=22 5=1.02 r=24 5=1.11 z=26 S=Ul z=28 S=I.30 z=30 5=1.39 z=32 S=1.48 z=34 5=1.58 X I M M I 1 I i I M I X

119 103 section 4.4 (Seki et al., 1955; Papadakis, 1966). The attenuation correction Aar is subtracted from the measured attenuation a' to get the true attenuation a. a = a' Aa (4.12) In general,

120 O Frequency (MHz) (a) 5r 4 ^w M 3 eo 3 2 O Fig Frequency (MHz) (b)

121 105

122 Dry G 1800 *? ~ 1200 CQ, iooo 800

123 107 LL\3\ i *j >> I 160 > J 1400 I 1200 al

124 % and for UU sandstones between 26.2% and 31.0%. From this graph is observed that Pwave velocity

125 Watersaturated 2300 f 2200 o "5 «2100 J «2000 > * Vp = R 2 =0.59 « Porosity (%) (a) 1100 Watersaturated <& 1000 S 900 *s ocu 800 CW </> R 2 = , Porosity (%) (b) Fig Phase velocityporosity relationships for: (a) P waves and (b) S waves. All measurements were made under watersaturated conditions. For P wave are considered all samples while for S wave only those samples with velocity information.

126 31 CTQ' 4^ to N ;±?rr o 5 < P «a

127 above Ill

128 S 2800 Watersaturated c 2600 a 2400 % 2200 CQ CU I 2000 p!< 1800

129 Watersaturated Clay content (%

130 they indicate that 114

131 Watersaturated I 2300 o 2200 "S O) Qu 4> O Permeability (md) Fig Pwave phase velocity

132 Watersaturated I J 800 O) I Permeability (md) Fig Swave phase velocity as a function of permeability for some sandstone samples from WOSPP.

133 fact, Swave phase velocity apparently increases with increasing permeability 117

134 118 SOi i i i 5 45 Watersaturated I 40 CQ 3 *s 35 o> g 20 4» 1ff > 15 CQ Swave attenuation coefficient (db/cm) Fig Ultrasonic data obtained from

135 S 35 OJ Tl V^ I «15 d< 10 O

136 120 Watersaturated O Permeability (md) Fig Pwave attenuation coefficient versus permeability for all the sandstone samples from WOSPP.

137 121 concluded that the attenuation of a highpermeability rock (>300 md) may be quite high, as indicated in Figure The experimental data shown in Figure 4.27 are in agreement with the results obtained

138 Watersaturated 120 I 100 'S O

139 ' 100. O O

140 124 5O 1 I * * I 35!= 30 I 25 *» g 20 A 15 Watersaturated Z direction O 10

141 125 under dry conditions (Figures 4.29b and 4.3Ob). In contrast, the UU sandstones apparently not shows a significant increment in their Pwave attenuation values after saturating they with water (Figures 4.29a and 4.3Oa). In each case, this increment of Pwave attenuation with porosity is lower than associated with permeability Effect of saturant fluid on P and Swave attenuation coefficient anisotropy

142 126 S 60 I 3 50 Dry O O 40 I 30 CJ B 20 wo! O I 10 IS l o I s 30.SJ '3 E M 1 10 CQ =? 5 &

143 127 PQ TJ 80, g Dry O LU sandstones 50

144 128

145 129 a Watersaturated YZ plane O O LU sandstones

146 Watersaturated XZ plane g 2.5 U C * 2.0 CQ I

147 131 anisotropy anisotropy and permeability anisotropy (Figure 4.33). These experimental relations suggests that there is a critical permeabilityanisotropy value above which the P wave attenuation anisotropy

148 ** 15 I 10 O) A ^ 5 a 2 CQ o 5 * 5 Watersaturated LU sandstones YZ plane r ^,.. A 0UU sandstones O 0 00 O O O O Ol CQ 10 O 15

149 Watersaturated O LU sandstones

150 and 4.36 it is evident that Pwave velocity anisotropy is not dependent on permeability anisotropy and keeps a constant value around of 0.0 for the entire permeability anisotropy range. The scarce phase velocity and attenuation coefficient data for S waves, due to the high attenuation of these kind of waves under watersaturated conditions, made it practically impossible to obtain any significant relationship between Swave velocity anisotropy and permeability anisotropy. In conclusion, Pwave attenuation coefficient is more suitable for estimating information about

151 135 16QQ UQQ Polarization direction 1 >> o UOQ um O, Sample number Fig Effect of polarization direction on Swave phase velocity for sandstone samples from WOSPP under dry conditions. Two polarization directions at 0 and 45 are shown.

152 Swave source transducer Swave source transducer Polarization of referenc Swave receiver transducer Swave receiver transducer Fig Definition

153 Polarization direction Sample number Fig Effect of polarization direction on Swave attenuation coefficient under

154 possibility that 138

155 Pressure Vessel Pulse Generator Oscilloscope Computer Fig Schematic diagram of apparatus used for Pwave phase and Pwave attenuation measurements under confining pressure conditions. U) VO Printer

156 Watersaturated Core O Internal pressure (psi) (a) Watersaturated Core

157 141 CHAPTERS Conclusions Important conclusions

158 142

159 143 But, Swave attenuation coefficient apparently is significantly influenced by polarization direction. The reason of this could be associated with the complex internal structure of these sandstones

160 CHAPTER 144

161 APPENDIX 145

162 APPENDIX 146

163 Isotropic: Having the same physical properties regardless of the direction in which they 147

164 Tortuosity: 148

165 APPENDIXC Abbreviations and symbols Im = Imaginary part of a complex number

166 150 APPENDIX D Data location

167 151 REFERENCES Akbar, N., Dvorkin, J. and Nur, A., 1993, Relating Pwave attenuation to permeability: Geophysics,

168 152 Biot, M. A., 1956a, Theory of propagation of elastic waves in a fluidsaturated solid. I, Lower frequency range:

169 153 Castagna, J. P., Batzle, M. L and Eastwood, R. L., 1985, Relationships between compressionalwave and shearwave velocities in clastic silicate rocks: Geophysics, 50, Cerveny,

170 154 Dellinger, J., 1991, Anisotropic seismic wave propagation: Ph.D. thesis, Stanford University. Diederix, K.M., 1982, Anomalous relationships between resistivity index

171 155 Geerstma, J. and Smit, D. C., 1961, Some aspects of elastic wave propagation in fluidsaturated porous solids: Geophys.,

172 156 Johnston, D. H. and Tokso z, M. N., 1980, Ultrasonic P and S wave attenuation in dry and saturated rocks under pressure:

173 157

174 158 Murphy, W. F., Ill, 1982, Effects of partial water saturation on attenuation in sandstones: J. Acoust. Soc. Am.,

175 Rathore, 159

176 Stainsby, S.D. 160

177 Toksoz, 161

178 162 Winkler, K. W. and Nur, A., 1982, Seismic attenuation: Effects of pore fluids and fnctional sliding: Geophysics,