- Email: [email protected]
Wave-velocity dispersion and rock microstructure
Journal Pre-proof Wave-velocity dispersion and rock microstructure Wei Cheng, Jing Ba, Li-Yun Fu, Maxim Lebedev PII:
S0920-4105(19)30887-3
DOI:
https://doi.org/10.1016/j.petrol.2019.106466
Reference:
PETROL 106466
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 17 May 2019 Revised Date:
11 August 2019
Accepted Date: 2 September 2019
Please cite this article as: Cheng, W., Ba, J., Fu, L.-Y., Lebedev, M., Wave-velocity dispersion and rock microstructure, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/ j.petrol.2019.106466. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1 2
Wave-velocity Dispersion and Rock Microstructure
3 4
Wei Chenga, Jing Baa*, Li-Yun Fub and Maxim Lebedevc
5
a. School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China
6
b. School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
7
c. WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Perth,
8
Western Australia, Australia.
9
Abstract
10
Porosity, fluid type and rock texture significantly affect acoustic wave
11
propagation, since velocity dispersion and attenuation in fluid saturated rocks are
12
mainly caused by wave-induced local fluid flow between microcracks and
13
intergranular pores. We analyze P-wave velocity dispersion as a function of porosity
14
to obtain information about the rock microstructure. The P-wave velocities in
15
water-saturated rocks are predicted from measurements in gas-saturated rocks, using
16
the Gassmann fluid substitution equation (the relaxed state). The dispersion is
17
estimated from the difference between this predicted velocity and the measured one,
18
where the latter corresponds to the unrelaxed state. We evaluate the wave dispersion
19
as a function of porosity for 112 carbonates, 128 sandstones and 56 volcanic rocks,
20
including our measurements for 86 tight rocks, showing that dispersion increases with
21
porosity in the low porosity range, but decreases in the high porosity range. The
22
dispersion peak occurs at a porosity of approximately 15 %. Double-porosity
23
poroelasticity modeling based on the local fluid-flow mechanism confirms this
24
behavior. The microcrack radius has a peak in the porosity range 15-19 % for all the
25
lithologies from our collection, while the behavior of microcrack porosity is less
26
evident. The dispersion peak may reveal the characteristics of lithological units, in
27
particular porosity, fluid type and rock microstructure.
28 29
Keywords: Wave propagation; P-wave velocity dispersion; Ultrasonic measurement;
30
Gassmann equation; Carbonates; Sandstones; Volcanic rocks; Porosity; Microcracks;
31
Poroelasticity
32 33 34
*Corresponding author: Jing Ba ([email protected])
35
1. Introduction
36
Rock anelasticity - velocity dispersion and attenuation in seismic waves - is
37
affected by porosity, texture and pore fluids. Studies on attenuation and dispersion are
38
essential in guiding seismic inversion and estimating the properties of rocks (e.g.
39
Pham et al., 2002). Jeong and Hsu (1995) showed that ultrasonic attenuation increases
40
with void content in carbon composites. Klimentos et al. (1990) established a
41
correlation between attenuation, clay content and porosity in sandstones based on
42
measurements. Velocity dispersion can be quantified if attenuation is known, since
43
these properties are related by the Kramers-Kronig relations (Mavko et al., 2009;
44
Müller et al., 2010; Carcione, 2014; Carcione et al., 2018). Dispersion reflects the
45
intrinsic properties of rocks and is closely related to porosity.
46
Three different rocks lithologies are considered here. Carbonates cover a range
47
of depositional facies, with considerable textural variability, showing a wide range of
48
pore sizes and types, and fluid distribution heterogeneity (Fedrizzi et al., 2018; Lopes
49
et al., 2014; Sharma et al., 2013). Some of the deep reservoir sandstones are highly
50
porous, but the tight sandstones have low porosity, low permeability and microcracks
51
(Anjos et al., 2003; Guo et al., 2018). The volcanic rocks underwent cooling,
52
solidification and the epidiagenesis stage, and can be characterized by a strong
53
heterogeneity and complex composition (Mao et al., 2015; Sruoga and Rubinstein,
54
2007).
55
Laboratory measurements of ultrasonic waves in rocks have been frequently used
56
to investigate the relations between the wave properties and rock properties. Han et al.,
57
(1986) measured the compressional (P-) and shear (S-) wave velocities of sandstones
58
at full saturation. Assefa et al. (2003) showed that these velocities decrease with
59
increasing porosity in carbonates, with the P-wave velocities decreasing
60
approximately twice as fast compared to the S-wave velocities. Adelinet et al. (2010)
61
investigated the elastic properties of basalt by using ultrasonic tests, confirming the
62
difference between the high- and low-frequency rock moduli under full saturation, a
63
difference that decreases when crack density decreases.
64
Gassmann equation can be used to predict the compressional wave velocity of a
65
water-saturated rock based on the properties of the dry-rock skeleton and fluid, i. e.,
66
using fluid substitution (Gassmann, 1951). However, it is only valid at the low
67
frequency limit, where the wave-induced pore fluid pressures are equilibrated
68
throughout the pore space (specifically, between the soft cracks and the stiff
69
intergranular pores) (Mavko and Nolen-Hoeksema, 1994; King and Marsden, 2002).
70
Adam et al. (2006) showed that Gassmann equation can give a good prediction at
71
seismic frequencies for carbonates with round pores or vugs. At ultrasonic frequencies,
72
the wave-induced fluid pressure gradient between soft and stiff pores does not
73
equilibrate in each wave cycle. This results in a stiffening effect, and the Gassmann
74
equation underestimates the compressional wave velocity. The velocity dispersion can
75
be estimated by computing the difference between the Gassmann prediction and
76
measurements at full liquid saturation (King and Marsden, 2002; Regnet et al., 2015).
77
For an undrained rock, the difference between the high- and low-frequency
78
moduli is interpreted as the effect of wave-induced squirt-flow (or local fluid flow)
79
between microcracks and intergranular pores (Adelinet et al., 2010). Dvorkin and Nur
80
(1993) proposed the Biot/squirt (BISQ) model, which incorporates both the Biot
81
global flow and the local flow into the same theoretical framework. The model was
82
applied for predicting compressional wave velocities in sandstones at sonic and
83
ultrasonic frequencies (Dvorkin et al., 1994, 1995). Recently, the double-porosity
84
model has been introduced, where two pore phases with different compressibilities are
85
considered to describe the velocity-dispersion effect due to wave-induced fluid flow
86
(Pride et al., 2004; Ba et al., 2016, 2017; Fu et al., 2018).
87
The dependence of the wave properties of common rocks on their microstructure
88
is not fully understood. We measure ultrasonic P- and S-wave velocities in 18
89
carbonates, 17 sandstones and 51 volcanic rocks at full-water and full-gas saturations,
90
and complement the dataset with experimental data collected from the literatures
91
(Regnet et al., 2015; Han et al., 1986; Wang, 2016a; Wang, 2016b; Guo et al., 2018;
92
King et al., 2000; Zamora et al., 1994). The velocity dispersion is estimated by using
93
the Gassmann equation and the experimental velocities at full-gas and full-water
94
saturations. The relation between dispersion and porosity is analyzed. A
95
double-porosity theory, developed by Ba et al. (2011, 2017), is adopted to model the
96
stiffening/dispersion effect for different lithologies. On the basis of this modeling
97
theory, we obtain the characteristics of the rock microstructutre.
98
2. Experimental Data
99
2.1. Experimental Set-up and Rock Specimens
100
The experimental set-up of Guo et al. (2009) is used for the ultrasonic-wave
101
measurements on 18 carbonates (5 limestones and 13 dolomites), 17 sandstones, and
102
51 volcanic rocks (25 rhyolites, 12 tuffs and 14 tufflavas). The experimental set-up
103
consists of a pulse generator, a digital oscilloscope, a high pressure vessel, the
104
acoustic testing unit, a confining pressure control unit, a pore pressure control unit
105
and a temperature control unit. The transmitting transducers are PZT-ceramic crystals
106
(Piezoelectric Ceramic transducer), which are used to generate P- and S-wave
107
velocities (VP and VS), respectively. The receiving transducer is connected to a
108
computer through a signal amplifier. The core is jacketed within rubber tubing, and
109
each endplate has a pore fluid inlet.
110
The carbonates are collected from Ordovician and Cambrian formations (> 4.0
111
km depth), West China, with low-moderate porosity, dissolved pores and rare clay.
112
The sandstones, collected from the Paleogene formation, in the Dongying sag, East
113
China (around 4.0 km depth), are composed of feldspar, quartz, and rare clay. The
114
volcanic rocks belong to the Lower Cretaceous formation, Songliao Basin, Northeast
115
China (around 3.6 km depth); the volcanic rocks exhibit low porosity and low
116
permeability, and are mainly composed of pyroclast and rare arfvedsonite.
117
Ultrasonic VP and VS, at the dominant frequency of 1 MHz, are measured for
118
each sample at full-water and full-gas (nitrogen) saturations states. In addition to our
119
measurements on the three lithologies, experimental data by Regnet et al. (2015), Han
120
et al. (1986), Wang (2016a), Wang (2016b), Guo et al. (2018), King et al. (2000) and
121
Zamora et al. (1994) are analyzed. Each dataset and the corresponding measurement
122
condition (including the pressure and temperature) are given in Table 1. The
123
measured temperatures for the 13 sets of rock samples are not the same, and in the
124
dispersion analysis of this work, the effect of temperature on fluid properties is
125
incorporated by Batzle and Wang (1992).
126
Figure 1 shows crossplots of VP and VS for all the data sets, at full-gas (dry) and
127
full-water saturations. The correlation of a linear fitting between VP and VS in
128
carbonates is the best, and that of volcanic rocks is the worst. The slope of VP versus
129
VS is 1.6 in carbonates, higher than those in sandstones and volcanic rocks. For each
130
lithology, the slope of VP versus VS at full gas saturation is higher than that at full
131
water saturation.
132
2.2. Determination of The Bulk Modulus of The Mineral (K0)
133
The bulk modulus of the solid (effective mineral grains) can be estimated by
134
using effective medium theories (Ba et al., 2016), if the mineral components, contents
135
and geometrical parameters are known. However, for most rocks, these properties can
136
hardly be obtained. Alternatively, rocks of the same lithology are classified into
137
subsets by analyzing the specimens with similar lithological characteristics and
138
minerals. A linear fit of the velocity-porosity relations in the low porosity range gives
139
an estimation of the effective solid modulus for the whole set (Vernik, 1994; Yan et
140
al., 2011). Figure 2a and 2b show the results for the limestones, sandstones, and
141
rhyolite rocks (porosity less than 8 %). For each of the three sets, VP and VS at zero
142
porosity are computed, and thus, K0 is obtained.
143
Modulus K0, given in Table 1, is obtained from the limestones, sandstones,
144
rhyolite, tuff and tufflava (our data), and from the results by Han et al. (1986), Wang
145
(2016a), Guo et al. (2018) and Zamora et al. (1994). For our dolomites and the
146
limestones of Regnet et al. (2015), the method is unreliable due to the lack of data in
147
the low porosity range, therefore for these rocks K0 is taken from Mavko et al. (2009).
148
K0 is 40.0 GPa for the sandstone set of King and Marsden (2002), and 89.2 GPa for
149
the carbonate set of Wang (2016b).
150
3. P-wave Velocity Dispersion
151
3.1. Gassmann Fluid Substitution
152
The Gassmann equation (Gassmann, 1951; Carcione, 2014) is used to estimate
153
the bulk modulus of the water-saturated rock ( K(sat) ) from velocity measurements of
154
the gas-saturated rock. Gas is assumed to cause no stiffening effect at ultrasonic
155
frequencies (Gist, 1994). Therefore, the gas-saturated ultrasonic experiments measure
156
a relaxed state and give the dry-rock bulk modulus, Kb. Gassmann equation is based
157
on the assumption that wave-induced fluid pressures are equilibrated throughout the
158
pore space, which means a completely relaxed state, i. e., the low-frequency (LF)
159
limit. The Gassmann equation is (LF) K (sat)
160
(LF) K 0 − K(sat)
=
Kf Kb + K0 − Kb φ ( K 0 − K f )
(1)
161
where Kf and K0 are the bulk moduli of fluid and mineral mixture, respectively, ϕ is
162
the rock porosity, and Kb is the bulk modulus of the rock skeleton without pore fluids
163
(LF) (e.g., Mavko et al., 2009; Carcione, 2014). K (sat) is computed from equation (1) for
164
each specimen, where K0 is determined in 2.2, the fluid properties are obtained at the
165
measurement conditions according to Batzle and Wang (1992).
166
The P-wave velocity dispersion is then estimated as the difference between the
167
(HF) measured P-wave velocity at ultrasonic frequencies (high-frequency, HF), VP(sat ) , and
168
(LF) the velocity obtained from the Gassmann equation, VP(sat) , as follows
169
170
Dispersion=
(HF) (LF) VP(sat) − VP(sat ) (LF) VP(sat)
.
(2)
3.2. Dispersion as a Function of Porosity in Tight Rocks
171
The velocity dispersion is estimated by applying equation (2) to the three sets of
172
tight rocks (carbonate, sandstone and volcanic rocks) with six subsets, i.e., dolomite,
173
limestone, sandstone, tuff, tufflava and rhyolite, as shown in Figure 3. The dispersion
174
is generally positive for the tight rocks, indicating that the measured ultrasonic
175
P-wave velocity of the saturated rock is higher than the predicted velocity by the
176
Gassmann equation, as expected. Similar results were reported by Wang (2001), King
177
et al. (2002) and Zaitsev and Sas (2004), and attributed to the presence of open
178
microcracks or compliant pores, and the related squirt-flow mechanism. However, in
179
most of these tight specimens, the dispersion is less than 5 %, and apparently
180
increasing with porosity, suggesting that the microcrack density increases accordingly.
181
It can be seen that the subsets of dolomite and limestone of carbonate (measured at
182
the same condition) have the same linear trend. Similarly, the three subsets of
183
volcanic rocks have a linear trend, and each subset cannot be discriminated from each
184
other on the basis of the dispersion. However, the three lithologies can be
185
distinguished, with the volcanic rocks having the highest dispersion and slope (0.33),
186
and carbonates having the lowest (0.14).
187
3.3. Relation Between Dispersion and Porosity
188
The porosities of our specimens are mainly less than 12 % (tight rocks). The
189
thirteen rock sets listed in Table 1 are considered to cover the full porosity range.
190
The measured conditions of these data reflect the actual in-situ conditions of typical
191
shallow geological formations. Figure 4 (a), (b) and (c) presents crossplots of
192
dispersion and porosity for the three lithologies. The most interesting fact is that
193
dispersion increases with porosity in the low porosity range (< 15 %), but decreases
194
for moderate to high porosities (> 15 %). A Gaussian fit of the different lithologies
195
shows that the dispersion has a peak at a porosity of approximately 15 % (15.7 %,
196
14.9 % and 14.4 %, for the carbonate, sandstone and volcanic rocks, respectively).
197
Figure 4d gives the histogram of P-wave velocity dispersion as a function of porosity
198
for the carbonates, sandstones and volcanic rocks. The trend validates that the peak of
199
P-wave velocity dispersion at a characteristic porosity can be expected in the
200
moderate porosity range (12-16 %) for the three lithologies.
201
The dispersion characteristics are less reliable for volcanic rocks, since there are
202
few data in the moderate-high-porosity range. However, the data in Figure 4c roughly
203
shows a similar trend as those of carbonates and sandstones. Negative values of the
204
dispersion in Figure 4a and 4b indicate that the same K0 for each set may not be so
205
reliable. However, there is no effective approach to precisely determine K0 for each
206
specimen, in view of a detailed lithological and mineralogical information. The
207
statistical analysis here shows the trend.
208
4. Poroelasticity Modeling of Wave Dispersion
209
4.1. Theory of Wave-induced Fluid Flow Due to Microcracks
210
The wave-induced local fluid flow between compliant microcracks and
211
intergranular pores causes the stiffening effect of the rock matrix at ultrasonic
212
frequencies, which results in the dispersion in rocks. Apparently, the microcrack
213
properties change with porosity and lead to the phenomena observed in Figure 4.
214
The double-porosity theory (Ba et al., 2011, 2017) is used to model the
215
microscopic local fluid-flow mechanism (see Appendix A for the governing equations
216
of wave propagation and the velocity prediction method). Figure 5 compares the
217
experimental data with the theoretical results for samples DT10, SD17 and RS24. The
218
basic rock properties are given in Supplementary Material; Kb is determined
219
according to the measurements in gas-saturated/dry rocks. The predictions at full
220
water saturation are based on poroelasticity modeling, where the optimization is
221
performed by using the inclusion (i. e., the cracked grain with microscopic
222
heterogeneity) radius, inclusion porosity and inclusion bulk modulus as free
223
parameters, which are limited to strict and reasonable ranges during modelling, and
224
the other fixed parameters can be measured or estimated from the measurements. We
225
obtain a set of optimal parameters for each rock by fitting the P-wave velocity of
226
saturated rocks at the corresponding experimental frequency. Details can be found in
227
the Supplementary Material. We take inclusion radii of 90 µm, 370 µm and 100 µm,
228
inclusion porosities of 0.90 %, 1.41 % and 0.28 %, and inclusion bulk moduli of 9.70
229
GPa, 2.00 GPa and 5.30 GPa, for the DT10, SD17 and RS24 samples, respectively.
230
The results show that the double-porosity theory yields the same prediction of the
231
Gassmann equation at the low frequency limit, and predicts the stiffening effect of the
232
rock matrix due to local fluid flow at ultrasonic frequencies. Moreover, the theory
233
predicts the P-wave velocity dispersion, compatible with the measured data at full
234
water saturation. Figure 5b shows the P-wave dissipation factor (inverse quality factor)
235
versus frequency, where the P-wave dissipation factor of the volcanic rock (RS24) is
236
the highest, and that of the sandstone (SD17) is the least.
237
4.2. Microfracture Properties as a Function of Porosity
238
The poroelasticity modeling is applied to the 112 carbonates, 128 sandstones,
239
and 56 volcanic rocks. Figure 6a and 6b show the microcrack radius and microcrack
240
porosity as a function of the total porosity, respectively. A Gaussian fit shows that the
241
microcrack radius R0 has peaks porosities of 16.16 %, 18.03 % and 18.27 % for
242
carbonates, sandstones and volcanic rocks, respectively, while the microcrack
243
porosity φ2 has peaks at porosities of 15.06 % and 19.00 % for carbonates and
244
sandstones, respectively. The correlation between φ2 and the rock total porosity is
245
generally worse than that of the R0 . For volcanic rocks, no peaks can be found for
246
φ2 as a function of porosity due to the lack of data at moderate and high porosities.
247
The P-wave dispersion as a function of R0 and φ2 in the cabonates is given in
248
Figure 7a and 7b, respectively. P-wave dispersion generally increases with R0 , while
249
no clear relation can be found between P-wave dispersion and φ2 .
250
Although there are differences between the different lithologies, it can be
251
concluded that in most of the rocks, the microcrack radius and porosity increase with
252
the rock total porosity in the low porosity range (< 15 %), having peaks in the
253
porosity range of 15-19 %, while they decrease in the high porosity range (> 19 %).
254
This behavior may be related to the rock composition, fabric and texture, which are
255
associated with processes such as diagenesis. A possible explanation concerning this
256
phenomenon can be related to the geological process of rock diagenesis. Due to the
257
consolidation and compaction of rocks, in the moderate-high porosity range,
258
micropores become flat and microcracks extend with the deeper burial and the higher
259
pressure, and simultaneously, the total rock porosity decreases. Some softer pores are
260
changed to flat microcracks, and their radii are larger than primary cracks. Therefore,
261
microcrack radius increases with a decreasing porosity in moderate-high porosity
262
range. However, in the low-moderate porosity range, when the burial depth or
263
overburden stress keeps increasing, and rock porosity keeps decreasing, some of the
264
soft microcracks tend to close, and consequently, microcrack radius decreases with a
265
decreasing porosity. Further research is required to understand how these processes
266
are related to the anelastic characteristic of the rocks.
267
5. Conclusions
268
We have performed ultrasonic measurements on three sets of tight rocks, namely,
269
18 carbonates, 17 sandstones and 51 volcanic rocks, at full gas and water saturated
270
conditions. Assuming that the rock is relaxed at full-gas saturation, the Gassmann
271
equation is used to predict the P-wave velocity at full water saturation and the
272
low-frequency (seismic) limit. Wave dispersion is then estimated as the difference
273
between the Gassmann prediction and the ultrasonic measurements. Dispersion
274
increases with porosity for the tight rocks of this study. The different lithologies can
275
be discriminated from the different linear slopes, with the volcanic rocks showing the
276
strongest dispersion. However, for each lithology, the subsets (e.g., dolomite and
277
limestone) cannot be discriminated from each other. Adding experimental data from
278
the literature, a statistical analysis on 13 data sets with 296 samples shows that the
279
P-wave dispersion has peaks at approximately 15 % porosity for all the lithologies,
280
which indicating that wave dispersion decreases with porosity in the high porosity
281
range, instead of increasing.
282
The double-porosity theory is used to model the P-wave dispersion, describing
283
the stiffening effects of the rock matrix due to the presence of microcracks and the
284
related wave-induced fluid flow. The results reveal that the microcrack radius and
285
porosity have peaks at moderate porosities for the three lithologies. This indicates that
286
the total porosity can be related to microcrack presence, in the sense that these have a
287
high density at moderate total porosities (15-19 %) for the three lithologies from our
288
collection. The geological mechanism explaining this fact is still unclear and further
289
research is required.
290
Appendix A: The Double-porosity Theory
291
The double-porosity theory (Ba et al., 2011, 2017) is used to model the
292
microscopic local fluid-flow mechanism. The host medium has stiff intergranular
293
pores with porosity φ1 , while the inclusions are grains containing compliant
294
microcracks with porosity φ2 . The governing equations for wave propagation are
295
N ∇ 2u + ( A + N )∇e + Q1∇(ξ1 + φ2ζ ) + Q2∇(ξ 2 − φ1ζ ) , && (1) + ρ U && (2) + b (u& − U & (1) ) + b (u& − U & (2) ) && + ρ U =ρ u 00
01
02
1
2
296
&& (1) − b (u& − U & (1) ) , && + ρ11U Q1∇e + R1∇(ξ1 + φ2ζ ) = ρ 01u 1
297
&& (2) − b (u& − U & (2) ) , && + ρ 22 U Q2∇e + R2∇(ξ 2 − φ1ζ ) = ρ 02u 2
298
φ2 (Q1e + R1 (ξ1 + φ2ζ )) − φ1 (Q2e + R2 (ξ 2 − φ1ζ )) ρ . η 1 = R02φ12φ2φ20 ( f ζ&& + ζ& ) φ10 κ1 3
(A1)
299
where u , U(1) and U(2) are the particle displacements of the rock frame, fluid in
300
intergranular pores, and fluid in inclusion microcracks, respectively, e , ξ1 and ξ2
301
are the corresponding displacement divergence fields, the scalar ζ represents the
302
variation of fluid content, and φ10 and φ20 are the absolute porosities of the
303
intergranular pores and cracked grains, respectively; φ2 =v2 ⋅ φ20 , where v2 is the
304
inclusion (cracked grains) volume content. The rock porosity is φ =φ1 +φ2 , R0 is the
305
inclusion radius, and κ1 , η and ρ f are the rock permeability, fluid viscosity and
306
fluid density, respectively. The stiffnesses A , N , Q1 , Q2 , R1 and R2 , the density
307
coefficients ρ 00 , ρ 01 , ρ 02 , ρ11 and ρ 22 , and the Biot dissipation coefficients b1
308
and b2 are determined on the basis of the rock and inclusion properties (Ba et al.,
309
2017). By substituting a plane P-wave kernel into equation (A1), we obtain a cubic
310
equation for P waves. The solutions yield the wave number k (Ba et al., 2011). Then,
311
the complex velocity is given by
v=
312
313
k
,
(A2)
where ω is the angular frequency, such that
1 vP = Re , v
314
315
ω
(A3)
is the phase velocity,
Q=
316
317
is the quality factor.
318
Acknowledgements
Re {v 2 }
Im {v 2 }
,
(A4)
319
The authors are grateful to the editor H. Wang and the two annonymous
320
reviewers for their help which improved the paper. Zhaobing Hao helped in the
321
ultrasonic measurements on rock specimens. This work is supported by the
322
Distinguished Professor Program of Jiangsu Province, China, the Cultivation Program
323
of the “111 Plan”, China (BC2018019), and the Fundamental Research Funds for the
324
Central Universities (2016B13114), China. Experimental data associated with this
325
article can be found in the Supplementary Material.
326
References
327
Adam, L., Batzle, M., Brevik, I., 2006. Gassmann fluid substitution and shear
328
modulus variability in carbonates at laboratory seismic and ultrasonic
329
frequencies. Geophysics, 71(6), P.F173–F183. https://doi.org/10.1190/1.2358494
330
Adelinet, M., Fortin, J., Guéguen, Y., Schubnel, A., Geoffroy, L., 2010. Frequency
331
and fluid effects on elastic properties of basalt: Experimental investigations.
332
Geophysical Research Letters, 37(2). https://doi.org/10.1029/2009GL041660
333
Anjos, S. M. C., Deros, L. F., Silva, C. M. A., 2003. Chlorite authigenesis and
334
porosity preservation in the Upper Cretaceous marine sandstones of the Santos
335
Basin, offshore eastern Brazil. International Association of Sedimentologists, 34,
336
291–316. https://doi.org/10.1002/9781444304336.ch13
337
Assefa, S., McCann, C., Sothcott, J., 2003. Velocities of ccompressional and shear
338
waves
in
limestones.
Geophysical
339
doi:10.1046/j.1365-2478.2003.00349.x
Prospecting,
51(1),
1–13.
340
Ba, J., Carcione, J. M., Nie, J. X., 2011. Biot‐ Rayleigh theory of wave propagation in
341
double-porosity media. Journal of Geophysical Research, 116, B06202.
342
doi:10.1029/2010JB008185
343
Ba, J., Zhao, J. G., Carcione, J. M., Huang, X. X., 2016. Compressional wave
344
dispersion due to rock matrix stiffening by clay squirt flow. Geophys. Res. Lett.,
345
43, 6186–6195. https://doi.org/10.1002/2016GL069312
346
Ba, J., Xu, W. H., Fu, L. Y., Carcione, J. M., Zhang, L., 2017. Rock anelasticity due
347
to patchy saturation and fabric heterogeneity: A double double-porosity model of
348
wave propagation. Journal of Geophysical Research-Solid Earth, 122(3),
349
1949–1976. https://doi.org/10.1002/2016JB013882
350 351
Batzle, M., Wang, Z., 1992. Seismic properties of pore fluids. Geophysics, 57(11), 1396–1408. https://doi.org/10.1190/1.1443207
352
Carcione, J. M., 2014. Wave Fields in Real Media. Theory and numerical simulation
353
of wave propagation in anisotropic, anelastic, porous and electromagnetic media,
354
Elsevier., Third edition, extended and revised.
355
Carcione, J. M., Cavallini, F., Ba, J., Cheng, W., Qadrouh, A., 2018. On the
356
Kramers-Kronig relations, Acta Rheologica.
357
https://link.springer.com/article/10.1007%2Fs00397–018-1119–3
358
Dvorkin, J., Nur, A., 1993. Dynamic poroelasticity: A unified model with the squirt
359
and
360
https://doi.org/10.1190/1.1443435
361
the
Biot
mechanisms.
Geophysics,
58(4):
524–533.
Dvorkin, J., Nolen-Hoeksema R., Nur A., 1994. The squirt-flow mechanism:
362
Macroscopic
description.
363
https://doi.org/10.1190/1.1443605
Geophysics,
59(3):
428–438.
364 365
Dvorkin, J., Mavko, G., Nur, A., 1995. Squirt flow in fully saturated rocks. Geophysics, 60(1): 97–107. https://doi.org/10.1190/1.1443767
366
Fedrizzi, R. M., Ceia, M. A. R. de, Missagia, R. M., Santos, V. H., Neto, I. L., 2018.
367
Artificial carbonate rocks: Synthesis and petrophysical characterization. Journal
368
Of
369
https://doi.org/10.1016/j.petrol.2017.12.089
Petroleum
Science
And
Engineering,
163,
303–310.
370
Fu, B. Y., Guo, J. X., Fu, L. Y., Glubokovskikh, S., Galvin, R. J., Gurevich, B., 2018.
371
Seismic dispersion and attenuation in saturated porous rock with aligned slit
372
cracks.
373
doi:10.1029/2018JB015918
374
Journal
of
gas-saturated
376
https://doi.org/10.1190/1.1443666
378
Research-Solid
Earth.
Gist, G. A., 1994. Interpreting laboratory velocity measurements in partially
375
377
Geophysical
rocks.
Geophysics,
59(7),
1100-1109.
Gassmann, F., 1951. Elastic waves through a parking of spheres. Geophysics, 16, 673–685. doi:10.1190/1.1437718
379
Guo, M., Fu, L., Ba J., 2009. Comparison of stress-associated coda attenuation and
380
intrinsic attenuation from ultrasonic measurements, Geophysical Journal
381
International, 178, 447-456. https://doi.org/10.1111/j.1365-246X.2009.04159.x
382
Guo, M. Q., Ba, J., Ma, R. P., Chen, T. S., Zhang, L., Pang, M. Q., Xie, J. Y., 2018.
383
P-wave velocity dispersion and attenuation in fluid-saturated tight sandstones:
384
Characteristics analysis based on a double double-porosity structure model
385
description.
386
doi:10.6038/cji2018L0678
387
Chinese
Journal
of
Geophysics,
61(3),
1053–1068.
Han, D. H., Nur, A., Morqan, D., 1986. Effects of porosity and clay content on wave
388
velocities
in
sandstones.
389
doi:10.1190/1.1442062
Geophysics,
51(11),
2093–2107.
390
Jeong, H., Hsu, D. K., 1995. Experimental analysis of porosity-induced ultrasonic
391
attenuation and velocity change in carbon composites. Ultrasonics, 33(3),
392
195-203. https://doi.org/10.1016/0041-624X(95)00023-V
393
King, M. S., Marsden, J. R., 2002. Velocity dispersion between ultrasonic and seismic
394
frequencies in brine-saturated reservoir sandstones. Geophysics, 67(1), 254–258.
395
https://doi.org/10.1190/1.1451700
396
King, M. S., Marsden, J. R., Dennis, J. W., 2000. Biot dispersion for P-and S-wave
397
velocities in partially and fully saturated sandstones. Geophysical Prospecting,
398
48(6), 1075–1089. doi:10.1111/j.1365-2478.2000.00221.x
399
Klimentos, T., McCann, C., 1990. Relationships among compressional wave
400
attenuation, porosity, clay content, and permeability in sandstones. Geophysics,
401
55(8), P998–1014. https://doi.org/10.1190/1.1442928
402
Lopes, S., M. Lebedev, C., Müller, T. M., Clennell, M. B., Gurevich, B., 2014. Forced
403
imbibition into a limestone: measuring P-wave velocity and water saturation
404
dependence on injection rate. Geophysical Prospecting, 62(5), 1126-1142.
405
doi:10.1111/1365-2478.12111
406
Mao, Z. G., Zhu, R. K., Luo, J. L., Wang, J. H., Du, Z. H., Su, L., Zhang, S. M., 2015.
407
Reservoir characteristics, formation mechanisms and petroleum exploration
408
potential of volcanic rocks in China. Petroleum Science, 12(1), 54–66.
409
doi:10.1007/s12182–014–0013–6
410
Mavko, G., Mukerji, T., Dvorkin, J., 2009. The Rock Physics Handbook: Tools for
411
Seismic Analysis of Porous Media, New York, Cambridge University Press.
412
Mavko, G., Nolen-Hoeksema, R., 1994. Estimating seismic velocities at ultrasonic
413
frequencies in partially saturated
414
https://doi.org/10.1190/1.1443587
rocks.
Geophysics,
59(2),
252-258.
415
Müller, T. M., Gurevich, B., Lebedev, M., 2010. Seismic wave attenuation and
416
dispersion resulting from wave-induced flow in porous rocks-A review.
417
Geophysics, 75(5), P. 75A147–175A164. https://doi.org/10.1190/1.3463417
418
Pham, N. H., Carcione, J. M., Helle, H. B., Ursin, B., 2002. Wave velocities and
419
attenuation of shaley sandstones as a function of pore pressure and partial
420
saturation.Geophysical Prospecting, 50, 615–627.
421
doi:10.1046/j.1365-2478.2002.00343.x
422
Pride, S. R., Berryman, J. G., Harris, J. M., 2004. Seismic attenuation due to
423
wave-induced flow. Journal of Geophysical Research: Solid Earth, 109(B1).
424
doi:10.1029/2003jb002639
425
Regnet, J. B., Robion, P., David, C., Fortin, J., Brigaud, B., Yven, B., 2015. Acoustic
426
and reservoir properties of microporous carbonate rocks: Implication of micrite
427
particle size and morphology. Journal of Geophysical Research:Solid Earth
428
banner, 120(2), 790–811. doi:10.1002/2014jb011313
429
Sharma, R., Prasad, M., Batzle, M., Vega, S., 2013. Sensitivity of flow and elastic
430
properties to fabric heterogeneity in carbonates. Geophysical Prospecting, 61(2),
431
270–286. doi:10.1111/1365–2478.12030
432
Sruoga, P., Rubinstein, N., 2007. Processes controlling porosity and permeability in
433
volcanic reservoirs from the Austral and Neuquén Basins, Argentina. AAPG
434
Bulletin, 91(1), 115–129. doi:10.1306/08290605173
435
Vernik, L., 1994. Predicting lithology and transport properties from acoustic
436
velocities based on petrophysical classification of siliciclastics. Geophysics,
437
59(3), 420–427. https://doi.org/10.1190/1.1443604
438 439 440
Wang, Z. Z., 2001. Fundamentals of seismic rock physics. Geophysics, 66(2), 398–412. https://doi.org/10.1190/1.1444931 Wang, D. X., 2016a. Study of the rock physics model of gas reservoirs in tight
441
sandstone.
Chinese
442
doi:10.1002/cjg2.30028
Journal
of
Geophysics,
59(12),
4603–4622.
443
Wang, Z. Z., 2016b. Research on the Effects of Pore Structure on the Elastic Wave
444
Properties in Carbonate Rocks,, Doctoral dissertation. Retrieved from CNKI.,
445
http://kns.cnki.net/kns/brief/default_result.aspx. Qingdao: China University of
446
Petroleum, (East China)
447
Yan, X. F., Yao, F. C., Cao, H., Ba, J., Hu, L. L., Yang, Z. F., 2011. Analyzing the
448
mid-low porosity sandstone dry frame in central Sichuan based on effective
449
medium
450
doi:10.1007/s11770–011-0293–1
theory.
Applied
Geophysics,
8(3),
163–170.
451
Zaitsev, V. Y., Sas, P., 2004. Effect of high-compliant porosity on variations of P- and
452
S-wave velocities in dry and saturated rocks: comparison between theory and
453
experiment.
454
http://vladimir.zaytsev.net/articles/2004_crack_PHMe.pdf
Physical
Mesomechanics,
7(1–2),
37–46.
455
Zamora, M., Sartoris, G., Chelini, W., 1994. Laboratory measurements of ultrasonic
456
wave velocities in rocks from the Campi Flegrei volcanic system and their
457
relation to other field data. Journal of Geophysical Research-Solid Earth, 99(B7),
458
13553–13561. https://doi.org/10.1029/94JB00121
459
460
Figure Captions
461
Figure 1. Crossplots of VP and VS for (a) 112 carbonates, (b) 128 sandstones and (c)
462
56 volcanic rocks at full gas and full water saturations. Liner fits are shown.
463
Figure 2. Linear fit of (a) VP and (b) VS and porosity in the low porosity range (< 8 %)
464
for the carbonates (circle), sandstones (square) and volcanic rocks (triangle) at full gas
465
saturation. The dashed lines represent the fit results.
466
Figure 3. Crossplot of P-wave velocity dispersion and porosity for the tight
467
carbonates (including dolomites and limestones), sandstones and volcanic rocks
468
(including tuffs, tufflavas, and rhyolite phases) in our measurements. The dashed lines
469
represent the regressions.
470
Figure 4. Crossplots of P-wave dispersion and porosity for the whole datasets of (a)
471
carbonates, (b) sandstones and (c) volcanic rocks. Gaussian fits are shown. (d)
472
Histogram of P-wave velocity dispersion as a function of porosity for the datasets of
473
carbonates, sandstones and volcanic rocks.
474
Figure 5. (a) Measured P-wave velocities in water-saturated sample DT10 (carbonate,
475
porosity: 11.75%), SD17 (sandstone, porosity: 9.6%) and RS24 (volcanic rock,
476
porosity: 10.5%) compared with the Gassmann low-frequency limit and the
477
double-porosity theoretical predictions (we show the experimental P-wave velocities
478
at full water saturation and at 1 MHz for the carbonates (filled circles), sandstones
479
(filled squares) and volcanic rocks (filled triangles), whereas the open symbols
480
represent full gas saturation). (b) The double-porosity theoretical predictions of
481
P-wave dissipation factor (inverse quality factor) as a function of frequency.
482
Figure 6. The crossplots of microcracks radius (a) R0 and porosity (b) φ2 and rock
483
total porosity for carbonates, sandstones and volcanic rock. Gaussian fits are shown.
484
Figure 7. The crossplots of P-wave velocity dispersion and microcrack radius (a) R0
485
and microcrack porosity (b) φ2 in carbonates.
486
487
Table Caption:
488
Table 1. Rock properties and measurement conditions Lithology
Measured by
Collected from
Samples
Porosity
Permeability
Density 3
K0
Pc
Pp
T
Frequency
(%)
(mD)
(g/cm )
(GPa)
(MPa)
(MPa)
(°C)
(MHz)
Fluid
Dolomite
This study
Tarim Basin et al.
DT1-13
4.99-16.87
0.08-162.75
2.32-2.69
91.0
80
10
140
1
Gas, Water
Limestone
This study
Tarim Basin et al.
LT1-5
0.71-2.50
0.01-1.56
2.63-2.67
56.3
70
10
140
1
Gas, Water
Limestone
Regnet et al. (2015)
Eastern Paris Basin
L_R1-90
2.12-25.76
0.01-0.88
2.12-2.74
63.7
-
0.1
20
0.5
Dry, Water
Carbonate
Wang (2016b)
Synthetic Carbonate
C_W1-4
21.20-23.10
55.90-77.20
2.13-2.19
89.2
-
0.1
20
0.25-0.5
Dry, Brine
Sandstone
This study
Dongying Sag, China
SD1-17
0.40-9.60
3.00-15.20
2.40-2.79
47.5
84-119
42-59
131-179
1
Gas, Water
Sandstone
Han et al. (1986)
Gulf of Mexico et al.
S_H1-70
4.08-29.82
0.01-194.80
1.79-2.49
34.7
40
1
22
0.6-1
Dry, Water
Sandstone
Wang (2016a)
Ordos Basin
S_W1-23
3.81-14.50
0.03-1.98
2.22-2.59
33.4
58
29
105
1
Gas, Water
Sandstone
Guo et al. (2018)
Sichuan Basin
S_G1- 10
3.03-13.35
0.001-1.32
2.30-2.61
31.5
45
10
22
-
Gas, Water
Sandstone
King et al. (2000)
Hydrocarbon
S_K1- 8
22.00-28.00
2.00-2600.00
2.51-2.65
40.0
70
30
20
0.3-0.9
Dry, Brine
reservoirs
489 490
Rhyolite
This study
Songliao Basin
RS1-25
0.50-12.60
0.01-0.14
2.31-2.68
44.5
60
30
95
1
Gas, Water
Tuff
This study
Songliao Basin
TS1-12
0.80-10.80
0.03-0.08
2.36-2.61
44.0
60
30
95
1
Gas, Water
Tufflava
This study
Songliao Basin
TLS1-14
3.40-10.40
0.04-0.08
2.36-2.53
34.4
60
30
95
1
Gas, Water
Volcanic rocks
Zamora et al. (1994)
San Vito
V_Z1- 5
5.00-20.00
0.002-44.67
2.19-2.57
40.0
-
0.1
20
1
Dry, Water
K0 is the bulk modulus of the mineral mixture; Pc is the confining pressure; Pp is the pore pressure and T is the temperature.
491
492 493 494
Figure 1.
495 496
Figure 2.
497
e
498 499 500
Figure 3.
501 502
Figure 4.
503
504 505 506
Figure 5.
507 508 509
Figure 6.
510 511
Figure 7.
Highlights 1. Acoustic wave dispersion peaks at a characteristic porosity around 15 % for different lithologies from our collection, including sandstone, carbonate and volcanic rock. 2. Poroelasticity modeling shows the microcrack radius and porosity have a peak in the porosity range 15-19 % for all the lithologies from our collection. 3. According to the relations between P-wave velocity dispersion and porosity, different lithologies can be discriminated for the tight rocks in this study.
S0920-4105(19)30887-3
DOI:
https://doi.org/10.1016/j.petrol.2019.106466
Reference:
PETROL 106466
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 17 May 2019 Revised Date:
11 August 2019
Accepted Date: 2 September 2019
Please cite this article as: Cheng, W., Ba, J., Fu, L.-Y., Lebedev, M., Wave-velocity dispersion and rock microstructure, Journal of Petroleum Science and Engineering (2019), doi: https://doi.org/10.1016/ j.petrol.2019.106466. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
1 2
Wave-velocity Dispersion and Rock Microstructure
3 4
Wei Chenga, Jing Baa*, Li-Yun Fub and Maxim Lebedevc
5
a. School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China
6
b. School of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
7
c. WA School of Mines: Minerals, Energy and Chemical Engineering, Curtin University, Perth,
8
Western Australia, Australia.
9
Abstract
10
Porosity, fluid type and rock texture significantly affect acoustic wave
11
propagation, since velocity dispersion and attenuation in fluid saturated rocks are
12
mainly caused by wave-induced local fluid flow between microcracks and
13
intergranular pores. We analyze P-wave velocity dispersion as a function of porosity
14
to obtain information about the rock microstructure. The P-wave velocities in
15
water-saturated rocks are predicted from measurements in gas-saturated rocks, using
16
the Gassmann fluid substitution equation (the relaxed state). The dispersion is
17
estimated from the difference between this predicted velocity and the measured one,
18
where the latter corresponds to the unrelaxed state. We evaluate the wave dispersion
19
as a function of porosity for 112 carbonates, 128 sandstones and 56 volcanic rocks,
20
including our measurements for 86 tight rocks, showing that dispersion increases with
21
porosity in the low porosity range, but decreases in the high porosity range. The
22
dispersion peak occurs at a porosity of approximately 15 %. Double-porosity
23
poroelasticity modeling based on the local fluid-flow mechanism confirms this
24
behavior. The microcrack radius has a peak in the porosity range 15-19 % for all the
25
lithologies from our collection, while the behavior of microcrack porosity is less
26
evident. The dispersion peak may reveal the characteristics of lithological units, in
27
particular porosity, fluid type and rock microstructure.
28 29
Keywords: Wave propagation; P-wave velocity dispersion; Ultrasonic measurement;
30
Gassmann equation; Carbonates; Sandstones; Volcanic rocks; Porosity; Microcracks;
31
Poroelasticity
32 33 34
*Corresponding author: Jing Ba ([email protected])
35
1. Introduction
36
Rock anelasticity - velocity dispersion and attenuation in seismic waves - is
37
affected by porosity, texture and pore fluids. Studies on attenuation and dispersion are
38
essential in guiding seismic inversion and estimating the properties of rocks (e.g.
39
Pham et al., 2002). Jeong and Hsu (1995) showed that ultrasonic attenuation increases
40
with void content in carbon composites. Klimentos et al. (1990) established a
41
correlation between attenuation, clay content and porosity in sandstones based on
42
measurements. Velocity dispersion can be quantified if attenuation is known, since
43
these properties are related by the Kramers-Kronig relations (Mavko et al., 2009;
44
Müller et al., 2010; Carcione, 2014; Carcione et al., 2018). Dispersion reflects the
45
intrinsic properties of rocks and is closely related to porosity.
46
Three different rocks lithologies are considered here. Carbonates cover a range
47
of depositional facies, with considerable textural variability, showing a wide range of
48
pore sizes and types, and fluid distribution heterogeneity (Fedrizzi et al., 2018; Lopes
49
et al., 2014; Sharma et al., 2013). Some of the deep reservoir sandstones are highly
50
porous, but the tight sandstones have low porosity, low permeability and microcracks
51
(Anjos et al., 2003; Guo et al., 2018). The volcanic rocks underwent cooling,
52
solidification and the epidiagenesis stage, and can be characterized by a strong
53
heterogeneity and complex composition (Mao et al., 2015; Sruoga and Rubinstein,
54
2007).
55
Laboratory measurements of ultrasonic waves in rocks have been frequently used
56
to investigate the relations between the wave properties and rock properties. Han et al.,
57
(1986) measured the compressional (P-) and shear (S-) wave velocities of sandstones
58
at full saturation. Assefa et al. (2003) showed that these velocities decrease with
59
increasing porosity in carbonates, with the P-wave velocities decreasing
60
approximately twice as fast compared to the S-wave velocities. Adelinet et al. (2010)
61
investigated the elastic properties of basalt by using ultrasonic tests, confirming the
62
difference between the high- and low-frequency rock moduli under full saturation, a
63
difference that decreases when crack density decreases.
64
Gassmann equation can be used to predict the compressional wave velocity of a
65
water-saturated rock based on the properties of the dry-rock skeleton and fluid, i. e.,
66
using fluid substitution (Gassmann, 1951). However, it is only valid at the low
67
frequency limit, where the wave-induced pore fluid pressures are equilibrated
68
throughout the pore space (specifically, between the soft cracks and the stiff
69
intergranular pores) (Mavko and Nolen-Hoeksema, 1994; King and Marsden, 2002).
70
Adam et al. (2006) showed that Gassmann equation can give a good prediction at
71
seismic frequencies for carbonates with round pores or vugs. At ultrasonic frequencies,
72
the wave-induced fluid pressure gradient between soft and stiff pores does not
73
equilibrate in each wave cycle. This results in a stiffening effect, and the Gassmann
74
equation underestimates the compressional wave velocity. The velocity dispersion can
75
be estimated by computing the difference between the Gassmann prediction and
76
measurements at full liquid saturation (King and Marsden, 2002; Regnet et al., 2015).
77
For an undrained rock, the difference between the high- and low-frequency
78
moduli is interpreted as the effect of wave-induced squirt-flow (or local fluid flow)
79
between microcracks and intergranular pores (Adelinet et al., 2010). Dvorkin and Nur
80
(1993) proposed the Biot/squirt (BISQ) model, which incorporates both the Biot
81
global flow and the local flow into the same theoretical framework. The model was
82
applied for predicting compressional wave velocities in sandstones at sonic and
83
ultrasonic frequencies (Dvorkin et al., 1994, 1995). Recently, the double-porosity
84
model has been introduced, where two pore phases with different compressibilities are
85
considered to describe the velocity-dispersion effect due to wave-induced fluid flow
86
(Pride et al., 2004; Ba et al., 2016, 2017; Fu et al., 2018).
87
The dependence of the wave properties of common rocks on their microstructure
88
is not fully understood. We measure ultrasonic P- and S-wave velocities in 18
89
carbonates, 17 sandstones and 51 volcanic rocks at full-water and full-gas saturations,
90
and complement the dataset with experimental data collected from the literatures
91
(Regnet et al., 2015; Han et al., 1986; Wang, 2016a; Wang, 2016b; Guo et al., 2018;
92
King et al., 2000; Zamora et al., 1994). The velocity dispersion is estimated by using
93
the Gassmann equation and the experimental velocities at full-gas and full-water
94
saturations. The relation between dispersion and porosity is analyzed. A
95
double-porosity theory, developed by Ba et al. (2011, 2017), is adopted to model the
96
stiffening/dispersion effect for different lithologies. On the basis of this modeling
97
theory, we obtain the characteristics of the rock microstructutre.
98
2. Experimental Data
99
2.1. Experimental Set-up and Rock Specimens
100
The experimental set-up of Guo et al. (2009) is used for the ultrasonic-wave
101
measurements on 18 carbonates (5 limestones and 13 dolomites), 17 sandstones, and
102
51 volcanic rocks (25 rhyolites, 12 tuffs and 14 tufflavas). The experimental set-up
103
consists of a pulse generator, a digital oscilloscope, a high pressure vessel, the
104
acoustic testing unit, a confining pressure control unit, a pore pressure control unit
105
and a temperature control unit. The transmitting transducers are PZT-ceramic crystals
106
(Piezoelectric Ceramic transducer), which are used to generate P- and S-wave
107
velocities (VP and VS), respectively. The receiving transducer is connected to a
108
computer through a signal amplifier. The core is jacketed within rubber tubing, and
109
each endplate has a pore fluid inlet.
110
The carbonates are collected from Ordovician and Cambrian formations (> 4.0
111
km depth), West China, with low-moderate porosity, dissolved pores and rare clay.
112
The sandstones, collected from the Paleogene formation, in the Dongying sag, East
113
China (around 4.0 km depth), are composed of feldspar, quartz, and rare clay. The
114
volcanic rocks belong to the Lower Cretaceous formation, Songliao Basin, Northeast
115
China (around 3.6 km depth); the volcanic rocks exhibit low porosity and low
116
permeability, and are mainly composed of pyroclast and rare arfvedsonite.
117
Ultrasonic VP and VS, at the dominant frequency of 1 MHz, are measured for
118
each sample at full-water and full-gas (nitrogen) saturations states. In addition to our
119
measurements on the three lithologies, experimental data by Regnet et al. (2015), Han
120
et al. (1986), Wang (2016a), Wang (2016b), Guo et al. (2018), King et al. (2000) and
121
Zamora et al. (1994) are analyzed. Each dataset and the corresponding measurement
122
condition (including the pressure and temperature) are given in Table 1. The
123
measured temperatures for the 13 sets of rock samples are not the same, and in the
124
dispersion analysis of this work, the effect of temperature on fluid properties is
125
incorporated by Batzle and Wang (1992).
126
Figure 1 shows crossplots of VP and VS for all the data sets, at full-gas (dry) and
127
full-water saturations. The correlation of a linear fitting between VP and VS in
128
carbonates is the best, and that of volcanic rocks is the worst. The slope of VP versus
129
VS is 1.6 in carbonates, higher than those in sandstones and volcanic rocks. For each
130
lithology, the slope of VP versus VS at full gas saturation is higher than that at full
131
water saturation.
132
2.2. Determination of The Bulk Modulus of The Mineral (K0)
133
The bulk modulus of the solid (effective mineral grains) can be estimated by
134
using effective medium theories (Ba et al., 2016), if the mineral components, contents
135
and geometrical parameters are known. However, for most rocks, these properties can
136
hardly be obtained. Alternatively, rocks of the same lithology are classified into
137
subsets by analyzing the specimens with similar lithological characteristics and
138
minerals. A linear fit of the velocity-porosity relations in the low porosity range gives
139
an estimation of the effective solid modulus for the whole set (Vernik, 1994; Yan et
140
al., 2011). Figure 2a and 2b show the results for the limestones, sandstones, and
141
rhyolite rocks (porosity less than 8 %). For each of the three sets, VP and VS at zero
142
porosity are computed, and thus, K0 is obtained.
143
Modulus K0, given in Table 1, is obtained from the limestones, sandstones,
144
rhyolite, tuff and tufflava (our data), and from the results by Han et al. (1986), Wang
145
(2016a), Guo et al. (2018) and Zamora et al. (1994). For our dolomites and the
146
limestones of Regnet et al. (2015), the method is unreliable due to the lack of data in
147
the low porosity range, therefore for these rocks K0 is taken from Mavko et al. (2009).
148
K0 is 40.0 GPa for the sandstone set of King and Marsden (2002), and 89.2 GPa for
149
the carbonate set of Wang (2016b).
150
3. P-wave Velocity Dispersion
151
3.1. Gassmann Fluid Substitution
152
The Gassmann equation (Gassmann, 1951; Carcione, 2014) is used to estimate
153
the bulk modulus of the water-saturated rock ( K(sat) ) from velocity measurements of
154
the gas-saturated rock. Gas is assumed to cause no stiffening effect at ultrasonic
155
frequencies (Gist, 1994). Therefore, the gas-saturated ultrasonic experiments measure
156
a relaxed state and give the dry-rock bulk modulus, Kb. Gassmann equation is based
157
on the assumption that wave-induced fluid pressures are equilibrated throughout the
158
pore space, which means a completely relaxed state, i. e., the low-frequency (LF)
159
limit. The Gassmann equation is (LF) K (sat)
160
(LF) K 0 − K(sat)
=
Kf Kb + K0 − Kb φ ( K 0 − K f )
(1)
161
where Kf and K0 are the bulk moduli of fluid and mineral mixture, respectively, ϕ is
162
the rock porosity, and Kb is the bulk modulus of the rock skeleton without pore fluids
163
(LF) (e.g., Mavko et al., 2009; Carcione, 2014). K (sat) is computed from equation (1) for
164
each specimen, where K0 is determined in 2.2, the fluid properties are obtained at the
165
measurement conditions according to Batzle and Wang (1992).
166
The P-wave velocity dispersion is then estimated as the difference between the
167
(HF) measured P-wave velocity at ultrasonic frequencies (high-frequency, HF), VP(sat ) , and
168
(LF) the velocity obtained from the Gassmann equation, VP(sat) , as follows
169
170
Dispersion=
(HF) (LF) VP(sat) − VP(sat ) (LF) VP(sat)
.
(2)
3.2. Dispersion as a Function of Porosity in Tight Rocks
171
The velocity dispersion is estimated by applying equation (2) to the three sets of
172
tight rocks (carbonate, sandstone and volcanic rocks) with six subsets, i.e., dolomite,
173
limestone, sandstone, tuff, tufflava and rhyolite, as shown in Figure 3. The dispersion
174
is generally positive for the tight rocks, indicating that the measured ultrasonic
175
P-wave velocity of the saturated rock is higher than the predicted velocity by the
176
Gassmann equation, as expected. Similar results were reported by Wang (2001), King
177
et al. (2002) and Zaitsev and Sas (2004), and attributed to the presence of open
178
microcracks or compliant pores, and the related squirt-flow mechanism. However, in
179
most of these tight specimens, the dispersion is less than 5 %, and apparently
180
increasing with porosity, suggesting that the microcrack density increases accordingly.
181
It can be seen that the subsets of dolomite and limestone of carbonate (measured at
182
the same condition) have the same linear trend. Similarly, the three subsets of
183
volcanic rocks have a linear trend, and each subset cannot be discriminated from each
184
other on the basis of the dispersion. However, the three lithologies can be
185
distinguished, with the volcanic rocks having the highest dispersion and slope (0.33),
186
and carbonates having the lowest (0.14).
187
3.3. Relation Between Dispersion and Porosity
188
The porosities of our specimens are mainly less than 12 % (tight rocks). The
189
thirteen rock sets listed in Table 1 are considered to cover the full porosity range.
190
The measured conditions of these data reflect the actual in-situ conditions of typical
191
shallow geological formations. Figure 4 (a), (b) and (c) presents crossplots of
192
dispersion and porosity for the three lithologies. The most interesting fact is that
193
dispersion increases with porosity in the low porosity range (< 15 %), but decreases
194
for moderate to high porosities (> 15 %). A Gaussian fit of the different lithologies
195
shows that the dispersion has a peak at a porosity of approximately 15 % (15.7 %,
196
14.9 % and 14.4 %, for the carbonate, sandstone and volcanic rocks, respectively).
197
Figure 4d gives the histogram of P-wave velocity dispersion as a function of porosity
198
for the carbonates, sandstones and volcanic rocks. The trend validates that the peak of
199
P-wave velocity dispersion at a characteristic porosity can be expected in the
200
moderate porosity range (12-16 %) for the three lithologies.
201
The dispersion characteristics are less reliable for volcanic rocks, since there are
202
few data in the moderate-high-porosity range. However, the data in Figure 4c roughly
203
shows a similar trend as those of carbonates and sandstones. Negative values of the
204
dispersion in Figure 4a and 4b indicate that the same K0 for each set may not be so
205
reliable. However, there is no effective approach to precisely determine K0 for each
206
specimen, in view of a detailed lithological and mineralogical information. The
207
statistical analysis here shows the trend.
208
4. Poroelasticity Modeling of Wave Dispersion
209
4.1. Theory of Wave-induced Fluid Flow Due to Microcracks
210
The wave-induced local fluid flow between compliant microcracks and
211
intergranular pores causes the stiffening effect of the rock matrix at ultrasonic
212
frequencies, which results in the dispersion in rocks. Apparently, the microcrack
213
properties change with porosity and lead to the phenomena observed in Figure 4.
214
The double-porosity theory (Ba et al., 2011, 2017) is used to model the
215
microscopic local fluid-flow mechanism (see Appendix A for the governing equations
216
of wave propagation and the velocity prediction method). Figure 5 compares the
217
experimental data with the theoretical results for samples DT10, SD17 and RS24. The
218
basic rock properties are given in Supplementary Material; Kb is determined
219
according to the measurements in gas-saturated/dry rocks. The predictions at full
220
water saturation are based on poroelasticity modeling, where the optimization is
221
performed by using the inclusion (i. e., the cracked grain with microscopic
222
heterogeneity) radius, inclusion porosity and inclusion bulk modulus as free
223
parameters, which are limited to strict and reasonable ranges during modelling, and
224
the other fixed parameters can be measured or estimated from the measurements. We
225
obtain a set of optimal parameters for each rock by fitting the P-wave velocity of
226
saturated rocks at the corresponding experimental frequency. Details can be found in
227
the Supplementary Material. We take inclusion radii of 90 µm, 370 µm and 100 µm,
228
inclusion porosities of 0.90 %, 1.41 % and 0.28 %, and inclusion bulk moduli of 9.70
229
GPa, 2.00 GPa and 5.30 GPa, for the DT10, SD17 and RS24 samples, respectively.
230
The results show that the double-porosity theory yields the same prediction of the
231
Gassmann equation at the low frequency limit, and predicts the stiffening effect of the
232
rock matrix due to local fluid flow at ultrasonic frequencies. Moreover, the theory
233
predicts the P-wave velocity dispersion, compatible with the measured data at full
234
water saturation. Figure 5b shows the P-wave dissipation factor (inverse quality factor)
235
versus frequency, where the P-wave dissipation factor of the volcanic rock (RS24) is
236
the highest, and that of the sandstone (SD17) is the least.
237
4.2. Microfracture Properties as a Function of Porosity
238
The poroelasticity modeling is applied to the 112 carbonates, 128 sandstones,
239
and 56 volcanic rocks. Figure 6a and 6b show the microcrack radius and microcrack
240
porosity as a function of the total porosity, respectively. A Gaussian fit shows that the
241
microcrack radius R0 has peaks porosities of 16.16 %, 18.03 % and 18.27 % for
242
carbonates, sandstones and volcanic rocks, respectively, while the microcrack
243
porosity φ2 has peaks at porosities of 15.06 % and 19.00 % for carbonates and
244
sandstones, respectively. The correlation between φ2 and the rock total porosity is
245
generally worse than that of the R0 . For volcanic rocks, no peaks can be found for
246
φ2 as a function of porosity due to the lack of data at moderate and high porosities.
247
The P-wave dispersion as a function of R0 and φ2 in the cabonates is given in
248
Figure 7a and 7b, respectively. P-wave dispersion generally increases with R0 , while
249
no clear relation can be found between P-wave dispersion and φ2 .
250
Although there are differences between the different lithologies, it can be
251
concluded that in most of the rocks, the microcrack radius and porosity increase with
252
the rock total porosity in the low porosity range (< 15 %), having peaks in the
253
porosity range of 15-19 %, while they decrease in the high porosity range (> 19 %).
254
This behavior may be related to the rock composition, fabric and texture, which are
255
associated with processes such as diagenesis. A possible explanation concerning this
256
phenomenon can be related to the geological process of rock diagenesis. Due to the
257
consolidation and compaction of rocks, in the moderate-high porosity range,
258
micropores become flat and microcracks extend with the deeper burial and the higher
259
pressure, and simultaneously, the total rock porosity decreases. Some softer pores are
260
changed to flat microcracks, and their radii are larger than primary cracks. Therefore,
261
microcrack radius increases with a decreasing porosity in moderate-high porosity
262
range. However, in the low-moderate porosity range, when the burial depth or
263
overburden stress keeps increasing, and rock porosity keeps decreasing, some of the
264
soft microcracks tend to close, and consequently, microcrack radius decreases with a
265
decreasing porosity. Further research is required to understand how these processes
266
are related to the anelastic characteristic of the rocks.
267
5. Conclusions
268
We have performed ultrasonic measurements on three sets of tight rocks, namely,
269
18 carbonates, 17 sandstones and 51 volcanic rocks, at full gas and water saturated
270
conditions. Assuming that the rock is relaxed at full-gas saturation, the Gassmann
271
equation is used to predict the P-wave velocity at full water saturation and the
272
low-frequency (seismic) limit. Wave dispersion is then estimated as the difference
273
between the Gassmann prediction and the ultrasonic measurements. Dispersion
274
increases with porosity for the tight rocks of this study. The different lithologies can
275
be discriminated from the different linear slopes, with the volcanic rocks showing the
276
strongest dispersion. However, for each lithology, the subsets (e.g., dolomite and
277
limestone) cannot be discriminated from each other. Adding experimental data from
278
the literature, a statistical analysis on 13 data sets with 296 samples shows that the
279
P-wave dispersion has peaks at approximately 15 % porosity for all the lithologies,
280
which indicating that wave dispersion decreases with porosity in the high porosity
281
range, instead of increasing.
282
The double-porosity theory is used to model the P-wave dispersion, describing
283
the stiffening effects of the rock matrix due to the presence of microcracks and the
284
related wave-induced fluid flow. The results reveal that the microcrack radius and
285
porosity have peaks at moderate porosities for the three lithologies. This indicates that
286
the total porosity can be related to microcrack presence, in the sense that these have a
287
high density at moderate total porosities (15-19 %) for the three lithologies from our
288
collection. The geological mechanism explaining this fact is still unclear and further
289
research is required.
290
Appendix A: The Double-porosity Theory
291
The double-porosity theory (Ba et al., 2011, 2017) is used to model the
292
microscopic local fluid-flow mechanism. The host medium has stiff intergranular
293
pores with porosity φ1 , while the inclusions are grains containing compliant
294
microcracks with porosity φ2 . The governing equations for wave propagation are
295
N ∇ 2u + ( A + N )∇e + Q1∇(ξ1 + φ2ζ ) + Q2∇(ξ 2 − φ1ζ ) , && (1) + ρ U && (2) + b (u& − U & (1) ) + b (u& − U & (2) ) && + ρ U =ρ u 00
01
02
1
2
296
&& (1) − b (u& − U & (1) ) , && + ρ11U Q1∇e + R1∇(ξ1 + φ2ζ ) = ρ 01u 1
297
&& (2) − b (u& − U & (2) ) , && + ρ 22 U Q2∇e + R2∇(ξ 2 − φ1ζ ) = ρ 02u 2
298
φ2 (Q1e + R1 (ξ1 + φ2ζ )) − φ1 (Q2e + R2 (ξ 2 − φ1ζ )) ρ . η 1 = R02φ12φ2φ20 ( f ζ&& + ζ& ) φ10 κ1 3
(A1)
299
where u , U(1) and U(2) are the particle displacements of the rock frame, fluid in
300
intergranular pores, and fluid in inclusion microcracks, respectively, e , ξ1 and ξ2
301
are the corresponding displacement divergence fields, the scalar ζ represents the
302
variation of fluid content, and φ10 and φ20 are the absolute porosities of the
303
intergranular pores and cracked grains, respectively; φ2 =v2 ⋅ φ20 , where v2 is the
304
inclusion (cracked grains) volume content. The rock porosity is φ =φ1 +φ2 , R0 is the
305
inclusion radius, and κ1 , η and ρ f are the rock permeability, fluid viscosity and
306
fluid density, respectively. The stiffnesses A , N , Q1 , Q2 , R1 and R2 , the density
307
coefficients ρ 00 , ρ 01 , ρ 02 , ρ11 and ρ 22 , and the Biot dissipation coefficients b1
308
and b2 are determined on the basis of the rock and inclusion properties (Ba et al.,
309
2017). By substituting a plane P-wave kernel into equation (A1), we obtain a cubic
310
equation for P waves. The solutions yield the wave number k (Ba et al., 2011). Then,
311
the complex velocity is given by
v=
312
313
k
,
(A2)
where ω is the angular frequency, such that
1 vP = Re , v
314
315
ω
(A3)
is the phase velocity,
Q=
316
317
is the quality factor.
318
Acknowledgements
Re {v 2 }
Im {v 2 }
,
(A4)
319
The authors are grateful to the editor H. Wang and the two annonymous
320
reviewers for their help which improved the paper. Zhaobing Hao helped in the
321
ultrasonic measurements on rock specimens. This work is supported by the
322
Distinguished Professor Program of Jiangsu Province, China, the Cultivation Program
323
of the “111 Plan”, China (BC2018019), and the Fundamental Research Funds for the
324
Central Universities (2016B13114), China. Experimental data associated with this
325
article can be found in the Supplementary Material.
326
References
327
Adam, L., Batzle, M., Brevik, I., 2006. Gassmann fluid substitution and shear
328
modulus variability in carbonates at laboratory seismic and ultrasonic
329
frequencies. Geophysics, 71(6), P.F173–F183. https://doi.org/10.1190/1.2358494
330
Adelinet, M., Fortin, J., Guéguen, Y., Schubnel, A., Geoffroy, L., 2010. Frequency
331
and fluid effects on elastic properties of basalt: Experimental investigations.
332
Geophysical Research Letters, 37(2). https://doi.org/10.1029/2009GL041660
333
Anjos, S. M. C., Deros, L. F., Silva, C. M. A., 2003. Chlorite authigenesis and
334
porosity preservation in the Upper Cretaceous marine sandstones of the Santos
335
Basin, offshore eastern Brazil. International Association of Sedimentologists, 34,
336
291–316. https://doi.org/10.1002/9781444304336.ch13
337
Assefa, S., McCann, C., Sothcott, J., 2003. Velocities of ccompressional and shear
338
waves
in
limestones.
Geophysical
339
doi:10.1046/j.1365-2478.2003.00349.x
Prospecting,
51(1),
1–13.
340
Ba, J., Carcione, J. M., Nie, J. X., 2011. Biot‐ Rayleigh theory of wave propagation in
341
double-porosity media. Journal of Geophysical Research, 116, B06202.
342
doi:10.1029/2010JB008185
343
Ba, J., Zhao, J. G., Carcione, J. M., Huang, X. X., 2016. Compressional wave
344
dispersion due to rock matrix stiffening by clay squirt flow. Geophys. Res. Lett.,
345
43, 6186–6195. https://doi.org/10.1002/2016GL069312
346
Ba, J., Xu, W. H., Fu, L. Y., Carcione, J. M., Zhang, L., 2017. Rock anelasticity due
347
to patchy saturation and fabric heterogeneity: A double double-porosity model of
348
wave propagation. Journal of Geophysical Research-Solid Earth, 122(3),
349
1949–1976. https://doi.org/10.1002/2016JB013882
350 351
Batzle, M., Wang, Z., 1992. Seismic properties of pore fluids. Geophysics, 57(11), 1396–1408. https://doi.org/10.1190/1.1443207
352
Carcione, J. M., 2014. Wave Fields in Real Media. Theory and numerical simulation
353
of wave propagation in anisotropic, anelastic, porous and electromagnetic media,
354
Elsevier., Third edition, extended and revised.
355
Carcione, J. M., Cavallini, F., Ba, J., Cheng, W., Qadrouh, A., 2018. On the
356
Kramers-Kronig relations, Acta Rheologica.
357
https://link.springer.com/article/10.1007%2Fs00397–018-1119–3
358
Dvorkin, J., Nur, A., 1993. Dynamic poroelasticity: A unified model with the squirt
359
and
360
https://doi.org/10.1190/1.1443435
361
the
Biot
mechanisms.
Geophysics,
58(4):
524–533.
Dvorkin, J., Nolen-Hoeksema R., Nur A., 1994. The squirt-flow mechanism:
362
Macroscopic
description.
363
https://doi.org/10.1190/1.1443605
Geophysics,
59(3):
428–438.
364 365
Dvorkin, J., Mavko, G., Nur, A., 1995. Squirt flow in fully saturated rocks. Geophysics, 60(1): 97–107. https://doi.org/10.1190/1.1443767
366
Fedrizzi, R. M., Ceia, M. A. R. de, Missagia, R. M., Santos, V. H., Neto, I. L., 2018.
367
Artificial carbonate rocks: Synthesis and petrophysical characterization. Journal
368
Of
369
https://doi.org/10.1016/j.petrol.2017.12.089
Petroleum
Science
And
Engineering,
163,
303–310.
370
Fu, B. Y., Guo, J. X., Fu, L. Y., Glubokovskikh, S., Galvin, R. J., Gurevich, B., 2018.
371
Seismic dispersion and attenuation in saturated porous rock with aligned slit
372
cracks.
373
doi:10.1029/2018JB015918
374
Journal
of
gas-saturated
376
https://doi.org/10.1190/1.1443666
378
Research-Solid
Earth.
Gist, G. A., 1994. Interpreting laboratory velocity measurements in partially
375
377
Geophysical
rocks.
Geophysics,
59(7),
1100-1109.
Gassmann, F., 1951. Elastic waves through a parking of spheres. Geophysics, 16, 673–685. doi:10.1190/1.1437718
379
Guo, M., Fu, L., Ba J., 2009. Comparison of stress-associated coda attenuation and
380
intrinsic attenuation from ultrasonic measurements, Geophysical Journal
381
International, 178, 447-456. https://doi.org/10.1111/j.1365-246X.2009.04159.x
382
Guo, M. Q., Ba, J., Ma, R. P., Chen, T. S., Zhang, L., Pang, M. Q., Xie, J. Y., 2018.
383
P-wave velocity dispersion and attenuation in fluid-saturated tight sandstones:
384
Characteristics analysis based on a double double-porosity structure model
385
description.
386
doi:10.6038/cji2018L0678
387
Chinese
Journal
of
Geophysics,
61(3),
1053–1068.
Han, D. H., Nur, A., Morqan, D., 1986. Effects of porosity and clay content on wave
388
velocities
in
sandstones.
389
doi:10.1190/1.1442062
Geophysics,
51(11),
2093–2107.
390
Jeong, H., Hsu, D. K., 1995. Experimental analysis of porosity-induced ultrasonic
391
attenuation and velocity change in carbon composites. Ultrasonics, 33(3),
392
195-203. https://doi.org/10.1016/0041-624X(95)00023-V
393
King, M. S., Marsden, J. R., 2002. Velocity dispersion between ultrasonic and seismic
394
frequencies in brine-saturated reservoir sandstones. Geophysics, 67(1), 254–258.
395
https://doi.org/10.1190/1.1451700
396
King, M. S., Marsden, J. R., Dennis, J. W., 2000. Biot dispersion for P-and S-wave
397
velocities in partially and fully saturated sandstones. Geophysical Prospecting,
398
48(6), 1075–1089. doi:10.1111/j.1365-2478.2000.00221.x
399
Klimentos, T., McCann, C., 1990. Relationships among compressional wave
400
attenuation, porosity, clay content, and permeability in sandstones. Geophysics,
401
55(8), P998–1014. https://doi.org/10.1190/1.1442928
402
Lopes, S., M. Lebedev, C., Müller, T. M., Clennell, M. B., Gurevich, B., 2014. Forced
403
imbibition into a limestone: measuring P-wave velocity and water saturation
404
dependence on injection rate. Geophysical Prospecting, 62(5), 1126-1142.
405
doi:10.1111/1365-2478.12111
406
Mao, Z. G., Zhu, R. K., Luo, J. L., Wang, J. H., Du, Z. H., Su, L., Zhang, S. M., 2015.
407
Reservoir characteristics, formation mechanisms and petroleum exploration
408
potential of volcanic rocks in China. Petroleum Science, 12(1), 54–66.
409
doi:10.1007/s12182–014–0013–6
410
Mavko, G., Mukerji, T., Dvorkin, J., 2009. The Rock Physics Handbook: Tools for
411
Seismic Analysis of Porous Media, New York, Cambridge University Press.
412
Mavko, G., Nolen-Hoeksema, R., 1994. Estimating seismic velocities at ultrasonic
413
frequencies in partially saturated
414
https://doi.org/10.1190/1.1443587
rocks.
Geophysics,
59(2),
252-258.
415
Müller, T. M., Gurevich, B., Lebedev, M., 2010. Seismic wave attenuation and
416
dispersion resulting from wave-induced flow in porous rocks-A review.
417
Geophysics, 75(5), P. 75A147–175A164. https://doi.org/10.1190/1.3463417
418
Pham, N. H., Carcione, J. M., Helle, H. B., Ursin, B., 2002. Wave velocities and
419
attenuation of shaley sandstones as a function of pore pressure and partial
420
saturation.Geophysical Prospecting, 50, 615–627.
421
doi:10.1046/j.1365-2478.2002.00343.x
422
Pride, S. R., Berryman, J. G., Harris, J. M., 2004. Seismic attenuation due to
423
wave-induced flow. Journal of Geophysical Research: Solid Earth, 109(B1).
424
doi:10.1029/2003jb002639
425
Regnet, J. B., Robion, P., David, C., Fortin, J., Brigaud, B., Yven, B., 2015. Acoustic
426
and reservoir properties of microporous carbonate rocks: Implication of micrite
427
particle size and morphology. Journal of Geophysical Research:Solid Earth
428
banner, 120(2), 790–811. doi:10.1002/2014jb011313
429
Sharma, R., Prasad, M., Batzle, M., Vega, S., 2013. Sensitivity of flow and elastic
430
properties to fabric heterogeneity in carbonates. Geophysical Prospecting, 61(2),
431
270–286. doi:10.1111/1365–2478.12030
432
Sruoga, P., Rubinstein, N., 2007. Processes controlling porosity and permeability in
433
volcanic reservoirs from the Austral and Neuquén Basins, Argentina. AAPG
434
Bulletin, 91(1), 115–129. doi:10.1306/08290605173
435
Vernik, L., 1994. Predicting lithology and transport properties from acoustic
436
velocities based on petrophysical classification of siliciclastics. Geophysics,
437
59(3), 420–427. https://doi.org/10.1190/1.1443604
438 439 440
Wang, Z. Z., 2001. Fundamentals of seismic rock physics. Geophysics, 66(2), 398–412. https://doi.org/10.1190/1.1444931 Wang, D. X., 2016a. Study of the rock physics model of gas reservoirs in tight
441
sandstone.
Chinese
442
doi:10.1002/cjg2.30028
Journal
of
Geophysics,
59(12),
4603–4622.
443
Wang, Z. Z., 2016b. Research on the Effects of Pore Structure on the Elastic Wave
444
Properties in Carbonate Rocks,, Doctoral dissertation. Retrieved from CNKI.,
445
http://kns.cnki.net/kns/brief/default_result.aspx. Qingdao: China University of
446
Petroleum, (East China)
447
Yan, X. F., Yao, F. C., Cao, H., Ba, J., Hu, L. L., Yang, Z. F., 2011. Analyzing the
448
mid-low porosity sandstone dry frame in central Sichuan based on effective
449
medium
450
doi:10.1007/s11770–011-0293–1
theory.
Applied
Geophysics,
8(3),
163–170.
451
Zaitsev, V. Y., Sas, P., 2004. Effect of high-compliant porosity on variations of P- and
452
S-wave velocities in dry and saturated rocks: comparison between theory and
453
experiment.
454
http://vladimir.zaytsev.net/articles/2004_crack_PHMe.pdf
Physical
Mesomechanics,
7(1–2),
37–46.
455
Zamora, M., Sartoris, G., Chelini, W., 1994. Laboratory measurements of ultrasonic
456
wave velocities in rocks from the Campi Flegrei volcanic system and their
457
relation to other field data. Journal of Geophysical Research-Solid Earth, 99(B7),
458
13553–13561. https://doi.org/10.1029/94JB00121
459
460
Figure Captions
461
Figure 1. Crossplots of VP and VS for (a) 112 carbonates, (b) 128 sandstones and (c)
462
56 volcanic rocks at full gas and full water saturations. Liner fits are shown.
463
Figure 2. Linear fit of (a) VP and (b) VS and porosity in the low porosity range (< 8 %)
464
for the carbonates (circle), sandstones (square) and volcanic rocks (triangle) at full gas
465
saturation. The dashed lines represent the fit results.
466
Figure 3. Crossplot of P-wave velocity dispersion and porosity for the tight
467
carbonates (including dolomites and limestones), sandstones and volcanic rocks
468
(including tuffs, tufflavas, and rhyolite phases) in our measurements. The dashed lines
469
represent the regressions.
470
Figure 4. Crossplots of P-wave dispersion and porosity for the whole datasets of (a)
471
carbonates, (b) sandstones and (c) volcanic rocks. Gaussian fits are shown. (d)
472
Histogram of P-wave velocity dispersion as a function of porosity for the datasets of
473
carbonates, sandstones and volcanic rocks.
474
Figure 5. (a) Measured P-wave velocities in water-saturated sample DT10 (carbonate,
475
porosity: 11.75%), SD17 (sandstone, porosity: 9.6%) and RS24 (volcanic rock,
476
porosity: 10.5%) compared with the Gassmann low-frequency limit and the
477
double-porosity theoretical predictions (we show the experimental P-wave velocities
478
at full water saturation and at 1 MHz for the carbonates (filled circles), sandstones
479
(filled squares) and volcanic rocks (filled triangles), whereas the open symbols
480
represent full gas saturation). (b) The double-porosity theoretical predictions of
481
P-wave dissipation factor (inverse quality factor) as a function of frequency.
482
Figure 6. The crossplots of microcracks radius (a) R0 and porosity (b) φ2 and rock
483
total porosity for carbonates, sandstones and volcanic rock. Gaussian fits are shown.
484
Figure 7. The crossplots of P-wave velocity dispersion and microcrack radius (a) R0
485
and microcrack porosity (b) φ2 in carbonates.
486
487
Table Caption:
488
Table 1. Rock properties and measurement conditions Lithology
Measured by
Collected from
Samples
Porosity
Permeability
Density 3
K0
Pc
Pp
T
Frequency
(%)
(mD)
(g/cm )
(GPa)
(MPa)
(MPa)
(°C)
(MHz)
Fluid
Dolomite
This study
Tarim Basin et al.
DT1-13
4.99-16.87
0.08-162.75
2.32-2.69
91.0
80
10
140
1
Gas, Water
Limestone
This study
Tarim Basin et al.
LT1-5
0.71-2.50
0.01-1.56
2.63-2.67
56.3
70
10
140
1
Gas, Water
Limestone
Regnet et al. (2015)
Eastern Paris Basin
L_R1-90
2.12-25.76
0.01-0.88
2.12-2.74
63.7
-
0.1
20
0.5
Dry, Water
Carbonate
Wang (2016b)
Synthetic Carbonate
C_W1-4
21.20-23.10
55.90-77.20
2.13-2.19
89.2
-
0.1
20
0.25-0.5
Dry, Brine
Sandstone
This study
Dongying Sag, China
SD1-17
0.40-9.60
3.00-15.20
2.40-2.79
47.5
84-119
42-59
131-179
1
Gas, Water
Sandstone
Han et al. (1986)
Gulf of Mexico et al.
S_H1-70
4.08-29.82
0.01-194.80
1.79-2.49
34.7
40
1
22
0.6-1
Dry, Water
Sandstone
Wang (2016a)
Ordos Basin
S_W1-23
3.81-14.50
0.03-1.98
2.22-2.59
33.4
58
29
105
1
Gas, Water
Sandstone
Guo et al. (2018)
Sichuan Basin
S_G1- 10
3.03-13.35
0.001-1.32
2.30-2.61
31.5
45
10
22
-
Gas, Water
Sandstone
King et al. (2000)
Hydrocarbon
S_K1- 8
22.00-28.00
2.00-2600.00
2.51-2.65
40.0
70
30
20
0.3-0.9
Dry, Brine
reservoirs
489 490
Rhyolite
This study
Songliao Basin
RS1-25
0.50-12.60
0.01-0.14
2.31-2.68
44.5
60
30
95
1
Gas, Water
Tuff
This study
Songliao Basin
TS1-12
0.80-10.80
0.03-0.08
2.36-2.61
44.0
60
30
95
1
Gas, Water
Tufflava
This study
Songliao Basin
TLS1-14
3.40-10.40
0.04-0.08
2.36-2.53
34.4
60
30
95
1
Gas, Water
Volcanic rocks
Zamora et al. (1994)
San Vito
V_Z1- 5
5.00-20.00
0.002-44.67
2.19-2.57
40.0
-
0.1
20
1
Dry, Water
K0 is the bulk modulus of the mineral mixture; Pc is the confining pressure; Pp is the pore pressure and T is the temperature.
491
492 493 494
Figure 1.
495 496
Figure 2.
497
e
498 499 500
Figure 3.
501 502
Figure 4.
503
504 505 506
Figure 5.
507 508 509
Figure 6.
510 511
Figure 7.
Highlights 1. Acoustic wave dispersion peaks at a characteristic porosity around 15 % for different lithologies from our collection, including sandstone, carbonate and volcanic rock. 2. Poroelasticity modeling shows the microcrack radius and porosity have a peak in the porosity range 15-19 % for all the lithologies from our collection. 3. According to the relations between P-wave velocity dispersion and porosity, different lithologies can be discriminated for the tight rocks in this study.