Cosentini, R.

Duca, S.

Musso, G.

English

UPCommons

Evaluation of the representativeness of shale samples on basis of 
analysis of elastic wave velocities 
 
 
Musso G.(1), Cosentini R. (1), Duca S.(2) 
 
 
 
(1) Dipartimento di Ingegneria Strutturale Edile e Geotecnica, Politecnico di Torino, Corso Duca degli Abruzzi 
24, 10129 Torino (Italy). guido.musso@polito.it ; renato.cosentini@polito.it  
(2) Geomechanica Laboratory, LAIP, Eni SpA, Upstream and Technical Services, via Maritano, 26, 20097 S. 
Donato Milanese (Italy). Silvia.Duca@eni.com 
 
 
 
 
Unconventional oil and gas reservoirs are playing a significantly increasing role in offsetting 
production losses due to declining conventional oil and gas production for the past decade. For this 
reason, one of the great challenges and opportunities facing the oil and gas industry today is 
identifying, quantifying and properly exploiting gas and oil resources in unconventional reservoirs, 
particularly shale. 
Shale comprises clay and silt-sized particles that have been consolidated into rock layers of extremely 
low permeability. This low permeability claims the use of intense fracturing in order to allow 
hydrocarbon production, and appropriate fracturing claims adequate advanced modeling. 
Unfortunately, the heterogeneities and high level of anisotropy contained in unconventional gas plays 
make it impossible to use the existing conventional techniques for many applications due to the need 
for higher precision information. 
While laboratory testing plays a fundamental role for geomechanical characterization, 
representativeness of laboratory samples is often questionable. For one, core-plug measurements are 
highly variable and they are unlikely to provide representative information at the scale of a reservoir 
model. For another, when delivered to the laboratories cores proceeding from shale formations are 
normally affected by a high number of fractures, mostly aligned along the sedimentation planes, 
which also represent preferential weakness planes. Spacing among fractures can be low that 
sometimes it is almost impossible preparing specimens of the size used in normal triaxial testing. . 
One of the main questions of fundamental importance for the set up of fracturing models is then 
whether these fractures are due to coring (stress relief effects) or are already present in the insitu 
formation – and to what extent samples have been damaged by coring. 
Wireline log data can provide information on the state of the material at in situ condition, although 
they do not allow a full geomechanical characterization. This work introduces preliminary results 
concerning a methodology aimed at merging information from both laboratory characterization and in 
situ logging to ascertain the rapresentativeness of shale samples tested in the laboratory. It relies on 
the conjugate analysis of the results of ultrasonic measurements performed in the laboratory, at 
increasing level of confinements, and on sonic measurements performed at the geostatic stress 
through wireline logging – together with concurring data from porosity logs and gamma ray logs. 
Representativeness of samples is evaluated on basis of the different wavelenth and travel distance of 
ultrasonic and sonic measurements. Ultrasonic measurements, performed in the laboratory, are taken 
at frequencies f of the order of the MegaHertz and on travel distances of the scale of a few tens of 
mm, while sonic logging measurements are taken at frequencies of the order of the kiloHertz along 
distances of the order of meters. Wavelength  can be evaluated through the expression: 
 
f
V  
 
where V is the elastic wave velovity, whose range is on the order of km/s. Since the answer recorded 
by the elastic wave depends on the scale of investigation, related to the wavelength, it follows that two 
different scales are investigated by the two different devices (order of the mm for the ultrasonic, order 
of the m for the sonic logs). 
Elastic wave velocities are known to depend on the elastic properties of the rock material constituents, 
on porosity, on the geometrical arrangement and bonds between the grains (structure effects, see e.g. 
Mavko et al., 2009), together with on stress conditions.  
The effect of structure and porosity on the elastic velocity at a reference stress, in the following 
denoted by , can be expressed by the following relationship:  
 
)()(  AF  
 
where is the velocity at reference stress p’0, A is the elastic velocity in the rock material constituents 
and  is porosity. The function F() introduces both the effects of porosity and of structure on the 
wave propagation. 
The effect of stress can be described by Hertz – Mindlin type laws, which foresee an exponential 
increase of velocity with stress p’: 
 





0p
ppV
'
')'(  
 
where the exponent  depends on the material and on the type of contacts between particles 
(according to the Hertz Mindlin original formulation - spherical grains with no bonding - it is equal to 
1/6). It is also recognised (Santamarina et al., 2001, Cha et al., 2009) that for a given meterial  can be 
related to  by a linear decay relationship: 
Ultrasonic measurements taken at increasing stress on mineralogically homogeneous shale samples, 
with different porosoties, are used to calibrate parameters of the function F() and of the  –  
relationship: a specific expression for F() is then obtained, which is representative of the structural 
state of the dataset of samples in the laboratory. Thus, the expression  

 pseudo (z)= AF(log (z))  
 
where  log is porosity recorded in logs, provides along the formation values of elastic wave velocities 
at reference stress for the structural state of the specimen dataset  pseudo (z).  
Supposing known the in situ stress p’(z), the actual value of  for the formation,  well (z), can be 
determined. This is achieved through optimization methods, minimizing at each depth the objective 
function g: 
 
 
2
0 




 




zV
'p
)z('p)z,,(g log  
 
where Vlog (z) is the elastic wave velocity measured by logs. The ratio SI 
 
)z(
)z()z(SI pseudo
well

  
 
is thus a ratio of the effects of structure on wave velocity in the rock formation compared to the 
effects of structure on the specimen dataset. If SI > 1, the structure of the formation is such that the 
elastic wave velocity is higher than in the specimen dataset at the same porosity – therefore we can 
infer that coring induced damage of the samples. On the other hand, if SI<1, the structure of the 
formation is such that the elastic wave velocity is lower than in the specimen dataset at the same 
porosity – possibly due to the effect of natural fractures: these are not investigated at the laboratory 
scale, but are relevant for the in situ measurements because of the higher wavelength. 
The method briefly described was used to evaluate the representativeness of some shale samples 
(location, depth and every other specific data are omitted because of industrial interest). In the 
following figure (on the left) strucutural index evaluated by P and S wave velocities are shown. SI 
values are above 1 highliting a coring induced damage of the samples. Coring effects are visible in the 
following figure (on the right) where X-ray computed tomographies of the cores for the depth 
indicated (shlightly shadow zone) are shown. It is possible to observe persistent horizontal fractures 
along the core. 
 
 
Figure 1: SI = well/pseudo versus depth for P-wave and S-wave (on the left), X-ray computed 
tomographies of the cores (on the right). 
 
These preliminary results indicate that the proposed method is able to ascertain the representativeness 
of shale samples tested in the laboratory. The advantage of the method relies on basing the evaluation 
on the mechanical response at small strains. This allows the introduction of a new “structural index”, 
through which quantify the representativeness of the laboratory samples, and that can contribute in 
converting the parameters obtained in the laboratory (e.g. from triaxial tests) into a reliable 
geomechanical model. 
 
References 
Cha, M., Cho, G.C. and J.C. Santamarina, 2009, Long-wavelength P-wave and S-wave propagation in 
jointed rock masses: Geophysics, 74, 5, E205-E214. 
Mavko G., Mukerji T. and J. Dvorkin, 2009, The Rock Physics Handbook: Tools for Seismic 
Analysis of Porous Media: Cambridge University Press, 2nd edition. 
Santamarina, J.C., Fam, M. and K.A. Klein, 2001, Soils And Waves: Particulate Materials Behavior, 
Characterization and Process: John Wiley, New York. 
 
 
  


Evaluation of the representativeness of shale samples on basis of analysis of elastic wave velocities

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Evaluation of the representativeness of shale samples on basis of analysis of elastic wave velocities

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