Preface: If we pass two weeks or so at our office without ever talking about the validity of handling geomechanical characterization merely by geophysical methods, I would consider it as an especial occasion. My alibi to this statement is a recent article authored by my colleagues Amy Fox and Carl Reine and published in the April issue of CSEG RECORDER. Certainly, such conversations are not only our company’s coffee break chit-chats but there are similar discussions that you may hear in a project meeting, a conference talk, or an university classroom. This article tries to elaborate more on this matter.
During the past two decades, the science of geomechanics has quickly widened its territory of practice from small-scale analysis of boreholes to large-scale study of reservoirs. This expansion has different reasons such as the appetite in unconventional plays, increasing public and industrial awareness of the issue of reservoir containment and caprock integrity, growing number of underground waste storage projects, and progress in production optimization for stress-sensitive reservoirs. The drastic change in the scale of regular geomechanical problems comes along with a requirement for significantly larger volumes of geomechanical data. In the borehole-scale studies, most of these data come from the wireline logs and laboratory tests on the core plugs. Usually, with some calibration and correlation, these data can fulfil the major requirements for building one-dimensional Mechanical Earth Models (1D MEMs) that are nearly good enough for wellbore stability modeling. With the increase in the scale of the problems, there seems to be a requirement for three-dimensional versions of these models (i.e., 3D MEMs) that need complete sets of geomechanical data for very large volumes of sedimentary rocks (Figure 1). In these cases, the wells are still the major benchmarks for constructing 3D MEMs but the major challenge is populating the missing data in the inter-well regions. Let’s remember that this is not a completely new issue for the petroleum industry as reservoir engineers have always been dealing with a similar problem although the nature of their required data is different than that of MEMs.
Figure 1. An Example of pesudo-3D MEM showing variation of static Young’s modulus for a CCS project (Source: Soltanzadeh and Hawkes, 2012).
Different approaches have been suggested and applied to encounter this problem such as sensitivity studies, probabilistic analyses, geostatistical modeling, and, of course, using seismic data. Among these solutions, the latter seems to be the only one that relies on real measurement of properties in the field and, thus, in the first glance, it seems to be the most acceptable approach. This is probably why we are seeing several works on using seismic data to determine different geomechanical parameters ranging from rock mechanical properties to in-situ stresses. Although this opportunity for large-scale data acquisition sounds appealing to oil and gas industry, there have been some loud concerns on the validity of these studies mostly stated by geomechanics specialists with backgrounds in rock mechanics who believe, in some cases, this approach may not be the most appropriate way to perform geomechanical characterization. They believe all the trust put by some practitioners in these models may be too excessive and unjustifiable.
Different Instruments, Different Scales, Different Behaviours
The roots of these ongoing disputes are probably the different viewpoints of these disciplines towards rock behaviour. On top of that, variations in measuring instruments, technologies, and methods used for characterization of rock behaviour play significant roles. The main objective of geophysicists and rock physicists is characterizing the behaviour of rock under the loadings imposed by wave propagation. This type of loading usually has very high frequencies (Figure 2) meaning the loads are applied in opposite directions for several times per each second [i]. This cyclic pattern of loading, that is a function of time, is commonly called dynamic loading and all the parameters that characterize the rock behaviour in response to this loading are called dynamic properties [ii]. In addition to high frequency, another characteristic of loadings imposed by wave propagation is their low strain amplitude that can only induce very small deformations in the rock. These deformations are extremely low and, therefore, it is always assumed that, under such loadings, rock will only deform within its reversible domain of mechanical behaviour (i.e., linear elastic behaviour) and not beyond that (i.e., plastic behaviour). This means that during every cycle, the induced rock deformations during each phase of loading will be completely removed by the immediately succeeding phase of unloading.
Figure 2. Frequency and amplitude ranges for different measurement methods of mechanical properties (Source: Hoffman, 2006).
It is commonly accepted that the behaviour of rock under such high-frequency and low-amplitude loadings does not necessarily describe the actual behaviour of rock when it undergoes subsurface operations such as production or injection. For example, loading and deformation of rocks induced by production is a very slow process that usually takes place during several years of operation and it is sometimes accompanied by significant rock deformations [iii] that are considerably larger than what is induced by elastic waves. This is the reason that several geomechanics engineers believe that the proper properties for describing the rock behaviour during subsurface operations must be measured using slow-paced loadings when the rock is let to deform large enough to simulate what may occur in the field. Unless with detail monitoring performed during the life time of reservoirs, there is no direct way to study this behaviour in the field. Thus, such studies are usually performed in the controlled condition of laboratories and on very small samples of rocks. In the laboratory tests designed for quantification of these behaviours, mechanical loadings with controlled rates are applied to resemble the actual loadings that occurs in the field. In such a loading process, rock is allowed to exceed the limits of its elastic behaviour (in other words, it passes its yield point) and starts behaving in an irreversible or plastic manner. In these tests, it is usual to let the rock fail under loading and even continue the test afterwards to study the rock’s post-failure behaviour. Usually, the samples in these tests are initialized with the closest estimation of in-situ stresses and some times with the ambient pore pressure (although it is common to do these tests on dry samples) in the field. These tests usually measure several parameters including elastic, plastic, and strength properties of the rock samples. Elastic properties found from these tests are usually called static or quasi-static elastic properties referring to the slow-paced loading applied during their measurements.
There are also different reasons to critique these lab tests for their misrepresentation of rock behaviour in its in-situ state in the field. One main reason is the fact that the core samples analysed in the lab are not under the influence of exact in-situ conditions experienced underground. The type of fluid, its compressibility, and pore pressure have significant influences on the mechanical behaviour of rocks. Several of these laboratory measurements are performed at dry conditions. Even for saturated samples, it is very difficult to perform a test with the exact fluid properties in the field, especially for the hydrocarbon-bearing formations. Another major issue is the effect of in-situ stresses on the rock samples. Although it is usually tried to apply the best estimates of the in-situ stresses during testing, it is almost impossible to do it perfectly due to the difficulty of measurement of in-situ stresses in the field and limitations of the lab apparatuses for applying the full stress tensor. Another major discrepancy between the lab results and the field behaviour of rocks is caused by the effect of sampling size. The samples used in the lab are tiny compared to the sampling sizes of geophysical measurements in the field. This issue becomes much more complex when the rock is heterogeneous or fractured. Usually core plugs in the lab are pieces of intact rock and their small sizes do not leave so much chance for accounting for fractures or large-scale heterogeneities. Core disturbance is not probably a less important issue leading to different behaviour of the rock. In reality, extending the results of laboratory tests to field conditions can sometimes lead to serious misunderstanding of rock behaviour. This is why, sometimes, valuable information found using in-situ measurements such as wireline sonic or seismic can provide so much information that we cannot find by lab work.
Apparently, both in-situ geophysical and lab measurements on the rock samples have their strengths and weaknesses for understanding the actual behaviour of rock in the field. Geophysical data represent the in-situ behaviour of rock but this behaviour is in response to a loading pattern that is not similar to what rock experiences during the actual subsurface operations. On the other hand, it may be possible to simulate this actual loading condition in the lab, but detaching the sample from its in-situ condition undermines the validity of these lab results for describing the actual rock behaviour as it happens in the field.
Data Integration, Does It Really Work?
The rock properties measured in the lab are preferred in most of geomechanical studies performed in the petroleum industry despite the fact that, sometimes, they may not represent the actual behaviour of rock in the field as mentioned above. Acquiring these data is usually expensive, time-consuming, and difficult while, on the other hand, wireline logs and seismic surveys can provide abundant volumes of data at a much lower cost and time. Such considerations are the main driving forces behind the attempts to correlate these two sets of data. These correlations come in different forms but the most famous ones are developed between static and dynamic elastic properties. These usually-linear correlations are widely used to estimate static properties based on sonic or seismic measurements. Also, there are so many other correlations used to calculate other parameters such as strength properties, pore pressure, and in-situ stresses as functions of geophysical measurements. Though implementing such correlations may seem a convenient and reasonable approach at the first glance, there might be some obstacles or concerns that may limit their validity.
Figure 3. Comparison of static and dynamic (measured in the lab and calculated for a dipole sonic log) Poisson’s ratio and Young’s modulus (Source: Fox and Reine, 2014).
The main concern is that the nature of different measurements are significantly dissimilar and there should be a requirement to have a correlation between these parameters. For instance, finding correlations between wireline sonic and strength properties of rock such as unconfined compressive strength (UCS) sometimes can be very difficult mainly because these parameters have been found at two completely different stages of rock deformation. Another concern is that such correlations are not always as strong as we expect them. For example, usually, there is much more chance to find a relatively acceptable correlation between dynamic and static Young’s moduli measured in the lab than between the two corresponding Poisson’s ratios. This can be because of the nature of Poisson’s ratio that is defined very differently in the dynamic and static tests in addition to its strong dependency to the loading frequency, lithology, pore pressure, and fluid content. This issue must be treated carefully as Poison’s ratio is a very important parameter with significant effects on several geomechanical problems. In practice, even the dynamic parameters used for creating such correlations are measured using ultrasonic waves on the same samples used for static measurements and not in the field. The ultrasonic measurements performed in the lab can be significantly different from that of sonic and seismic done in the field due to the effects of several factors such as wave frequency, fluid content, pore pressure, in-situ stresses, and sample disturbance (Figure 3). Some may try to reduce this difference by theoretical adjustments, for example, by implementing the Gassman’s equations to consider the effects of formation fluid content on the wave velocities when the ultrasonic laboratory tests are conducted on dry samples. These adjustments may not always be convenient as there are so many factors involved that are either difficult or expensive to account for.
How Many Birds Can We Kill with Just Two Stones?
How many rock properties are measured in geophysical measurements? The answer is not a long list, the most common parameters are usually only two: compressional and shear wave transit times and if we can acquire density from other measurements/estimations we will use that, as well. There is no doubt that these two critical parameters can efficiently capture so much about the behavioural characteristics of the rock and its filling fluid but the main question is ‘how many geomechanical rock parameters can be derived from just these two parameters?’ There are so many common prescriptions in the industry that claim to be able to provide numerous parameters such as static elastic properties, strength properties, pore pressure, in-situ stresses, anisotropy parameters, and lithological types from these parameters. The critics are probably right in doubting the excessive trust put in these calculations as it may not be reasonable to reduce several independent parameters related to so many complex physical processes occurring during millions of years to only two or three parameters. Perhaps, sometimes, we have to compromise as there are not so many other choices to quantify geomechanical properties of rocks but it is important to acknowledge that these extrapolations of data from a couple of parameters to almost everything required can be imprecise and disproportionate.
So many complex geomechanical parameters are claimed to be directly calculated based on dynamic elastic properties. The major problem with such calculations is not just that the dynamic elastic properties may not be valid for such calculations but it is also about using simplistic models (e.g., linear elastic solutions) used to find the desired parameters. For instance, breakdown pressure is a parameter that can be hardly determined even by using complex methods while there are cases where the simplistic Kirch’s solution is used to calculate this parameter.
Another example is the geophysical estimation of in-situ stresses using seismic data that is strongly criticised for its simplistic assumptions such as uniaxial deformation pattern, elastic behaviour, and ignoring the effect of faults and fractures and oversimplification of tectonic effects. In the geomechanics community, field tests based on fracturing (i.e., micro- or mini-frac tests) are usually considered the most practical and accurate approaches to measure the least principal stress (in many cases it is equal to minimum horizontal stress, Shmin). As a common way of practice, these measurements are usually used by geophysicists and petrophysicists to calibrate their calculation of Shmin based on seismic or sonic data. This seems to be a reasonable method to reduce the uncertainty if a good number of direct measurements for calibration is available. This issue becomes much more complex when it comes to the estimation of maximum in-situ horizontal stress (SHmax) that is extremely difficult to measure. Special geomechanical techniques such as reverse wellbore stability analysis are usually recommended to constrain the magnitude of SHmax. However, some practitioners insist in determining this important parameter by using simple equations based on elastic properties acquired from seismic or sonic. The cross-dipole sonic logs used by geophysics to determine in-situ stress anisotropy of the rock is another example that is criticized because its measurements may be strongly influenced by the intrinsic anisotropy of rock or fracture networks. A similar example is using these measurements to determine the orientation of horizontal stress that is usually questioned for similar reasons.
The Last Word
Apparently, the mechanical behaviour of rock is strongly influenced by the measuring systems including the measurement methods and tools. In reality, each of the geophysical and lab data are only capable of quantifying some particular characteristics of rock in response to some specific loading patterns at very specific conditions. As told by the ancient allegory of The Elephant in the Dark Room [iv] (Figure 4), it seems that each of these measuring systems can only describe certain behaviour of rocks in specific conditions that are usually different from the real behaviour of rock during subsurface operations. Thus, in reality, none of these approaches is confidently capable of capturing the rock behaviour as it may happen in the field and over-emphasising on their accuracy does not help much. Even, sometimes, it may not be straightforward to develop correlations between these different sets of data. Nevertheless, it is important to understand and value the significance of all these data for geomechanical characterization, while always acknowledge their limitations in defining the real rock behaviour. Continuous field monitoring along with reverse modelling and history matching throughout the operational life of a field are probably the best we can do to evaluate the roles of these data in describing realistic behaviour of rocks.
Figure 4. “Blind monks examining an elephant” by Hanabusa Itchō (1652–1724). Source: Wikipedia
More to Read on this Subject
Value of Integrated Geophysics by Amy Fox and Carl Reine, CSEG RECORDER, April 2014, Vol. 39, No. 04 Geomechanics: Bridging the Gap from Geophysics to Engineering in Unconventional Reservoirs by Kurt Wikel, CSEG RECORDER, May 2011, Vol. 36, No. 05 The Evolving Role of Geophysics in Exploration: From Amplitudes to Geomechanics by Eric Andersen, 2011 CSPG CSEG CWLS Convention
When geophysics met geomechanics: Imaging of geomechanical properties and processes using elastic waves by Stephen A. Hall, Mechanics of Natural Solids, 2009, pp 147-175.
Geomechanics and geophysics for Reservoir Management by Erling Fjaer, Revue Européenne de Génie Civil, Volume 10, Issue 6-7, 2006
[i] Frequencies are usually about 10-100 Hz for seismic and microcosmic measurements and about 10 kHz for wireline sonic measurements. The ultrasonic measurements performed on the core plugs in the lab can be as high as 500 kHz.
[ii] Although these rock properties have a long list (e.g., Poisson’s ratio, Young’s modulus, shear modulus, bulk modulus, etc.), in reality, there are only two impedances or wave velocities that we need to measure to calculate these parameters: compressional or primary wave velocity (Vp) and shear or secondary wave velocity (Vs). Probably, the simplest parameter derived from these velocities is the ratio of these velocities (Vp/Vs) that is usually considered as one of the most useful parameters for lithological classification of rocks. This parameter has a simple relation to one of the most important geomechanical properties, dynamic Poisson’s ratio (vd), as follows:
If density of rock (rb) is also known (either from wireline logs or lab measurements), it is also possible to find several of other dynamic properties of rock such as shear modulus (Gd), Young’s modulus (Ed) , and bulk modulus (Kd) using the following simple equations:
[iii] There are several examples of significant compaction and subsidence of the ground surface induced by reservoir compaction during production. Some famous examples are Wilmington Oil Field, California; Goose Creek Field, Texas; Ekofisk Oil Field, North Sea; Lake Maracaibo, Venezuela; San Joaquin Valley, California each showing several meters of subsidence.
[iv] This eastern allegory (most famously narrated by the Persian poet, Rumi) is about some men who were too eager to see an elephant for the first time, so they rushed to its place in the dark of night. When they came out, everyone had his own description of the creature. The one who only got the chance to touch its leg described the elephant as a tree trunk, the one who rubbed its ears said that it was like a fan, the other who felt its nose believed it was like a drain pipe, etc. Each person described some of the gigantic animal’s body members quite precisely but it was not easy for them to know that this is only a part of the whole truth about it.