Tuesday, December 11, 2018

The Promise of Elastic Anisotropy

In certain rocks, sound waves travel at different directions. This characteristics, called elastic tence of aligned features such as fractures, microcracks, fine-scale layers or mineral grains. Combining anisotropy from petrophysics, geology and reservoir engineering may reveal a connection between these alignments and paths.

For most of this century, oilfield theory and practice assumed that waves propagate equally fast in all directions. That is, rocks have isotropic wave velocities.  But waves travel through some rock with different velocities in different directions. This phenomenon, called elastic anisotropy, occurs if there is a spatial ordering of crystals, grains, cracks, bedding planes, joints or fractures- essentially an alignment of strengths or weakness - on a scale smaller than the length of the wave. This alignment causes waves to propagate fastest in the stiffest direction. 

The existence of elastic anisotropy has been largely ignored by exploration and production geophysicist - and for good reasons. The effect is often small. With standard surface seismic measurement techniques most reservoir rocks show directional velocity differences of only 3 to 5% , which may often ben neglected. Moreover, processing data under the assumptions of an isotropic earth is already a challenge; the cost of adding the complications of anisotropy must be justified by improvements in the final seismic image. At most, anisotropy has usually been considered noise that must be filtered out, not as a useful indicator of rock properties.

However, with recent advances in acquisition, processing and interpretation of elastic data , the reasons for ignoring anisotropy are no longer valid. New acquisition hardware and measurement techniques designed to highlight anisotropy reveal highly anisotropic velocities in ultrasonic, sonic and seismic data. This article looks at the evidence for anisotropy, the best way to measure it, and how to use it to enhance reservoir description and optimize development. 

The two requirements for anisotropy - alignment in a preferential direction and at a scale smaller that of the measurement - can be understood through anologies. For the effect of alignment, imagine driving a car in an anisotropic city where streets in the north-south direction have a 30-mile-per-hour speed limit, while the east-west streets have a 50-mile-per-hour limit. East-west drivers will spend less time traveling a given distance than north-south drivers. And drivers will take east-west streets whenever possible. In an anisotropic rock, waves do the same thing, traveling faster along layers of cracks than across them. 

For the effect of scale, a less than perfect but interesting analogy is an insect on a leaf in a forest. The insect sees leaves and branches branching off in random direction : up, down, left, right and everywhere in between. A the scale of the insect, there is no preffered direction of tree growth. There are heterogenieties- sharp discontinuities between leaf and no leaf- but at the insect scale the forest is isotropic. However, to an insect a kilometer away from the forest, the trees appear neatly aligned vertically. To it, the anisotropic nature of the forest is revealed.

Similiarly, a small wavelength wave passing through a packet of thick isotropic layers of differing velocities senses the isotropic velocity of each layer.The wave sees discontinuities at each boundary , but if the wave is small enough to fit several wavelengths in every layer, the layers will still appear isotropic, and no alignment of the discontinuities will be apparent. However, a wave with a wavelength much longer than the layer thickness will not sample layers individually, but as a packet. The packet of layers act as an anisotropic material. The orientation of the layer boundaries is now perceived by the wave-and as one of the fastest directions of travel. And if the individual layers are made of aligned anisotropic grains, as is the case with shales, the anisotropic is even more pronounced.

Anisotropy is then one of the few indicators of variations in rock that can even must be studied with wavelengths longer than the scale of the variations. For once, using 100-ft [30-m] wavelength seismic waves, we can examine rock structure down to the particle scale. However, seismic waves are unable to determine whether the anisotropy is due to alignment at the particle scale or at a scale nearer the length of the wave. In the words of one anisotropy specialist, " The seismic wave is a blunt instrument in that it cannot tell us whether anisotropy is from large or small structures."

Two Types of Anisotropy

There are two styles of alignment in earth materials- horizontal and vertical - and they give rise to two types of anisotropy. Two oversimplified but convenient models have been created to describe how elastic properties, such as velocity or stiffness, vary in the two types. In the simplest horizontal, or layered , case, elastic properties may vary vertically , such as from layer to layer , but not horizontally. Such a material is called tranversely isotropic with a vertical axis of symmetry (TIV). Waves generally travel faster horizontally, along layers, than vertically. Detecting and quantifying this type of anisotroy are important for correlation purposes, such as comparing sonic logs in vertical and deviated dwwells, and for borehole and surface seismic imaging and studies of amplitude variation with offset (AVO).

The simplest case of the second type of anisotropy corresponds to a material with aligned vertical weaknesses such as cracks or fractures, or with unequal horizontal stresses. Elastic properties vary in the direction crossing the fractures, but not along the plane of the fracture. Such a material is called tranversely isotropic with a horizontal axis of symmetry (TIH). Waves travelling along the fracture direction- but within the competent rock-generally travel faster than waves crossing the fractures. Identifying and measuring this type of anisotropy yield information about rock stress and fracture density and orientation. These parameters are important for designing hydraulic fracture jobs and for understanding horizontal and vertical permeability anisotropy. 

More complex cases, such as dipping layers, fractured layered rocks or rocks with multiple fracture sets, may be understood in terms of superposition of the effects of t he individual anisotropies. 

Identifying these types of anisotropy requires understanding how waves are  affected by them. Early encounters with elastic anisotropy in rocks were documented about forty years ago in field and laboratory experiments. Many theoretical papers, too numerous to mention, address this subject, and they are not for beginners. However, it's easy to visualize waves propagating in an anisotropic material. First picture the isotropic case of circular ripples that spread across the surface of a pool of water disrupted by the toss of a pebble. In "anisotropic water" , the ripples would no longer be circular, but almost - not quite - an ellipse. Quantifying the anisotropy amounts to describing the shape of the wavefronts with terms such as ellipticity and anellipticity. In anisotropic rocks, waves behave similarly, expanding in nonspherical, not-quite ellipsoidal wavefronts. 

Waves come in three styles , all of which involve tiny motion of particles relative to the undisturbed material: in isotropic media, compressional waves have particle motion parallel to the direction of wave propagation, and two shear waves have particle motion in planes perpendicular to the direction of wave propagation.

In fluids, only compressional waves can propagate, while soilds can sustain both compressional and shear waves.  Compressional waves are sometimes called P waves, sound waves or acoustic waves, and shear waves are sometimes called S waves. The two are recognized as elastic waves. In a given material, compressional waves nearly always travel faster than shear waves.

When waves travel in an anisotropic material, they generally travel fastest when their particle motion is aligned with the material's stiff direction. For P waves, the particle motion direction and the propagation direction are nearly the same. When S waves travel in a given direction in an anisotropic medium, their particle motion becomes polarized in the material's stiff ( or fast) and compliant (or slow) directions. The waves with differently polarized motion arrive at their destination at different times - one corresponding to the fast velocity, one to the slow velocity. This phenomenon is called shear-wave splitting, or shear-wave birefringence - a term, like anisotropy, with origins in optics. Splitting occurs when shear waves travel horizontally through a layered (TIV) medium or vertically through a fractured (TIH) medium.

Since most geophysical applications place the energy source on the surface, waves generally propagate vertically. Such waves are sensitive to TIH anisotropy, and are therefore useful for detecting vertically aligned fractures. Any stress field can also produce TIH anisotropy if the two horizontal stresses are unequal in magnitude. Vertically traveling P waves by themselves cannot detect anisotropy, but by combining information from P waves traveling in more than one direction, either type of anisotropy can be detected. One approach is to combine vertical and horizontal P waves - such as those which arrive at borehole receivers from distant sources. Another technique compares P waves traveling at different azimuths. Two drawbacks to these compressional-wave methods are that horizontal wave propagation is difficult to achieve except in special acquisition geometries, and that travel paths for P waves are different, introducing into interpretation additional potential differences other than anisotropy. Shear waves, on the other hand, allow a differential measurement in one experiment by sampling anisotropic velocities with two polarizations along the same travel path, giving a greater sensitivity for anisotropy than P waves in multiple experiments. 

Compressional and shear waves of all wavelengths can be affected by anisotropic velocities, as long as the scale of the anisotropy is smaller than the wavelength. In the oil field, the scales of measurement parallel those in the analogy of the insect in a tree in a forest- the insect represents the ultrasonic scale, the tree trunk radius is similiar to the sonic scale and the height of the trees is the scale of the borehole seismic wavelength. The following sections describe how anisotropy is being used to investigate rock properties at each of those scales. 

At the Insect Scale

Wavelenghts in most sedimentary rocks are small - 0.25 to 5 mm for 250 kHz ultrasonic laboratory experiments, and they are four times smaller at 1 MHz. Ultrasonic laboratory experiments on cores show evidence for both layering and fracture related anisotropy in different rock types. While shales generally lead the pack in the relative between velocities of a given wave type in fast and slow directions, experimentalists no longer deliver laboratory results in such simple terms. Instead of the two numbers, P- and S-wave velocities, elastic properties are often characterized by plots of velocity variation around some axis of symmetry. This variation of velocity with angle of propagation has implications for the validity of many empirical relationships that have been established, linking velocity to some other rock property. 

Since ultrasonic laboratory measurements at 0.25 to 5 mm wavelength detect anisotropy, this indicates that the spatial scale of the features causing the anisotropy is much smaller than that wavelength. The main cause of elastic anisotropy in shales appears to be layering of clay platelets on the micron scale due to geotropism - turning in the earth's gravity field- and compaction enhances the effect. 

Laboratory experiments also show the effect of directional stresses on ultrasonic velocities, confirming that compressional waves travel faster in the direction of applied stress. One explanation of this may be that all rocks contain some distribution of microcracks, random or otherwise. As stress is  applied, cracks oriented normal to the direction of greatest stress will close, while cracks aligned with the stress direction will open. In most cases, waves travel fastest when their particle motion is aligned in the direction of the opening cracks. 

Measurements made on synthetic cracked rocks show such results. And computer simulations indicate that rock with an initially isotropic distribution of fractures shows anisotropic fluid flow properties when stressed. Fluid flow is greatest in the direction of cracks than remain open under applied stress, but the overall fluid flow can decrease, because cracks perpendicular to the stress direction, which would feed into open cracks, are now closed.

 At the Tree Trunk Scale

Both types of anisotropy, TIV and TIH, are also detected at the next target scale, approximately the size of a borehole radius, with the DSI Dipole Shear Sonic Imager tool.  At this scale, the most common evidence for TIV layering anisotropy comes from different P-wave velocities measured in vertical and highly deviated or horizontal wells in the same formation  -faster horizontally than vertically. But the same can be said for S-wave velocities. For years, whenever discrepancies appeared between sonic velocities logged in vertical and deviated sections, log interpreters sought explanations in tool failure or logging conditions. Now that anisotropy is better understood, the discrepancies can be viewed as additional petrophysics information. Log interpreters expect anisotropy and look for correlation between elastic anisotropy and anisotropy of other log measurements, such as resistivity.

Fracture- or stress-, induced elastic anisotropy has also been detected by sonic logs through shear-wave splitting. In formations with TIH anisotropy, shear waves generated by transmitters on the DSI tool split into fast and slow polarizations. The fast shear waves arrive at the receiver array before the slow shear waves. Also, the amount of shear wave energy arriving at the receivers varies with tool azimuth as the tool moves up the borehole, rotating on its way.

Detecting anisotropy in DSI waveform data is easy, but using the data to compute the orientations of the split shear waves is a bit trickier. If travel time and arrival energy could be measured for every azimuth at every depth, the problem would be solved, but that would require a stationary measurement. Logging at 1800 ft/hour [ 550 m / hr] , the DSI tool fires its shear sonic pulse alternately from two perpendicular transmitters to an array of similiarly oriented receivers, and the pulse splits into two polarizations. As the tool moves up the borehole, four components -from two transmitters to each of two receivers - of the shear wavefield are recorded. The four components measured at every level, along with a sonde orientation from a GPIT General Purpose Inclinometer Tool measurement , can be manipulated to simulate the data that would have been acquired in a stationary measurement. These data determine the fast and slow  directions, but cannot distinguish between the two. Including the travel-time difference information allows identification of the fast shear-wave polarization direction, which in turn is the orientation of aligned cracks, fractures or the maximum horizontal stress. 

In an example from a well operated by Texaco, Inc. in California , the fast shear-wave polarization direction obtained from such DSI measurements corresponds to fracture azimuths extracted from an FMI fullbore formation Microimager image. 

Amoco exploration and Production used information about shear velocities to optimize hydraulic fracture design in the Hugoton field of Kansas, USA. A key parameter for hydraulic fracture design is closure stress. Closure stress is related through rock mechanics models to Poisson's ratio, which is a function of the P- and S-wave velocities.

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