Reading the Rocks
A SwRI geophysicists have created a new algorithm that uses cross-dipole sonic data to estimate formation properties around the borehole
By Jorge O. Parra, Ph.D. and Dawn Domaschk
Petroleum exploration companies rely on sophisticated analyses of the geologic formations from which they hope to produce oil and gas. The subsurface geology of a hydrocarbon reservoir typically consists of sedimentary rock such as shale, limestone or sandstone. In large part, the productive potential of a well drilled into the reservoir depends not just on the permeability and porosity of the formation in which the hydrocarbons occur, but also on the amount and distribution of fractures into which the hydrocarbons tend to gather and flow. Thus, it is important to know in what direction from the borehole these elements of non-uniformity, or anisotropy, occur in greatest numbers, and also whether they are oriented horizontally, vertically or at an angle relative to a well. The answers offer valuable clues for production-improving strategies, such as directional drilling from the original borehole outward into the formation.
In particular, reservoirs formed by sand and shale sequences are characterized by mineral distributions and cracks. Anisotropy can occur in different axes. In layered sedimentary formations, the effective stiffness properties in the vertical plane (perpendicular to the earth’s surface) are differ¬ent from the properties as seen at more horizontal planes. The axis of symmetry in this case assumes vertical transverse isotropy (VTI), where the same effective material properties exist in any azimuth direction that can represent a well intercepting a horizontal shale sequence.
Also, naturally fractured reservoirs, like those typically formed by carbonate or limestone, exhibit a different type of anisotropy called fracture-induced anisotropy, which is related to fracture permeability or porosity. Because of stress exerted by overlying formations, naturally fractured reservoirs can be formed by vertical or tilted fractures, or both. For example, the vertical fractures are oriented parallel to the well, and the axis of symmetry is perpendicular to the borehole axis. In this case the anisotropy is horizontal transverse isotropy (HTI).
Sonic well logging provides an electronic profile of a geologic formation by reading the refracted patterns of sonic waves sent through it. The process can involve a simple unipole technique that is delivered in the well, in which a single sensor measures a compressional (or primary) wave as it travels through the formation from an acoustic source in the borehole. More sophisticated data can be gathered using the cross-dipole method, so named because it sends dual, or dipole, pressure signals outward directionally, at right angles from each other, such that their pathways cross at the center of the borehole. These signals are detected as shear waves, so-called because, as they encounter non-uniform subsurface features, such as vertical fracture, they split into faster and slower waves. Shear waves naturally travel slower than the compressional wave but are more sensitive to anisotropy. The paths and arrival times of the shear waves are detected and compared at an array of sensors set farther up on the sonic tool at known distances from the signal source at the bottom.
Cross-dipole data can be acquired in deviated, or non-vertical, wells that intercept thick shale formations, such as those that are usually drilled offshore, for estimating the stiffness properties surrounding the well. These properties are important to determine vertical and horizontal seismic velocities of the shale, and the fracture-induced anisotropy properties of the reservoir. In this case, velocity refers to the speed with which seismic signals propagate through a soft or hard formation. Since a signal passes more quickly through harder, more solid rock, sonic-derived velocity yields important clues to hardness and continuity.
Stress-induced anisotropy is also an important property in the characterization of reservoirs. This includes tectonic and borehole stresses and their orientations. These properties affect well stability (breakouts) and the ability to hydro-fracture a well in order to increase its production.
Shear wave anisotropy is a robust method to determine stress directions. In more complex fracture reservoirs, cross-dipole information is integrated with other well logs; in particular when fractures are not oriented vertically. In this case, the cross-dipole provides only the effective measure of stiffness properties of the fracture zone. To obtain the intrinsic properties of the fractures, further processing and fracture modeling, combined with other well log information, are common practices.
Cross-dipole data acquisition and processing are mainly offered by large service companies to the oil and gas industry. A few small companies also provide full waveform sonic processing for quality control for some oil companies. It is becoming critical for these companies to seek a second opinion when important decisions need to be made based on the well log data, either for 3-D surface seismic ties or reservoir characterization. The lack of modeling capabilities and inversion techniques for quality control of cross-dipole sonic inversion is a prime motivator for advancing the state of the art in this area.
A team of geophysicists from Southwest Research Institute (SwRI) has developed an algorithm based on the inversion of two realistic data sets that were computer-generated using a boundary element technique. This technique allows simulating cross-dipole micro-seismograms for several sensors as a function of depth by including the change of physical properties of the rock at each source position. The resulting synthetic data sets were used as a substitute for actual observed data for creating the inversion algorithm. The objectives of this application were to test and verify the algorithm to develop a protocol for inverting actual cross-dipole sonic logs.
To develop such an inversion technique, it is important to understand the wave phenomena associated with vertical as well as deviated wells, especially the different wave mode interactions with anisotropic formations and the well, when cross-dipole sonic tools are used. The wave motion generated by the dipole source in the borehole produces a unidirectional displacement in the borehole fluid that generates strong flexure wave modes (or guided waves) in the formation. These waves gently shake the entire borehole and the flexure modes propagate up and down the borehole and also along the borehole-formation interface. The wave modes are detected by sensors located at some distance from the source. Because the dipole source is unidirectional, it yields the velocity and the variations of the formation as well as their location on the azimuth surrounding the borehole. This is the concept that led to development of cross-dipole acoustic tools by the service industry.
The SwRI team used the Transformed Boundary Integral Equation (TBIE) method to simulate cross-dipole responses representing wells drilled vertically into formations with horizontal layering, and for horizontal wells drilled into formations that have vertical fractures. This rigorous, full-waveform approach has a number of advantages: The well boundary conditions are satisfied in the model and there are no limitations in the well geometry regarding well diameter and the angle of well deviation. The software can simulate acoustic waveforms for a sonic tool having source dipoles placed in horizontal x and y axes and positioned in the center of a vertical borehole. The tool’s axis of symmetry lies along the vertical z axis, thereby assuming an x,y,z Cartesian system of coordinates.
The dipole sources are in the bottom of the sonic tool. An array of 12 sensors is oriented higher on the tool in a vertical plane along the x axis, and 12 more sensors are set in a vertical plane along the y axis. The SwRI team’s example assumed a tool with the first receiver set 2.7 meters away from the source, and with 15 centimeters between sensors on each plane. The transmitter, or source, dipoles are fired to generate shear waves that 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 the tool’s azimuth as the tool moves up the borehole, rotating as it moves upward. When waves are propagated into an anisotropic material, they generally travel fastest when their direction of motion is aligned with the stiffest material. They travel slower through the softer, more pliant segments of the material. The shear waves’ motion becomes polarized in the material’s stiff (or fast) and pliant (or slow) directions. Thus, waves with differently polarized motion arrive at their destination at different times, one corresponding to the fast velocity and the second corresponding to the slow velocity. This phenomenon is called shear-wave splitting. Splitting can occur when shear waves travel horizontally through a layered medium or vertically through a fractured medium.
The computer model allows simulation of synthetic data by following the real measurement procedure. The tool fires its directional shear sonic pulse alternately from its two transmitters (the cross dipoles) along the horizontal x and y axes to an array of similarly oriented receivers, and the pulse splits into two polarizations. As the tool is moved up the borehole, four components (from the two transmitters to each of two receivers of the shear wavefield) are recorded. These four components are named XX, XY, YX, and YY (XX represents the component of a dipole placed in the x axis and receivers in the x-plane; alternatively, XY is the component of a dipole placed in the x axis and receivers in the y-plane).
The TBIE method allows the production of accurate and efficient synthetic full-waveform sonic logs (monopole, dipole, quadrupole, etc.), and it is particularly efficient when a large number of receivers are involved. In the example, 21 depth-dependent isotropic properties were generated. To generate the data set with synthetic waveforms for the inversion, one must calculate a 3-D image consisting of the cross-dipole component in each of three planes (XX, XY and YY) for each of the 12 receivers, or 36 micro-seismograms in all for each depth. The input model parameters were plotted together as a function of depth with the inversion results.
Inversion method and results
The SwRI team developed and applied a new method for the inversion of parameters of fast and slow shear wave velocities and azimuth angles from cross-dipole logs. The geophysicists transformed the three-dimensional object function into three one-dimensional object functions under the same anisotropic conditions, while keeping the original object function’s redundancy of information. The transform was facilitated through a change of variables and subsequent mathematical treatments. In the three-dimensional object function, the fast shear wave slowness, slow shear wave slowness, and slow shear azimuth are coupled unknowns. The three one-dimensional object functions, after the transformation, are uncoupled functions of these same three parameters. This important change allows the algorithm to extract the unknowns separately, with greater accuracy than current techniques, thus eliminating the need for human guessing of the initial parameters.
The current global minimization method used by the industry requires the simultaneous inversion of the three unknown anisotropy parameters. Unfortunately, however, this method is numerically inefficient and sometimes unreliable. In particular, the global minimization algorithm — or any non-linear inversion algorithm — requires an initial human guessing of the parameters. The SwRI-developed algorithm, on the other hand, has been validated by abundant synthetic data without initial human guessing. The SwRI geophysicists applied the inversion algorithm to the cross-dipole waveform data for limestone and shale models. The inversion results showed that the azimuth angle of anisotropy matched the exact synthetic model data perfectly at all depths, regardless of the type of formation or the degree of anisotropy. On the other hand, the agreement between the inverted and exact shear wave velocities was quite good, close to 97 percent. It currently takes about one hour to complete the inversion of cross-dipole data taken at about 20 depth locations of a formation. Thus, there remains some room for improvement in both accuracy and efficiency.
Extension to deviated wells
The SwRI team is currently extending the algorithm to invert cross-dipole sonic logs acquired in deviated wells, or in vertical wells intercepting a tilted geological formation. The current state of the art is to invert standard compressional sonic logs that are acquired in deviated wells to extract the parameter of anisotropy. This approach requires the logs to be acquired in multiple boreholes with known deviation angles. However, no work has been reported on inversion based solely on cross-dipole data. In its approach to inverting intrinsic shear-wave data from deviated wells, the SwRI team required data from at least two known, distinct deviation angles. The team extended the TBIE method to include deviated wells to generate synthetic data for testing the extended algorithm.
Based on existing borehole array processing algorithms, the SwRI geophysical team has developed a new method for inverting cross-dipole sonic waveforms. The inversion algorithm, based on the new object functions, successfully separates and extracts unknowns, and the processing is fast and reliable. The team verified the results using a large amount of reliable synthetic waveform data for vertical boreholes. The agreement between the inverted and input shear wave velocities is about 97 percent.
The SwRI team is the first to verify the inversion results using a large amount of reliable synthetic waveform data for vertical wells in various formations. The software will be applied to process real cross-dipole data from vertical wells. The algorithm is being extended to also be able to process cross-dipole data acquired in deviated wells. Pending verification of the algorithm’s performance with actual cross-dipole data, the technology may be commercialized or provided as a service by the Institute in the future.
Questions about this article? Contact Parra at (210) 522-3284 or firstname.lastname@example.org.