Shiyu Xu

Modeling elastic properties in carbonate rocks

Carbonate (limestone and dolomite) reservoirs account for approximately 50% of oil and gas production worldwide. However, seismic responses in carbonate rocks are poorly understood. In addition, DHI ranking and AVO classification systems developed for clastic rocks are unlikely to be applicable to carbonate rocks. An accurate and physically sound carbonate rock physics model is needed to address these technical issues.

An approximation for the Xu‐White velocity model

In 1995, S. Xu and R. E. White described a method for estimating compressional and shear-wave velocities of shaley sandstones from porosity and shale content. Their model was able to predict the effect of increasing clay content on compressional-wave velocity observed in laboratory measurements. A key step in the Xu-White method estimates dry rock bulk and shear moduli for the sand/shale mixture. This step is performed numerically by applying the differential effective medium method to the Kuster-Toksoz equations for ellipsoidal pores. This step is computationally intensive. Using reasonable assumptions about dry rock elastic properties, this step can be replaced with a set of approximations for dry rock bulk and shear moduli. Numerical experiments show an extremely close match between velocities obtained with these approximations and velocities computed with the differential effective medium method. These approximations simplify the application of the Xu-White method, and make the method computationally more efficient. They also provide insight into the Xu-White method. For example, these approximations show how the Xu-White model is related to the critical porosity model.

Stress-induced Anisotropy In Unconsolidated Sands And Its Effect On AVO Analysis

Summary In a recent rock physics study, anomalously high Vp/Vs ratios were observed relative to expectations in unconsolidated reservoir sands at shallow burial depths. For the wet sands, the Vp/Vs ratios were high relative to the surrounding shales. The wet sands also had high Vp/Vs ratios relative to laboratory measurements. For gas sands, the Vp/Vs ratios observed in logs were high relative to laboratory measurements of dry samples. For oil sands, the observed Vp/Vs ratios were high relative to predictions using existing rock physics models. The observed behavior cannot be explained using factors such as porosity, lithology, clay content, pressure, temperature, compaction or cementation. However, the observed behavior can be explained as a result of stressinduced anisotropy. Since the vertical stress is normally much higher than the horizontal stresses in a relaxed sedimentary basin, the compressional wave is fast in the vertical direction, but the shear wave is slow. This consequently gives high Vp/Vs ratios in the vertical direction. A rock physics model that includes the effect of differential stress was applied to compute anisotropic elastic parameters. Preliminary results show that its effect on Vp/Vs can be bigger than the fluid effect (oil versus gas). The model has also been applied to two deepwater wells. We observed significant improvement in S-wave log prediction and in the predicted AVO behavior compared to the observed seismic response.

Stress-induced Velocity Anisotropy of Unconsolidated Sand Under Realistic Reservoir Stress Conditions

Ultrasonic velocity measurements were made on dry and oil saturated samples/cores of unconsolidated sands to investigate the stress-induced velocity anisotropy under realistic reservoir stress conditions. Instrumentation was arranged to simultaneously measure five velocities (axial P, axial S, radial P, radial S polarized radially, and radial S polarized axially) and the axial and radial deformation of the samples in a single run.

Intrinsic P- And S-wave Attenuation of Carbonate Reservoir Rocks From Seismic, Sonic, to Ultrasonic Frequencies

New measurements of Pand S-wave velocity dispersion in carbonate reservoir rocks from seismic (<100Hz) to sonic (~10kHz) and ultrasonic (~1MHz) frequencies were analyzed to derive the frequency-domain intrinsic attenuation spectrum. Three rock samples were analyzed, all with porosity in the same range: one sample had high permeability and two had low permeability. We used the standard linear solid model to describe the twin relationship between velocity dispersion and attenuation. The analysis led to the following observations: (1) P-wave attenuation (1/Qp) and S-wave attenuation (1/Qs) are similar in each of the frequency bands(seismic, sonic, ultrasonic): 1/Qp ~ 1/Qs; (2) The attenuation spectrum in each frequency band has an associated characteristic relaxation distance; (3) For a given carbonate reservoir rock, attenuation in the ultrasonic frequency band can be “anomalously” high (Q~1) but still be “normal” (Q~10-100) in the seismic frequency band.

The Effect of Fabric-Controlled Layering On Compressional And Shear Wave Propagation In Carbonate Rock

Mixed chemical and clastic sedimentary processes form carbonate rock with fine bedding that results in a weakly directed fabric. Laboratory experiments were performed to determine the effect of fabric-controlled layering on compressional and shear wave propagation. X-ray tomographic scans of the sample found a density variation among the layers that ranged from 1700 kg/m 3 to 2300 kg/m 3 in a cubic sample 100 mm on edge. Wavefront imaging results show that the density contrasts among the layers produced energy confinement. The amplitude and arrival time of the compressional and shear waves are affected by saturation of the sample with water, i.e., by changing the impedance contrast among the layers. Seismic monitoring of the fluid-front during saturation indicates that the fine bedding also affects the hydraulic properties of the sample.

P-Wave Seismic Anisotropy In a Fractured Carbonate Reservoir: A Case Study From EastTexas

Summary We present a case study where we calculated P-wave seismic anisotropy for a land, 3D seismic survey at a gas field in east Texas. We calculated the azimuthal AVO (AzAVO) and azimuthal velocity (AzNMO) anisotropy. We compared the results with interpreted faults, fractures from oriented core, image logs, present day stress, and a dipole sonic log. High- anisotropy anomalies align with faults on the flanks of the structure. Low seismic anisotropy characterizes the crest of the structure, and may be an artifact of an associated amplitude shadow. Locally, orientations predicted from seismic anisotropy agree with our subsurface fracture observations. Full quantitative fracture interpretation is restricted, however, by signal noise, local reduction in inversion quality by an amplitude artifact, and limited subsurface fracture correlation.

Sensitivity Study of PP and PS AVO on Azimuthal Anisotropy

Multicomponent seismic data offer not only seismic reflections of pure compressional wave (PP) but also of converted shear waves (PSV and PSH) resulting from conversions at stratum interfaces in the subsurface. Different types of waves have different responses to subsurface geology. The reflection amplitude responses of different types of waves have been investigated and compared through a numerical modeling study. The shot-receiver offset and azimuthal angle have been varied relative to the subsurface anisotropy symmetry direction. Our results show that PSV data are more sensitive to azimuthal anisotropy than PP data. This makes the converted wave a better tool for subsurface azimuthal anisotropy (or fracture) detection. The study also demonstrates that the higher-order term in PP-wave amplitude versus offset (AVO) expression (beyond the traditional intercept and slope terms) can be important for fracture detection. Feasibility modeling study before field application is essential to better understand the relative importance of each term in the azimuthal AVO response and the appropriate incidence angle range for azimuthal anisotropy detections.

Case Studies of Using Far and Ultra-Far Seismic Data in Deep-Water Nigeria Erha North Field: Beauty and the Beast

This paper highlights the complexity and challenges associated with deep-water exploration and development in Nigeria. The Erha North field Reservoir-300 was discovered using the block-wide 2000 seismic survey. A shallow channel severely attenuated the seismic image at the reservoir level. A new 2005 seismic survey was shot perpendicular to the shallow channel and improved the imagibility of the reservoirs by undershooting the shallow channel. ExxonMobil’s Pre-migration Spectral Shaping (EM_PreSS) technique further enhanced the data quality. The EM_PreSS ultra-far 38-48° angle stack provided the best well tie in the Erha North Phase I development area. The significantly improved seismic data quality greatly increased interpretation confidence and impacted the business decision to not drill appraisal well Erha Far-East (EFE) and instead to drill the exploration well Erha North-East (ENE). The Erha NE prospect is located 7 km away from the center of the Erha North field, with the primary target in Reservoir-300. The seismic response at the up-dip of the prospect is similar to the hydrocarbon response observed at the Erha North field, but lacks conformance to structure - an expected DHI element. The original hole (OH) targeted an up-dip location and encountered multiple gas and oil sands, in both primary and secondary reservoirs. However, the primary target Reservoir-300 was penetrated with two separated thin gas-on-oil sands. No water sand was penetrated. A determination was made that such highly compartmentalized reservoir could not be developed economically. Down-dip from the Erha NE original hole discovery, a strong low-impedance amplitude anomaly was observed on the ultra-far (38-48°) angle stack. No other angle stack showed a similar strong low-impedance response and no other DHI attributes were observed. This amplitude response was neither similar to other known hydrocarbon responses nor to known water leg responses. Geophysical modeling results could not rule out the possibility of down-dip hydrocarbon presence by using reasonable rock properties assumptions. Given the high resource uncertainty, the operator determined it would be beneficial to test the down-dip location before Phase II development starts. The down-dip side-track (ST) well was drilled and penetrated a thick clean water-bearing sand. Post- drill modeling suggested that abnormally high anisotropy in the sand could be the cause of the ultra-far low impedance amplitude anomaly.

Effective medium models from x‐ray microtomography images.

A novel method is described where an effective medium model is generated from a 3‐D x‐ray microtomography image of a rock sample. In contrast to current modeling practice, material phases are not assigned idealized geometries, like spheroids. Instead, strain concentration tensors are computed numerically for the true phase geometries observed in the 3‐D image. In this method, a 3‐D image of x‐ray attenuation is converted into a 3‐D elastic properties volume, the strain field is computed within the volume, and the strain concentration tensors, which quantify the contribution of each grain and pore type to the bulk elastic properties, are calculated from the strain field. From only one representative sample of a rock type and with no assumptions about grain or pore shape, an effective medium model is generated that specifies the effective elastic tensor as a function of the various mineral and pore volume fractions. The method is demonstrated by generating effective medium models for several rock types. The...