A homogeneous anisotropic effective‐medium model for saturated thinly layered sediments is introduced. It is obtained by averaging over many layers with different poroelastic moduli and different saturating fluids. For a medium consisting of a stack of vertically fractured horizontal layers, this effective medium is orthorhombic. We derive the poroelastic constants that define such media in the long‐wavelength limit as well as the effective large‐scale permeability tensor. The permeability shows strong anisotropy for large porosity fluctuations. We observe pronounced effects that do not exist in purely elastic media. At very low frequencies, seismic waves cause interlayer flow of pore fluid across interfaces from more compliant into stiffer layers. For higher frequencies, the layers behave as if they are sealed, and no fluid flow occurs. The effective‐medium velocities of the quasi‐compressional waves are higher in the no‐flow than in the quasi‐static limit. Both are lower than the high‐frequency, i.e., ray‐theory limit. Partial saturation affects the anisotropy of wave propagation. In the no‐flow limit, gas that is accumulated primarily in the stiffer layers reduces the seismic anisotropy; gas that is trapped mainly in layers with a more compliant frame tends to increase the anisotropy. In the quasi‐static limit, local flow keeps the anisotropy constant independent of partial saturation effects. For dry rock, no‐flow and quasi‐static velocities are the same, and the anisotropy caused by layering is controlled only by fluctuations of the layer shear moduli. If the shear stiffness of all layers is the same and only the compressive stiffness or saturation varies, only the ray‐theory velocity exhibits anisotropy.

No abstract

S U M M A R YThe phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10-100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P-wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.

No abstract

The measured geophysical response of sand–shale sequences is an average over multiple layers when the tool resolution (seismic or well log) is coarser than the scale of sand–shale mixing. Shale can be found within sand–shale sequences as laminations, dispersed in sand pores, as well as load bearing clasts. We present a rock physics framework to model seismic/sonic properties of sub‐resolution interbedded shaly sands using the so‐called solid and mineral substitution models. This modelling approach stays consistent with the conceptual model of the Thomas–Stieber approach for estimating volumetric properties of shaly sands; thus, this work connects established well log data‐based petrophysical workflows with quantitative interpretation of seismic data for modelling hydrocarbon signature in sand–shale sequences. We present applications of the new model to infer thickness of sand–shale lamination (i.e., net to gross) and other volumetric properties using seismic data. Another application of the new approach is fluid substitution in sub‐resolution interbedded sand–shale sequences that operate directly at the measurement scale without the need to downscale; such a procedure has many practical advantages over the approach of “first‐downscale‐and‐then‐upscale” as it is not very sensitive to errors in estimated sand fraction and end member sand/shale properties and remains stable at small sand/shale fractions.

Improper planning and execution of deepwater drilling programs can lead to high costs and unsafe conditions. Proper well planning requires reliable estimates of the expected pore fluid pressure and formation strength prior to drilling. Such pressure predictions are based on integrated seismic and offset well data. A new, rock model-based approach especially suited for deepwater pore pressure imaging is introduced here and applied in an example of a deepwater Gulf of Mexico well. P- and S- velocities were determined both at an offset well and for the future drilling location, using prestack seismic full waveform inversion. Both predicted velocities were later verified with log measurements. Using the new model, a significant pore pressure increase at depth was predicted before drilling the well and verified while drilling (Figure 1). For the entire well, the predicted and measured pore pressure gradients agree within half a pound per gallon equivalent mudweight (Figure 1). The shear velocity, and the extracted shear modulus, proved to be excellent indicators of low effective stresses, corresponding to overpressured formations (Figure 2). Introduction It has been common practice to predict pore pressure before drilling from conventional seismic stacking velocities with a normal compaction trend analysis using, for example, the well-known Eaton approach (Eaton, 1972). Velocities that appear to be slower than the ‘normal velocities’ are indicative of overpressure, which then is quantified using an empirical equation. However, there are several problems with this approach. First, conventional seismic stacking velocities are usually unsuitable for pressure prediction since they are not "rock or propagation velocities" (Al-Chalabi, 1994). Second, these velocities lack resolution in depth. Third, in a deepwater environment, sediment loading often has been so fast that pressures in these sediments are above hydrostatic (geopressured) right below the mud line - unlike, for example, on the continental shelf of the Gulf of Mexico (Dutta, 1997). This prevents development of a normal compaction trend, thus invalidating the entire approach in the deepwater. Our new approach is trendline independent and uses a deepwater rock model for geopressure analysis. The model (or approach) is based on several seismic attributes, such as velocities and amplitudes and is calibrated with offset well information. Pore pressure is calculated as the difference between overburden stress and effective stress. The effective stress affects the grain-to-grain contacts of clastic, sedimentary rock, and consequently, the velocities of seismic waves propagating through such rock (Domenico, 1984; Dutta, 1997). The rock model has various components: relations between porosity, lithology and velocity, clay dehydration, and transformations relating both density and Poisson's ratios of the sediments to effective stresses acting on the matrix framework. The key inputs that drive the rock model are velocities (P and S) obtained from a variety of velocity tools. Iterative velocity calibration and interpretation are two essential steps in the prediction process to ensure that the velocity fields are within the realm of expected rock or propagation velocities. In the following study, we demonstrate how the P- and S- velocities used in a Gulf of Mexico example were derived using prestack waveform inversion and we describe the rock model in more detail.

No abstract

With support of the SEG Research Committee, the authors of this paper organized a special session at the 2011 SEG Annual Meeting focused on the environmental challenges of developing tight, unconventional hydrocarbon reservoirs with special emphasis on the controversial hydraulic fracturing technology. Goals of the session were to support a better understanding of the challenges from the environmental perspective and to discuss possible solutions to these challenges through improving existing methods and developing novel exploration and stimulation techniques. Recognized unconventional resource experts brought their perspectives to the special session to highlight these challenges and work toward bringing the community together for solutions. It is evident that advances in horizontal drilling and multistage fracturing technologies have had significant influence on the global spread of the exploration for and production from gas shale and shale oil reservoirs.