William A. Olsson

Theoretical and experimental investigation of compaction bands in porous rock

Field investigators have recently discovered thin, tabular zones of pure compressional deformation that they called compaction bands. These bands were found in association with shear bands and were postulated to be genetically related to them. At the laboratory scale, compaction bands have been noticed in association with boreholes and preexisting, artificial shear cracks subjected to compressive stress fields. Natural compaction bands are noticeable in outcrops because of their resistance to weathering; however, they may be more difficult to discern on freshly cut rock surfaces such as drill core or borehole walls. Because of the much reduced porosity in the compaction bands, these structures are potentially important as permeability barriers in reservoirs and aquifers in porous rocks. For bands associated with boreholes, the crushed material can be washed into the borehole contributing to sand production and possibly altering the stability of the borehole. This paper examines a theoretical framework that explains these features as a constitutive instability leading to localized compaction in a way completely analogous to shear strain localization. Conventional triaxial experiments on Castlegate sandstone resulted in compaction bands. In addition, thick deformation bands having normals at low angles to the maximum compression are present in some specimens.

Compaction localization in porous rock

Experimental work on shear localization in porous sandstone led to the observation of nonuniform compaction. By analogy with shear localization, the process is referred to as compaction localization. To gain insight into the process of compaction localization, acoustic emission locations were used to define and track the thicknesses of localized zones of compaction during axisymmetric compression experiments. Zones of acoustic emission, demarcating the boundaries between the uncompacted and compacted regions, developed and moved parallel to the sample axis at velocities an order of magnitude higher than the imposed specimen shortening rate. Thus tabular zones of compaction were found to grow (thicken) in the direction of maximum compressive stress. These structures may form due to tectonic stresses or as a result of local stresses induced during production of fluids from wells, resulting in barriers to fluid (oil, gas, water) movement in sandstone reservoirs.

Quasistatic propagation of compaction fronts in porous rock

Abstract Recent experimental studies have observed the quasistatic propagation through rock of planar porosity discontinuities. In this process, one or more, initially thin, compacted layers appear at the yield point of the stress–strain curve and then grow by thickening in the direction of maximum compression at constant stress. Strain localization theory was previously applied to compaction to explain the initial formation of the compacted zones. This paper describes the growth of the compaction zones, that is, the propagation of their boundaries, in terms of shock wave analysis. The ratio of the applied shortening rate to the velocity of the boundary is related to the porosity change across the boundary. A small but consistent peak at the yield point of the stress–strain curve is explained by the model.

Reexamination of fault angles predicted by shear localization theory

This paper reexamines orientations of shear bands (fault angles) predicted by a theory of shear localization as a bifurcation from homogeneous deformation. In contrast to the Coulomb prediction, which does not depend on deviatoric stress state, the angle between the band normal and the least (most compressive) principal stress increases as the deviatoric stress state varies from axisymmetric compression to axisymmetric extension. This variation is consistent with the data of Mogi (1967) on Dunham dolomite for axisymmetric compression, extension and biaxial compression, but the predicted angles are generally less than observed. This discrepancy may be due to anisotropy that develops due to crack growth in preferred orientations. Results from specialized constitutive relations for axisymmetric compression and plane strain that include this anisotropy indicate that it tends to increase the predicted angles. Measurements for a weak, porous sandstone (Castlegate) indicate that the band angle decreases with increasing inelastic compaction that accompanies increasing mean stress. This trend is consistent with the predictions of the theory but, for this rock, the observed angles are less than predicted.

A mechanical model for multiply-oriented conjugate deformation bands

A unique suite of three pairs of conjugate deformation band sets is present in Jurassic sandstones in the southeastern corner of the San Juan basin, northwestern New Mexico. In order of sequential development, these conjugate pairs are oriented to form each of the three principal conjugate attitudes: (1) upright Xs, (2) plan-view Xs, and (3) recumbent Xs. The symmetry axes of the three different X-geometries at this location are parallel, suggesting that the three systems are genetically related. A relatively simple stress history, with the horizontal stresses striking northeast and southeast and varying in magnitude but not in orientation, plausibly explains this suite of sequentially developed conjugate structures. In this model, the upright Xs formed with dip-slip, normal offset under the initial conditions where the overburden was the maximum stress and the northeast-striking horizontal stress was the intermediate stress. Plan-view Xs with strike-slip offset formed next, as the northeast-striking stress increased (due to northeastward Laramide translation of the Colorado Plateau and interaction with the local basement-cored Nacimiento Uplift) to become the maximum stress, leaving the overburden stress as the intermediate stress although unchanged in magnitude. As the northeast-directed horizontal compressive stress continued to increase, it eventually created a condition where the horizontal stresses equaled or exceeded the overburden stress, resulting in small-scale thrusting along the recumbent Xs. The proposed mechanical model shows that shear stress levels dropped temporarily after the formation of the upright Xs, providing a hiatus in deformation and making the deformation at the next stage distinct, without overlap. The three systems of intersecting conjugate deformation bands that resulted have severely compartmentalized potential reservoirs in this unit, and illustrate why similar high-porosity, deformation-banded units can have low hydrocarbon production rates despite otherwise good reservoir potential.

Development of anisotropy in the incremental shear moduli for rock undergoing inelastic deformation

Abstract New experimental data on the evolution of two incremental shear moduli have been obtained for rock undergoing inelastic deformation. Changes in the incremental shear moduli during increasing axial straining probably reflect the development of a deformation-induced, anisotropic fabric resulting from accumulation of oriented damage. These incremental moduli occupy a prominent position in a constitutive equation for the plane deformation of inelastic solids that has evolved over nearly 30 years to include pressure-sensitivity, compressibility and plastic non-normality. This equation is often used in analyses of strain localization. One of the moduli, G, governs shearing parallel to the coordinate axes, and the other one, G ∗ , governs shearing at 45° to the coordinate axes. They both were measured on the loading branch of the constitutive equation. The modulus for shearing at 45° was also measured on the unloading branch, where it is called G ∗ . Though the predicted onset of strain localization for this type of constitutive model is a strong function of G ∗ /G , there appears to have been no such data collected for rock. Experiments to obtain estimates of these incremental moduli were conducted on solid cylinders and thin-walled tubes of Tennessee marble during axisymmetric compression under fluid confining pressures of 60 MPa. All three moduli were equal to the isotropic elastic value of E/2(1 + ν) ≃ 30 GPa in the elastic range of axisymmetric compression, but then the moduli decreased with increasing axial strain up to 0.01, always with G ∗ ≤ G ∗ ≤ G , and the ratio G ∗ /G decreased markedly. The decreased ratio, G ∗ /G , allows strain localization to occur earlier in a program of axial straining than would be predicted for a similar material that did not exhibit such a change in moduli.

The effect of slip on the flow of fluid through a fracture

To measure the changes in fluid volume flow rates through an artificial fracture undergoing slip, silicone oil was pumped through a sawcut in welded tuff in the radial flow geometry during rotary shear. The flow rates at constant normal stress and constant fluid pressure gradient were measured at different amounts of fracture slip. The fluid volume flow rate for a smooth fracture increases at first then decreases with ongoing slip. For a rougher fracture the flow rate decreases over the whole range of slip. The results have implications for fluid withdrawal from reservoirs and underground waste disposal.

Natural fracture distributions in sinuous, channel-fill sandstones of the Cedar Mountain Formation, Utah

A set of regional natural fractures, present in the sandy to conglomeratic, fluvial, channel-fill deposits of the Cedar Mountain Formation (east-central Utah) has a consistent west-northwest strike regardless of the local axial orientations of the sinuous channels. The fracture-producing stresses were not significantly refracted by the mechanical-property contrast between the channel-fill sandstones and the encasing overbank mudstones. In addition, fracture spacing along the sinuous channel axes is relatively constant between one-half and one-third of the bed thickness for both large fractures that cut the full thickness of the channel deposits and for smaller fractures in the thinner, component beds. Fracture spacing was apparently not affected by the variations in stress amplification that commonly result from differently oriented stiff inclusions in a ductile matrix. Therefore, in the absence of other structures, fracture intensity and the orientation of fracture-related maximum horizontal permeability in sinuous elongated reservoirs will be relatively constant regardless of the orientation of the long axis of the reservoir. Whether maximum permeability trends along, oblique, or across such reservoirs, and the relative drainage efficiency of horizontal versus vertical wellbores drilled into them, will vary only with the local trend of the channel axis.

Natural gas production problems : solutions, methodologies, and modeling.

Natural gas is a clean fuel that will be the most important domestic energy resource for the first half the 21st centtuy. Ensuring a stable supply is essential for our national energy security. The research we have undertaken will maximize the extractable volume of gas while minimizing the environmental impact of surface disturbances associated with drilling and production. This report describes a methodology for comprehensive evaluation and modeling of the total gas system within a basin focusing on problematic horizontal fluid flow variability. This has been accomplished through extensive use of geophysical, core (rock sample) and outcrop data to interpret and predict directional flow and production trends. Side benefits include reduced environmental impact of drilling due to reduced number of required wells for resource extraction. These results have been accomplished through a cooperative and integrated systems approach involving industry, government, academia and a multi-organizational team within Sandia National Laboratories. Industry has provided essential in-kind support to this project in the forms of extensive core data, production data, maps, seismic data, production analyses, engineering studies, plus equipment and staff for obtaining geophysical data. This approach provides innovative ideas and technologies to bring new resources to market and to reduce the overall environmental impact of drilling. More importantly, the products of this research are not be location specific but can be extended to other areas of gas production throughout the Rocky Mountain area. Thus this project is designed to solve problems associated with natural gas production at developing sites, or at old sites under redevelopment.

A constitutive model for frictional slip on rock interfaces

Abstract The shear stress required for frictional slip on rock interfaces is known to depend on the history of the slip velocity. At least one physical model that predicts this behavior also indicates that memory of past normal stresses may persist. A constitutive equation that incorporates memory of both past slip velocities and past normal stresses is proposed, and the appropriate physical property functions are identified. Once measured, these functions allow the computation of the shear stress on a slipping interface for general loading histories.