Brian George Davidson Smart

A constitutive law for low‐temperature creep of water‐saturated sandstones

An accurate predictive model for the long-term strength of the continental lithosphere is important in a range of geophysical and geodynamic problems. While laboratory experiments are consistent with Mohr-Coulomb brittle faulting in the cold, upper continental crust, there is increasing evidence that time-dependent processes may also be important in these rocks, even at low temperature. However, there is some ambiguity as to the exact form of the constitutive law for describing time-dependent behavior of upper crustal rocks. Here we present results of room temperature creep experiments on a suite of water-saturated sandstones spanning a range of petrophysical and rheological properties and underlying deformation mechanisms. On physical and microstructural grounds our analysis suggests that a modified power law creep, of the form ˙ A(d f) , where d is the differential stress and f is the long-term failure (fundamental) strength, provides a more complete description of the experimental data. In particular, the parameters can be used to differentiate between sandstone types, with A, f, and varying systematically with cementation state, rock rheology, and confining pressure. The fundamental strength (f) for time-dependent deformation varies much more than the other parameters of the distribution, making it a potentially sensitive indicator of underlying creep mechanisms. Further tests would be needed to prove the constitutive law on a wider range of rock types and to prove that the three-parameter model is statistically better in the general case.

A TRUE TRIAXIAL CELL FOR TESTING CYLINDRICAL ROCK SPECIMENS

In this paper a new true triaxial cell, capable of routine testing of cylindrical rock core plugs under realistic 3-D polyaxial stress states, has been conceived by the author, the design of which is outlined. The cell presents the opportunity to develop enhanced realism when testing cylindrical rock specimens. The cell effectively enables an existing compression machine to be converted into a true triaxial machine for the testing of core. The stress state generated by the cell has been shown to significantly influence microcrack development, macroscopic shear failure and permeability.

Stress sensitivity of fractured reservoirs

Abstract A fractured reservoir has a rock mechanical character which can be described by considering it to be built up from intact rock bounded by mechanical discontinuities. These discontinuities have been formed by natural processes and comprise fractures which normally make a steep angle to bedding, and the frequently ignored bedding-plane parallel discontinuities caused by, for example, weak clay-rich layers in clastics, or stylolites in carbonates. Both the intact rock and the discontinuities exhibit sensitivity to stress. In the case of the intact rock, this expresses itself as a pore geometry sensitivity which influences permeabilities and capillary pressures, with the changes being influenced by the stress-state. In the case of the discontinuities, three types of permeability changes are proposed, depending upon the stress and strain which develops across the discontinuity. Importantly, all the constitutive laws for permeability stress-sensitivity can now be incorporated in simulations. While allowing for these effects complicates the simulation of fractured reservoirs, the enhanced realism brought to the simulation should improve the efficacy of the reservoir management.

Modeling combined fluid and stress change effects in the seismic response of a producing hydrocarbon reservoir

Editors note: A fuller version of this article can be downloaded in pdf format from the GUMPA project Web site at the following URL - http://www.pet.hw.ac.uk/research/gumpa/index.html The exploration and production of hydrocarbons are generally accomplished with the aid of 3-D seismic to image reservoir structure and, in some instances, reservoir properties and direct hydrocarbon indicators. Repeated seismic surveys over a period are termed time-lapse seismic (and sometimes 4-D seismic ). Changes observed in the seismic character with time have been attributed to impedance changes as a result of production (e.g. Gawith and Gutteridge, 1996). These changes have been used in a few producing fields to monitor reservoir performance. Identifying observed differences in repeat 3-D surveys and relating these to either in-situ saturation or stress-state changes, or both, has been difficult because of the lack of control data. It has been noted that in some fields (Watts et al., 1995), the sensitivity to stress changes can be very much greater than the sensitivity to saturation changes. In other fields (Landro et al., 1999), the saturation changes are thought to be more significant. To aid understanding, a need for greater integration of geophysics and reservoir engineering has been noted and was the motivation for this study (Jack, 2001). There is a limited window of opportunity in a fields producing life when there are sufficient changes (saturation or stress) in the subsurface to show a surface seismic response. These changes have to be monitored before the field has reached significant decline for the observed changes to be exploited for reservoir management (through in-fill drilling for by-passed, compartmentalized or attic oil). Reservoir modeling is an essential tool for managing the development of and production from hydrocarbon reservoirs. Many technical issues however surround the realism and validity of the models on which management decisions are based. …

Predicting Rock Mechanical Properties from Wireline Porosities

The rock mechanical behaviour of reservoir rocks is important in the design and implementation of drilling and production programmes. Traditionally rock mechanical properties are obtained from direct measurement on core samples or from mechanical calculations on acoustic wireline log measurements. This paper reports the rock mechanical properties of many different reservoir rocks of different porosities. This has led to the development of a new method of predicting rock mechanical properties directly from porosity. The paper discusses the measurement of experimentally derived porosity, elastic moduli and fracture strength parameters and the interpretation of these mechanical properties results into direct correlations with porosity. The application of these results to obtain continuous rock mechanical property plots of the reservoir from wireline derived porosity is discussed. The practical use of these rock mechanical property profiles in drilling, production and enhanced reservoir simulation is also emphasised. Porosity (Φ), modulus of elasticity (E), Poissons Ratio (ν), uniaxial compressive strength (UCS), cohesion (τ 0 ), angle of internal friction (ψ), and triaxial stress factor (k), were measured on samples from a wide range of North Sea reservoirs using a conventional triaxial testing machine. This paper describes the procedure used and presents the correlations obtained from plotting each of the rock mechanical properties against porosity. The derivation of wireline porosities along with empirical corrections are presented and the results of applying the correlations to these wireline derived porosities to produce continuous rock mechanical property plots are discussed. Logs were calibrated to core-measured values to reveal realistic elastic and inelastic moduli profiles. The continuous property logs provide a reasonable estimate of the possible behaviour at discrete points throughout the reservoir interval, but they are limited in their description of the behaviour of individual beds as coherent bodies. A technique has been developed to pick out these individual beds and assess how they will perform as Rock Mechanical Coherent Units, i.e. sets of beds that perform in a similar or dissimilar manner to adjacent layers. Finally a discussion on how the results are used to aid production and generate enhanced reservoir simulation will be presented.

Strength characteristics and shear acoustic anisotropy of rock core subjected to true triaxial compression

Abstract Results are presented from an initial experimental programme aimed towards evaluating the capabilities of a new true triaxial cell, designed to apply independent and unequal principal stresses to the curved surfaces of cylindrical core plugs. A series of discrete failure tests on dry specimens from two sandstone lithologies exhibiting different deformation, strength and poroperm characteristics, were conducted under azimuthal stress anisotropy ( σ 2 > σ 3 ) with σ 1 being applied axially. The true triaxial cell consistently orientates induced brittle shear fractures so that they strike parallel to the direction of σ 2 , and slip against the direction of least confinement, σ 3 . Both peak (fracture) and residual (friction) strengths are shown to be strongly dependent on the magnitude of the applied σ 2 , as well as on that of σ 3 . Results from multi-failure state testing using the conventional “triaxial” compression configuration are contrasted with discrete failure tests conducted in the true triaxial cell, by means of the familiar von Mises and extended 3-D Griffith criteria. Digitised records of shear-waves obtained at 40, 60 and 80% of peak failure strength during true triaxial testing, show clear evidence of progressively increasing stress-induced “splitting” or birefringence between the arrival of the faster S1(∥ σ 2 ) and the slower S2(∥ σ 3 ) shear-wave. Microseismic data and macroscopic observations from discrete failure tests performed within the true triaxial cell, are thus supportive of a brittle deformation mechanism involving stress-induced dilatant microcracks extending parallel to σ 2 and opening against σ 3 , progressively coalescing with increasing σ 1 to form a pervasive fault also oriented by the applied 3-D stress field.

A rock test cell with true triaxial capability

Conventional so-called triaxial test cells apply the axial stress to a cylindrical sample using steel platens, with the confining stress developed via an annulus of hydraulic fluid retained by a liner in a pressure cell. This does not allow differentiation between the two principal stresses around the core and inhibits the realism with which the rocks can be tested, for example in determining the effect of the intermediate principal stress on the strength of the sample.This paper describes the development and application of a new test cell – believed to be the first in the world – which enables truly triaxial stresses to be applied to cylindrical core samples, opening up the possibility to test rocks routinely in a more realistic manner. An array of 24 trapped tubes replace the single annulus which usually generates the uniform radial stress. Selective pressurization of the tubes enables differential radial stresses to be generated, while axial stresses are applied as before through steel platens. The first results of multi-state failure and permeability stress sensitivity of samples tested in the cell are presented. These demonstrate the influence of the intermediate principal stress on measured rock properties and the orientation of induced fracture planes.

Ape-Modelling of Fluid/Rock Deforrnation of Sandstone Cores in Laboratory Stress-Cells

Anisotropic poro-elasticity (APE) is a model for the evolution of fluid-saturated microcracked rock undergoing (pre-fracturing) deformation.

Permeability prediction using stress sensitive petrophysical properties

The correlation of stress sensitivity to various petrophysical parameters was studied by analysis of experimental results from a range of sandstone core plugs tested hydrostatically at room temperature. The parameters measured were: compressional wave velocity, porosity, permeability and electrical resistivity. More detailed information on the effects of sorting and grain size distributions was obtained from experiments on artificial, unconsolidated sandstone cores. The measurements showed a high degree of stress sensitivity, which was different for each core but, broadly, could be classified as either high or low stress sensitivity. Cores from the high permeability clean sand were less stress sensitive than the cores from the low permeability coarsening-upwards sequence and the petrophysical values when combined into a synthetic log distinguished between the two lithologies. The results were compared to the predictions of a simple asperity deformation model. The experimental results and the model suggested a possible logging strategy to deduce permeability, by varying wellbore pressure.

Influence of driving stress on cataclastic deformation and permeability in well cemented sandstones

Abstract Although many mechanisms for fault sealing have been identified, the microscale processes involved are still not well understood. This paper reports continuous steady-state permeability on core plugs deformed triaxially at effective confining pressures from 6.9 MPa to 55.2 MPa and with slip displacements of up to 3 mm in order to better understand the coupling between mechanical deformation and fluid flow response. The results also experimentally quantify the influence of in-situ remote driving stress on cataclastic deformation associated with varying degrees of fault slip displacement. The permeability response is seen to vary systematically from a linear to an exponential decrease with increasing effective stress. This behaviour is related to microstructural textures and in particular to grain size of comminuted gouge material. An empirical law relating fault sealing and deformation is presented.