hydraulic-fracturing treatment. However, mechanically weak zones may fail due to the drawdown between the MDT packers (see “ Test- ing Weak Sands,” page 24). To avoid this, the MDT technique can be used in cased holes.15 To predict how a sand-management comple- tion will perform over the life of the reservoir, information is also needed about the impact of depletion on reservoir stresses. This information, usually a single number called the reservoir- stress path, can be calculated approximately from the elastic properties of the reservoir and surrounding rock, or calculated more accurately using a full-fi eld geomechanical model, or mea- sured by examining hydraulic fracture records from different stages in the development of the fi eld, if such data exist.
Modern sonic logging devices, such as the DSI tool, measure shear-wave anisotropy to determine in-situ stress directions in both hard, fast formations and soft, slow formations.16
Static rock properties are derived from labo- ratory tests. In the laboratory, the effective stress on the rock sample governs failure, but sample size, shape, moisture content and defects also influence failure. A failure envelope is con- structed using data from several compression tests, in which peak axial stress points are typi- cally plotted against the different confining pressures used during the tests (below). Labora- tory test data greatly enhance the overall knowledge of reservoir rock strength and can be used to calibrate log-derived values. However, performing these tests requires specialized equipment, and acquiring representative rock samples may be diffi cult, if not impossible.
Model Behavior
Predicting sand-production behavior starts with developing a mechanical earth model (MEM) to understand a field’s geomechanics.17
These These
tools also provide crucial rock-mechanics param- eters to assess formation strength and predict sand-production problems. Measured values of compressional traveltime (tc) and shear travel- time (ts) are used to calculate dynamic elastic properties, including Poisson’s ratio (ν) and Young’s modulus (E).
250 200 30 150 100 5 50 0 0 0 0.2 0.4 0.6 0.8 1.0 Axial strain, %
Confining pressure MPa
0 5
10 20 30 40 50
Peak axial stress MPa
31 71
100
151 174 196 224
1.2 1.4 1.6 150 100 50 0 0 10 20 30 40 Confining pressure, MPa 50 60 10 20
200 250
Red Hollington sandstone: porosity ~28%
models are especially important when trying to assess the impact of a given completion method on weak rocks. In its most basic form— one dimension (1D)— an MEM contains information on vertical and horizontal stresses, pore pres- sure, rock strength, rock properties and geologic data, such as formation dip. An MEM can use additional inputs from geological and geophysi-
Red Hollington sandstone: porosity ~28% 50 40
cal models that defi ne tectonic features, such as faults and folds. Reservoir models that describe field-depletion or pressure-maintenance responses can also be input to an MEM. A well- constructed three-dimensional (3D) MEM allows engineers and geoscientists to determine the state of stress in a reservoir and surrounding strata at any location within a fi eld. Sand-prediction models focus on failure of reservoir rock and migration of disaggregated sand grains resulting from well-completion practices. Information about the mechanisms that drive sand production is not easily obtained from downhole observations, so much of the knowledge relating to sand prediction has come from laboratory research.
Scientists at Schlumberger Cambridge Research Center (SCR) and Schlumberger Reservoir Completions Technology Center (SRC) conducted perforation-stability experiments on rock samples of different strengths, providing data to develop simulation software that predicts sand failure in weak rocks. These experiments examined sand-production tendencies at various stresses and fl ow rates to study the effects of per- foration hole size, formation grain size and completion geometry— perforation and wellbore orientation— in relation to the principal stresses
> Constructing a failure envelope. Reservoir rocks are tested in the laboratory to acquire axial stress and strain data at different con ning pressures (top left). Normally, each con ning pressure used during testing is plotted against the peak axial stress that occurs before failure (right), allowing the internal friction angle to be estimated.
Spring 2004
15
Axial stress, MPa
Peak axial stress, MPa
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