Intermediate cec model papers

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Intermediate cec model papers

That is, for small strains, the elements of the stress and strain tensors are related through where Furthermore, the strain response occurs instantaneously as soon as the stress is applied, and it is reversible—that is, after removal of a load, the material will be in the same state as it was before the load was applied.

A plot of stress vs. However, in real rocks, the moduli increase as a function of effective stress, particularly at low stress. Some of this increase is reversible nonlinear elasticitybut some of it is irreversible plasticity or end-cap compaction. To make matters even more complicated, rocks also exhibit time-dependent behavior, so that an instantaneous stress change elicits both an instantaneous and a time-dependent response.

These anelastic effects can be seen in laboratory experiments, as shown in Fig. Sample 1 was maintained at its saturated condition; Sample 2 was cleaned and dried before testing modified after Moos and Chang [1].

At the top of Fig. As in most experiments of this type, a cylindrical rock sample is jacketed with an Intermediate cec model papers soft sleeve and placed in a fluid-filled pressure cell. The fluid pressure surrounding the sample is increased slowly, and the fluid pressure confining stress and sample axial and circumferential strains are measured.

Intermediate cec model papers

To identify the various deformation processes that occur in this unconsolidated sand, the stress is slowly increased at a constant rate and then held constant until the sample stops deforming. Then the pressure is decreased to approximately half of the previous maximum pressure.

After that, the pressure is increased at the same rate until the next pressure step is completed. This process continues until the desired maximum pressure is achieved, and then the sample is slowly unloaded and removed from the pressure cell.

Stress-strain curve All aspects of typical rock behavior can be seen in the stress-strain curve plotted on the bottom of Fig. At low pressure, the sample is soft, and there is a rapid increase of stiffness with pressure nonlinear elasticity owing to crack closure, as well as an increase in stiffness caused by irreversible compaction.

Once the pressure increase stops, the sample continues to deform, with deformation rate decreasing with time time-dependent creep.

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Reloading follows the purely elastic unloading path until the maximum previous pressure has been reached, after which additional plastic deformation begins to occur again as the material resumes following the compaction curve.

All of these effects can be seen in situ, including the difference between the loading and unloading response. Measurements of P-wave and S-wave velocity made on this sample during the experiment by measuring the time of flight of pulses transmitted axially along the sample were used to calculate the dynamic shear G and bulk K moduli with Eq.

The implications of the results for pore pressure prediction are discussed later in this chapter. This dispersion frequency-dependence of the moduli also is typical of reservoir rocks, and it is the justification for empirical corrections applied to sonic log data to convert from the dynamic moduli measured by the sonic log to static moduli that are used to model reservoir response.

These considerations can become very important when modeling and predicting how the wellbore will respond during and after drilling. In the discussion of wellbore stability that follows, however, we will assume that the rock is purely elastic and only briefly discuss the implications of more complicated rheological models.

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Compaction and end-cap plasticity When rocks are loaded past a certain point, they will no longer behave elastically. This process is referred to as shear-enhanced compaction because, in general, the effect occurs at lower mean stress as the shear stress increases.

Compaction trends are shown as arcs bounding the data from the right, and they define end caps of the stress regime within which the rock at a given porosity can exist. Values of porosity decrease as the end caps move outward, owing to material compaction that is caused by the increase in confining stress.Results.

The primary olfactory centers in this species dominate the brain and are composed of many elongate olfactory glomeruli. The secondary olfactory centers that receive an input from olfactory projection neurons are almost equally large as the olfactory lobes .

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