This is the Vp versus Porosity cross plot for a large carbonate data set, color-coded for shale volume (Vshale). Notice the inverse correlation between velocity and porosity. (Data courtesy of Prof. Gary Mavko of Stanford University; images courtesy of OHM/Rock Solid Images)
Reservoir characterization, especially reservoir monitoring, has become an integral part of the E&P strategy. The goal of reservoir characterization is to see how the hydrocarbons are distributed in the reservoir. Among the many parameters used to describe the reservoir, the main ones are porosity, fluid saturation, and permeability. In reservoir monitoring, the objective is to find out how reservoirs change with time during production and enhanced recovery efforts. In both of these areas, rock physics play an important role.

Traditional reservoir characterization uses downhole measurements to help obtain information about the reservoir rocks. These measurements typically consist of a standard suite of logs: resistivity, gamma ray, neutron porosity, and acoustic logs. These logs are often (but not always) supplemented with measurements from cores. Together, these logs provide information about the porosity of the reservoir and whether the reservoir is saturated with gas, oil, or water. Specialty logs like NMR and Stoneley wave logs provide estimates of formation permeability. These estimates are model-based and are not direct measurements of permeability, unlike production testing.

This figure shows the effect of triaxial stress on P and S wave velocities as a function of direction. The S wave splits into two different polarizations traveling with different velocities. There is a complex relationship between stresses and velocities.
Core measurements provide more details about the rock formations and at a scale more detailed than those obtainable from logs. However, core recovery is expensive and done only at selected intervals of the well. In addition to providing an additional set of measurements to correlate with the log measurements such as porosity and permeability, core analysis provides important information about the mineralogy of the rock, the solid part that makes up the rock matrix, which can be difficult to obtain using conventional logs.

With the core and log information in hand, the petrophysicist builds a rock physics model of the formation using one of a number of different rock physics models.

These models range from pure empirical relationships to models developed on specific geometries of the pore space. The tool of choice is usually the cross-plot.

One of the most common ones is the velocity-porosity cross-plot. This cross-plot establishes a relationship between the compressional (P)-wave velocity of the formation and the porosity of the rock; in general, the faster the rock, the smaller the porosity. However, mineralogy also affects the velocity of the rock. Knowing the mineralogy, the petrophysicist selects the rock physics model that best suits the data. With the rock physics model in hand, the petrophysicist can predict the properties of the reservoir if the fluid and saturation condition changes from one location to another.

Time-lapse reservoir monitoring

Changes in P wave velocity with effective stress (pressure) as a function of different fluid saturation are shown in a Berea sandstone core sample.
Time-lapse or 4-D monitoring of reservoirs presents a new challenge to the petrophysicist: changes in the state of stress of the formation. Whether one is producing or injecting fluids into the rock, the pore fluid pressure in the rock changes. The effective stress state of a rock is the overburden stress minus the pore fluid pressure in most cases. By changing the pore fluid pressure, the effective stress on the rock changes. This change affects all aspects of the rock and is quite complex to understand. Some of the specific changes are:
• Significantly increasing P-wave velocity with increasing effective stress;
• Increased shear (S)-wave velocity with effective stress, but not simply proportional to the change in P-wave velocity;
• Decreased permeability with increasing effective stress;
• Decreased electrical resistivity with increasing effective stress;
• Decreased porosity (though only slightly) with increasing effective stress; and
• Changing gas and water/oil effects on P and S wave velocities with effective stress.

With these complex changes, simple rock physics models, such as velocity-porosity relationships based on cross-plots, can lead to erroneous conclusions. A velocity change induced by a change in pore fluid pressure can be mistaken for porosity or changes in fluid type. Similar complexities exist for other empirical relationships such as porosity-permeability. The primary reason for this is that the change in stress fundamentally affects the geometry of the pore space inside the rock, especially those thin crack-like spaces that often act as conduits for fluid flow and passage of electrical currents.

To properly interpret the changes in seismic signature for time-lapse monitoring, it is critical to use a rock physics model that can handle stress changes. Both empirical and theoretical models exist, but currently these have too many parameters that cannot be measured directly from downhole logging measurements and surface seismic measurements. These models need to be constrained using core measurements of properties as a function of stress. The core measurements are not routinely available.

Fluid monitoring using electromagnetic methods

In addition to time-lapse reservoir monitoring using seismic methods, recent developments in controlled-source electromagnetic (CSEM) measurements make the technology possible for this purpose. CSEM is attractive because electromagnetic measurements are superior to seismic ones for the purpose of discriminating hydrocarbons from water. However, this poses an additional challenge for the geophysicists and reservoir engineers, as these data need to be jointly interpreted. To do that properly requires a rock physics model that can model resistivity as well as elastic behavior.

Combining resistivity and elastic properties modeling in a rock physics model is not straightforward. Elastic properties mainly depend on the amount and shape of the pore space, whereas resistivity (and to a large extent permeability) depends on how the pore space is connected. A rock model needs to be able to combine the two to do the job properly. There are such rock physics models proposed, but none currently are being widely applied.

Stress-induced anisotropy

Perhaps the most challenging part of understanding the rock physics behind time-lapse monitoring is the issue of stress-induced anisotropy. The stresses in the earth are not simply hydrostatic, i.e., the same in all directions.

In general the stresses are at least uni-axial (usually implying that the horizontal stresses are equal but different from the vertical stress), and more likely, tri-axial (the two principal horizontal stresses and the vertical stress are all different). As the pore fluid pressure changes, the relative effective stresses on the rock change, resulting in different amounts of velocity changes in different directions. This is known as stress-induced anisotropy. Similar changes happen to formation resistivity and permeability.

There have been few experimental data on stress-induced anisotropy on cores since these measurements are difficult and expensive. Models have been proposed to model stress-induced anisotropy, both at the core and at the field scale. Though these models are complex and not well-tested, they also have the ability to model the resistivity, permeability, and elastic properties in a constant manner. More work needs to be done to test the usefulness and applicability of these models.

Changes in physical properties of a reservoir over time are complex. It is only by developing and understanding the underlying rock physics that the appropriate measurements can be made so the changes in the reservoir can be interpreted properly.

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