Question

Using a schematic plot explain what is the equivalent matrix stress method for prediction of abnormal pore pressure?

Answer 1

Using the schematic and also plot Methods that treat the problem correctly are often referred to as equivalent matrix stress methods. The basis of the approach is summarized in Fig. In this example, the top set of plots shows data recorded over a normally compacted section. The mean stress and pore pressure are shown as a function of depth at the left. Because the effective stress increases with depth, the porosity decreases with depth, as shown in the middle. If the porosity-stress function is a power law, it will plot as a straight line in linear-log space. There is, in fact, no restriction on the functional form of the porosity-stress function. The lower set of plots in Fig. show the effect of an increase in pore pressure below a certain depth, as represented by the dashed line that diverges from the hydrostatic line in the lower left plot. In this case, the pore pressure in the overpressured zone increases at the same rate as the mean stress, such that the effective stress is constant. The plot of log ? vs. ? follows the compaction trend only until it reaches the depth of overpressure, after which there is no change in either porosity or effective stress (lower right plot). This type of profile is typical of regions in which a pore-pressure increase is caused by the inability of the pore fluids to escape during burial and compaction.

In general, effective stress methods must be calibrated, preferably using log data. However, they can also be calibrated empirically using approaches similar to those used to select trend lines, and they account explicitly for local changes in overburden and other stresses. The equation plotted in Fig. is an example of relationships of the form

Use of Athy’s original parameters is not recommended because they were based on analysis of overconsolidated shales from Oklahoma and thus are not applicable to young sediments. An appropriate algorithm for Athy’s method is to solve the following set of equations.

and f is the acoustic formation factor and is derived by calibration; ?tma is the matrix transit time. This type of relationship allows extension to account for effects such as cementation and thermal transformations by modifying the functional form of the exponent.