Pore Pressure and Methods of Analysis Section 3 PPFG Modeling Principles Parts 4, 5, and 6

Part 4.???Resistivity Models

Resistivity responds to the geochemistry of the rock.

The resistivity of a formation is indicative of the geochemistry. The water-filled porosity in the formation is part of the geochemical constituents the resistivity tool is measuring. Formation water is approximately 400 times more conductive than the typical rock matrix. A change in water-filled porosity is detected by the resistivity tool, and the trend of porosity decline due to compaction can be determined by applying a trend to the resistivity log at similar shale intervals.

Figure 17.???????????The Normal Compaction Trend of a Resistivity Model and Pore Pressure Calculation

Part 5.???Sonic Models

???????????????Sonic travel time responds to the physical property of the rock.

???????????????The acoustic travel time of a formation is indicative of the physical property. The water-filled porosity in the formation contributes to the acoustic travel time the sonic tool is measuring. The acoustic travel time of water is approximately 3 to 4 times the acoustic travel time of the typical rock matrix. A change in water-filled porosity is detected by the sonic tool, and the trend of porosity decline due to compaction can be determined by applying a trend to the sonic log at similar shale intervals.

Figure 18.???????????The Normal Compaction Trend of a Sonic Travel Time Model and Pore Pressure Calculation

Part 6.???Centroid Relationship Between Permeable and Impermeable Rock

???????????????The centroid theory assumes a dipping permeable formation is bound by an impermeable formation, and at some point along the boundary the pressure of the permeable formation is equal to the pressure of the impermeable formation. This depth is called the “centroid”.

???????????????The permeable rock has effective porosity (hydraulically connected pore spaces). The pressure at any depth is equal to the hydraulic head of the fluid column within the permeable rock. The impermeable rock does not have effective porosity (refer to the introduction of this course and the discussion of permeability with respect to clock time and geologic time). The pressure at any depth is determined by the compaction of the surrounding geology. Below the centroid, the impermeable rock pressure is greater than the permeable rock pressure. Above the centroid, the impermeable rock pressure is less than the permeable rock pressure.

Figure 19.???????????Hydraulic Pressure Calculations Within a Permeable Sand Bounded by Impermeable Clay

A well is drilled at balance and penetrated a sand body at the centroid depth of 10,000 ft. Pore pressure gradient of the sand and shale at the centroid is 11.6 ppg, which is 0.6 psi/ft. The pressure at the centroid is (0.0519*11.6*10,000) psi, which is 6020 psi.

At 1,000 feet above the centroid, the shale pressure decreased by 0.6 psi/ft, or 602 psi. The shale pressure 1,000 feet above the centroid is 6020-602, which is 5418 psi at 9,000 ft. The pressure gradient for 5418 psi at 9,000 feet is 11.6 ppg.

The sand contained water and the measured pressure at the centroid depth was 6020 psi. The formation water has a pressure gradient of 0.44 psi/ft. At 1,000 feet above the centroid, the sand pressure decreased by 0.44 psi/ft, or 440 psi. The sand pressure above the centroid is 6020-440, which is 5580 psi. The pressure gradient for 5580 psi at 9,000 feet is 11.94 ppg.

At 1,000 feet below the centroid, the shale pressure increased by 0.6 psi/ft, or 602 psi. The shale pressure 1,000 feet below the centroid is 6020+602, which is 6622 psi at 11,000 feet. The pressure gradient for 6622 psi at 11,000 feet is 11.6 ppg.

At 1,000 feet below the centroid, the sand pressure increased by 0.44 psi/ft, or 440 psi. The sand pressure 1,000 feet below the centroid is 6020+440, which is 6460 psi. The pressure gradient for 6460 psi at 11,000 feet is 11.32 ppg.

Figure 20.???????????Centroid Example Calculation Solution Spreadsheet

???????????????The psi per foot is linear with depth. The equivalent pressure gradient calculations are not linear with depth. Graphical solutions using a linear trend to project a centroid value over a significant depth interval will not be accurate. The centroid value for pressure gradient must be calculated.