Shales are very fine-grained, clastic rocks that lose porosity through compaction. Sedimentary basins typically contain about 70% shale, Figure 1. Quantifying shale properties helps with predrill geologic and seismic interpretation, basin modeling, and wellbore design. Knowing shale properties can also improve safety and reduce drilling well costs by overcoming wellbore stability issues.

Because shales lose porosity via compaction, they have been used to forecast and quantify pore pressure. Though, only one of the many controls on shale porosity is effective stress. The key to proper shale pore* *pressure interpretation is isolating the effective stress control on porosity. Overpressure knowledge is important because it affects drilling safety and costs, hydrocarbon column seal integrity, and rock and fluid acoustical properties.

Traditional pore pressure models use shale resistivity, acoustic velocities, and/or exponential porosity loss, which do not properly identify or isolate all the variables and components of compaction. Though, in the defense of practitioners of these techniques, it is only recently with the widespread use of non-water based mud that non-altered shale bulk density measurements are representative of insitu conditions.

Compaction is a reduction in bulk volume or thickness (i.e. porosity loss) in fine-grained sediments, due to continually-deposited material that compresses the underlying sediments. Compaction components include: mechanical, thermal, and chemical changes to the shale. Mechanical changes are associated with increasing effective stress (overburden stress); thermal changes are due to increasing temperature with depth (geothermal gradient), and chemical-changes come from diagenesis (transformation of smectite to illite). A robust compaction- based, pore pressure model must account for all these components, as well as variable shale lithology, to correctly isolate the pore pressure effect on mechanical compaction.

The model outlined here uses the cation exchange capacity (CEC, meq/g) of the bulk shale as a surrogate for mineralogy and grain size. CEC is a measurement of the amount of exchangeable charge per unit mass of dry sample and is derived from well logs, similar to a published method. The process involves several steps to link the different elements into the final model. At the “heart” of the compaction model are water desorption isotherms.

**Developing the model**

The use of water vapor desorption isotherms, a technique historically used to quantify the water associated with pure clays provides a surprisingly rigorous shale compaction model. Water vapor desorption isotherms, derived from published studies of Na-exchanged clays, clay mixtures, and shales properly model the controls on shale porosity. These isotherms are simply a chart of the water content of the sample (g/g) plotted against the relative humidity as it is decreased from 100%, Figure 2a. A general trend arises when the water content is normalized by the CEC, Figures 2a and 2b.

Soil scientists and civil engineers have noted that the compaction of finegrained soils collapses to a trendline when the water content (or the volume equivalent porosity) is normalized by the CEC or a surrogate such as the liquid limit or total surface area, when plotted against effective overburden stress. Both the liquid limit and total surface area correlate extremely well with CEC.

The relative humidity converts to effective overburden stress via the thermodynamic Kelvin equation: where, Pe is effective overburden stress (psi), C is a constant (14.7) to convert units, R is the gas constant (0.083liters atm/mole K), T is absolute temperature of the isotherms (297K), Vw is partial molar volume of pure water (0.018 liters/mole), and p/po is the relative humidity.

Figure 2b does not represent a true compaction model because the chart was developed only with data measured at about 75 °F. The geothermal gradient must be incorporated to properly account for thermal compaction. Then the model can be properly applied to temperatures associated with oil and gas drilling. Again, water sorption isotherms prove up to the task.

The sample’s sorption isotherm at a higher temperature has less water for a given relative humidity (i. e., effective stress state, Eq.1). The thermal effects on compaction are accounted for by applying the thermodynamic Clausius- Clapeyron equation to the isotherms trendline, Figure 2b. This permits the mechanical compaction component (e.g., pore pressure via effective stress) to be isolated from the thermal and chemical compaction component as well as variable mineralogy. Figure 3 shows graphically how the general trendline is adjusted by temperature.

**Applying the model**

The pore pressure calculated from the compaction model outlined here is truly porosity based. Because of extremely low permeability in shale, it is impossible to calculated shale pore pressure to directly verify the model. Therefore, the pore pressure derived from this model has to be compared to inferred pore pressure from drilled mud weights deemed correct and measured pressures in adjacent sands with little structural relief.

Inputs to the model are water content normalized by the CEC (WC/ CEC), and insitu temperature. The WC is the mass equivalent of porosity. Porosity is calculated from the bulk density curve, using a grain density of 2.73 and a water density of 1 g/cc. In petrophysical lingo, it is considered “total porosity.” As previously stated, the CEC is derived from well logs using a modified published technique. The insitu temperature is derived from the geothermal gradient. Figure 3 shows how WC/CEC and temperature results in a graphically derived relative humidity (p/po). This relative humidity, converts to effective stress (Pe) via Eq. 1 and is repeated on a foot by foot basis for the shale in the interpreted well. Pore pressure is then determined by rearranging the where, Pp is model derived pore pressure, OB is total overburden pressure, commonly derived from integration of the density log and Pe is derived from relative humidity (Eq. 1). All units are psi.

There is excellent agreement between the modeled shale pore pressure outlined here with pore pressure inferred from drilled mud weights and pressures measured in interbedded sands illustrated in Figure 4. Since, shale is so abundant and challenging to drill, a robust compaction model will help explorers and drillers by properly modeling seismic, forecasting geologic technical risk, decrease well costs, and improve drilling safety. **OE**

**Jim Krushin** is a consulting oil and gas geologist with over 30 years experience, working in the US and internationally. He worked for 15 years at Amoco Production Co. in Houston, Texas and Tulsa, Oklahoma in exploration and exploitation. His interests include quantifying reservoirs, seals, pore pressure, and shales. He earned BS and MS degrees in geology from the University of Pittsburgh and is a graduate of Amoco’s Petrophysics Training program, where he researched shale petrophysical properties.