1.2.1 Units and Dimensions

Before we proceed, a word on units and dimensions is in order. All quantities in physics must either be dimensionless or have dimensions. All units can be expressed in terms of mass [M], length [L], and time [T]. In equations, the units must be consistent; there is no need for conversion factors. However, care is needed for quantities, such as pressure. It is force per unit area. The dimension of force is [ML⁻¹T⁻²]; but if the unit of length is feet and the unit of pressure is pounds per square inch, or psi (as is commonly used in the US drilling community), a conversion factor is required, since these are inconsistent mixed units. In SI units, such conversion factors are not needed because all the units are consistent. The lack of inconsistency of units using the American system is known to have created a massive headache between the two drilling communities – those who use the SI units (some communities in Europe, for example) and those who do not use SI units. We shall discuss this further in this chapter in the context of pore pressure measurements.

As mentioned, pore pressure has the dimension of force per unit area. In the SI system, the unit of pressure is pascal (Pa), and in the British system, the unit is pounds per square inch (psi). We note that 1 Pa = 1.4504 × 10⁻⁴ psi. This is a rather small unit, and for most practical applications, it is customary to use either kilopascal (KPa) or megapascal (MPa). Drillers, engineers, and well loggers still use the British system, while the academicians prefer the SI system. Therefore, a fluency in both type of units is a must. We will be using the mixed system throughout the book. However, whenever possible, we will provide the SI or British system equivalents.

1.2.2 Hydrostatic Pressure

Sedimentary rocks in formations are composed of solid material and fluids in the porous network. Hydrostatic or normal pressure, $P_h$ , is the pressure caused by the weight of a column of fluid and is given by

$P_h={\displaystyle \underset{0}{\overset{z}{\int }}{\rho }_f}(z)gd\mathrm{z+Pair} \approx {\rho }_{f}gz+P_{air}$(1.1)

where z is the column height of the fluid, ${\rho }_f$ is the density of the fluid, g is the acceleration due to gravity, and $P_{air}$ denotes the pressure due to the atmosphere. The size and shape of the fluid column have no effect on hydrostatic pressure. The approximation on the right-hand side of equation (1.1) assumes that ${\rho }_f$ is constant and z is the depth below sea level or the land surface. Hydrostatic pore pressure increases with depth; the gradient at a given depth is dictated by the fluid density at that depth. This is because the water or brine density is not constant. Water tends to expand with rising temperature but contracts with rising pressure. As we shall see later, between the two processes in the subsurface (i.e., increase in temperature and pressure), thermal expansion with increasing depth is greater than the mechanical compression. There are other factors that affect the water density, such as dissolved salt – the solubility of salt also increases with depth. Subsurface brines are more saline than the ocean water. This increase in total dissolved salt increases the density of water. The net effect is that the water (brine) density is a complex function of temperature, pressure, and total dissolved solids. If a subsurface formation is in the hydrostatic condition, it implies that there is an interconnected and open pore system from the earth’s surface to the depth of measurement. To summarize, the fluid density depends on various factors, such as fluid type (oil, water, or gas), concentration of dissolved solids (i.e., salts and other minerals), and temperature and pressure of the fluid and gases dissolved in the fluid column. In Appendix A we provide some practical empirical relationships for physical properties of brine, gas, and oil needed for quantitative analysis of geopressure.

We strongly recommend that those who wish to pursue quantitative evaluation of geopressure use those equations for density and velocity of brine, gas, and oil (“dead” and “live”) in a computer code. This will enable them to evaluate the true hydrostatic pressure as well as the pressure due to gas and oil columns of various heights. Here “dead” oil designates oil without any dissolved gas, whereas “live” oil means it contains dissolved gas.

What would a pressure versus depth plot such as the one in Figure 1.1 look like for a reservoir rock containing gas, oil, and water? An example is given in Figure 1.2 for the case of a reservoir filled with gas, oil, and water (brine). The slope changes are due to the density contrast between different kinds of fluids (gas, oil, brine), as discussed earlier. This kind of plot is very useful for determining the height of a hydrocarbon column in a reservoir. The discrete data points show actual measurements of pore pressure in a reservoir. Typically, not many measurements are carried out, as measurements are expensive in a real petroleum well; petroleum engineers make these discrete measurements and then look for slope changes to determine gas–oil and oil–water contacts, which yield the hydrocarbon column height. Eventually, seismic data are used along with geologic structure maps of a prospect to map these contacts in 3D. Volumetric calculations resulting from these measurements, along with uncertainty estimates, are used to determine the ultimate value of the asset.

1.2.3 Head

We introduce some terminology commonly used in fluid dynamics and relevant to geopressure. In the subsurface, fluids always move, although the speed at which they move is small in the human timescale. It is not so in the geologic timescale. The definitions that we gave in Section 1.2.2 are for fluids in the static condition. In fluid mechanics literature, the word head is commonly used. Head refers to a vertical dimension and has the dimension of length [L]. There are various types of heads.

A pressure head (also termed as static pressure head or static head) is the vertical elevation of the free surface of water above the point of interest. It is given by

$\psi =P/\gamma =P/\rho g$(1.2)

where

• $\psi$ is the pressure head (length, typically in units of m)

• P is the fluid pressure (force per unit area, typically in units of Pa)

• $\gamma$ is the specific weight (force per unit volume, typically in units of Newton/m³)

• $\rho$ is the density of the fluid (mass per unit volume, typically in kg/m³)

The term hydraulic head or piezometric head is used to specify a specific measurement of liquid pressure above a datum. It is composed of three terms: velocity head ($h_v$ ), elevation head ($z_{\text{elevation}}$ ), and pressure head ($\psi$ ). The following is referred to as the head equation:

$C=h_v+z_{\text{elevation}}+\psi$(1.3)

Here C is a constant for the system (referred to as the total head) that appears in the context of the Bernoulli equation for incompressible fluids in hydrodynamics, which states that an increase in fluid speed occurs simultaneously with a decrease in pressure (Reference StreeterStreeter, 1966). The velocity head (also referred to as kinetic head) is the head due to the energy of movement of the water. (In subsurface flow through porous rocks, this is negligible.) The elevation head is the elevation of the point of interest above a datum, usually sea level or the land surface.

1.6.1 Subpressure

Subpressure formations are those in which the pore pressure is below the hydrostatic pressure. Such pressure conditions are known to exist in many depleted oil reservoirs, in areas with withdrawal of ground water and attendant local subsidence and in lenticular reservoirs closely associated with shales in areas that have undergone erosion. Since pore pressure gradient is datum dependent, the local topography plays a significant role. Pressure gradients can be either lower or higher than the hydrostatic pressure gradient. In Figures 1.7a–c, we show three possibilities where the outcrop elevation and the well site elevation determine the pore pressure gradient as measured in that well bore. Figure 1.7a shows the normal pressure situation where the well elevation is the same as the outcrop elevation. The pressure gradient at the wellbore is 0.465 psi/ft (0.0105 MPa/m). Figure 1.7b shows the abnormally high pore pressure situation where the well elevation is lower than the outcrop elevation. The pore pressure at the wellbore is 0.465 psi/ft × 13,000 ft = 6045 psi (41.6787 MPa), leading to a pressure gradient of 6045 psi/10,000 ft = 0.6045 psi/ft (0.01360 MPa/m). Figure 1.7c shows a situation where abnormally low or subnormal pressure occurs where the well elevation is higher than the outcrop elevation. In this case, the pore pressure at the well site is 0.465 psi/ft × 7000 ft = 3255 psi (22.4483 MPa) leading to a pressure gradient of 3255/10,000 ft = 0.3255 psi/ft (0.007323 MPa/m) which is lower than the normal pressure gradient. We note that subpressures are relatively uncommon except for depleted reservoirs. Proximity to a mountain range is also a feature that relate to subpressures – it provides a sink through which water is abstracted from the basins.

Figure 1.7 Effect of datum on pore pressure gradient. (a) Well elevation is the same as that of the outcrop elevation. (b) Well elevation is lower than the outcrop elevation leading to an abnormally high-pressure gradient. (c) Well elevation is higher than the outcrop elevation, leading to an abnormally low-pressure gradient.

1.6.2 Fracture Pressure

In oil field terminology, fracture pressure is the pressure that causes a formation to fracture and the circulating fluids to be lost. Normally it is expressed as the fracture gradient or the fracture pressure divided by the depth. In this way, it determines the maximum mud weight that can be used to drill a well bore at a given depth. Hence it is an important parameter for mud weight design in both the drilling planning stage and in the drilling stage. If the mud weight is higher than the fracture gradient of the formation the well bore will undergo tensile failure, causing losses of drilling mud or even lost circulation. In practice, fracture pressure is measured from various types of leak-off tests (LOT). A leak-off test is performed to estimate the maximum amount of pressure or fluid density that the test depth can hold before leakage and formation fracture may occur. This measurement is usually made at the casing points. There are several approaches to calculate fracture gradient. We shall discuss this in details later (Chapters 2 and 4).

1.6.3 Equivalent Circulation Density (ECD)

This is an important concept in drilling. Hydrostatic weight of the mud is intended to balance the formation pressure under “static” condition. During drilling, mud pumps are turned on and the situation is no longer static. In this case, the borehole geometry introduces pressure loss based on drag on the fluid as it passes through the various components of the fluid flow path during drilling such as standpipe, drillstring components, open hole, and casing. The mud pumps supply the pressure that forces drilling mud down the drill string to the bottom of the hole and up again to the surface. As the drilling mud exits the bit nozzles, the mud has to flow through the annular space between the drill string and the borehole wall. Contact is made between the drilling mud and the borehole wall as the drilling mud flows upward to the surface. This contact creates “drag” as the result of friction and the drilling mud loses some of the pressure supplied by the pump in order to overcome this frictional drag. This pressure loss is absorbed by the formation. Equivalent circulating density (ECD) is the effective density that combines current mud density and annular pressure drop. Thus, ECD in ppg = (annular pressure loss in psi) ÷ 0.052 ÷ true vertical depth (TVD) in ft + (current mud weight in ppg). This is why the ECD is always greater than the mud density under static condition. The greater the vertical distance through which the drilling mud has to travel until it reaches the surface, the higher are the pressure drop and ECD. Note that ECD is a function of the true vertical depth and not the measured depth. Measured depth includes the horizontal section in deviated wells but ECD only depends on the true “vertical” depth. Acquired solids (cuttings), the type of mud and its temperature also affect ECD.

1.8.1 Guide for Safe Drilling Practices

Even though the petroleum industry has a good safety record, drilling through high pressured formations is known to pose serious drilling challenges. Blowouts are also known to occur occasionally. Some of the reasons are listed above. While catastrophic events are rare, what is not rare is the nonproductive drilling time spent during a drilling operation as shown in Figure 1.11. About 95 percent of the incidents involves problems related to drilling performance. In addition, ~5–25 percent of the well cost is a result of inadequate drilling performance. As the data shows, ~30–40 percent of the operations cost during drilling are related to overpressure. Some estimates put the total loss to the industry as high as $3.0 billion annually. For serious problems such as those due to loss of circulation of drilling mud into the surrounding formation or influx of the formation fluid into the borehole (Figure 1.11), the nonproductive downtime could be as long as seven days or higher – for deepwater drilling activities where daily rig rates could be as high as $200 million, the losses could be very high. In the extreme case, if the formation pressure encountered during drilling is much higher than planned, it would be impossible to drill through to the target at deeper depths and to set proper casing as there may not be enough casing string left. This would result in abandoning the well without reaching its target and thus causing huge losses.

Figure 1.11 Time lost during drilling (nonproductive time or NPT) as known in the petroleum industry. About 30–40 percent of NPT are due to issues related to overpressure. Fishing is a term used by the driller to retrieve any tool lost in a borehole.

We mentioned earlier that quantitative analysis of geopressure is important as it impacts the mud program while drilling a well. Mud program refers to designing a formal plan for drilling fluid requirements in general and specific maintenance need, namely, choosing drilling fluid for a specific well with predictions and requirements at various intervals of the wellbore depth. It consists of details on the mud type; composition, density, rheology, filtration and other properties. The density is especially important because they must fit with the casing design program and to ensure wellbore pressures are properly controlled as the well is drilled deeper. Good drilling fluid or mud (as is known in the industry) with proper density is necessary to ensure that no formation fluid influx occurs into the wellbore. This is particularly important while drilling in high pressured wells that require increasing the fluid density (or mud weight) with depth. However, a best practice dictates that the drilling fluid density or the mud weight must not be too high as compared to the true formation pressure. If not, it can cause a serious drilling problem known as lost circulation with unwanted consequences such as formation of thick mud filtration between the well bore and the formation, poor cementing job, and so on. (There are other uses of a good drilling fluid: remove cuttings expeditiously from beneath the drill bit; transport cuttings to the surface without degradation; economically deliver a wellbore suitable for formation evaluation and completion and control torque on drill string, particularly in deviated wells.) Thus, variation of geopressure with depth is perhaps the key parameter that dictates designing a good mud program.

There is another importance of geopressure that impacts safety. As we will learn in this book that high pressures usually occur in thick shale formations with considerably higher water (brine) content compared with the normally pressured case. The types of drilling fluid used depend on the pressure regime. In the low-pressure regime, cost-effective water-base drilling fluid (with bentonite mud) is commonly used. For higher pressured wells, the industry uses oil-base drilling fluid. It is expensive and affects the rate of penetration of the drill bit. Thus, a transition from water-base mud to oil-base mud at a specific depth is highly influenced by the details of the quantitative profile of geopressure with depth.

1.8.2 Exploration Use

In the context of exploration for hydrocarbon, a proper quantification of pore fluid pressure in 3D is highly desirable as it can suggest a path for hydrocarbon migration through porous formations and subsequent trapping, either stratigraphically or structurally favored environments (faults, folds, etc.). Thus, the hydrodynamics of a sedimentary basin is greatly impacted by the distribution of pressured fluids, and an analysis may reveal the proper location to drill (or to avoid) and the expected height of hydrocarbon column in the prospect area. The economics of drilling for hydrocarbon is impacted in two major ways by the presence of overpressure in sedimentary basins. First, one would like to know the depth of an economic basement, if any. This is defined as the depth where the pore pressure is so high (and the vertical effective stress is so low) that the likelihood of fracturing the rock by natural causes such as hydraulic fracturing or rock movement due to earthquake can cause the hydrocarbon trap to mitigate and the oil and gas accumulation to escape from the reservoir. Figure 1.12, developed for a part of the Gulf of Mexico (Reference Dutta, Moller-Pedersen and KoestlerDutta, 1997b), shows such a map in which color codes indicate potential areas of possible seal failure due to high pore pressure. Each square block of that figure represents a federal lease area – a block that is 9 sq mi. The red colors indicate areas with possibility of low effective stresses (~500 $\pm 250\text{psi}).$ Maps such as the one in Figure 1.12 could be used to high-grade the prospect inventory (possibility of seal mitigation) and assign a potential hazard index to those areas with extremely low effective stresses for drilling. Second, the explorer of hydrocarbons would like to know the depth of the top of the onset of overpressure (Figure 1.13) and the distribution of overpressure in 3D (Figure 1.14). As we shall see later, the hydrocarbon column height in a reservoir is greatly impacted by the magnitude of overpressure in the reservoir – higher the overpressure, the lower will be the total hydrocarbon column height. This is because the buoyancy force due to hydrocarbon will contribute further to the existing high pore pressure of the fluids, thus raising the likelihood of seal leakage and eventually seal failure.

Figure 1.12 Effective stress and seal failure map in a large area of the Gulf of Mexico (see inset) as predicted from a combination of surface seismic and basin modeling. Red indicates high probability of seal failure. Taken from Reference Dutta, Moller-Pedersen and KoestlerDutta (1997b). The range of effective stress is from 0 to 5000 psi.

Figure 1.13 Two-way time to the top of overpressure for the same area as shown in Figure 1.12. Blue indicates shallow overpressure. Taken from Reference Dutta, Moller-Pedersen and KoestlerDutta (1997b). The scale is two-way time (twt); the range is 0-8000 ms.

Figure 1.14 Seismic-based map of distribution of pore pressure in 3D. Annotation shows “sweet” spots for exploration and identifies areas for “drilling” through risky zones. The size of the cube is ~600 sq. mi. in area and 5 s deep (in time). From Dutta and Khazanehdari (2006).

Recent studies have indicated another use for quantification of geopressure for exploration. This is related to defining a better seismic velocity model for seismic imaging. Traditionally, seismic velocities are obtained by various inversion processes (we will study this in Chapter 5) that produce velocity models that are inherently nonunique and potentially ambiguous. Recent studies (Reference Dutta, Yang, Dai, Chandrasekhar, Dotiwala and RaoDutta et al., 2014, Reference Dutta, Deo, Liu, Krishna, Kapoor and Vigh2015a, Reference Dutta, Yang, Liu, Lawrence and Cue2015b; Reference Le, Pradhan, Dutta, Biondi, Mukerji and LevinLe et al., 2018) have shown that imposing a pore pressure constraint on the derived seismic velocity model and demanding that the velocity model yield a physically plausible pore pressure model, namely, the predicted pore pressure be equal or higher than the hydrostatic pore pressure and be less than the fracture pressure, for example, yields a better seismic image of the subsurface. An example is provided in Figure 1.15. Figure 1.15a shows the legacy image using conventional velocity analysis (tomography based anisotropic velocity analysis) while the one in Figure 1.15b (that used a constrained anisotropic velocity model (tomography) – constrained by plausible range of pore pressure) shows a marked improvement. Not only is the velocity lowered (a consequence of high pore pressure) but the seismic energy is more focused resulting in a better illumination of the image of the potential deep targets for exploration. We shall discuss this approach for building a common velocity modeling for pore pressure and imaging in detail in Chapter 6.

Figure 1.15 Use of seismic data to improve the image of subsurface formations in a velocity model. (a) An image based on a legacy anisotropic velocity model. (b) An improved image based on an anisotropic velocity model that uses pore pressure constraint on the velocity model. The image is better focused. This led to a better well path trajectory to reach the deeper target. After Reference Dutta, Yang, Dai, Chandrasekhar, Dotiwala and RaoDutta et al. (2014).

Over the last several decades, our quest for hydrocarbon exploration and drilling has taken us to the frontiers of the deepwater where sizable accumulations have been found. These activities have pointed to a link between high pore pressures and potential risk to the environment. We have seen the risk of blowouts of pressured aquifer sands in the shallow part of the stratigraphy below seabed (Reference Ostermeier, Pelletier, Winker, Nicholson, Rambow and CowanOstermeier et al., 2002). These are known in the industry as shallow-water-flow (SWF) sands – it is a deepwater phenomenon and deals with aquifer pressured sands held by a thin veneer of clay. Drilling through these sands can cause blowouts and serious damages to the environment. This is a near-surface geologic phenomenon and the quantification of pore pressure is difficult but necessary so that adequate precautions (avoidance, for example) can be undertaken. In Figure 1.16, we show a compilation of many other geological causes of geohazards – not all of which are related to high pore pressure. An example is the gas hydrates in deepwater that exist in the environment similar to the place where SWF sands occur. In Chapter 11 we shall discuss how to quantify some of these geohazards and the role of geopressure.

Figure 1.16 A schematic compilation of geological causes of geohazards.

1.8.3 Seals, Seal Capacity, and Pore Pressure

Hydrocarbon exploration is fundamentally about recognizing three things in a sedimentary basin: existence of source rocks (source), a reservoir or container for hydrocarbon to migrate into (reservoir), and a seal or a lid to contain the hydrocarbon (seal). Geopressure impacts all of these and in addition, it facilitates the primary and secondary migration of hydrocarbon (Reference Tissot and WelteTissot and Welte, 1978). In a scholarly article, Reference WattsWatts (1987) describes three types of seals: hydrodynamic, caprock, and fault. Hydrodynamic seals are controlled by excess hydrodynamic head above hydrocarbon accumulation. In this case hydrocarbon column reaches equilibrium when hydrocarbon buoyancy pressure is balanced by a downward hydrodynamic flow force, as shown in a schematic diagram in Figure 1.17 in an anticlinal reservoir under the condition of increasing action of flowing water (brine). Under hydrostatic conditions (no flow), oil and gas would simply rise (top figure), according to the principle of buoyancy, to the highest available part of the trap. Under hydrodynamic conditions, however, it is not necessary that hydrocarbon (oil or gas) rises in the crest position of the structure. Fault-related seals are those that prohibit fluid migration through the faulted regions and these are controlled by the entry pressure of largest interconnected pore throats across the fault planes. Sealing faults are caused mainly by clay smear (very low permeability) or a variety of diagenetic processes (Reference Tissot and WelteTissot and Welte, 1978).

Figure 1.17 Hydrocarbon distribution in an anticlinal reservoir under the conditions of increasing action of flowing water (brine).

Modified after Reference Tissot and WelteTissot and Welte (1978).

In the petroleum industry, caprock is defined as any nonpermeable formation that may trap oil, gas or water, thus preventing it from migrating to the surface. Caprock is essential to create a reservoir of oil, gas or water beneath it and is a primary target for the petroleum industry. It can be overpressured as is the case for almost all Tertiary Clastic basins. According to Reference Tissot and WelteTissot and Welte (1978), caprock seals can be of two types: membrane and hydraulic. The membrane seal integrity is mostly controlled by the entry pressure of largest interconnected pore throats, while this is not the case for hydraulic seals where seal breach occurs mainly due to hydraulic fractures (typically due to high overpressure).

Seal capacity refers to the hydrocarbon column height that the caprock can retain before capillary forces allow migration of the hydrocarbon into, and possibly through, the pore system of the caprock. Seal capacity is affected by both the physical properties of seal including its pore pressure state and the properties of the hydrocarbon. When hydrocarbon begins to fill in a reservoir, the pore space of that reservoir is usually filled with water (formation water). As hydrocarbon has a lower density than the formation water occupying the pore space, the hydrocarbon rises upward through the reservoir due to buoyancy (the density difference between hydrocarbon and water). Greater the density difference between the two phases is, so is the buoyant force that pushes the less dense, more buoyant hydrocarbon-phase upward.

The upward movement of the hydrocarbon through the pore system is resisted by capillary pressure. Capillary pressure is defined as the pressure required to displace the formation water from the pores and pore throats of the seal. The capillary pressure $P_c$ is known as the displacement pressure in the petroleum industry, and it is given by (Reference BergBerg, 1975)

$P_C=\frac{2\gamma \cos \theta }{r}$(1.19)

where $\gamma$ is the interfacial tension (dynes/cm) between hydrocarbon (oil or gas) and brine, $\theta$ is the contact angle (degrees), and $r$ is the pore throat radius (cm). Reference Clayton and HayClayton and Hay (1994) showed the following relation for the thickness of the hydrocarbon column $T_H$ :

$T_H=\frac{2\gamma \cos \theta }{r({\rho }_w-{\rho }_h)g}-\frac{\Delta P}{({\rho }_w-{\rho }_h)g}$(1.20)

where ${\rho }_w$ is the density of the formation water (brine), ${\rho }_h$ is the density of the trapped hydrocarbon, $g$ is the acceleration due to gravity, and $\Delta P$ is the overpressure in reservoir relative to the seal (caprock). The first part of the right-hand side of equation (1.20) gives the column height under normal or hydrostatic pore pressure conditions (seal capacity), and the second part gives a correction for excess reservoir overpressure. In Figure 1.18 we show the range of seal capacities of different rock types as documented in AAPG Wiki. This figure was compiled from published displacement pressures based upon the mercury capillary curves. Column heights were calculated using a 35°API oil at near-surface conditions with a density of 0.85 g/cm³, an interfacial tension of 21 dynes/cm, and a brine density of 1.05 g/cm³. Data were compiled from Reference SmithSmith (1966), Reference Thomas, Katz and TedThomas et al. (1968), Reference SchowalterSchowalter (1979), Reference Wells and AmafueleWells and Amaefule (1985), Reference Melas and FriedmanMelas and Friedman (1992), Reference Vavra, Kaldi and SneiderVavra et al. (1992), Reference BoultBoult (1993), and Reference Shea, Schwalbach, Allard, Ebanks, Kaldi and VavraShea et al. (1993). The figure suggests that (1) shales can trap thousands of feet of hydrocarbon (normally pressured case), (2) most clean sands can trap up to 50 ft or less column of oil, and (3) poor quality sands and siltstones can trap 50–400 ft of oil. Carbonates have a wide range of displacement pressures. Some carbonates can seal as much as 1500–6000 ft of oil.

Figure 1.18 Range of measured seal capacities of oil accumulation for different rock types.

Modified after a figure from the AAPG Wiki at http://wiki.aapg.org/Seal_capacity_of_different_rock_types.

We note that higher the overpressure, lower is the hydrocarbon column height. This is clear from the following:

$H_{hc, \max }=\frac{FP-RP}{({\rho }_w-{\rho }_{hc})g}$(1.21)

where

• $H_{hc,\max }$ = maximum hydrocarbon column height

• FP = fracture pressure or the pore pressure at which hydraulic fracturing occurs

• RP = reservoir pressure or the pore pressure of the brine-filled reservoir

• ${\rho }_w$ = density of brine

• ${\rho }_{hc}$ = density of hydrocarbon

The fracture and reservoir pressure should be estimated or measured at the crest of the structural closure. Equation (1.21) shows why a study of geopressure is so important – as reservoir pressure increases (due to some overpressure mechanisms), the hydrocarbon column height decreases. It impacts both hydrocarbon accumulation and migration from source to reservoir. It also defines the seal integrity of caprock, namely, whether hydraulic fracture would occur or not. Compaction and diagenesis during burial cause a progressive reduction in pore throats in most seal lithologies. This affects seal capacity. In addition, the interfacial tension of the hydrocarbons changes with depth and affects seal capacity. Most importantly, the interfacial tension of oil and gas changes at different rates and impacts the seal capacity.

1.8.4 Permeability and Fluid Flow in Porous Rocks

Rocks are porous material composed of solid grains, void spaces and fluids in the void spaces. Reference DarcyDarcy (1856) showed that the fluid flow rate in a porous rock is linearly related to the pressure gradient. The flow equation can be expressed generally as

$Q=-\frac{\kappa A}{\mu }gradP$(1.22)

where Q is the vector fluid volumetric velocity, A is the cross-sectional area normal to the pressure gradient, $\mu$ is the fluid viscosity, and $\kappa$ is the permeability (it is a tensor) with units of area. The unit of permeability commonly used is Darcy. We shall discuss how permeability affects fluid flow and contributes to geopressure in Chapter 3 in detail. The ability of fluids to flow is controlled by the permeability $\kappa$ that is of great importance in the petroleum industry. Formations that transmit fluids readily, such as sandstones, are described as permeable and tend to have many large, well-connected pores. Impermeable formations, such as silts and shales, tend to be finer grained or of mixed grain sizes, with smaller, fewer, or less interconnected pores. Absolute permeability is defined as that permeability measured when a single fluid is present in the rock. Its dimension is of an area. Relative permeability is the ratio of permeability of a particular fluid at a particular saturation to the absolute permeability of that fluid at full saturation. It is a dimensionless quantity. Calculation of relative permeability enables us to compare different abilities of each fluid to flow in the presence of the other. The presence of more than one fluid generally hinders flow. Effective permeability is a measure of permeability when two immiscible fluids occupy the same pore space of a rock, the movement of each is influenced by the other, and by their saturations. The following are the typical ranges of the individual permeability of common rock types:

• Conventional oil and gas reservoirs ~ milli-Darcy (10⁻³ Darcy)

• Tight sands, coal and some shales ~ micro-Darcy (10⁻⁶ Darcy)

• Some coals and most shales ~ nano-Darcy (10⁻⁹ Darcy)

Permeability of sediments is related to porosity $\varphi$ and therefore, it will decrease with compaction as rocks are buried. The Kozeny–Carman equation (Reference KozenyKozeny, 1927; Reference CarmanCarman, 1937) describes the relationship between permeability $\kappa$ , porosity, and grain diameter d, as follows:

$\kappa =B\frac{{\varphi }^3}{{(1-\varphi )}^2}{d}^2$(1.23)

where $B$ is a constant that includes tortuosity of the rock. The porosity exponent of 3 in equation (1.23) is valid for very clean sandstones. Higher exponents are more appropriate of clays and shales (Reference Bourbie, Coussy and ZinsznerBourbie et al., 1987).

In this chapter we introduced a host of definitions related to pore pressure and drilling. In Appendix B the readers will find a glossary of some of the commonly used terms introduced in this chapter as well as those used in the industry.