Petroleum Engineers Association

Pore Pressure Prediction from Well Logs

1. Abnormal Pore Pressure

Abnormal pore pressures, particularly overpressures, can greatly increase drilling non-productive
time and cause serious drilling incidents (e.g., well blowouts, pressure kicks, fluid influx) if the
abnormal pressures are not accurately predicted before drilling and while drilling. Overpressures can
be generated by many mechanism, such as compaction disequilibrium (under-compaction),
hydrocarbon generation and gas cracking, aquathermal expansion, tectonic compression (lateral
stress), mineral transformations (e.g., illitiza- tion), and osmosis, hydraulic head and hydrocarbon
buoyancy (Swarbrick and Osborne, 1998; Gutierrez et al., 2006). In nearly all cases where compaction
disequilibrium has been determined to be the primary cause of overpressuring, the age of the rocks
is geologically young.

One of the major reasons of abnormal pore pressure is caused by abnormal formation compaction
(compaction disequilibrium or under-compaction). When sediments compact normally, formation
porosity is reduced at the same time as pore fluid is expelled. During burial, increasing overburden
pressure is the prime cause of fluid expulsion. If the sedimentation rate is slow, normal compaction
occurs, i.e., equilibrium between increasing overburden and the reduction of pore fluid volume
due to compaction (or ability to expel fluids) is maintained (Mouchet and Mitchell, 1989). This
normal compaction generates hydrostatic pore pressure in the formation. Rapid burial, however,
leads to faster expulsion of fluids in response to rapidly increasing overburden stress. When the
sediments subside rapidly, or the formation has extremely low permeability, fluids in the sediments
can only be partially expelled.

The remained fluid in the pores of the sediments must support all or part of the weight of overly
sediments, causing the pressure of pore fluid increases, i.e., abnormally high pore pressure. In this
case, porosity decreases less rapidly than it should be with depth, and formations are said to be under-
compacted or in compaction disequilibrium. The overpressures generated by under-compaction in
mudrock-dominated sequences may exhibit the following characteristic: the abnormal pore pressure
change with depth is sub-parallel to the lithostatic (overburden) pressure gradient (Swarbrick et al.,
2002). The compaction disequilibrium is often recognized by higher than expected porosities at a
given depth and the porosities deviated from the normal porosity trend. However, the increase in
porosity is not necessary caused merely by under- compaction and it could be caused by other
reasons, such as micro-fractures induced by hydrocarbon generation. Therefore, both under-
compaction and hydrocarbon generation may cause porosity increase and abnormal pressure. Thus,
by knowing the normal porosity trend and measured formation porosities (can be obtained from well
log data), one can calculate the formation pore pressure.

1.1. Pore pressure and pore pressure gradient

Pore pressure is one of the most important parameters for drilling plan and for geomechanical and
geological analyses. Pore pressures are the fluid pressures in the pore spaces in the porous formations.
Pore pressure varies from hydrostatic pressure, to severely overpressure (48% to 95% of the
overburden stress). If the pore pressure is lower or higher than the hydrostatic pressure (normal pore
pressure), it is abnormal pore pressure. When pore pressure exceeds the normal pressure, it is
overpressure.
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The fundamental theory for pore pressure prediction is based on Tirzah and Boot’s effective stress law
(Biot, 1941; Terzaghi et al., 1996). This theory indicates that pore pressure in the formation is a
function of total stress (or overburden stress) and effective stress. The overburden stress, effective
vertical stress and pore pressure can be expressed in the following form:
(𝜎𝑉 − 𝜎𝑒 )
𝑝= (1)
𝛼
Where 𝑝the pore is pressure; 𝜎𝑉 is the overburden stress; 𝜎𝑒 is the vertical effective stress; and α is
the Biot effective stress coefficient. It is conventionally assumed α=1 in geopressure community.

Pore pressure can be calculated from Eq. (1) when one knows overburden and effective stresses.
Overburden stress can be easily obtained from bulk density logs, while effective stress can be
correlated to well log data, such as resistivity, sonic travel time/ velocity, bulk density and drilling
parameters (e.g., D exponent). Fig. 1 demonstrates the hydrostatic pressure, formation pore pressure,
overburden stress and vertical effective stress with the true vertical depth (TVD) in a typical oil and
gas exploration well. The pore pressure profile with depth in this field is similar to many geologically
young sedimentary basins where overpressure is encountered at depth. At relatively shallow depths
(less than 2000 m), pore pressure is hydrostatic, indicating that a continuous, interconnected column
of pore fluid extends from the surface to that depth. Deeper than 2000 m the overpressure starts,
and pore pressure increases with depth rapidly, implying that the deeper formations are
hydraulically isolated from shallower ones. By 3800 m, pore pressure reaches to a value close to
the overburden stress, a condition referred to as hard overpressure. The effective stress is
conventionally defined to be the subtraction of pore pressure from overburden stress (refer to Eq.
(1)), as shown in Fig. 1. The increase in overpressure causes reduction in the effective stress.

Figure 1. Hydrostatic pressure, pore pressure, overburden stress, and effective stress in a borehole

The pore pressure gradient is more practically used in drilling engineering, because the gradients
are more convenient to be used for determining mud weight (or mud density), as shown in Fig. 2.
The pore pressure gradient at a given depth is the pore pressure divided by the true vertical depth.
The mud weight should be appropriately selected based on pore pressure gradient, wellbore stability
and fracture gradient prior to setting and cementing a casing. The drilling fluid (mud) is applied in the
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form of mud pressure to support the wellbore walls for preventing influx and wellbore collapse during
drilling. To avoid fluid influx, kicks and wellbore instability in an open whole section, a heavier mud
pressure than the pore pressure is needed. However, when mud weight is higher than the fracture
gradient of the drilling section, it may fracture the formation, causing mud losses or even lost
circulation. To prevent wellbore from hydraulic fracturing by the high mud weight, as needed where
there is overpressure, casing needs to be set to protect the overlying formations from fracturing, as
illustrated in Fig. 2.

Figure 2Pore pressure gradient, fracture gradient, overburden stress gradient (lithostaticgradient), mud weight, and casing
shoes with depth. In this figure, the pore pressure and overburden gradients are converted from the pore pressure and
overburden stress plotted in Fig. 1.

1.2. Fracture pressure and fracture gradient

Fracture pressure is the pressure required to fracture the formation and cause mud loss from wellbore
into the induced fracture. Fracture gradient can be obtained by dividing the true vertical depth from
the fracture pressure. Fracture gradient is the maximum mud weight; therefore, it is an important
parameter for mud weight design in both drilling planning stage and while drilling. If mud weight is
higher than the formation fracture gradient, then the wellbore will have tensile failure (be fractured),
causing losses of drilling mud or even lost circulation. Fracture pressure can be measured directly
from downhole leak-off test (LOT). There are several approaches to calculate fracture gradient. The
following two methods are commonly used in the drilling industry; i.e., the minimum stress method
and tensile failure method.

1.3. Minimum stress for lower bound of fracture gradient

The minimum stress method does not include any accommodation for the tensile strength of the rock,
rather it represents the pressure required to open and extend a pre-existing fracture in the formation.
Therefore, the minimum stress represents the lower bound of fracture pressure. The minimum stress
is the minimum principal in-situ stress and typically equal to the fracture closure pressure, which can
be observed on the decline curve of a leak-off test following the breakdown pressure (Zhang et al.,
2008).
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1
𝜎𝑚𝑖𝑛 = (𝜎 − 𝑝) + 𝑝 (2)
1−𝑣 𝑉
Where 𝜎𝑚𝑖𝑛 is the minimum in-situ stress or the lower bound of fracture pressure; 𝑣 is the Poisson's
ratio, can be obtained from the

1 𝑣𝑝 2
2 ( 𝑣𝑠 ) − 1
𝑣=
𝑣𝑝 2
( ) −1
𝑣𝑠
When the open fractures exist in the formation, the fracture gradient may be even lower than the
minimum stress.

Matthews and Kelly (1967) introduced a variable of effective stress coefficient for fracture gradient
prediction:

𝑃𝐹𝐺 = 𝐾𝑜 (𝑂𝐵𝐺 − 𝑃𝑝𝑔 )𝑃𝑝𝑔

Where 𝑃𝐹𝐺 is the formation fracture gradient; Ppg is the formation pore pressure gradient; OBG is the
overburden stress gradient; 𝐾𝑜 is the effective stress coefficient, 𝐾𝑜 = 𝜎′𝑚𝑖𝑛 /𝜎′𝑉 ; 𝜎′𝑚𝑖𝑛 is the
minimum effective in-situ stress; 𝜎′𝑉 is the maximum effective in-situ stress or effective overburden
stress. In this method the values of 𝐾𝑜 were established based on fracture threshold values derived
empirically in the field. The 𝐾𝑜 can be obtained from LOT and regional experiences.

Formation breakdown pressure for upper bound of fracture gradient

For intact formations, only after a tensile failure appeared in the wellbore can mud loss occur. In this
case, fracture pressure/gradient can be calculated from Kirsch's solution when the minimum
tangential stress is equal to the tensile strength (Haimson and Fairhurst, 1970; Zhang and Roegiers,
2010). This fracture pressure is the fracture breakdown pressure in LOT (Zhang et al., 2008). For a
vertical well, the fracture breakdown pressure or the upper bound of fracture pressure can be
expressed as follows:

𝑃𝐹𝑃 𝑚𝑎𝑥 = 3𝜎𝑚𝑖𝑛 − 𝜎𝐻 − 𝑝 − 𝜎𝑇 + 𝑇𝑜

Where 𝑃𝐹𝑃 𝑚𝑎𝑥 the upper bound of fracture is pressure; 𝜎𝐻 is the maximum horizontal stress; 𝜎𝑚𝑖𝑛 is
the minimum horizontal stress or minimum in-situ stress; 𝜎𝑇 is the thermal stress induced by the
difference between the mud temperature and the formation temperature, and 𝑇𝑜 is the tensile
strength of the rock.

Neglecting tensile strength and temperature effect and assuming 𝜎𝐻 is approximately equal to 𝜎𝑚𝑖𝑛 ,
the previous equation can be simplified to the following form:

𝑃𝐹𝑃 𝑚𝑎𝑥 = 2𝜎𝑚𝑖𝑛 − 𝑝 (5)

Substituting Eq. (2) into Eq. (5), the upper bound of fracture pressure can be expressed as:
2𝑣
𝑃𝐹𝑃 𝑚𝑎𝑥 = (𝜎 − 𝑝) + 𝑝 (6)
1−𝑣 𝑉
Compared this upper bound of fracture pressure (Eq. (6)) to the lower bound of fracture pressure (Eq.
(2)), the only difference is the constant in front of effective vertical stress (𝜎𝑉 − 𝑝). This upper bound
of fracture gradient can be considered as the maximum fracture gradient, or the bound of lost
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circulation (Zhang et al., 2008). Therefore, the average of the lower bound and upper bound of
fracture pressures can be used as the most likely fracture pressure, i.e.:
3𝑣
𝑃𝐹𝑃 = (𝜎 − 𝑝) + 𝑝 (7)
2(1 − 𝑣) 𝑉
Where 𝑃𝐹𝑃 is the most likely fracture pressure.

1.4. Pore pressure in a hydraulically connected formation

Before introducing methods of well-log-based pore pressure prediction, it should be noted that the
methods are based on the shale (mudrock) properties, and the pore pressures obtained from these
methods are the pressures in shales. For the pressures in sandstones, limestones or other
permeable formations, the pore pressure can be obtained by either assuming that the shale pressure
is equal to the sandstone pressure, or using centroid method (Dickinson, 1953; Traugott, 1997;
Bowers, 2001) and using lateral flow model (Yardley and Swarbrick, 2000; Meng et al., 2011) to do
calculation. In either centroid method or lateral flow model, the principle is similar and based on the
following equation (Eq. (8)) for a hydraulically connected and fully saturated formation.

Where a laterally extensive inclined aquifer or a hydrocarbon- bearing formation exists, deep
overpressure regions are connected to shallower regions by a permeable pathway. Fluid flow along
such an inclined formation can cause pore pressures at the crest of a structure to increase. The
pressures in a hydraulically connected formation can be calculated based on the difference in the
heights of fluid columns, i.e.:

Where p1 is the formation fluid pressure at depth of Z1; p2 is the formation fluid pressure at depth of
Z2; ρf is the in-situ fluid density; g is the acceleration of gravity.

Therefore, for a permeable aquifer or hydrocarbon-bearing formation if we know the formation

pressure at a certain depth, then the pressures at other depths can be obtained from Eq. (8). The
calculation and principle is relatively simple. However, to perform this calculation, we need to know
the connectivity and extension area of the formation. In other words, we need to distinguish each
individual fluid compartment and seal, which can be determined from regional geology, well logging
data and drilling data (Powley, 1990). Fig. 3 shows an example of calculating formation pressure in
an oil-bearing sandstone using the fluid flow model (Eq. (8)). When the formation pressure and
pressures in other wells using Eq. (8). When the formation is hydraulically connected and
saturated with the same

Formation pressures in the four wells should follow a single fluid gradient. Fig. Three demonstrates
that Eq. (8) Gives an excellent prediction. Therefore, when the geologic structure, fluid pressure
and density in a well are known, the fluid pressures in other wells located in a hydraulically connected
formation can be fairly predicted. It should be noted that the permeability magnitude and its variation
might affect the hydraulic connectivity of a formation. For extremely low permeable formations (e.g.,
shale gas formation), the applicability of Eq. (8) may be limited.

Pore pressure gradient is different in a formation when it is saturated with different fluids. In each
fluid column, the pore pressure can be calculated using Eq. (8) with the density of the fluid saturated
in this column. Fig. 4 shows a hydraulically connected formation filled with gas, oil and water/brine. If
we know the fluid pressure at a depth, fluid densities, and depths of water–oil contact (WOC) and
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oil–gas contact (OGC), then we can use Eq. (8) to calculate the pressures at other depths. Therefore,
in Location A (the crest) the gas pressure can be expressed as follows:

Where ρg is the in-situ gas density; Pb is the pore pressure in Location B; pA is the pore pressure in
Location A.

Figure 3 . Schematic cross section (left) showing four wells in a hydraulically connected oil-bearing sandstone compartment
and the fluid pressures in different wells (right). Measured fl uid pressures (dots) in these wells match the calculated pore
pressures (line) with an oil gradient of 0.9 g/cm3

In Location B (oil–gas contact), the oil pressure can be obtained from the following equation:

Where ρo is the in-situ oil density; pC is the pore pressure in Location C; pB is the pore pressure in
Location B.

If the formation is only saturated with water, then the pressure in Location A is:

Compared the pressure (pA) in the crest to the water/brine pressure (pwA) at the same depth, the pore
pressure increment induced by oil and gas column in the crest (location A in Fig. 4) can be expressed
in the following form (i.e., Δpog = pA− pwA):

Where Δpog is the pore pressure increment induced by the oil and gas columns; ρw is the in-situ
water/brine density; hg is the height of gas column; ho is the height of the oil column. It should be
noted that gas density is highly dependent on pressure. Therefore, the in-situ gas density should be
used for the calculations. Normally, the gas column height is not very large; hence, in the
aforementioned equations gas density is assumed a constant value. This pore pressure elevation
(Δpog in Eq. (9)) is caused by hydrocarbon buoyancy effect due to density contrasts between
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hydrocarbon and brine. The pressure elevation due to the difference in densities gradually decreases
from the maximum value at the top of the reservoir to zero at the water and hydrocarbon contact.

Figure 4 A schematic reservoir saturated with gas, oil and water (left) and pore pressure elevated by oil and gas columns
and density contrast between water and oil, gas in a reservoir. This density contrast cause pore pressure increase in
Location A compared to the one caused only by water/brine gradient. The right figure shows pore pressure elevated by
hydrocarbon columns in a hydraulically connected formation.

2. Methods for Pore Pressure Prediction

Hottmann and Johnson (1965) were probably the first ones to make pore pressure prediction from
shale properties derived from well log data (acoustic travel time/velocity and resistivity). They
indicated that porosity decreases as a function of depth from analysing acoustic travel time in Miocene
and Oligocene shales in Upper Texas and Southern Louisiana Gulf Coast. This trend represents the
“normal compaction trend” as a function of burial depth, and fluid pressure exhibited within this
normal trend is the hydrostatic. If intervals of abnormal compaction are penetrated, the resulting data
points diverge from the normal compaction trend. They contended that porosity or transit time in
shale is abnormally high relative to its depth if the fluid pressure is abnormally high.

Analysing the data presented by Hottmann and Johnson (1965), Gardner et al. (1974) proposed an
equation that can be written in the following form to predict pore pressure:

Where pf is the formation fluid pressure (psi); σV is expressed in psi; αV is the normal overburden stress
gradient (psi/ft); β is the normal fluid pressure gradient (psi/ft); Z is the depth (ft); Δt is the sonic transit
time (μs/ft); A and B are the constants, A1 =82,776 and B1 = 15,695. Later on, many empirical equations
for pore pressure prediction were presented based on resistivity, sonic transit time (interval velocity)
and other well logging data. The following sections only introduce some commonly used methods of
pore pressure prediction based on the shale properties.

2.1. Pore pressure prediction from resistivity

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In young sedimentary basins where under-compaction is the major cause of overpressure, e.g., the
Gulf of Mexico, North Sea, the well-log-based resistivity method can fairly predict pore pressure. Eaton
(1972, 1975) presented the following equation to predict pore pressure gradient in shales using
resistivity log:

Where Ppg is the formation pore pressure gradient; OBG is the overburden stress gradient; Png is the
hydrostatic pore pressure gradient (normally 0.45 psi/ft or 1.03 MPa/km, dependent on water
salinity); R is the shale resistivity obtained from well logging; Rn is the shale resistivity at the normal
(hydrostatic) pressure; n is the exponent varied from 0.6 to 1.5, and normally n =1.2. Eaton's resistivity
method is applicable in pore pressure prediction, particularly for young sedimentary basins, if the
normal shale resistivity is properly determined (e.g., Lang et al., 2011). One approach is to assume
that the normal shale resistivity is a constant. The other approach includes to accurately determining
the normal compaction trend line, which will be presented in Section 3.1 to address this issue.

Pore pressure prediction from interval velocity and transit time

Eaton's method

Eaton presented the following empirical equation for pore pressure gradient prediction from sonic
compressional transit time:

Where Δtn is the sonic transit time or slowness in shales at the normal pressure; Δt is the sonic transit
time in shales obtained from well logging, and it can be derived from seismic interval velocity. This
method is applicable in some petroleum basins, but it does not consider unloading effects. This limits
its application in geologically complicated area, such as formations with uplifts. To apply this method,
one needs to determine the normal transit time (Δtn).

2.1.1. Bowers' method

Bowers (1995) calculated the effective stresses from measured pore pressure data of the shale and
overburden stresses (using Eq. (1)) and analysed the corresponded sonic interval velocities from well
logging data in the Gulf of Mexico slope. He proposed that the sonic velocity and effective stress have
a power relationship as follows:

Where vp is the compressional velocity at a given depth; vml is the compressional velocity in the
mudline (i.e., the sea floor or the ground surface, normally vml≈5000 ft/s, or 1520 m/s); A and B are
the parameters calibrated with offset velocity versus effective stress data. Rearranging Eq. (7) and
considering σe =σV− p, the pore pressure can be obtained from the velocity as described in Eq. (7), as:
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For Gulf of Mexico wells, A =10–20 and B =0.7–0.75 in the English units (with p, σV in psi and vp, vml in
ft/s). Eq. (8) can also be written in terms of transit time simply by substituting 106/Δt for vp and 106/Δtml
for vml:

Where Δtml is the compressional transit time in the mudline, normally Δtml =200 μs/ft or 660 μs/m.
The effective stress and compressional velocity do not follow the loading curve if formation uplift or
unloading occurs, and a higher than the velocity in the loading curve appears at the same effective
stress. Bowers (1995) proposed the following empirical relation to account for the effect of unloading
curves:

Where σe, vp, vml, A and B are as before; U is the uplift parameter; and

Where σmax and vmax are the estimates of the effective stress and velocity at the onset unloading. In
absence of major lithology changes, vmax is usually set equal to the velocity at the start of the velocity
reversal. Rearranging Eq. (10) the pore pressure can be obtained for the unloading case:

Where pulo is the pore pressure in the unloading case. Bowers' method is applicable to many
petroleum basins (e.g., the Gulf of Mexico). However, this method overestimated pore pressure when
shallow formation is poorly- or un-consolidated, because the velocity in such a formation is very slow.

2.1.2. Millers Method

The Miller sonic method describes a relationship between velocity and effective stress that can be
used to relate sonic/seismic transit time to formation pore pressure. In Miller's sonic method, an input
parameter “maximum velocity depth”, dmax, controls whether unloading has occurred or not. If dmax
is less than the depth (Z), unloading has not occurred; the pore pressure can be obtained from the
following equation (Zhang et al., 2008)

Where vm is the sonic interval velocity in the matrix of the shale (asymptotic travel time at infinite
effective stress, vm =14,000–16,000 ft/s); vp is the compressional velocity at a given depth; λ is the
empirical parameter defining the rate of increase in velocity with effective stress (normally 0.00025);
dmax is the depth at which the unloading has occurred.

If dmax≥ Z, then unloading behaviour is assumed, the pore pressure in the unloading case is calculated
from the following equation:
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Where am is the ratio of slopes of the virgin (loading) and unloading velocities in the effective stress
curves σul (normally am =1.8) and am = vp/vulo; σul is the effective stress from unloading of the sediment;
vulo is the velocity where unloading begins.

Tau model

A velocity-dependent pore pressure prediction method was proposed by Shell through introducing a
“Tau” variable into the effective stress equation (Lopez et al., 2004; Gutierrez et al., 2006):

Where As and Bs are the fitting constants; τ is the Tau variable, and τ = (C−Δt)/ (Δt− D); Δt is the
compressional transit time either from sonic log or seismic velocity; C is the constant related to the
mudline transit time (normally C =200 μs/ft); and D is the constant related to the matrix transit time
(normally D=50μs/ft). Then, the pore pressure can be calculated from Eq. (14) using Eq. (1), i.e.:

The best fitting parameters in the Gulf of Mexico are As =1989.6 and Bs =0.904 (Gutierrez et al., 2006).
Tau model and Miller's method are similar to Bowers' method. The advantage of Miller's method and
Tau model is that both the effects of the matrix and mudline velocities are considered on pore
pressure prediction.

3. Adapted Eaton's methods with depth-dependent normal compaction trendlines

3.1. Eaton's resistivity method with depth-dependent normal compaction trend line

In Eaton's original equation, it is difficult to determine the normal shale resistivity or the shale
resistivity in the condition of hydrostatic pore pressure. One approach is to assume that the normal
shale resistivity is a constant. However, the normal resistivity (Rn) is not a constant in most cases, but
a function of the burial depth, as shown in Fig. 5. Thus normal compaction trendline needs to be
determined for pore pressure prediction. Based on the relationship of measured resistivity and burial
depth in the formations with normal pressures, the following equation of the normal compaction
trend of resistivity can be used (refer to Fig. 5):

Figure 5 Schematic resistivity (a) and pore pressure (b) in an undercompacted basin. The inclined line in (a) represents the
resistivity in normally compacted formation (normal resistivity, Rn). In the under-compacted section the resistivity (R)
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reversal occurs, corresponding an overpressured formation in (b). In the under-compacted/overpressured section, resistivity
is lower than that in the normal compaction trendline(Rn). In the fi gure, σV = lithostatic or overburden stress; σe = the
effective vertical stress; pn = normal pore pressure; p= pore pressure.

Where Rn is the shale resistivity in the normal compaction condition; R0 is the shale resistivity in the
mudline; b is the constant; and Z is the depth below the mudline. Substituting Eq. (16) into Eq. (5), the
Eaton's resistivity equation can be expressed in the following form:

Where: R is the measured shale resistivity at depth of Z; R0 is the normal compaction shale resistivity
in the mudline; b is the slope of logarithmic resistivity normal compaction trendline.

3.2. Eaton's velocity method with depth-dependent normal compaction trendline

Slotnick (1936) recognized that the compressional velocity is a function of depth, i.e., velocity
increases with depth in the subsurface formations. Therefore, the normal compaction trendline of
travel time should be a function of depth. The oldest and simplest normal compaction trend of seismic
velocity is a linear relationship given by Slotnick (1936) in the following form:

Where v is the seismic velocity at depth of Z; v0 is the velocity in the ground surface or at the sea floor;
k is a constant. Sayers et al. (2002) used this relationship as the normally pressured velocity for pore
pressure prediction. A normal compaction trend for shale acoustic travel time with depth in the
Carnarvon Basin was established by fitting an exponential relationship to averaged acoustic travel
times from 17 normally pressured wells (van Ruth et al., 2004):

Where Δtn is the acoustic transit time from the normal compaction trend at the depth of investigation
(μs/m); Z is in meters.

A similar relationship was used for a petroleum basin in Brunei (Tingay et al., 2009):

Based on the data of the measured sonic transit time in the formations with normal pore pressures,
as illustrated in Fig. 7, the following general relationship of the normal compaction trend of the transit
time is proposed (refer to Appendix B for derivations):

Where Δtm is the compressional transit time in the shale matrix (with zero porosity); Δtml is the mudline
transit time; and c is the constant. Substituting Eq. (21) into Eq. (6), the modified Eaton's sonic
equation can be expressed in the following form:
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4. New theoretical models of pore pressure prediction

4.1. Pore pressure prediction from porosity

As introduced before, the under-compaction is the primary reason to cause formation overpressured,
which occur primarily in rapidly subsiding basins and in rocks with low permeability. The indicators of
under-compaction are higher pore pressure and larger formation porosity than those in the normal
compaction condition. It is commonly accepted that porosity decreases exponentially as depth
increases in normally compacted formations (e.g., Athy, 1930):

Where ϕ is porosity; ϕ0 is the porosity in the mudline; Z is the true vertical depth below the mudline;
c is the compaction constant in 1/m or 1/ft. The same relationship exists in porosity and effective
stress (e.g., Dutta, 2002; Flemings et al., 2002; Peng and Zhang, 2007).

Where a is the stress compaction constant in 1/psi or 1/MPa.

As discussed previously, porosity is an indicator (a function) of effective stress and pore pressure,
particularly for the overpressures generated from under-compaction and hydrocarbon cracking.
Therefore, pore pressure can be estimated from formation porosity. Fig. 6 illustrates how to identify
under-compaction and overpressure from porosity profile. When the porosity is reversal, the under-
compaction occurs and overpressure generates. The starting point of the porosity reversal is the top
of under-compaction or top of overpressure. In the formation with under-compaction, porosity and
pore pressure are higher than those in the normally compacted one.

Efforts have been made to use porosity data for predicting pore pressure in shales and mudstones.
For instance, Holbrook et al. (2005) presented porosity-dependent effective stress for pore pressure
prediction. Heppard et al. (1998) used an empirical porosity equation similar to Eaton's sonic method
to predict pore pressure using shale porosity data. Flemings et al. (2002) and Schneider et al. (2009)
also applied porosity–stress relationships to predict overpressures in mudstones.

The author derived a theoretical equation for pore pressure prediction from porosity according to
normal compaction trend of porosity (Zhang, 2008).
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Figure 6Schematic porosity (a) and corresponding pore pressure (b) in a sedimentary basin. The dash porosity profile in (a)
represents normally compacted formation. In the overpressured section, the porosity reversal occurs (heavy line). In the
overpressured section, porosity is larger than that in the normal compaction trendline (ϕn).

Where ϕ is the porosity in shale at depth of Z, can be obtained from sonic or density logs, ϕ0 is the
porosity in the mudline (in the ground surface or sea floor); Z is the depth below the mudline; c can
be obtained from the normal compaction porosity trendline in Eq. (28). From Eq. (26) the pore
pressure, overburden stress and porosity have the following relationship

The primary difference between Eq. (27) and other existing pore pressure-porosity equations is that
the pressures calculated from Eq. (27) are dependent on depths. In other words, the normal
compaction trendline of porosity is not a constant, but a function of depth.

When porosity (ϕ) at an interested depth is greater than the normal porosity (ϕn) at the same depth,
the formation has overpressure. The normal compaction porosity trendline can be determined from
the following equation (rewritten from Eq. (24)):

4.2. Pore pressure prediction from transit time or velocity

Porosity (ϕ) in Eqs. (26) and (27) can be obtained from density and sonic logs or from seismic interval
velocity. The following equation represents one of the methods to calculate porosity from
compressional velocity/transit time proposed by Raiga-Clemenceau et al. (1988):

Where x is the exponent to be determined from the data. In a study of compaction in siliciclastic rocks,
predominantly shales, in the Mackenzie Delta of northern Canada, Issler (1992) obtained laboratory
measurements of porosity in shales and determined a value of 2.19 for the exponent x and used a
fixed value of shale transit time, Δtm =67 μs/ft

Substituting Eq. (29) into Eq. (26), the pore pressure can be predicted from the compressional transit
time/velocity, i.e.:
 Petroleum Engineers Association

Where Cm is the constant related to the compressional transit time in the matrix and the transit time
in the mudline.

Porosity is often estimated by the empirical time average equation presented by Wyllie et al. (1956):

Where Δtf is the transit time of interstitial fluids.

Substituting Wyllie's porosity-transit time equation into Eqs. (26) and (27), we obtain the following
equations to calculate pore pressure gradient (Ppg) and pore pressure (p)

The normal compaction trendline of the transit time in Eqs. (32) and (33) can be obtained from the
following equation:

This normal compaction trend allows the normal transit time to approach the matrix transit time at a
very large depth, which is physically correct as Chapman (1983) pointed out. Unlike other methods,
this proposed sonic method (Eqs. (32), (33)) uses a normal compaction trendline that is asymptotic to
matrix transit time and therefore better represents the compaction mechanism of the sediments. The
other advantage of this model is that the calculated pore pressures are dependent on depth, and both
effects of the matrix and mudline transit time are considered

References

Athy, L.F., 1930. Density, porosity, and compaction of sedimentary rocks. AAPG Bull. 14 (1), 1–24.

Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12 (1), 155–164.

Bowers, G.L., 1995. Pore pressure estimation from velocity data; accounting for overpressure
mechanisms besides undercompaction. SPE Drilling and Completions, June, 1995, pp. 89–95.

Bowers, G.L., 2001. Determining an Appropriate Pore-Pressure Estimation Strategy, Paper OTC 13042.

Matthews, W.R., Kelly, J., 1967. How to predict formation pressure and fracture gradient. Oil Gas J.
65, 92–106.

Burrus, J., 1998. Overpressure models for clastic rocks, their relation to hydrocarbon expulsion: a
critical reevaluation. In: Law, B.E., Ulmishek, G.F., Slavin, V.I. (Eds.), Abnormal pressures in
hydrocarbon environments: AAPG Memoir, 70, pp. 35–63.
 Petroleum Engineers Association
Meng, Z., Zhang, J., Wang, R., 2011. In-situ stress, pore pressure and stress-dependent permeability in
the Southern Qinshui Basin. Int. J. Rock Mech. Min. Sci. 48 (1),122–131.

Chapman, R.E., 1983. Petroleum geology. Elsevier.

Daines, S.R., 1982. Prediction of fracture pressures for wildcat wells. JPT 34, 863–872.

Davies, R.J., Swarbrick, R.E., Evans, R.J., Huuse, M., 2007. Birth of a mud volcano: East Java, 29 May
2006. GSA Today 17 (2). doi:10.1130/GSAT01702A.1.

Dickinson, G., 1953. Geological aspects of abnormal reservoir pressures in Gulf Coast Louisiana. AAPG
Bull. 37 (2), 410–432.

Dodson, J.K., 2004. Gulf of Mexico ‘trouble time’ creates major drilling expenses. Offshore 64 (1).

Dutta, N.C., 2002. Geopressure prediction using seismic data: current status and the road ahead.
Geophysics 67 (6), 2012–2041.

Eaton, B.A., 1968. Fracture Gradient Prediction and Its Application in Oilfield Operations Paper
SPE2163 JPT 25–32.

Eaton, B.A., 1972. The Effect of Overburden Stress on Geopressures Prediction from Well Logs Paper
SPE3719 JPT 929–934 Aug., 1972.

Eaton, B.A., 1975. The Equation for Geopressure Prediction from Well Logs. Society of Petroleum
Engineers of AIME. paper SPE 5544.

Flemings, P.B., Stump, B.B., Finkbeiner, T., Zoback, M., 2002. Flow focusing in overpressured
sandstones: theory, observations, and applications. Am. J. Sci. 302, 827–855.

Gardner, G.H.F., Gardner, L.W., Gregory, A.R., 1974. Formation velocity and density — the diagnostic
basis for stratigraphic traps. Geophysics 39 (6), 2085–2095.

Gutierrez, M.A., Braunsdore, N.R., Couzens, B.A., 2006. Calibration and ranking of porepressure
prediction models. The leading Edge, Dec., 2006, pp. 1516–1523.

Haimson, B.C., Fairhurst, C., 1970. In situ stress determination at great depth by means of hydraulic
fracturing. In: Somerton, W.H. (Ed.), Rock Mechanics — Theory and Practice. Am. Inst. Mining. Eng.,
pp. 559–584.

Heppard, P.D., Cander, H.S., Eggertson, E.B., 1998. Abnormal pressure and the occurrence of
hydrocarbons in offshore eastern Trinidad, West Indies. In: Law, B.E., Ulmishek, G.F., Slavin, V.I. (Eds.),
Abnormal Pressures in Hydrocarbon Environments: AAPG Memoir, 70, pp. 215–246.

Holand, P., Skalle, P., 2001. Deepwater Kicks and BOP Performance. SINTEF Report for U.S. Minerals
Management Service.

Holbrook, P.W., Maggiori, D.A., Hensley, R., 2005. Real-time pore pressure and fracture gradient
evaluation in all sedimentary lithologies. SPE Form. Eval. 10 (4), 215–222.

Hottmann, C.E., Johnson, R.K., 1965. Estimation of formation pressures from log-derived shale
properties Paper SPE1110 JPT 17, 717–722.

Hubbert, M.K., Willis, D.G., 1957. Mechanics of hydraulic fracturing. Pet. Trans. AIME 210, 153–163.
 Petroleum Engineers Association
Issler, D.R., 1992. A new approach to shale compaction and stratigraphic restoration, Beaufort-
Mackenzie Basin and Mackenzie Corridor, Northern Canada. AAPG Bull. 76, 1170–1189.

KSI, 2001. Best practice procedures for predicting pre-drill geopressures in deep water Gulf of Mexico.
DEA Project 119 Report Knowledge Systems Inc. Lang, J., Li, S., Zhang, J., 2011. Wellbore stability
modeling and real-time surveillance for deepwater drilling to weak bedding planes and depleted
reservoirs. SPE/IADC 139708 presented at the SPE/IADC Drilling Conference and Exhibition held in
Amsterdam, The Netherlands, 1–3 March 2011.

Law, B.E., Spencer, C.W., 1998. Abnormal pressures in hydrocarbon environments. In:

Law, B.E., Ulmishek, G.F., Slavin, V.I. (Eds.), Abnormal Pressures in Hydrocarbon Environments: AAPG
Memoir, 70, pp. 1–11.

Lopez, J.L., Rappold, P.M., Ugueto, G.A., Wieseneck, J.B., Vu, K., 2004. Integratedshared earth model:
3D pore-pressure prediction and uncertainty analysis. The Leading Edge, Jan., 2004, pp. 52–59.

Morley, C.K., King, R., Hillis, R., Tingay, M., Backe, G., 2011. Deepwater fold and thrust belt
classification, tectonics, structure and hydrocarbon prospectivity: a review. Earth-Sci. Rev. 104, 41–
91.

Mouchet, J.-C., Mitchell, A., 1989. Abnormal Pressures while Drilling. Editions TECHNIP, Paris.

Nelson, H.N., Bird, K.J., 2005. Porosity-depth Trends and Regional Uplift Calculated from Sonic Logs,
National Reserve in Alaska. Scientific Investigation Report 2005–5051 U.S. Dept. of the Interior and
USGS.

Peng, S., Zhang, J., 2007. Engineering Geology for Underground Rocks. Springer.

Powley, D.E., 1990. Pressures and hydrogeology in petroleum basins. Earth-Sci. Rev. 29, 215–226.

Raiga-Clemenceau, J., Martin, J.P., Nicoletis, S., 1988. The concept of acoustic formation factor for
more accurate porosity determination from sonic transit time data. Log Analyst 29 (1), 54–60.

Sayers, C.M., Johnson, G.M., Denyer, G., 2002. Predrill pore pressure prediction using seismic data.
Geophysics 67, 1286–1292.

Schneider, J., Flemings, P.B., Dugan, B., Long, H., Germaine, J.T., 2009. Overpressure and consolidation
near the seafloor of Brazos-Trinity Basin IV, northwest deepwater Gulf of Mexico. J. Geophys. Res.
114, B05102.

Slotnick, M.M., 1936. On seismic computation with applications. Geophysics 1, 9–22.

Swarbrick, R.E., Osborne, M.J., 1998. Mechanisms that generate abnormal pressures: an overview. In:
Law, B.E., Ulmishek, G.F., Slavin, V.I. (Eds.), Abnormal Pressures in Hydrocarbon Environments: AAPG
Memoir, 70, pp. 13–34.

Swarbrick, R.E., Osborne, M.J., Yardley, G.S., 2002. Comparison of overpressure magnitude resulting
from the main generating mechanisms. In: Huffman, A.R.,

Bowers, G.L. (Eds.), Pressure Regimes in Sedimentary Basins and their Prediction: AAPG Memoir, 76,
pp. 1–12.

Terzaghi, K., Peck, R.B., Mesri, G., 1996. Soil Mechanics in Engineering Practice, 3 rd Edition. John Wiley
& Sons.
 Petroleum Engineers Association
Tingay, M.R.P., Hillis, R.R., Swarbrick, R.E., Morley, C.K., Damit, A.R., 2009. Origin of overpressure and
pore-pressure prediction in the Baram province, Brunei. AAPG Bull. 93 (1), 51–74.

Traugott, M., 1997. Pore pressure and fracture gradient determinations in deepwater. World Oil,
August, 1997.

van Ruth, P., Hillis, R., Tingate, P., 2004. The origin of overpressure in the Carnarvon Basin, Western
Australia: implications for pore pressure prediction. Pet. Geosci. 10, 247–257.

Wyllie, M.R.J., Gregory, A.R., Gardner, L.W., 1956. Elastic wave velocities in heterogeneous and porous
media. Geophysics 21, 41–70.

Yardley, G.S., Swarbrick, R.E., 2000. Lateral transfer: a source of additional overpressure? Mar. Pet.
Geol. 17, 523–537.

York, P., Prithard, D., Dodson, J.K., Dodson, T., Rosenberg, S., Gala, D., Utama, B., 2009. Eliminating
non-productive time associated drilling trouble zone. OTC20220 Presented at the 2009 Offshore Tech.
Conf. Held in Houston.

Zhang, J., 2008. Unpublished reports and training notes. Zhang, J., Roegiers, J.-C., 2005. Double
porosity finite element method for borehole modeling. Rock Mech. Rock Eng. 38, 217–242.

Zhang, J., Roegiers, J.-C., 2010. Discussion on “Integrating borehole-breakout dimensions, strength
criteria, and leak-off test results, to constrain the state of stress across the Chelungpu Fault, Taiwan”.
Tectonophysics 492, 295–298. Zhang, J., Standifird, W.B., Lenamond, C., 2008. Casing ultradeep,
ultralong salt sections in deep water: a case study for failure diagnosis and risk mitigation in record-
depth well. Paper SPE 114273 Presented at SPE Annual Technical Conference and Exhibition, 21–24
September 2008, Denver, Colorado, USA.